Control and measurement of clamping and machining forces in intelligent fixturing

CONTROL AND MEASUREMENT OF CLAMPING AND MACHINING FORCES IN INTELLIGENT FIXTURING RAWTHER ASHIQUL HAMEED (B.Eng.(Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my supervisors Associate Professor M.A. Mannan and Professor A.Y.C. Nee who shared their wealth of knowledge and research expertise and constantly helped me with their insightful advice and seemingly endless research ideas that made my stint under them a truly learning and enriching experience. Being a novice to research and struggling to meet their globally acclaimed standards and excellence, their friendly spirit, support and rapport have been a real source of motivation and enhancement of my research acumen. It was truly a great opportunity and rewarding experience to have worked under them. I would express my appreciation and gratitude to Mr SC Lim, Mr CS Lee and Mr CH Tan for their support with all the experimental work needed for this research. Their friendly gesture and air of informality made the experimental part of this work as light as it could get. i TABLE OF CONTENTS Acknowledgements i Table of Contents ii List of Figures v List of Tables Summary viii ix CHAPTER 1 INTRODUCTI ON .........................................................................................1 1.1 RESEARCH M OTIVATION ..............................................................................................2 1.3 ORGANISATION OF THE THESIS ....................................................................................4 CHAPTER 2 LITERATURE REVIEW.............................................................................5 2.1 BASIC FIXTURE D ESIGN ...............................................................................................5 2.2 LOCATING PRINCIPLE ..................................................................................................5 2.3 REQUIREMENTS OF A FIX TURE.....................................................................................6 2.4 BASIC CLAMPING FORCE CONTROL ............................................................................8 2.5 FIXTURE HARDWARE DEVELOPMENT .........................................................................9 2.6 CUTTING FORCE M ODELS AND CUTTING FORCE M EASUREMENT ...........................10 2.7 DYNAMIC FORCE M EASUREMENT .............................................................................12 2.8 FIXTURE M ODELS AND D EVELOPMENTS ...................................................................13 2.9 EFFECT OF FRICTION IN FIXTURING..........................................................................15 ii CHAPTER 3 CUTTING FORCE MEASUREMENT IN A FIXTURING SET-UP WITH INSTRUMENTED LOCATORS ......................................................................................17 3.1 INTRODUCTION ...........................................................................................................17 3.2 STABILITY ANALYSIS ..................................................................................................21 3.3 FORCE DISTRIBUTION IN END - MILLING ....................................................................22 3.4 RELATIONSHIP BETWEEN CUTTING, CLAMPING, LOCATOR AND FRICTIONAL FORCES ...........................................................................................................................................24 3.5 DETERMINATION OF THE CUTTING FORCES .............................................................26 3.6 EXPERIMENTAL PROCEDURE .....................................................................................27 3.6.1 Instrumented Locators........................................................................................27 3.6.2 Experimental Set -up ...........................................................................................29 3.7 RESULTS AND ANALYSIS .............................................................................................30 3.7.1 Analysis of Engagement time .............................................................................34 3.7.2 Quantitative Analysis with the Model Developed Based on Planar Stability Analysis .......................................................................................................................................34 3.8 PERFORMANCE ANALYSIS ..........................................................................................43 3.9 ADVANTAGES WITH THE D EVELOPED M EASURING S YSTEM ....................................44 3.10 DISADVANTAGES OF THE D EVELOPED S YSTEM.......................................................45 CHAPTER 4 FORCE MEASUREMENT IN A DYNAMOMETER OUTSIDE ASSOCIATED WORKSPACE ENVELOPE ..................................................................47 4.1 INTRODUCTION ...........................................................................................................47 4.2 STATIC LOADING TEST FOR THE D YNAMOMETER ....................................................47 iii CHAPTER 5 DEVELOPMENT OF A CLAMPING ELEM ENT USING DIRECTTORQUE CONTROL ........................................................................................................52 5.1 INTRODUCTION ...........................................................................................................52 5.2 DIRECT TORQUE CONTROL OF DC M OTOR ..............................................................53 5.3 CONTROL M ECHANISM ..............................................................................................54 5.4 M ECHANICAL S YSTEM ...............................................................................................56 CHAPTER 6 OPTIMISATION OF MINIMUM CLAMPING FORCE.......................59 6.1 INTRODUCTION ...........................................................................................................59 6.2 ALGORITHM FOR OPTIMISATION ...............................................................................60 6.3 EXPERIMENTAL S ET- UP ..............................................................................................61 6.3 OPTIMISATION TECHNIQUE USING LINEAR PROGRAMMING....................................62 6.4 OVERALL S YSTEM INTEGRATION ..............................................................................69 CHAPTER 7 CONCLUSIONS AND FUTURE WORK ................................................71 7.1 CONCLUSIONS .............................................................................................................72 7.2 CONTRIBUTIONS .........................................................................................................72 7.3 SCOPE FOR FUTURE WORK........................................................................................73 REFERENCES ...........................................................................................................................................................75 iv LIST OF FIGURES FIGURE 1.1 TYPICAL FIXTURE ASSEMBLY [CARR LANE 1995]..............................................1 FIGURE 2.1 THE 3-2-1 LOCATING PRINCIPLE [X IAO 1998] ...................................................6 FIGURE 3.1 FORCE PLATE (K ISTLER, 9253A) .....................................................................19 FIGURE 3.2 AN ILLUSTRATION OF LOADING OUTSIDE ENVELOPE......................................20 FIGURE 3.3 CUTTING AND CLAMPING FORCES [J ENG 1995] ..............................................22 FIGURE 3.4 CUTTING, CLAMPING AND LOCATOR FORCES ACTING ON A PRISMATIC PART 24 FIGURE 3.5 UNIAXIAL FORCE S ENSOR ......................... ERROR ! BOOKMARK NOT DEFINED.28 FIGURE 3.6 D ESIGN OF THE INSTRUMENTED LOCATOR WITH UNIAXIAL FORCE SENSOR ..28 FIGURE 3.7 EXPERIMENTAL SET- UP WITH THE LOCATORS AND CLAMPS PLACED ON THE DYNAMOMETER ....................................................................................................29 FIGURE 3.8 SCHEMATIC DRAWING IN PLAN VIEW OF THE EXPERIMENTAL SET- UP ...........30 FIGURE 3.9 THE END MILLING OPERATION WITH THE ENGAGEMENT ANGLE SHOWN .......31 FIGURE 3.10 FORCE RECORDED FROM THE X-AXIS OUTPUT OF THE DYNAMOMETER ......32 FIGURE 3.11 FORCE RECORDED FROM CLAMP1, FAA .......................................................33 FIGURE 3.12 FORCE RECORDED FROM LOCATOR 1, FA.....................................................33 FIGURE 3.13 (A) FORCE DATA RECORDED FROM CLAMP FAA ...........................................35 FIGURE 3.13 (B) FORCE DATA RECORDED FROM CLAMP FAA ...........................................35 FIGURE 3.13 (C) FORCE DATA RECORDED FROM LOCATOR FA..........................................36 FIGURE 3.13 (D) FORCE DATA RECORDED FROM LOCATOR FB ..........................................36 FIGURE 3.13 ( E) FORCE DATA RECORDED FROM LOCATOR FC..........................................36 FIGURE 3.13 ( F) FORCE DATA RECORDED FROM LOCATOR FD ..........................................37 v FIGURE 3.13 ( G) FORCE DATA RECORDED FROM LOCATOR FE..........................................37 FIGURE 3.13 ( H) FORCE DATA RECORDED FROM LOCATOR FF ..........................................37 FIGURE 3.13 ( I) FORCE DATA RECORDED FROM X-AXIS OF DYNAMOMETER .....................38 FIGURE 3.13 (J ) FORCE DATA RECORDED FROM Y-AXIS OF DYNAMOMETER .....................38 FIGURE 3.13 ( K) FORCE DATA RECORDED FROM Z-AXIS OF DYNAMOMETER ....................38 FIGURE 3.14 THE GEOMETRIC PARAMETERS FOR THE 3-2-1 LOCATOR SET - UP OF THE WORKPIECE...........................................................................................................39 FIGURE 4.1 S ET- UP FOR STATIC LOADIN G ...........................................................................48 FIGURE 4.2 S ET- UP FOR STATIC LOADIN G ...........................................................................49 FIGURE 4.3 (A) FORCE ALONG THE Z-AXIS OF THE DYNAMOMETER ..................................50 FIGURE 4.3 (B) FORCE ALONG THE Y-AXIS OF THE DYNAMOMETER ..................................50 FIGURE 5.1 DC M OTOR- TORQUE CONTROLLER ................................................................55 FIGURE 5.2 M OTOR OPERATING CHARACTERISTICS .........................................................57 FIGURE 5.3 CALIBRATION GRAPH .......................................................................................58 FIGURE 6.1 OPTIMISATION SCHEME ...................................................................................60 FIGURE 6.2(A) PLAN VIEW OF THE SET - UP...........................................................................61 FIGURE 6.2(B) ISOMETRIC VIEW OF THE SET - UP .................................................................62 FIGURE 6.3 (A) COMPONENT OF CUTTING FORCE FT ..........................................................65 FIGURE 6.3 (B) COMPONENT OF CUTTING FORCE FF ..........................................................65 FIGURE 6.3 (C) COMPONENT OF CUTTING FORCE FA ..........................................................65 FIGURE 6.4 FORCE APPLIED BY CLAMP FBB.......................................................................66 FIGURE 6.5 FORCE APPLIED BY CLAMP FBB.......................................................................66 FIGURE 6.6 O UTPUT FROM THE OPTIMISATION SOLVER .....................................................68 FIGURE 6.6 SCHEMATIC REPRESENTATION OF THE SYSTEM INTEGRATION. ......................70 vi LIST OF TABLES TABLE 3.1 CUTTING DATA FOR THE EXPERIMENTS PERFORMED……………….40 TABLE 3.1 ERROR VALUES AS A PERCENTAGE OF MEASURED FORCE…………41 TABLE 3.3 RMS VALUE OF THE ERRORS……………………………….……………….42 vii SUMMARY Accuracy and precision are the most important aspects of any machining operation. This is greatly dependent on the stability of the workpiece, which is in turn decided by the effectiveness and performance of the workholding device. Workholding in any manufacturing process is performed by the fixturing elements. Fixture design and implementation is dependent on the forces acting on the workpiece, which are predominantly the cutting and the clamping forces. Every machining process, especially those that involve the control of the fixturing forces in flexible manufacturing systems, require the measurement of clamping and cutting forces. This research addresses pertinent issues in both cutting force measurements and control of the clamping force and an attempt is made to solve the problems associated with the existing systems. The study and development in this work include the following: A novel force measurement technique in a fixturing arrangement with instrumented locators has been developed. Earlier works on the study of the stability of the workpiece with a spatial stability analysis is incorporated in this work to develop the force measuring system. A detailed study and experimental investigation into the performance of the dynamometer is carried out. The developed system aims to overcome some problems associated with the dynamometer and provide a viable alternative for force measurement in real time during a machining operation. There is no prior work to establish the relationship between the forces obtained using the locators based on the 3-2-1 locating principle and forces obtained from a dynamometer. This study could lead to the feasibility of fixturing set-ups with instrumented locators as a viable alternative to a dynamometer. ix An attempt is made to design a simple controllable electro-mechanical clamping element. Using the principle of direct torque control of a permanent magnet DC motor, a clamping system is developed. A rack and pinion mechanism is used to convert the rotary motion of the clamp to linear motion of the clamping element and the torque is controlled in the region of zero speed of the motor, which keeps wear and tear to a minimum. An optimisation method to determine the minimum optimal clamping force using linear programming is derived. This technique aims to simplify the process of optimisation and provides a methodology to find an estimate of the minimum clamping force through an iterative procedure so that control of clamping forces can be realised outside a laboratory environment. x Chapter 1 Introduction CHAPTER 1 INTRODUCTION Fixturing is one of the salient features of any manufacturing system, to ensure workpiece stability and hence good quality and accuracy of the finished products. A fixture is a mechanical device that locates, supports and secures the workpiece in an accurate and definite orientation relative to the process co-ordinate system. The stability of the workpiece is vital to achieve the desired dimensional tolerances in any machining operation. A mechanical fixture normally consists of several components such as locators, clamps, supports and the fixture body. Fixtures are either dedicated or flexible depending on the intended application. Figure 1.1 shows a typical machining fixture assembly. It consists of six locators that are passive and two clamping elements that are active during the machining process. Figure 1.1 A typical fixture assembly [Carr Lane 1995] The National University of Singapore 1 Chapter 1 Introduction 1.1 Research Motivation With the increase in demand for high precision products, various advanced manufacturing processes have been developed. However, one important aspect for achieving high precision and reducing distortion has often been overlooked. It is the clamping system used for securing the workpiece to be machined. Clamping forces provided by present day clamps are ironically constant in both magnitude and position, though a machining process is dynamic in both direction and magnitude of the cutting force. So it is imperative to make the clamping element capable of adjusting itself in accordance with the cutting force. It is seen in most cases, during manual clamping, that a workpiece is clamped with as much force as possible to ensure that it does not disengage during a machining process. This inevitably leads to deformation, especially in thin-walled workpieces, which could prove to be rather costly. Hence there is a need to develop and enhance the fixturing systems and contribute to the on–going research to make fixtures robust and dynamic in nature. In a fixturing system, it is vital to know the optimal clamping forces. In order to determine these values, the cutting forces have to be known. The accuracy of the available analytical and empirical cutting force models is limited by the various factors that usually cannot be accounted for in real machining conditions. In order to overcome the inaccuracies in force measurement using developed force models, one can measure the cutting forces in real time with a multi-component piezo-electric dynamometer. However, a dynamometer has many inherent drawbacks when its application in a real machining environment is considered e.g constraint on the volume of operation, high associated costs and substantial weight cause limitations to its application in certain environments. So, The National University of Singapore 2 Chapter 1 Introduction there is a need to develop an alternative force measuring system that can overcome these drawbacks found in a dynamometer. In an ideal fixturing system, both the location and magnitude of the clamping force are controllable in real time, ensuring optimal workholding at all times. A more practical and cost effective approach is to have off-line optimisation of the location of the clamping forces and on-line optimisation of the clamping force magnitudes. However, real time optimisation and control of clamping forces is still seen only in a laboratory environment due to high associated costs and expertise required. Hence there is a need for a simplified method with which one can determine the optimal clamping force and to develop an easily controllable clamping element. 1.2 Research Objectives • To develop a system to measure the cutting forces on-line during an end-milling process. • To conduct a sufficient number of experiments with various cutting parameters to validate the developed system. • To demonstrate the competency and advantages of the developed force measuring system against the dynamometer. • To design and develop a controllable electro-mechanical clamping element. • To develop a simplified system to optimise the minimum clamping force required during an end-milling operation. The National University of Singapore 3 Chapter 1 Introduction 1.3 Organisation of the Thesis • Chapter 2 gives a survey of the literature related to this research. • Chapter 3 presents the development of the cutting force measurement system in a fixturing arrangement with instrumented locators. The principle of spatial stability analysis is explained and its application to determine the cutting forces is demonstrated. Results of several experiments conducted are illustrated and the validity of the system is studied. • Chapter 4 demonstrates the advantages of the system developed over the dynamometer with regard to the volume of operation. Experiments conducted to study the behaviour of the dynamometer when force measurement is attempted outside its associated workspace envelope is explained. • Chapter 5 presents the design and development of an electro-mechanical clamping element using direct-torque control. The characteristics of the clamping element are illustrated. • Chapter 6 presents a simple optimisation technique to determine the minimum clamping force to be applied to ensure workpiece stability. • Chapter 7 states the main contributions of this work and recommendations for future research. The National University of Singapore 4 Chapter 2 Literature Review CHAPTER 2 LITERATURE REVIEW 2.1 Basic Fixture Design A fixture is a workholding device that is used to locate and hold workpieces securely in order to ensure that the manufacturing operation can be performed successfully [Hoffman 1980]. Fixture design is an essential and integral part of all the manufacturing operations. Good fixture design is important to achieve the required dimensional tolerances. With increase in demand for high precision machining with shrinking tolerances, good fixture design is imperative. It has been shown that the fixture cost can be upto 10–20% of the total manufacturing cost [Grippo 1988]. Skilled fixture designers are also hard to find [Finegold 1994]. Furthermore, an important problem encountered in conventional fixturing operation is the discrepancy between the constant clamping forces, fixed both in magnitude and points of application, and the dynamic cutting forces on the workpiece which may vary both in magnitudes and direction during machining. To overcome these problems of conventional clamping, there is a need to have a formal science-based approach for the analysis and synthesis of fixtures used in manufacturing. This shows the importance of fixturing in manufacturing processes and the need for research and development in this field. One of the first researches on experimental characterization of fixture-workpiece systems was conducted by Shawki and Abdel Al [Shawki 1965]. In recent times various advances have been made and many different models have been developed to analyse and enhance fixture designs. The National University of Singapore 5 Chapter 2 Literature Review 2.2 Locating Principle A workpiece has six degrees of freedom in 3D space. It can move in 12 directions corresponding to the translational motion along the co-ordinate axes and rotational motion about them. In order to restrain the motion of the workpiece, clamps and locators are used. Clamps are active elements, which apply force on the workpiece and locators are passive elements, which act as a datum. As far as possible, the 3-2-1 locating principle is used to locate a typical prismatic workpiece [Nee 1995]. Figure 2.1 shows a typical fixture set-up with an arrangement using the 3-2-1 locating principle. The primary locating plane is usually the one with the largest surface area and located using three points, arresting two rotational motions and one linear motion [Cecil 1996]. The secondary plane is the next largest surface and located using two points, which arrest one rotational and one linear motion. The tertiary plane has one locator restraining the last linear motion. The 3-2-1 locating principle is widely used in machining fixtures, as locating repeatability, part accessibility and detachability are inherent features of this principle. Figure 2.1 The 3-2-1 locating principle The National University of Singapore 6 Chapter 2 Literature Review 2.3 Requirements of a fixture Some general requirements of a fixture are listed below [Hoffman 1980] • Accurate location and total restraint of workpiece during machining • Limited deformation of the workpiece • No interference between workpiece and fixuring elements Chan et al classified the requirements for a good fixture as their ability to control various physical aspects of the workpiece during machining [Chan 1999]. • Geometric control – The fixture must be able to ensure the stability of the workpiece. For good geometric control, the workpiece must come into contact with all the locators in an exactly repeatable way irrespective of operator skill. • Dimensional control – The fixture must be able to choose the right position for the locators and orientation for the workpiece. Good dimensional control exists when irregularities on workpiece surface do not interfere with the location of the workpiece • Mechanical control – The fixture must be able to make correct placement of the clamping forces. Good mechanical control is achieved when the changes in the force of clamping do not affect the location of the workpiece. Asada came up with the following set of constraints to be observed while designing a viable fixture [Asada 1985]. • Deterministic location – A workpiece is said to be kinematically restrained when no motion occurs when there is loss of contact with any locator. Locating errors due to locators and locating surfaces of the workpiece should be minimised in The National University of Singapore 7 Chapter 2 Literature Review order to accurately and uniquely position the workpiece within the machine coordinate frame. • Total constraint – All movements of the workpiece should be restrained. Clamps apply forces that prevent the workpiece from any motion once it is located. The workpiece must be held in static equilibrium to withstand all the possible external forces or disturbances. • Contained deformation – Workpiece deformation during a machining operation must be kept to a minimum to achieve the tolerance specifications. • Geometric constraint – Geometric constraint guarantees that all fixturing elements have an access to the datum surface. They should ensure that the fixture components do not interfere with cutting tools during machining. A good fixture requires desirable characteristics such as quick loading and unloading, minimum number of components and a design equipped for multiple cutting operations [Sakurai 1991]. It is also desirable to have fixtures that can be used for both dry and wet cutting conditions, are capable of accommodating workpieces of various sizes, are configurable to workpieces of different shapes, require little set-up time, do not demand great expertise and keep associated costs to a minimum. 2.4 Basic Clamping Force Control Control of clamping forces online is an important feature implemented in recent fixturing systems to overcome the drawbacks of conventional fixturing arrangements with constant clamping forces, which are usually applied manually. The National University of Singapore 8 Chapter 2 Literature Review In order to achieve dynamic clamping, pneumatic, hydraulic and elecromechanical clamping systems are used. Electro-mechanical clamping is generally preferred as it is more convenient to use, has a fast response time, is easy to control and has a high resolution and very good precision. Pneumatic and hydraulic clamps are also used to meet specific requirements. Sollie [Sollie 1997] developed an electro-mechanical clamping element based on hybrid position-force control using a stepper motor. Linear actuators can be used for the same purpose [Chan 1999]. Cutkosky et al [Cutkosky 1982] developed a programmable clamping device for turbine blades. Lee et al [Lee 1999] proposed a methodology where piezo-ceramic crystals can be used to clamp and control the workpiece. Many other types of clamping elements have been developed to control the clamping forces online. 2.5 Fixture Hardware Development Commonly used fixturing hardware systems are classified into three types: dedicated, modular and hybrid [Trappey 1990]. Dedicated fixtures are those which are fabricated to suit a specific workpiece. Modular fixtures are more flexible and configurable to suit workpieces of different shapes and sizes. The latter is generally preferred, as it is very cost efficient. Hybrid fixtures are a combination of both dedicated and modular fixture types. Liu [Liu 1994] presented a systematic methodology for conceptual design on modular fixtures. Hou and Trappey [Hou 2001] developed a computer-aided fixture design system for comprehensive modular fixtures. Lin et al [Lin1997] developed a knowledge-based system for conceptual and layout modular fixture design developed on an intelligent CAD system. The National University of Singapore 9 Chapter 2 Literature Review Dedicated fixtures are becoming increasingly less popular with the rapid advancement of Flexible Manufacturing Systems (FMS) that require automated fixturing capabilities. The replacement of dedicated fixtures by modular fixturing systems seems to be a trend in the manufacturing field [Liu 1994]. There are many advanced fixturehardware systems developed in recent research works. A numerically controlled clamping system was developed by Tuffentsammer [Tuffentsammer 1981] to speed up loading and clamping of single part machining in an FMS. Chan et al [Chan 1991] developed an automatically reconfigurable fixturing system for robotic assembly. Shirinzadeh [Shirinzadeh 1993] also developed a similar fixture for robotic assembly that could be setup, adjusted and changed automatically. Du and Lin [Du 1998] developed a three-fingered automated flexible fixturing for planar objects. 2.6 Cutting Force Models and Cutting Force Measurement For any flexible manufacturing system, it is important to know the cutting forces during the machining operation. The knowledge of the cutting forces helps to determine the clamping forces required and hence the design of the fixturing system. There have been many models developed for the purpose of measurement of cutting forces in a machining operation. Koenigsberger and Sabberwal [Koenigsberger 1961] developed one of the first analytical models, which assumed that the instantaneous cutting forces were proportional to the chip area on the cutter. Further studies were made to verify the cutting force assumption and explored the effects of the cutting geometry on the force system characteristics. They developed nomograms to relate the cutting The National University of Singapore 10 Chapter 2 Literature Review geometry to average forces, maximum forces and power requirements in milling operations. This was a pioneering force measurement technique using an analytical model. Many empirical models have also been developed. One of the earliest empirical models was developed by Armarego and Brown [Armarego 1969]. The model was formulated by performing a number of experiments and measuring the cutting forces. Tlusty and McNeil [Tlusty 1975] performed empirical analysis to study the dynamics of cutting in end milling. Ber et al [Ber 1988] developed an empirical method to determine the cutting forces in end milling using specific force analysis. Altintas [Altintas 2000] developed an analytic approach to calculate the specific cutting forces as a function of cutting parameters. Lee and Altintas [Lee 1996] developed a general mechanics and dynamics model for helical end milling. Engin and Altintas [Engin 2001] presented a generalized mathematical model to suit most helical end-mills. Kline [Kline 1982a] developed a model assuming that the cutting force is proportional to the chip cross-sectional area. He based his model on one of the early works done by Martelloti [Martelloti 1945] on the analysis of the milling process. Kline et al [Kline 1982b] developed a model to predict the cutting forces applied to cornering cuts. Kline and De Vor [Kline 1983] also presented a detailed account on the effect of runout on the cutting force in end milling. Using the models developed various force measurement techniques have been developed. Altintas and Spence [Altintas 1991] developed end-milling force algorithms for CAD systems. Armarego and Deshpande [Armarego 1994] developed force prediction models for CAD/CAM systems. Yun et al [Yun 2001] developed a 3-D cutting force prediction model using cutting condition independent co-efficients in end milling. The National University of Singapore 11 Chapter 2 Literature Review Other methods for force measurement have also been developed using different techniques. Li et al [Li 2000] developed a new method for measurement of cutting force using current sensors. Cutting forces could be measured using a neuro-fuzzy technique, with current sensors installed on the a.c. servomotors of a CNC turning centre. Kim et al [Kim 1999] developed a cutting force measurement method in contour NC milling processes using current signals of the servomotors. Ozel and Altan [Ozel 2000] developed a Finite Element Method to measure cutting forces during an end-milling operation. 2.7 Dynamic Force Measurement A multi-component piezo-electric dynamometer has been widely accepted as a standard for dynamic force measurements, especially for milling and turning processes. The use of the dynamometer has been extended to many other applications as well. Seker et al [Seker 2002] designed and constructed a dynamometer for measurement of cutting forces during machining with linear motion. Gupta et al [Gupta 1988] developed a sensor based drilling fixture with two dynamometers and a standard vise. It was used to study the relationship between clamping forces and machining forces. Tounsi and Otho [Tounsi 2000] studied the problem of distortion of the delivered signals in a dynamometer and developed a method to compensate for it. Kim et al [Kim 1997] developed a combined-type tool dynamometer, which can measure the static cutting force and the dynamic cutting force together by using strain gauges and a piezo-film accelerometer. The National University of Singapore 12 Chapter 2 Literature Review 2.8 Fixture Models and Developments Various fixture models have been developed to analyse the clamping forces, cutting forces, synthesis of fixture layout, stability and optimal clamping. Early work in fixture analysis neglected the effects of friction, system inertia and damping which were considered as important entities for fixture analysis in later works. Rigid body models and contact elasticity models are the two major approaches undertaken. Laximinarayana [Laximinarayana 1978] applied the screw theory to model a rigid object constrained by frictionless point contacts. Laximinarayana’s work on ‘form closure’ was further extended to “force closure” for workpiece stability [Chou 1989]. Asada and By [Asada 1985] used rigid body model without friction for deriving the condition for total constraint of a workpiece. They formulated the condition for deterministic positioning for a workable fixture and analysed the stability using the screw theory. De Meter [De Meter 1992] used the screw theory approach for stability analysis of machining fixtures with distinct contact geometries. Lee and Cutkosky [Lee 1991] analysed the stability of the workpiece in a fixture using the concept of a force and moment limit surface. Nnaji et al [Nnaji 1988] determined the fixture locating points based on the singularity of the force matrix. Salisbury and Roth [Salisbury 1982] used the wrench theory to analyse force closure. Tao et al [Tao 1998a] proposed an optimal clamping scheme based on computational geometry of the contacting wrenches. Jeng et al [Jeng 1995] used spatial stability analysis for determining minimum clamping force. It was extended further by Xiao [Xiao 1998], who used genetic algorithm to solve it. To overcome the disadvantage of static indeterminacy, in rigid body modelling, various elasticity models for the fixture-workpiece system have been developed in recent The National University of Singapore 13 Chapter 2 Literature Review years. This effectively reduces the error due to the rigid body assumption but considerably increases the intensity of computations required. These models generally presume elasticity at the vicinity of contact and consider the remaining part of the workpiece as rigid [Johnson 1985]. Hockenberger and De Meter [Hockenberger 1996] used contact models specific to a workpiece, empirically determined by analysing workpiece static displacement. Mittal et al [Mittal 1991] modelled each locating and clamping element as a translational spring damper actuator. The deformation was determined by allocating the stiffness matrix for the fixturing elements. A similar approach was made by Gui et al [Gui 1996] by using a linear spring model for the fixturing elements to determine the minimum clamping force. Li and Melkote [Li 1999] used elastic contact mechanics principles with quasi-static and dynamic models to determine the contact forces. Various automated fixture design systems have been developed for the purpose of layout optimisation and determining the optimal clamping force. Non-linear programming is largely used for the former and linear programming for the latter. Ferriera et al [Ferriera 1985] presented a rule-based expert sytem for automated fixture design, suitable for general machining operations. Markus et al [Markus 1984] developed an expert system to assist the selection and positioning of locators and clamps. Boerma and Kals [Boerma 1989] presented an automated rule-based system for the selection of fixture setups. Nee and Kumar [Nee 1991] designed a system that used a predefined library for the synthesis of a fixture. Tao et al [Tao 1998b] used computational geometry approach for automatic generation of clamping forces. Finite Element Method (FEM) approach has also been widely used for fixtureworkpiece modelling. Lee and Haynes [Lee 1987] conducted one of the earliest researches The National University of Singapore 14 Chapter 2 Literature Review by applying FEM to study the deformation of workpiece, the clamping forces, the stress distribution and other characteristics of fixturing system by modelling the workpiece as a deformable body completely accounting for the elasticity of workpiece and fixture. Trappey et al [Trappey 1995] used FEM to ensure minimal deformation and maximum workpiece accuracy. Sakurai [Sakurai 1991] used FEM to implement an automated fixture design and set-up planning system. FEM approaches are generally very robust and do not have the assumptions that are usually found in other approaches but they tend to be computationally intensive and the model could be rather complex to simulate. 2.9 Effect of Friction in Fixturing In many of the early works on fixture models [Laxminarayana 1978, Asada 1985], friction was not considered. However, it is friction which plays a major role in work holding in most fixturing applications [Lee 1987]. In recent years, many approaches on frictional fixture force analysis have been reported. The addition of friction to the rigid body model makes the analysis significantly more complicated [Mason 1988]. Friction is primarily due to the adhesive forces arising from surface roughness between the workpiece and fixture surfaces. For fixturing applications, static friction is considered, which is the adhesive force between surfaces when there is no relative motion. Couloumb’s law best describes static friction, which is used for most fixture analysis [Mishra 1989]. Sinha and Abel [Sinha 1990] assumed that the Coloumb friction acts on each contact to calculate the frictional and normal contact forces. Kerr and Roth [Kerr 1986] developed a Coloumb friction model for point contacts in hand grasping and used linear programming to obtain the optimal grasping forces. Fuh and Nee [Fuh 1994] The National University of Singapore 15 Chapter 2 Literature Review described a frictional fixture workpiece model that considers the kinematics and dynamic aspects of the fixturing processes. Wu et al [Wu 1995] developed a fixturing verification system based on multiple frictional contacts. De Meter [De Meter 1994] analysed the restraint of fixtures based on the friction developed in the contact surfaces. Li et al [Li 2001] modelled the frictional contact between the workpiece and the fixture element as an elastic half-space subjected to distributed normal and tangential loads. Lee and Haynes [Lee 1987] accounted for Coulomb friction and its effect on the fixture performance in their FEM analysis. The National University of Singapore 16 Chapter 3 Cutting Force Measurement CHAPTER 3 CUTTING FORCE MEASUREMENT IN A FIXTURING SET-UP WITH INSTRUMENTED LOCATORS 3.1 Introduction Cutting force is one of the most sensitive indicators of machining performance. Force measurement is an important aspect in machining performance analysis, flexible manufacturing systems, precision machining, intelligent fixturing and other advanced manufacturing systems. In the analysis of fixturing systems, it is imperative to know the optimal clamping forces for the synthesis of fixtures and determination of their locations and magnitude of clamping forces. In order to determine these values, the cutting forces have to be known. There are many empirical and analytical models available for modelling and determining the cutting forces [Armarego 1969, Tlusty 1975, Ber 1988, Kline 1982a, Altintas 2000]. However, the accuracy of the available analytical and empirical force models is limited by the various factors that usually cannot be accounted for in real machining conditions, like cutter run-out, tool and workpiece deflection, wear of tool and other factors leading to inaccuracies. In order to overcome the inaccuracies in force measurement using developed force models, one can measure the cutting forces in real time with a multi-component piezo-electric dynamometer that has very high accuracy, sensitivity and response time. This method is widely accepted as a standard for force measurement. Quartz is a piezoelectric material that yields an electrical charge when mechanically loaded. Quartz dynamometer performs as a force transducer and the forces The National University of Singapore 17 Chapter 3 Cutting Force Measurement acting on the quartz elements are directly converted into proportional electrical signals. The mechanical stress induced in the quartz measuring element by the force to be measured, which can be either tensile or compressive, produces the output signal with only minimal mechanical deflection. This is a very important factor when measuring very slow, quasi-static forces. The high rigidity is also important when measuring dynamic forces as it provides for a high natural frequency thus allowing the measurement of very fast force pulses. Two pairs of shear-sensitive quartz elements for Fx and Fy together with one pair for compression for Fz result in a very compact 3-component sensor. However, high accuracy and precision may not be required for many force measuring applications. Though measurements with a dynamometer are very precise, there are many inherent drawbacks when its application in real machining environment is considered. Figure 3.1 shows a force plate (Kistler, 9253A) that has a surface dimension of 600 mm x 400 mm. The associated workspace envelope extends to upto 300mm perpendicular to the surface of the force plate. This is the largest available piezo-electric multi-component dynamometer and it can accommodate workpieces no larger than 400 mm x 600 mm x 300 mm. Every dynamometer has an associated workspace envelope. Machining must take place within this envelope for the dynamometer to measure the forces accurately. The National University of Singapore 18 Chapter 3 Cutting Force Measurement Figure 3.1 Force Plate (Kistler, 9253A) For machining larger parts, it is not feasible for accurate force measurement. Figure 3.2 shows schematically, a workpiece that is not completely enclosed by the workspace envelope of the dynamometer. This makes it difficult for one to measure the cutting forces accurately. Furthermore, in an industrial environment, machinists are reluctant to use dynamometers due to the lack of instrumentation knowledge and associated high costs. The cost of the dynamometer is high and the weight of a large-sized dynamometer could be over 100 kgs, which is inconvenient for many applications. These are some of the reasons why piezo-electric multi-component dynamometers, which are commonly used for research and development purposes in a laboratory environment, are seen to have a rather limited application in a real manufacturing environment. Hence there is a need to develop an alternate device that can overcome the disadvantages of a standard piezo-electric dynamometer but is versatile, less expensive and can be accepted to be an alternate force measurement system with accuracy acceptable for usual applications. The National University of Singapore 19 Chapter 3 Cutting Force Measurement Figure 3.2 An illustration of a case when a workpiece can exceed the allowable machining envelope associated with the dynamometer In this work, it is proposed that six instrumented locators with uniaxial force sensors positioned according to the 3-2-1 locating principle be considered as a feasible alternative to the dynamometer. The force outputs from the sensors can be used to obtain the three components of the cutting force acting on the workpiece. It can be shown that the six instrumented locators can act as a substitute for the dynamometer within good tolerance limits. This would effectively overcome the disadvantages that are inherent in a dynamometer. The instrumented locators are capable of accommodating workpieces of any size and configuration. As opposed to the dynamometer, which has a constrained volume and the workpiece has to be accommodated within that volume, the instrumented locators can be distributed around the workpiece without imposing any constraint on the workpiece geometry. Furthermore, the cost of acquiring the components to develop the system with instrumented locators is only about 10% of the cost of the dynamometer which can be The National University of Singapore 20 Chapter 3 Cutting Force Measurement purchased. The handling of the instrumented locators is better as the space occupied is very small and there is no significant addition to the load on the machine table. In this chapter, an effort is made towards achieving the aforementioned objective, cutting force measurement in a fixturing set-up with instrumented locators which can be an alternative force measuring system to the dynamometer. The design and development of the proposed force measuring system and the series of experiments that were performed to validate the accuracy of the system under dynamic loading conditions are demonstrated in detail. 3.2 Stability Analysis Planar stability analysis [Jeng 1995] was used to analyse workpiece stability with one clamping plane that could be further extended to spatial stability analysis in multiple clamping planes. The Instantaneous Centre of Motion property is used for the analysis. ICM Property [Jeng 1995] – For all points P ∈ of clamping plane Π such that the clamping moment about P is greater than or equal to the cutting moment about P, clamping is stable. The difficulty in the minimum clamping force analysis is that the direction and often times, the magnitude of the friction forces are indeterminate. The direction of a friction force can be determined only when the location of the ICM is assumed. One has to note that the ICM does not actually exist for a stable clamping but assumed for the purpose of analysis. Figure 3.3 shows the general configuration of clamping a prismatic workpiece, where FN,1, FN,2 and FN,3 are the three clamping forces. For the stability of plane XOY, the The National University of Singapore 21 Chapter 3 Cutting Force Measurement clamping forces and the reaction forces that are normal to the clamping plane are the only forces counterbalancing the external forces (FCX + FCY). In case of fixturing with one clamping plane, stability analysis can be carried out by taking into account the friction forces, which are due to the fixturing forces normal to the clamping plane and external forces that are parallel to the plane, such as FCX and FCY. Figure 3.3 Cutting and Clamping forces [Jeng 1995] The National University of Singapore 22 Chapter 3 Cutting Force Measurement 3.3 Force Distribution in End-milling Clamps are active elements that exert force on the workpiece during workholding. Locators that are used to locate the orientation of the workpiece and deliver reaction forces. In this analysis, the workpiece is considered as a rigid body and friction in all contact surfaces is taken into account. Clamping forces are the primary fixturing forces and the friction forces associated with the clamping forces are substantial. The locator forces are relatively smaller but have to be maintained at non-zero values to ensure no loss of contact between the workpiece and the fixture to ensure workpiece stability. External forces are the cutting forces and the weight of the workpiece. In this work, the weight of the workpiece is assumed to be small compared to the other forces and can be neglected in the analysis. Friction forces are attributed to static friction that exists in the region of contact between the workpiece and fixturing elements. Coulomb friction law is applied to determine the friction forces -µFn ≤ Ff ≤ µFn (3.1) One has to note that the fixturing forces are not normal to the boundary contact surface due to the presence of frictional forces. The forces referred to as clamping forces and locator forces refer to the normal component of the fixturing forces. All the forces acting on a prismatic workpiece during end milling are shown in Figure 3.4. The forces FAA, FBB are the forces exerted by the clamps and the forces FA, FB, FC, FD, FE and FF are the reaction forces of the locators. Ff, Ft and Fa are the cutting forces. T1, T2 and T3 are the cutting torques. The forces without labels are the friction forces. The National University of Singapore 23 Chapter 3 Cutting Force Measurement Figure 3.4 Cutting, clamping and locator forces acting on a prismatic part 3.4 Relationship between Cutting, Clamping, Locator and Frictional Forces Using stability condition for a rigid body (Beer 1997), the balance of force and moments give equations (3.2) to (3.7) x1, x2 , x3, x4, y1, y2, z1, z2 , z3 and z4 are the dimensions that can be input by the user after setting up a certain configuration. The subscripts fx, fy and fz (e.g. (FB)fx ) refer to the component of friction in the x, y, and z directions, respectively, of the various forces. Subscript c refers to the co-ordinates of the cutter position. Equilibrium of forces along the X-direction Ft + FF + (FD)fx + (FE)fx = FBB + (FA)fx + (FB)fx + (FC)fx + (FAA)fx The National University of Singapore (3.2) 24 Chapter 3 Cutting Force Measurement Equilibrium of forces along the Y-direction Fa = FA + FB + FC + (FD)fy + (FE)fy + (FF)fy + (FAA)fy + (FBB)fy (3.3) Equilibrium of forces along the Z-direction Ff + FAA + (FF)fz = FD + FE + (FA)fz + (FB)fz + (FC)fz + (FBB)fz (3.4) Equilibrium of moments about X axis z3 (FA) + z3 (FB) + z1 (FC) + y1 (FD) + y1 (FE) + z4 (FD)fy + z4 (FE)fy + z2 (FBB)fy + z2 (FF)fy + y2 (FBB)fz + T3 = zc (Fa) + y1(FF)fz + y2 (FAA) + yc (Ff) (3.5) Equilibrium of moments about Y axis z3 (FA)fx + z3 (FB)fx + x2 (FAA) + xc (Ff) + z1 (FC)fx +z2 (FBB) + x2 (FAA) = T1 + x1 (FD) + x3 (FE) + x4 (FBB)fz + x2 (FC)fz + x3 (FA)fz + x1 (FB)fz + z2 (FF) + z4 (FE)fx + z4 (FD)fx + zc (ft) (3.6) Equilibrium of moments about Z axis x3(FA) + x1(FB) + x2(FC) + x1(FD)fy + x3(FE)fy + x2(FAA)fy + y2 (FAA)fx + x4(FBB)fy + y2(FBB) = T2 + y1(FD)fx + y1(FE)fx + yc (Ft) + y1(FF) + xc (Fa) The National University of Singapore (3.7) 25 Chapter 3 Cutting Force Measurement 3.5 Determination of the Cutting Forces Equations (3.2) to (3.7) relate the various forces that are acting on the workpiece during the machining process. The aim of the developed relationship is to enable the determination of the three components of the cutting force Fx*, Fy*, Fz*. The known variables in the equations are the six locator forces (FA, FB, FC, FD, FE, and FF) and the two clamping forces (FAA and FBB), which are obtained from the sensors placed on them. It has to be noted that the equations developed are not limited to any particular shape or size of the workpiece but can be configured with input given by a user to suit any configuration. The equations obtained are complete and do not involve any assumptions. They relate all the forces and torques that are involved. For well-finished metal surfaces, the contact friction has co-efficient of friction, µ values ranging from 0.1 to 0.3. If the contact area is small, µ takes values closer to the lower limit. In the present experiment, as the locators have a hemispherical shape, the contact area is very small and the µ value is found to be about 0.1-0.15. For rubber-metal contact, µ is about 0.3 to 0.65. In the present experiment, the clamps have a hard rubber layer which has a rough surface and the contact area is also quite large as the face of the clamp is flat and the value of µ was found to be about 0.5-0.65. Slipping condition is assumed for the analysis and the friction in the contacts is estimated with the assumed position of the ICM. It has to be noted that these assumptions will add to the error in the analysis, however these errors cannot be totally avoided to solve a system which is statically indeterminate. The National University of Singapore 26 Chapter 3 Cutting Force Measurement A program was written in Matlab for solving the equations. The known variables are the locator forces and the clamping forces that will be input into the program and the unknowns output by the program will be the cutting forces and the cutting torques. 3.6 Experimental Procedure Experiments were performed with a fixturing set-up made on a dynamometer. Series of tests were conducted to establish the validity of the system developed. In order to achieve this, force measurements were recorded concurrently from the dynamometer, instrumented locators and the clamps. The following sections explain the experimental setup, details of the conducted experiments and the analysis of the results. 3.6.1 Instrumented Locators In the fixturing arrangement for this work, there is a need to measure the locating forces in real time, accurately. In order to achieve this, instrumented locators were designed with uniaxial force sensors (Kistler: Slim Line Sensor, 9134A). Figure 3.6 shows different types of uniaxial Slim Line Force Sensors. It is capable of measuring forces with very high precision and has a very fast response time. The sensor used is capable of measuring a compressive force of upto 30kN. For the purpose in this work, the fixturing forces are all compressive forces and hence can be measured with the above-mentioned sensor. The National University of Singapore 27 Chapter 3 Cutting Force Measurement Figure 3.6 Uniaxial Force Sensors [Kistler] The sensor has to be placed on the locator and pre-loaded. The locators were designed and the sensor pre-loaded to 3kN which is 10% of the maximum force value of the sensor. The sensor has very high linearity above this value and can be considered extremely accurate with error less than 0.1%. Figure 3.7 shows the instrumented locator with the pre-loaded uniaxial force sensor. Figure 3.7 Design of the instrumented locator with uniaxial force sensor The National University of Singapore 28 Chapter 3 Cutting Force Measurement 3.6.2 Experimental Set-up The experiment requires measuring the forces from the clamps, locators and the dynamometer simultaneously during a machining operation. This will facilitate the analysis to validate the cutting force measurements calculated from the instrumented locator set up against the cutting force measured by the dynamometer. Figure 3.8 shows the locating and clamping elements mounted on the dyanamometer (Kistler, 9253A). Figure 3.8 Experimental set-up with the locators and clamps placed on the dynamometer The workpiece and the locators were set up according to the 3-2-1 locating principle. The workpiece (180 mm x 180 mm x 120 mm) was mounted on a large dynamometer. A schematic drawing of the set-up with the dimensions indicated is shown in Figure 3.9. Charge amplifiers and tape recorders were used to obtain and record the The National University of Singapore 29 Chapter 3 Cutting Force Measurement output forces. The force values were recorded simultaneously from the dynamometer, the clamps and the locators, so that concurrent values from these components can be analysed. The data were converted to ASCII format for analysis. Figure 3.9 Schematic drawing in plan view of the experimental set-up 3.7 Results and Analysis A series of end-milling tests were conducted with a 32 mm diameter tungsten carbide indexable insert for various cutting parameters and the force values were recorded. With the obtained force data, various aspects of the force details were analysed. The analysis includes a comparison between the engagement periods and validation of the mathematical model developed through a quantitative analysis. The National University of Singapore 30 Chapter 3 Cutting Force Measurement 3.7.1 Analysis of Engagement time The force pattern in end milling has a peak during the engagement of each flute and for a four-fluted end-mill, there will be four peaks in one rotation. In order to show the concurrence between the dynamometer and the locator forces, the engagement period was calculated and checked for both force values. For instance, take a particular machining process for the cutting condition of axial depth of cut (ax) = 8 mm, radial depth of cut (ar) = 8 mm, rotational speed (rs) = 1500 rpm, feed rate (f) = 120 mm/min, diameter of cutter (d) = 32mm. Figure 3.10 The end milling operation with the engagement angle shown θ = Cos-1 (1 –2*ar/d) The National University of Singapore (3.8) 31 Chapter 3 Cutting Force Measurement The engagement time for a single tooth is given by t = (θo/ 360o)* T, where T is the time for one rotation of the cutter. For the cutting parameters for this particular cut, θ = Cos-1 (1 –2*8/32) = 60o and T= 60/1500 s, the engagement time, t = 6.7 ms. To compare the engagement time, force outputs are taken from the X-axis output of the dynamometer and from the locator and the clamp in the same direction. The force pattern for a period of 100ms is shown in figure 3.11. The displayed data has a sampling rate of 2400 samples per second t Force (Newton) 1000 800 600 400 200 0 -200 -400 1 291 581 871 1161 1451 1741 2031 2321 Sample Figure 3.11 Force recorded from the X-axis output of the dynamometer The engagement time, t for a certain engagement period chosen from the data for a sampling period is given by t = [∆t / (sample rate in total period)]* (total period) where ∆t is the sampling period. From Figure 3.11, for a particular engagement period from sample 1461 to 1624, the time of engagement is given by t = [(1624 – 1461) / (2400)] * 100 ms = 6.8 ms. The force from Clamp 1, FAA is shown in Figure 3.12. The graph shown is for a captured period of 100 ms. The displayed data has a sampling rate of 1200 samples per second The National University of Singapore 32 Chapter 3 Cutting Force Measurement t Force (Newton) 1750 1700 1650 1600 1550 1500 1450 1 143 285 427 569 711 853 995 1137 Sample Figure 3.12 Force recorded from Clamp1, FAA From Figure 3.12, for a particular engagement period from sample 567 to 646, the time of engagement is given by t = [(646 – 565) / (1200)] * 100 ms = 6.8 ms. The force from Locator 1, FA is shown in Figure 3.13 The graph shown is for a captured Force (Newtons) period of 100 ms. The displayed data has a sampling rate of 1200 samples per second 700 600 500 400 300 200 100 0 t 1 140 279 418 557 696 835 974 1113 Sample Figure 3.13 Force recorded from Locator 1, FA From Figure 3.13, for a particular engagement period from sample 567 to 646, the time of engagement is given by t = [(665 – 584) / (1200)] * 100 ms = 6.8 ms The National University of Singapore 33 Chapter 3 Cutting Force Measurement The engagement time is found by smoothing the graphs. The region corresponding to the engagement of the flute is seen by a significant rise in the force and hence the time is determined. The engagement times found to be same from the dynamometer, locator and the clamps serves as a preliminary measure that there is concurrence in the response between them for engagement and disengagement of the cutter. This however does not credit the accuracy of the actual magnitude of the measured forces. The analysis of the engagement times proved as an early indicator that the responses during the cutting time of the flute is same for the forces measured from the different equipments and thus the analysis can be continued for the magnitude of the forces, which is of primary concern, illustrated in the next section. 3.7.2 Quantitative Analysis with the Model Developed Based on Planar Stability Analysis It is to be noted that the sampling interval for the outputs from the dynamometer during the engagement period should be divided by two (as the sampling frequency for the 8-channel DAT recorder is half that of the 4-channel DAT recorder). From the corresponding output force value of the dynamometer, the appropriate force values were chosen from the instrumented locators and clamps. This was done with much care and the values obtained were substituted into the Matlab program. The program was developed using Cramer’s rule [Kreyszig 1999]. A Matlab program was written to prompt the values of the nine variables, which were obtained from the clamp and locator outputs. The program allows the user to input the dimensions for different configurations, making it possible for the equations to be applicable to different set-ups. The National University of Singapore 34 Chapter 3 Cutting Force Measurement Fx, Fy and Fz are principally the values to be determined using the output from the sensors. The cutting force components (Fx*, Fy*, Fz*) thus obtained using the set of equations, were compared with the cutting force components (Fx, Fy and Fz) directly measured using a dynamometer. Table 3.1 displays the various cutting conditions under which the tests were performed. The force data captured for one of the end-milling process is shown is shown in Figures 3.14 (a) – 3.14 (k). A summary of the results is shown in Table 3.2. Force (Newtons) Force in the clamp FAA 1500 1000 500 0 1 201 401 601 801 1001 Sample Figure 3.14 (a) Force data recorded from clamp FAA Force (Newtons) Force in clamp FBB 1800 1600 1400 1200 1 201 401 601 801 1001 Sample Figure 3.14 (b) Force data recorded from clamp FBB The National University of Singapore 35 Chapter 3 Cutting Force Measurement Force (Newton) Force in locator FA 1200 1000 800 600 1 201 401 601 801 1001 Sample Figure 3.14 (c) Force data recorded from locator FA Force (Newton) Force in Locator FB 1100 900 700 500 1 201 401 601 801 1001 Sample Figure 3.14 (d) Force data recorded from locator FB Force (Newton) Force in locator FC 1000 500 0 1 201 401 601 801 1001 Sample Figure 3.14 (e) Force data recorded from locator FC The National University of Singapore 36 Chapter 3 Cutting Force Measurement Force (Newton) Force in locator FD 200 100 0 -100 -200 1 201 401 601 801 1001 Sample Figure 3.14 (f) Force data recorded from locator FD Force (Newton) Force in locator FE 150 100 50 0 1 201 401 601 801 1001 Sample Figure 3.14 (g) Force data recorded from locator FE Force (Newton) Force in locator FF 200 100 0 -100 1 201 401 601 801 1001 Sample Figure 3.14 (h) Force data recorded from locator FF The National University of Singapore 37 Chapter 3 Cutting Force Measurement Force (Newton) Force in the X axis of the dynamometer 2000 1000 0 -1000 1 401 801 1201 1601 2001 2401 Sample Figure 3.14 (i) Force data recorded from X-axis of dynamometer Force (Newton) Force in the Y axis of the dynamometer 2000 1000 0 -1000 1 401 801 1201 1601 2001 2401 Sample Figure 3.14 (j) Force data recorded from Y-axis of dynamometer Force (Newton) Force in the Z axis of the dynamometer 400 200 0 -200 -400 -600 1 401 801 1201 1601 2001 2401 Sample Figure 3.14 (k) Force data recorded from Z-axis of dynamometer The National University of Singapore 38 Chapter 3 Cutting Force Measurement The validity of the equations was tested by using the obtained force data. The values for the parameters in equations (3.2) to (3.7) are dependent on the set-up configuration. Figure 3.15 shows a schematic representation of the dimensional variables of an example layout. Figure 3.15 The geometric parameters for the 3-2-1 locator set-up of the workpiece Table 3.1 gives the cutting data of the various milling operations that were performed and recorded. Material: Aluminium Cutter: Tungsten Carbide Indexable insert with 00 helix angle. (4-flute) The National University of Singapore 39 Chapter 3 Cutting Force Measurement Test Number Feed rate (10-2mm/tooth) Speed (m/min) Axial depth of cut (mm) Radial Depth of Cut (mm) 1 3.125 120.6 6 4 2 3.125 120.6 8 8 3 2.00 150.6 8 8 4 3.125 120.6 10 8 5 2.00 150.6 10 10 6 2.00 150.6 8 10 7 2.50 120.6 4 4 8 2.50 150.6 10 10 9 2.50 120.6 6 6 10 2.50 150.6 6 6 11 2.50 150.6 8 6 12 2.50 150.6 4 8 13 2.50 150.6 10 8 14 3.125 120.6 8 10 15 2.00 150.6 4 6 16 2.00 150.6 10 10 17 3.125 120.6 8 6 18 2.50 120.6 8 4 Table 3.1 Cutting data for the experiments performed The National University of Singapore 40 Chapter 3 Cutting Force Measurement Test Number Fx (N) Fy (N) Fz (N) (Fx)* (N) (Fy)* (N) (Fz)* (N) ex (%) ey (%) ez (%) 1 225 590 65 235 667 49 4 13 -25 2 382 1017 57 350 1056 47 -8 4 -18 3 306 831 72 341 876 90 11 5 25 4 348 1312 83 367 1198 112 5 -9 35 5 506 1133 184 395 1316 143 -22 16 -23 6 562 919 123 544 867 114 -3 -6 -7 7 139 352 40 172 447 53 24 27 33 8 610 1215 134 577 986 115 -5 -19 -15 9 291 634 71 270 619 56 -7 -2 -21 10 276 804 144 308 784 97 12 -2 -32 11 343 954 66 322 965 78 -6 1 18 12 146 1003 87 152 1187 65 4 18 -25 13 598 1063 79 542 1090 86 -9 3 9 14 411 1124 45 440 953 66 7 -15 47 15 155 634 56 171 625 48 10 -1 -14 16 369 1425 148 348 1382 124 -6 -3 -16 17 405 861 49 352 887 66 -13 3 35 18 522 944 85 481 976 64 -8 3 -25 Table 3.2 Error values as percentage of the measured force The National University of Singapore 41 Chapter 3 Cutting Force Measurement Figures 3.14(a) to 3.14(k) show the force recorded from the clamps, locators and the dynamometer. In order to check the validity of the equations and calculate the errors, a random point is chosen from one of the output and the corresponding point is chosen for the 10 other outputs. Using these values the errors are measured. For each of the cutting parameters shown in Table 3.1, the forces at one particular point in time are used to calculate the forces represented in Table 3.2. More points can be chosen for each set of parameters to have a larger data to statistically study the accuracy of the developed system. However, the number of data analysed was considered sufficient to make the conclusions in the error of the system. Future work could integrate the system developed with software that can automatically gather the discrete points corresponding to the various force outputs in the entire sampling range which can be used to establish the continuous force output for the entire sampling range. Table 3.2 gives the actual values of the cutting forces Fx, Fy and Fz, as measured directly by a dynamometer and the values Fx*, Fy* and Fz* that were calculated using the equations formulated. ex, ey and ez give the respective error values as a percentage of the measured force. The r.m.s values of the errors are shown in table 3.3 Error RMS value ex (%) 10.6 ey (%) 11.2 ez (%) 25.5 Table 3.3 RMS value of error The National University of Singapore 42 Chapter 3 Cutting Force Measurement 3.8 Performance Analysis The dynamometer has a very high accuracy of force measurement within the associated workspace envelope. Care was taken to ensure that the machining operation was performed within this envelope. The forces obtained from the dynamometer can therefore be considered as the accurate values of the cutting forces, which are used to determine the errors in the force values obtained using the system with the instrumented locators. It can be seen that the error values for X-axis and the Y-axis are rather small and the error values are within 12 % of the actual force values as measured by the dynamometer. The percentage error values from the Z-axis are fairly large as one can see that the actual force values are small due to the 00 helix angle of the cutter. So the noise picked up by the signals become more pronounced causing the discrepancy. However, it can be noted that the force along the Z-axis, Fz < 10-12% (SQRT (Fx2+Fy2)). Hence it does not affect the accuracy of the resultant cutting force significantly. Consequently, the error values from Zaxis are not a good indication of the system developed but the errors in X- and Y- axis show the accuracy of the system of force measurement using instrumented locators. A piezo-electric dynamometer is capable of measuring the cutting force with less than 0.1% error within its workspace envelope but this high accuracy may not be a requirement for many applications. In typical machining processes, where clamping is done manually, it can be noted that the clamping force can be much higher than what is needed, in fact it can even be 100% higher than what is required to avoid slippage during machining. The inaccuracies observed in the developed method with instrumented locators are therefore within acceptable limits. It is well known that, in order to keep workpiece deformation to the minimum possible extent, it is imperative to clamp with as little force as The National University of Singapore 43 Chapter 3 Cutting Force Measurement required. However, due to manual clamping and the lack of a viable force measuring device, the workpieces are quite often heavily over-clamped. This system with instrumented locators allows the cutting forces to be measured and would, in turn, allow the minimum clamping forces to be estimated providing a feasible solution to overcome this problem. Further development in this direction would become a source of encouragement to employ intelligent and adaptable fixturing beyond the laboratory environment. 3.9 Advantages with the Developed Measuring System The system developed with the instrumented locators establishes a novel and convenient method of force measurement at low cost with reasonable accuracy. As opposed to a piezo-electric dynamometer, which has a constraining workspace envelope, the developed system is capable of accommodating workpieces of any shape and size, as the force sensors can be placed around the workpiece to suit its geometry, hence the inaccuracies due to exceeding size constraints can be overcome. For instance, the dynamometer used for the experiments in this work has a certain associated volume beyond which all the forces cannot be measured accurately. Milling operations performed outside this limiting workspace are likely to produce inaccurate force recordings. This is due to the fact that the moments induced by forces acting outside the limiting envelope would become considerable and cannot be accommodated by the dynamometer. Static loading tests were performed to confirm the effect of loading a workpiece outside the workspace envelope. This is demonstrated in detail in Chapter 4. The National University of Singapore 44 Chapter 3 Cutting Force Measurement By using the instrumented locators, one could eliminate this problem as the sensors in the locators are in all the three orthogonal planes and placed at different levels. Any high moment values can be accounted for. Furthermore, it is also possible to make this system more sensitive than a dynamometer as sensors with different ranges and gains can be used for different locators depending on the force experienced in a particular axis or plane. It also has to be noted that the system developed is not designed for any particular workpiece shape or geometry but can be configured to accommodate a wide variety of workpieces with input parameters given by the user. The cost of the system developed is only about 10% of the cost of a dynamometer. This would be a major encouragement for applications beyond the laboratory environment. The dynamometer used is about 90 kgs and 600 mm x 400 mm, which occupies significant space and it adds considerable load to the machine table and also makes it difficult to handle. The space occupied by instrumented locators is very small and there is no significant addition to the load on the machine table. 3.10 Disadvantages of the Developed System There are also several disadvantages of the developed system that cannot be overlooked. For each configuration, a new set of parameters has to be chosen and it can be tedious for non-prismatic components. Though the equations need not be altered, the user input variables have to be changed for each configuration. This would eventually lead to an increase in set-up time. Furthermore, the overall set-up takes more time as compared to the dynamometer as each of the sensors must be separately connected and calibrated. However, this can be overcome by using an industrial terminal. Unlike the dynamometer, which has all the connections concealed inside the base plate, instrumented locators have The National University of Singapore 45 Chapter 3 Cutting Force Measurement wired connections, which could clutter the workspace area and make wet cutting questionable. This could possibly be overcome by the use of wireless sensors. The National University of Singapore 46 Chapter 4 Force Measurement Outside Workspace Envelope CHAPTER 4 FORCE MEASUREMENT ERRORS OUTSIDE THE ASSOCIATED WORKSPACE ENVELOPE OF A DYNAMOMETER 4.1 Introduction Moments caused by loading at significant distances from the dynamometer surface cannot be accommodated by the dynamometer. Due to this, there exists a specification of a workspace envelope for each dynamometer beyond which, the moment values become pronounced and machining forces cannot be accounted for accurately. This chapter attempts to illustrate the inherent drawback in the dynamometer due to this constraint on the volume of operation, which is not present in the force measurement system developed in this work. 4.2 Static Loading Test for the Dynamometer In order to determine the accuracy of a dynamometer for loading conditions outside the allowable workspace envelope, a series of static loading tests were performed. A load of 9 kg was placed on the dynamometer. Using a 20 kg mass and pulley system, a force was applied along the Y-axis of the dynamometer at various heights as shown in Figure 4.1. The mass of 9kg provides a force precisely in the Z-axis. The set-up was made to accommodate the loading in the Y-axis at different levels. In theory, the Z-axis of the dynamometer should record a constant force, irrespective of the loading in the Y-axis. Experiments were conducted to verify this. The National University of Singapore 47 Chapter 4 Force Measurement Outside Workspace Envelope Figure 4.1 Set-up for static loading (Actual set-up) The dynamometer has a calibrated workspace envelope, which allows loading upto a height of 50mm above the dynamometer. Horizontal load in the Y-axis was applied at heights of 50mm, 100mm, 150mm, 200mm and 250mm as shown in Figure 4.2. The National University of Singapore 48 Chapter 4 Force Measurement Outside Workspace Envelope Figure 4.2 Set-up for static loading (Schematic) The height of application of the load on the workpiece was gradually increased and the resulting forces recorded along the Z-axis of the dynamometer are shown in Figure 4.3(a). The corresponding variation on the Y-axis is shown in Figure 4.3(b). The National University of Singapore 49 Chapter 4 Force Measurement Outside Workspace Envelope 140 Force (N) 130 120 110 100 90 80 50 100 150 200 250 Height (mm) Figure 4.3 (a) Force along the Z-axis of the dynamometer 200 Force (N) 180 160 140 120 100 80 50 100 150 200 250 Height (mm) Figure 4.3 (b) Force along the Y-axis of the dynamometer It was noted that the forces along the Y-axis was constant but the force along the Z-axis increased steadily. By applying a linear fit, this variation can be represented as Z = Z0 + M*Ry (4.1) where Z is the force recorded along the Z-Axis of the dynamometer, Z0 is force recorded along the Z-axis at the boundary of the workspace envelope, M the force gradient The National University of Singapore 50 Chapter 4 Force Measurement Outside Workspace Envelope corresponding to the force equivalent of the moment produced and Ry is the moment arm, which is the veritical distance from the level of the dynamometer. One would expect the loading in the Y-axis not to affect the force measured along the Z-axis of the dynamometer. This is usually the case when the loading is within the workspace envelope. However, as one can see from Figure 4.3 (a), the measured value of the force recorded along the Z-axis changes considerably as the position of the load becomes higher. The calibrated accuracy for the dynamometer is applicable only within the allowable workspace. This causes significant error values when the loading point was moved further away from the workspace envelope. Forces recorded in one axis are no longer independent of the forces acting in another orthogonal axis. This clearly shows a major disadvantage in force measurements of machining large-sized workpieces that cannot be encompassed within the workspace envelope of a dynamometer. This substantiates the critical advantage in the developed force measurement system that is not constrained by size or shape of the workpiece. The National University of Singapore 51 Chapter 5 Development of a Clamping Element CHAPTER 5 DEVELOPMENT OF A CLAMPING ELEMENT USING DIRECTTORQUE CONTROL 5.1 Introduction In work-holding operations, the application of excessive clamping forces would lead to distortion and thus dimensional inaccuracy of a workpiece. This problem is common in industries, which manufacture thin-walled components requiring high precision, such as aerospace parts and hard disk drive casings. The cause of such a problem is the conventional practice of manually applying the largest clamping force available to ensure that the workpieces are secured against perturbations caused by dynamic cutting force during machining. In an actual machining operation, cutting forces change throughout the course of the machining operation, causing the clamping force requirements to change in tandem. In an ideal fixturing system, both the location and magnitude of the clamping force are controllable in real time, ensuring optimal workholding at all times. A more practical and cost effective approach is to have off-line optimisation of the location of the clamping forces and on-line optimisation of the cutting force magnitudes. In this chapter, the design and development of a clamping element based on direct torque control is explained. The mechanical design, control mechanism and the performance of the developed system are demonstrated. A series of experiments that were conducted to study the repeatability, resolution and accuracy of the system are illustrated. The National University of Singapore 52 Chapter 5 Development of a Clamping Element 5.2 Direct Torque Control of DC Motor There have been several force controlled clamping elements developed in the past. Sollie and Mannan [1997] developed a force-controlled clamping element based on the cutting force model developed by Altintas and Spence [Altintas 1991] and the fixture model developed by Gui et al [Gui 1996], which introduces the localised contact rigidity between workpiece and the fixturing elements by using virtual springs for analysis. The control technique used is a hybrid position/force control developed by Raibert and Craig [Raibert 1981] and Whitney [Whitney 1987]. In this system, controlled armature voltage of the PMDC motor is transformed through a screw actuator into a linear motion to apply the clamping force. A soft compression spring is introduced between the screw actuator and the workpiece to make the system compatible with the model by Gui [Gui 1996]. The hybrid position force controller developed by Sollie uses a stepper motor (which can also be replaced with any actuator) to realise the position control and a force sensor is used for force control. The method proposed in this work requires a simple DC motor and does not require a force sensor. The torque is controlled in the region of zero speed of the motor. The feasibility of this system is due to the directly proportional relationship that exists between the developed torque and armature current. The developed torque and the armature current are related as below T = kφI a (5.1) where, T is the developed torque, k is a constant, Ia is the armature current and φ is the magnetic flux. As the magnetic flux under normal operating condition is almost constant, The National University of Singapore 53 Chapter 5 Development of a Clamping Element as a PMDC motor is used, the developed torque (5.1) is directly proportional to current. Hence the developed torque can be controlled by the armature current Ia. The control of armature current is in turn achieved by controlling the armature voltage Va applied to the motor (using a chopper). The transfer function between the armature current and the armature voltage of the motor is given by: I a (s) G Eb ( s ) = + D( s ) (Ra + La s ) (Ra + La s ) (5.2) where Eb(s) is the back emf term dependent on the speed. With angular velocity being zero in the present case, there is no back emf. So the transfer function between the armature current and the armature voltage is given by I a ( s) G = D( s ) (Ra + La s ) (5.3) where, Ra is the armature resistance and La is the armature inductance. 5.3 Control Mechanism The control scheme employed for deriving a varying torque is shown in Figure 5.3. It employs a Permanent Magnet DC (PMDC) motor for delivering a variable torque at zero speed. The motor ratings are as below. Rated armature voltage - 24 V Maximum continuous current - 252 mA Maximum continuous torque - 13.9 mNm Stall torque - 33.1 mNm The National University of Singapore 54 Chapter 5 Development of a Clamping Element The control scheme employs a two-quadrant chopper that is realized using two MOSFETs (S1 and S2). S1 and S2 are switched in complement to each other at a high frequency (50 kHz). Such a two-quadrant chopper can handle both positive and negative torques (armature currents). However, the machine speed (armature voltage) cannot be reversed. In the present control scheme, the motor operates only in the first quadrant of the speed-torque plane. Hence, MOSFET S2 can also be replaced by a power diode. However, as the voltage drop and hence the power loss in a power diode are generally higher than those in a MOSFET, use of MOSFET S2 gives a higher efficiency. Ia Vdc 1-D S1 S2 D + Va PMDC motor DRIVER Ia PWM + K + Iref Proportional Controller Figure 5.2 DC Motor- Torque controller The National University of Singapore 55 Chapter 5 Development of a Clamping Element The applied armature voltage is controlled by the duty ratio D of S1. The relation between the applied armature voltage Va and duty ratio D of S1 is given by Va = D * Vdc (5.4) where Vdc (= 24 V) is the dc source voltage. Considering (5.2), the control input-toarmature current (D-to-Ia) transfer function of the motor can be written as I a ( s) G = D( s ) (Ra + La s ) (5.5) where, G is the dc gain. It can be seen from (5.5) that the control-to-output transfer function is similar to that of a simple first order system. Robust stability and performance objectives can be easily achieved. A simple high gain proportional controller has been used to realize the desired control of the armature current. The motor current reference is derived from external sources (precision supply / DAC of a computer). When the reference signal is derived from a DAC, the resolution of the reference signal depends on the associated quantization process. The actual motor current is sensed and is compared with the current reference to generate the armature current error. This error is amplified by a high gain proportional controller K (Figure 5.2) and is fed to the PWM comparator for generating the duty ratio pulses for S1 and S2. 5.4 Mechanical System In the proposed method, the linear motion of the clamp is achieved using a simple rack and pinion system. The factors that are to be considered for the clamp to deliver the required force are the size of rack and pinion to control the moment arm and the maximum The National University of Singapore 56 Chapter 5 Development of a Clamping Element allowable stall torque. The developed prototype was fabricated to deliver a maximum force of 150N. Figure 5.3 shows the torque-speed characteristics of the selected PMDC motor. The control of torque (force) is achieved at zero speed of the motor, which corresponds to the X-axis of Figure 5.3. In Figure 5.3, the shaded area is the region of continuous operation under nominal loading conditions of the motor. To avoid overheating, the maximum continuous torque under zero speed should not exceed 14 mNm. Hence with a gear ratio of 200:1 a maximum torque of 2.8 Nm can be delivered. This translates to a force of 150 N with the chosen moment arm of the rack and pinion. n[rpm] 7000 6000 5000 4000 3000 2000 1000 0 0 10 20 30 40 50 M [mNm] Figure 5.3 Motor Operating Characteristics The National University of Singapore 57 Chapter 5 Development of a Clamping Element For calibration purpose, a piezoelectric sensor was used to measure the clamping force. A series of tests were conducted and the forces developed for different armature currents were measured, as shown in Figure 5.4. Force (Newton) Force - Current Calibration 150 100 50 0 0 50 100 150 200 250 300 Current (mA) Figure 5.4 Calibration Graph As one can expect, the calibration graph does not pass through the origin as current is drawn under no load condition to compensate for motor losses such as eddy current and hysteresis losses. The calibration factor was found to be 0.5N/mA. An accuracy of +/- 0.2 N was noted using a DAC of 10-bit word length. This error is less than 1% of the maximum force delivered. Further reduction of error can be achieved by employing a DAC of a longer word length. This shows that the developed clamping element and control mechanism performs with good accuracy and resolution. The National University of Singapore 58 Chapter 6 Optimisation of Minimum Clamping Force CHAPTER 6 OPTIMISATION OF MINIMUM CLAMPING FORCE 6.1 Introduction As mentioned in the previous chapters, it is important in Flexible Manufacturing Systems to determine the minimum allowable clamping force to secure the workpiece in a stable position. Keeping the clamping forces to a minimum reduces the deformation of the workpiece. However, care must be taken to ensure that the workpiece does not slip. In other words, the clamping force must ensure that the locators are in contact with the workpiece throughout the machining process. There have been many researchers in the past who have attempted to optimise the location of the clamping positions off-line and optimise the clamping forces online. It can be noted that non-linear programming is used for the optimisation of the clamping positions and linear programming used for optimisation of the clamping force. However, real time optimisation and control of clamping forces is still seen only in a laboratory environment due to its complexity, high associated costs and expertise required. This chapter presents a technique developed to simplify the process of optimisation and provide a methodology to easily obtain an estimate of the minimum clamping force through an iterative procedure. The method is developed with cutting force measurements performed with instrumented locators as shown in Chapter 3. This effectively reduces the cost involved in using the dynamometer. Windows-based optimisation software TORA [Hamdy 2003] is used for the purpose of linear programming. The National University of Singapore 59 Chapter 6 Optimisation of Minimum Clamping Force 6.2 Algorithm for Optimisation The optimisation follows an iterative procedure as illustrated in Figure 6.1. The first machining operation is performed applying sufficient clamping force to ensure that the workpiece remains stable. The machining process is repeated with the same cutting parameters and the clamping force is progressively optimised for each subsequent machining operation to reach the final optimal clamping force. Initial clamping done with sufficient clamping force. Measure Cutting, Clamping and Locator forces during machining. Optimisation of the clamping forces with the measured force data. Does the optimal value differ significantly from the applied clamping force? No Yes Repeat machining with the new optimal clamping force. Optimal clamping reached Figure 6.1 Optimisation Scheme The National University of Singapore 60 Chapter 6 Optimisation of Minimum Clamping Force 6.3 Experimental Set-up The fixturing set-up follows the 3-2-1 locating principle. The clamping forces are provided by the electro-mechanical clamps with the rack and pinion mechanism, with direct-torque control, which was developed as mentioned in Chapter 5. All forces from the locators are measured during each machining process. The set-up is shown in Figures 6.2(a) and 6.2(b). Figure 6.2(a) Plan view of the set-up The National University of Singapore 61 Chapter 6 Optimisation of Minimum Clamping Force Figure 6.2(b) Isometric view of the set-up 6.4 Optimisation Technique using Linear Programming Initially, the workpiece was clamped with a pre-determined sufficient securing force and the machining operation was performed. The locator forces and clamping forces were recorded for the operation. Equations (3.2) to (3.7) establish the relationship to determine the cutting forces using the measured values of the clamping forces and locator forces. With the data recorded, the cutting force for the entire machining operation can be determined. With the same cutting parameters, the machining operation was repeated. The clamping forces can be optimised for this operation, as the cutting forces are already known. The National University of Singapore 62 Chapter 6 Optimisation of Minimum Clamping Force Linear Optimisation is done using TORA [Hamdy 2003]. TORA optimisation is a Windows-based software that offers various modules such as linear programming. It is a simple-to-use and user-friendly software, which can be used in automated mode to directly obtain the final solution of the problem or in tutorial mode to study each iteration leading to the optimal solution. The components of the cutting forces are known from the data of the first cut. For the workpiece to remain stable there must be no loss of contact between any of the locators and the workpiece. So, all the locator forces must be maintained at positive values. As a linear programming methodology is used, the clamping forces have to be optimised one at a time, first FAA can be optimised by using the data for FBB from the first cut and vice versa. With these conditions and assumptions, the linear programming model is given below, where the notation follows figure 3.4 Minimise FAA subject to equations (3.2) to (3.7) and the constraints -µAA (FAA) < (FAA)fx < µAA (FAA) (6.1) -µAA (FAA) < (FAA)fy < µAA (FAA) (6.2) -µBB (FBB) < (FBB)fz < µBB (FBB) (6.3) -µBB (FBB) < (FBB)fy < µBB (FBB) (6.4) α1 < FBB < α2, (6.5) β1 < Ft < β2, (6.6) χ1 < Fa < χ2, (6.7) δ1 < Ff < δ2 (6.8) FA > 0 (6.9) The National University of Singapore 63 Chapter 6 Optimisation of Minimum Clamping Force FB > 0 (6.10) FC > 0 (6.11) FD > 0 (6.12) FE > 0 (6.13) FF > 0 (6.14) µAA and µBB refer to the co-efficient of friction associated with the clamping forces FAA and FBB respectively and µAA = µBB = 0.5 Constraints (6.1) to (6.4) are obtained by applying the Coulomb’s law of static friction, which is usually used for analysis of workholding devices [Mishra 1989]. All possible contact forces are bounded by a convex friction cone [Tao 1998a]. The limiting values of the cone are given by the product of the co-efficient of static friction and the normal force. In constraints (6.5) to (6.8), α1, α2, β1, β2, χ1,χ2, δ1and δ2 are the values obtained from the data of the first cut. These values correspond to the region of maximum cutting force, which are used to determine the minimum clamping force. Constraints (6.9) to (6.14) are included to ensure that the workpiece does not lose contact with the locators. To illustrate the optimisation technique, the following example is shown for a particular end-milling operation. The forces recorded from the instrumented locators and the clamps are used to tabulate the cutting forces for the first operation. Figures 6.3 (a), 6.3 (b) and 6.3 (c) show the components of the cutting force. Figure 6.4 is the force applied by clamp FBB. The National University of Singapore 64 Chapter 6 Optimisation of Minimum Clamping Force Force (Newtons) Component of Cutting force Ft 800 600 400 200 0 -200 1 -400 250 499 748 997 1246 1495 1744 1993 2242 Sample Figure 6.3 (a) Component of Cutting force Ft Force (Newtons) Component of cutting force, Ff 1000 500 0 1 272 543 814 1085 1356 1627 1898 2169 -500 Sample Figure 6.3 (b) Component of Cutting force Ff Force (Newtons) Component of cutting force, Fa 300 200 100 0 -100 1 263 525 787 1049 1311 1573 1835 2097 2359 Sample Figure 6.3 (c) Component of Cutting force Fa The National University of Singapore 65 Chapter 6 Optimisation of Minimum Clamping Force Force (Newtons) Force applied by clamp FBB 900 850 800 750 700 1 130 259 388 517 646 775 904 1033 1162 Sample Figure 6.4 Force applied by clamp FBB The force values that are shown in the Figures 6.3 (a), 6.3 (b), 6.3 (c) and 6.4 are used to determine the values of α1, α2, β1, β2, χ1,χ2, δ1and δ2. By applying the results of the first cut to the constraints, the optimisation model is solved using TORA linear programming to minimise the clamping force FAA. The output of the solver is given in Figure 6.6. The optimal minimum clamping force, FAA, is found to be 593N. The corresponding values of the other variables are also shown for this minimum clamping force. The negative force shown for friction indicates that the direction of force is opposite to the initial assumption of direction. The force recorded in FAA during the first cut is shown in Figure 6.5. Force (Newtons) Force applied by clamp FAA 1800 1700 1600 1500 1400 1 137 273 409 545 681 817 953 1089 Sample Figure 6.5 Force applied by clamp FAA The National University of Singapore 66 Chapter 6 Optimisation of Minimum Clamping Force It can be noted that the optimal value of force obtained is much lower than the force with which it was clamped during the first cut. This clearly shows that workpieces are heavily overclamped and the clamping force can be reduced considerably. One has to note that the value obtained through optimisation as 593 N is under very ideal conditions and under the estimation of various factors. This can be considered as the absolute least clamping force required. Hence an estimate can be made between the calculated optimal value and the measured value of the clamping force. This will efficiently reduce the clamping force and repetitive measurements will lead to a convergence in the minimal optimal clamping force that is required to keep the workpiece stable. Similarly, FBB can be optimised by using the data obtained for FAA. The National University of Singapore 67 Chapter 6 Optimisation of Minimum Clamping Force Figure 6.6 Output from the optimisation solver α1, α2, β1, β2, χ1,χ2, δ1and δ2 are obtained from Figures 6.3 (a), 6.3 (b), 6.3 (c) and 6.4 corresponding to the region of maximum cutting forces from the data of the first cut. This is done as the maximum clamping force requirement will be when the cutting forces are maximum. The optimisation of the clamping force is performed using these values. A second machining operation is performed with the determined optimal value. New force data will be obtained for Ft, Ff, Fa and FBB. This force data, in turn will be used to obtain a The National University of Singapore 68 Chapter 6 Optimisation of Minimum Clamping Force new set of values of α1, α2, β1, β2, χ1,χ2, δ1and δ2. In this manner, iteratively the final optimal clamping force will be achieved when there is no significant difference in the value of the clamping force applied and the optimal value obtained for the subsequent operation. 6.5 Overall System Integration The integrated system is schematically shown in Figure 6.6. A main PC is used to perform the operations of control and optimisation. The clamping force value is output through the DAC port. The analogue force values from the locators are fed back to the PC through the ADC port. From the data of the force values collected, the parameters for the constraints of the optimisation are determined. Linear programming is performed to determine the optimal clamping value and the new clamping force value is sent to the DAC port to change the clamping force value for the subsequent operation. The process is repeated till the final optimal minimum clamping force is achieved. The National University of Singapore 69 Chapter 6 Optimisation of Minimum Clamping Force Power converter and control Clamp Ia + Reference Ia Current Locator force Ref ADC DAC Data Analysis PC Optimisation F to Ia Figure 6.6 Schematic representation of the system integration The National University of Singapore 70 Chapter 7 Conclusions and Future Work CHAPTER 7 CONCLUSIONS AND FUTURE WORK 7.1 Conclusions Comparing the advantages and the disadvantages of the developed force measurement system with a standard force dynamometer, it can be seen that in spite of the longer set-up time and lesser accuracy as compared to a laboratory type piezo-electric dynamometer, the devised system can be an effective solution towards the realization of intelligent fixturing and other force measurement applications beyond the laboratory environment. From the static loading tests performed on the dynamometer, it can be seen clearly that the dynamometer has a limited workspace and the calibrated sensitivity is not applicable outside the workspace envelope. However, the developed system does not have any constraint on the allowable machining envelope and is universally applicable for workpieces of any size. This is a significant advantage of the developed system with instrumented locators over a dynamometer. The developed system also eliminates the concern of high costs associated with a dynamometer. Control of clamping force is achieved with an electro-mechanical clamping device based on direct-torque control. The control scheme is achieved by controlling the current reference to the motor controller. The motion of the motor is converted to linear motion of the clamp through a rack and pinion mechanism. The torque is controlled in the region of zero speed of the motor, which keeps wear and tear to a minimum. The prototype developed can provide a maximum clamping force of 150 N, with a resolution of +/- 0.2 N. The calibration factor between the current reference and force output was found to be 0.5N/ mA. It does not require a spring and the motor is always stationary as stall torque is The National University of Singapore 71 Chapter 7 Conclusions and Future Work used for application of the force. There is no force feedback, hence there is no need for a force sensor. For the application of minimum optimal clamping force during an end-milling operation, an optimisation technique is developed based on spatial stability analysis. The optimisation is simple technique achieved with linear programming and improved through a series of iterations. The optimisation gives a good estimate for the minimal allowable clamping force by using the data obtained from the first machining operation. This process is repeated progressively, till there is convergence of the clamping force values. Although the developed scheme does not vary and control the clamping forces during the machining process real-time, it gives a low cost and easily achievable methodology to decide the initial clamping force to ensure workpiece stability during machining. 7.2 Contributions The contributions from this work can be summarised as follows • Development of a force measurement system with instrumented locators in a fixturing set-up according to the 3-2-1 locating principle • Experimental demonstration of the validity of the fixturing set-up and its competency and advantages over the dynamometer, especially with regard to the constraint on the volume of operation • Development of an electromechanical clamping element based on the principle of direct torque control • Development of a minimum clamping force optimisation technique with linear programming The National University of Singapore 72 Chapter 7 Conclusions and Future Work 7.3 Scope for Future Work There exists tremendous scope for future research to enhance the systems developed and to contribute more towards research in Flexible Manufacturing Systems in the field of cutting force measurements, control of clamping forces and optimisation of clamping forces. Some of the areas that have promising scope for further research are as follows • System integration with automation The system developed to measure the cutting forces in a fixturing set-up with instrumented locators requires the operator to measure the geometric configuration of the fixture and the relative position of the various fixturing elements for each configuration. Integrating the system with Computer Aided Drawing (CAD) system can relieve this task. A system can be developed where the fixture-workpiece model can be designed and the location of the fixturing points on the drawing will automatically generate the geometric parameters for calculating the cutting forces. • System integration with automated optimised fixturing points A number of researches have been concluded and a great deal of research is continuing to optimise the clamping locations and developing expert fixturing systems. If the optimisation of the clamping positions can be interfaced with the aforementioned CAD system, then the entire system will be a robust automated force measuring system where the optimisation system decides the best points for the fixture-workpiece contact and the CAD system can simultaneously generate the parameters for calculating the cutting forces. Another possible development would The National University of Singapore 73 Chapter 7 Conclusions and Future Work be the on-line optimisation of the clamping positions interfaced to the system and an automated mechanism to clamp according to the optimisation performed. Concurrently, the parameters for cutting force measurement can be generated for each optimal set-up. • More advanced motion conversion system The clamping element designed and developed based on direct torque control can be improved by using a rack and pinion of a higher module or using another mechanical or electro-mechanical system to convert the rotary motion to linear motion that will overcome the inherent drawbacks in geared systems. There exist possible alternatives such as linear actuators and plunger solenoids but they add significant cost to the system. There is scope to develop an alternate motion conversion mechanism for this purpose. • Real time optimisation Though the developed optimisation scheme gives a low cost and easily achievable methodology to decide the initial clamping force to ensure workpiece stability during machining, it does not vary and control the clamping forces during the machining process in real-time. This is a possible area to extend the developed system to an integrated system where the optimisation can take place in real-time and the clamping forces controlled likewise. The National University of Singapore 74 References REFERENCES [Altintas 1991] Altintas Y and Spence A. End Milling Force Algorithms for CAD Systems, Annals of the CIRP, 40(l), pp. 31-34, 1991. [Altintas 2000] Altintas Y. Manufacturing Automation, Cambridge University Press, 1st edition, 2000. [Armarego 1969] Armarego E and Brown J. The Machining of Metals, Prentice-Hall, New Jersey, 1969. [Armarego 1994] Armarego E.J.A and Deshpande N.P. Force Prediction Models and CAD/CAM Software for Helical Tooth Milling Processes, End-milling and Slotting Operations, International Journal of Production Research, 32 (7). pp. 1715-1738, 1994 [Asada 1985] Asada H and By A.B. Kinematic Analysis of Workpart Fixturing for Flexible Assembly with Automatically Reconfigurable Fixtures, IEEE Journal of Robotics and Automation, 1(2), pp. 86-94, 1985. [Beer 1997] Beer F.P and Johnston E. R. Vector Mechanics for Engineers: Statics and Dynamics, McGraw-Hill. New York, 1997. [Ber 1988] Ber A, Rotberg J and Zombach A. Method for Cutting Forces in End Milling, Annals of CIRP, 37(1). pp. 37-40, 1988. The National University of Singapore 75 References [Boerma 1989] Boerma J.R and Kals H.J.J. Fixture Design with FIXES: the Automated Selection of Positioning. Clamping and Support Features for Prismatic Parts, Annals of the CIRP, 38. pp. 399-402. 1989. [Carr lane 1995] Carr Lane Manufacturing Co. Modular Fixturing Handbook 2nd Edition, 1995. [Cecil 1996] Cecil J, Mayer R and Hari U. An Integrated Methodology for Fixture Design, Journal of Intelligent Manufacturing, 7, pp. 95-106, 1996. [Chan 1991] Chan K.C. 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Force measurement is an important aspect in machining performance analysis, flexible manufacturing systems, precision machining, intelligent fixturing and other advanced manufacturing systems In the analysis of fixturing systems, it is imperative to know the optimal clamping forces for the synthesis of fixtures and determination of their locations and magnitude of clamping forces In order to determine... fixturing system, both the location and magnitude of the clamping force are controllable in real time, ensuring optimal workholding at all times A more practical and cost effective approach is to have off-line optimisation of the location of the clamping forces and on-line optimisation of the clamping force magnitudes However, real time optimisation and control of clamping forces is still seen only in. .. three clamping forces For the stability of plane XOY, the The National University of Singapore 21 Chapter 3 Cutting Force Measurement clamping forces and the reaction forces that are normal to the clamping plane are the only forces counterbalancing the external forces (FCX + FCY) In case of fixturing with one clamping plane, stability analysis can be carried out by taking into account the friction forces, ... [Du 1998] developed a three-fingered automated flexible fixturing for planar objects 2.6 Cutting Force Models and Cutting Force Measurement For any flexible manufacturing system, it is important to know the cutting forces during the machining operation The knowledge of the cutting forces helps to determine the clamping forces required and hence the design of the fixturing system There have been many... constant in both magnitude and position, though a machining process is dynamic in both direction and magnitude of the cutting force So it is imperative to make the clamping element capable of adjusting itself in accordance with the cutting force It is seen in most cases, during manual clamping, that a workpiece is clamped with as much force as possible to ensure that it does not disengage during a machining. .. dynamometer for measurement of cutting forces during machining with linear motion Gupta et al [Gupta 1988] developed a sensor based drilling fixture with two dynamometers and a standard vise It was used to study the relationship between clamping forces and machining forces Tounsi and Otho [Tounsi 2000] studied the problem of distortion of the delivered signals in a dynamometer and developed a method to compensate... to determine the friction forces -µFn ≤ Ff ≤ µFn (3.1) One has to note that the fixturing forces are not normal to the boundary contact surface due to the presence of frictional forces The forces referred to as clamping forces and locator forces refer to the normal component of the fixturing forces All the forces acting on a prismatic workpiece during end milling are shown in Figure 3.4 The forces FAA,... forces FAA, FBB are the forces exerted by the clamps and the forces FA, FB, FC, FD, FE and FF are the reaction forces of the locators Ff, Ft and Fa are the cutting forces T1, T2 and T3 are the cutting torques The forces without labels are the friction forces The National University of Singapore 23 Chapter 3 Cutting Force Measurement Figure 3.4 Cutting, clamping and locator forces acting on a prismatic part... sizes, are configurable to workpieces of different shapes, require little set-up time, do not demand great expertise and keep associated costs to a minimum 2.4 Basic Clamping Force Control Control of clamping forces online is an important feature implemented in recent fixturing systems to overcome the drawbacks of conventional fixturing arrangements with constant clamping forces, which are usually applied... manufacturing cost [Grippo 1988] Skilled fixture designers are also hard to find [Finegold 1994] Furthermore, an important problem encountered in conventional fixturing operation is the discrepancy between the constant clamping forces, fixed both in magnitude and points of application, and the dynamic cutting forces on the workpiece which may vary both in magnitudes and direction during machining To overcome ... the forces acting on the workpiece, which are predominantly the cutting and the clamping forces Every machining process, especially those that involve the control of the fixturing forces in flexible... manufacturing systems, require the measurement of clamping and cutting forces This research addresses pertinent issues in both cutting force measurements and control of the clamping force and an... of the location of the clamping forces and on-line optimisation of the clamping force magnitudes However, real time optimisation and control of clamping forces is still seen only in a laboratory