contour error analysis of precise positioning for ball screw driven stage using friction model feedforward

Available online at www.sciencedirect.com ScienceDirect Procedia CIRP 26 (2015) 712 – 717 12th Global Conference on Sustainable Manufacturing Contour error analysis of precise positioning for ball screw driven stage using friction model feedforward N.A Rafana,*, Z Jamaludina, T.H Chiewa , L Abdullaha, M.N Maslana a Control Systems of Machine Tools Research Group, Faculty of Manufacturing Engineering, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya,76100 Durian Tunggal, Melaka, Malaysia * Corresponding author Tel.: +606-3316424; fax: +606-3316424 E-mail address: aidawaty@utem.edu.my Abstract This paper presents contouring error analysis using various classical feedforward controllers A circular motion is performed using an XY positioning stage with specified amplitude and velocities This study applied single Static friction model, Generalized Maxwell Slip (GMS) model and combination of both models together with feedforward Proportional-Integral-Derivative (PID) controller Contour error in term of quadrant glitch is measured by respective angle in each quadrant of circular motion Due to stick slip motion during velocity reversal generate glitches near zero velocity Root-mean-square error (RMSE) is calculated based on radial error of circular motion to show variance of errors towards average The results are experimentally shown that glitches have higher reduction in lower velocity by comparing between applied with and without friction feedforward controller Better reduction in contour errors improves precision of machine tools and hence increases productivity © 2014 2015 The Elsevier B.V © The Authors Authors Published Published by by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of Assembly Technology and Factory Management/Technische Universität Berlin Peer-review under responsibility of Assembly Technology and Factory Management/Technische Universität Berlin Keywords: ball screw driven system; friction compensation; contouring motion; quadrant glitches; feedforward Introduction The ball screw driven are mostly used because of great capabilities in velocity and acceleration, high efficiency and simple pre-stressing [1] Furthermore, ball screw has high service life without stick-slip effect [2] Because of that reason, it is dominantly chosen in machine construction market However, Pritschow [1] discusses on linear motors against the ball screw drives that the form resonant system with low natural frequency and thus limit the overall bandwidth Gordon and Hillery [3]describe a high speed cutting machine development by using linear motors A linear motor which is an electromagnetic actuator is composed of two rigid parts supported by linear bearing, offers several advantages such as low inertia, better performance, increased accuracy and reduced complexity A model based feedforward controller is introduced as friction compensation by Tjahjowidodo et al [4] This model adopted various friction model from Coulomb model to GMS model It is found that Coulomb and Stribeck effect is for motion with high displacement while GMS is effective in presenting friction behavior in pre-sliding regime Furthermore, feedback compensation is better than feedforward compensation for fast response and low steady state error Jamaludin et al [5] has illustrated friction behavior for presliding and sliding regime by a feedforward friction force compensation based on GMS model In addition to the model, an inverse-model-based disturbance observer and repetitive controller are introduced to reduce friction induced quadrant glitch However, the compensation designed not able to compensate cutting force higher harmonics Lampaert [6] did a comparison between model and nonmodel based friction compensation techniques in pre-sliding regime GMS and disturbance observer is been experimented to the weak feedback controller GMS appears to be good in position tracking error while proposed disturbance observer gives best feedforward friction compensation result However, higher reference trajectories increasing position error Thus, 2212-8271 © 2015 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of Assembly Technology and Factory Management/Technische Universität Berlin doi:10.1016/j.procir.2014.08.021 713 N.A Rafan et al / Procedia CIRP 26 (2015) 712 – 717 GMS is best in reducing errors since disturbance observer has only compensated disturbance up to limited bandwidth This paper is organized as follows Section provides an overview of friction compensation models applied to compensate friction while sliding and pre-sliding regime Section describes relationship between quadrant glitch magnitudes with feed rate in CNC machine Section covers experimentation works and result of applied friction compensation model onto ball screw driven positioning stage Section concludes the finding and gives recommendation for future works Friction compensation model This section discusses various friction compensation model to compensate friction occurred while sliding and pre-sliding regime Much research has been done to compensate friction especially on ball screw driven positioning It has been studied that nonlinear frictions caused by a ball screw driven are Stribeck effect and rolling friction [2] Whereas static friction affects the circular contour accuracy at near zero velocity and begins to move [7] Armstrong et al [8] highlights two important behaviours: • Elastically deformed and rise in pre-sliding regime • Plastically deformed and rise to static friction Pre-sliding regime is where breakaway point occurred Presliding displacement is a breakaway displacement Xi [9] stated that the static friction is at maximum value when breakaway displacement has been reached Static friction drop to zero when breakaway displacement is in the end Al-Bender and Lampaert [10] defines that pre-sliding is where friction force dominantly a hysteresis non-local memory of the displacement In many years, research is continuously done on compensating friction based on presliding regime Dahl, Lugre, Leuven model and Generalized Maxwell Slip (GMS) are compensation model based on presliding regime and hysteresis with nonlocal memory [8,7,11,12] In 1995, LuGre model was introduced by Canudas et al [11] LuGre model is a new improved friction model for control of the system with friction It includes Stribeck effect, hysteresis, spring-like characteristic for stiction and varying break-away force This model presents experimentally observed of friction behavior In 2000, Swevers et al [13] introduced Leuven model that is an improved LuGre model This model has been modified by Lampaert et al [14] which provide continuous friction force and solve the problem on stack overflow in implementation of hysteresis force In 2003, Lampaert et al [7] presented a Generalized-Maxwell-Slip friction model or GMS model After that, GMS model has been studied and illustrated in simulation for both pre-sliding and sliding regimes by Al Bender et al [10] The extended Maxwell which is assessed via Monte Carlo experiment became an effective method for feedforward control of the system with friction In recent years, a study on modified GMS is aggressively done by few researchers Smoothed GMS friction model and M-GMS have been introduced to provide smooth connection between sliding regimes [15][16] Contouring error- Quadrant glitch Motion error is one of important error that affect the accuracy of machine High friction occurs especially at motion reversal Glitch focus at quadrant location during circular motion is a direct result of it Circular cutting process is performed on CNC milling machine according to ISO 2304:1996(E) Quadrant glitch analysis is performed using measurement at the roundness of circular workpiece where the magnitudes of the glitches at the quadrant position are identified Tracking error analysis based on radial error recorded by roundness measurement Tracking error is the different between ideal designed and stimulated tracking position with the actual tracking position on the machine During the circular motion performed on a CNC milling machine, the X axis and Y axis motion on XY table is moved in sinusoidal form The non-linear behaviour of friction at motion reversal will cause glitches to form at the quadrant position of the circular workpiece The magnitude of quadrant glitches depends on the square of the feed rate Roundness measurement is a measure of the sharpness of a particle’s edges and corners The measuring equipment used is MAHR MMQ-44 roundness tester machine FORMTESTER MMQ-44 roundness tester is features with three measuring axes (C,Z and X) and an automatic centering and tilting table It is controlled by FORM-PC, a measuring, control and evaluation program The analysis involves two different federate with same spindle speed Table shows the parameter setup for the experiment Table Parameter set up for cutting experiment Diameter of circular path 30 mm Spindle speed Feedrate 1000 rpm 250 mm/min 500 mm/min 1.5 mm Depth of cut The results of roughness measurement for work pieces cut with feed rate 250 and 500 mm/min are shown in Fig Fig 1(a) and 1(b) demonstrate radial error with respect to angle in degree of circular workpiece Whereas, Fig (c) and (d) show quadrant glitches at each quadrant angle a [mm] [degree] 714 N.A Rafan et al / Procedia CIRP 26 (2015) 712 – 717 b [mm] [degree] c Position y [mm] d Position y [mm] Position x [mm] Position x [mm] Fig Experimental setup Fig (a) Linear centered roundness measurement with feed rate 250 mm/min (b) Linear centered roundness measurement with feed rate 500 mm/min (c) Circular centered roundness measurement with feedrate 250 mm/min (d) Circular centered roundness measurement with feedrate 500 mm/min Table shows the result of quadrant glitch based on different federate From the table, it can be seen that motion accuracy of CNC machine tools increases as operating speed increases Table Result of quadrant glitch based on different feedrate Feedrate (mm/min) 250 500 Radial error (μm) 12.91 10.98 Magnitude of quadrant glitch (μm) 2.2 90 1.7 180 0.5 3.5 270 2.5 Fig Block diagram of system with friction feedforward compensation Table Parameter applied for experiment Experimental setup and result 4.1Experimental setup Friction feedforward compensation is validated by experiments For circular motion, x and y axis are defined with sinusoidal wave (cosine and sine wave) respectively Sinusoidal wave with amplitude 30 mm is applied to evaluate the compensation performance of the reversal motion The tracking performance of axes is analysed with three different velocities; mm/s, mm/s and mm/s Fig and Fig illustrates the experimental setup and block diagram of applied friction feedforward compensation with PID controller for each axis respectively Table shows parameter setup for both axes Parameter Source of signal Amplitude (mm) Bias Frequency (rad/sec) Phase (rad) Sample time (s) Kp (V/mm) Ki (V/mm·s) Kd (V·s/mm) Velocity (mm/s) X axis Cosine Y axis Sine 30 f*2*pi pi/2 1/2000 1.2051 0.0012051 0.0060257 1.32 0.0008248 0.006805 2,3,4 Friction behaviour categorised in sliding and pre-sliding regime Hence, important parameters to be identified including Coulomb friction, Stribeck friction, Stribeck velocity, number of elementary blocks, stiffness and viscous Friction behaviour in sliding regime is analysed by static friction model This model is dependent to the sliding velocity ν It considers Coulomb, viscous and Stribeck friction The Stribeck effect represents a decreasing effect of friction forces respectively Vs is Stribeck velocity and Stribeck shape factor δ Equation is applied to identify static friction model Table shows identified parameters for static friction model Đ Ff Q đFc  (Fs  Fc ) exp ă  ă Vs â à á ẵ ¾ ˜ sign ν °¿ (1) 715 N.A Rafan et al / Procedia CIRP 26 (2015) 712 – 717 Table Parameter for static friction model α1  α  α  α ¦W Parameter Fc Fs σ 1/Vs k1  k  k  k K0 x-axis 0.5 3.8 0.15 y-axis 0.15 1.00 4.3 0.2 k2  k3  k4 k3  k4 In pre-sliding regime, the Generalized Maxwell-Slip (GMS) model consists of friction properties of Stribeck curve, the hysteresis function and frictional memory It has elements of Maxwell slip, which is parallel of N elementary slip-blocks and spring [5,7,17] The dynamic behavior of elementary slip block and spring is described as below: dFi kiX (2) dt dFi dt F · § sign(X ) C ăă D i  i áá s(X ) â (3) k4 i Ka (5) Kb Kc Table Parameter of GMS model Parameter α1 α2 α3 α4 k1 k2 k3 k4 x-axis 0.0625 0.1375 0.1 0.0125 46.4286 61.9047 10.4167 6.25 y-axis 0.1795 0.3532 0.068 0.0352 120.2877 100.6 20.404 2.926 The total friction force F is the summation of the output of all elementary state models and viscous term σ F (X ) N ¦ F (X )  V ˜ X (t ) i (4) i In term of GMS model, displacement is dominant and hysteretic with non-local memory behaviour This behaviour is represented with a virgin curve The virgin curve as in Fig is constructed based on sinusoidal excitation of amplitudes of μm and 40 μm with frequency of Hz N, elementary slip blocks in this study is N=4 yielding to 13 parameters (αi’s and ki’s ) total from each elements Based on virgin curve, GMS parameter is identified as in Equation (5) Table shows GMS model parameters applied for this study 4.2 Experimental result XY stage is run with sinusoidal waves at both X and Y axes to perform a circular motion for minimum cycles The experiment is done at different velocities; mm/s, mm/s and mm/s Based on experimental results, it demonstrates the most effective implementation of PID and friction feedforward compensation model is when velocity is mm/s Fig shows XY plot and radial error of circular motion for a different condition of model implementation The system has been implemented by static friction model, GMS model and combination of static and GMS model Table compares experimental data in term of contour error and tracking error Table RMS Error and tracking error of quadrant glitch magnitude Velocity (mm/s) Fig Virgin curve for GMS model Friction model Contour error Tracking error RMSE RMSE at X 0.0029 RMSE at Y 0.0027 no feedforward static 0.0006496 Max error 0.0031 0.000806 0.0025 0.0013 0.000799 GMS 0.0008901 0.0034 0.0028 0.0025 Static + GMS 0.0007961 0.0037 0.0013 0.000911 no feedforward static 0.0008909 0.004 0.0042 0.0039 0.0009434 0.0037 0.0015 0.0008741 GMS 0.000727 0.0034 0.0042 0.0037 Static + GMS 0.0008144 0.0034 0.0013 0.0009235 no feedforward static 0.0009551 0.0052 0.0055 0.0053 0.0009754 0.0038 0.0013 0.001 GMS 0.0008682 0.0056 0.0058 0.0049 Static + GMS 0.0009522 0.0036 0.0012 0.0011 716 N.A Rafan et al / Procedia CIRP 26 (2015) 712 – 717 position y [mm] without friction feedforward with static 40 40 20 20 20 0 0 -20 -20 -20 -20 -20 20 position x [mm] 40 -40 -40 -3 x 10 3 2 1 0 20 40 -40 -40 -20 20 40 -40 -40 -3 x 10 -20 20 40 180 270 360 -3 x 10 x 10 1 0 -1 -1 -1 -1 -2 -3 -20 -3 a Static + GMS 40 20 -40 -40 radial error [mm] with GMS 40 -2 -2 90 180 270 angle [degree] 360 -3 90 180 270 360 -3 -2 90 180 270 360 -3 90 b Fig XY plot and radial error of circular motion at mm/s Based on XY plot and radial error of circular motion as illustrated as Figure 5, a list of magnitude of quadrant glitches is measured to show the comparison of glitches according to friction model applied Table shows the comparison of magnitude glitches for velocity of mm/s, mm/s and mm/s c Table Magnitude of quadrant glitches based on radial error of circular motion Velocity Angle Magnitude of quadrant glitches (mm) (mm/s) (degree) Without friction feedforward With static With GMS with static +GMS 0.00308 0.00245 0.003364 0.002896 90 0.00181 0.00127 0.002389 0.001747 180 0.001098 0.00083 0.001045 0.000872 270 0.0009279 0.00032 0.001051 0.000707 0.003975 0.00242 0.003426 0.002387 90 0.002579 0.00175 0.002619 0.002008 180 0.001098 0.0026 0.002265 0.002566 270 0.001425 0.00056 0.00175 0.000906 0.005156 0.00378 0.005557 0.003557 90 0.003193 0.00234 0.002853 0.002287 180 0.001807 0.00248 0.001937 0.002669 270 0.001864 0.00125 0.002276 0.001445 Fig Percentage error reduction at velocity (a) mm/s (b) mm/s (c) mm/s The compensation of quadrant glitch magnitude is analyzed based on root mean square error (RMSE) The results have demonstrated that RMSE of tracking error is clearly viewed compared to contour error Overall, RMSE of tracking error at Y axis is lower than X axis However, there is no significant reduction of RMSE in contour error regardless compensation model By comparing different friction feedforward compensation model, static friction model shows a significant reduction for all velocities In another point of view, better reduction with implementation of static friction represents that the friction in sliding regime is accountable to be compensated compared to pre-sliding regime Fig compares percentage error reduction at each quadrant at different velocities Each quadrant categorized with positive y axis (pos y), positive x axis (pos x), negative y axis (neg y) and negative x axis (neg x) as in Fig N.A Rafan et al / Procedia CIRP 26 (2015) 712 – 717 Fig Quadrant assigned for x and y axis Based on the results of percentage error reduction in Fig 6, lower velocity produces higher reduction The observed result shows that percentage error reduction is higher at each quadrant especially by static friction model The reduction is much higher when implemented a combination of static and GMS friction model In term of quadrant, it is illustrated that negative Y provides a better reduction among another quadrant Conclusion The aim of study is to reduce or eliminate contouring error in order to improve machine tools precision The present study was designed to determine the effect of PID and friction compensation model feedforward on ball screw driven positioning stage It is shown that PID controller with friction feedforward provides no sufficient enough to compensate friction in the system It is found that only lower velocity gives better reduction in error Besides that, RMSE of tracking error at Y axis is more likely compensate compared to X axis Further research may explore the effectiveness of another controller such as Cascade controller with friction compensation model feedforward towards ball screw driven positioning stage Acknowledgements This research was supported by Universiti Teknikal Malaysia Melaka (UTeM) and Fundamental Research Grant Scheme (FRGS) with reference no FRGS/2013/FKP/ICT02/02/3/F00158 References [1] G Pritschow, “A comparison of linear and conventional electromechanical dives,” CIRP Annals-Manufacturing Technology, vol 47, no 1, 1998 [2] Y Altintas, A Verl, C Brecher, L Uriarte, and G Pritschow, “Machine tool feed drives,” CIRP Annals - Manufacturing Technology, vol 60, no 2, pp 779–796, Jan 2011 [3] S Gordon and M T Hillery, “Development of a high-speed CNC cutting machine using linear motors,” Journal of Materials Processing Technology, vol 166, no 3, pp 321–329, Aug 2005 [4] T Tjahjowidodo, F Al-Bender, H Van Brussel, and W Symens, “Friction characterization and compensation in electro-mechanical systems,” Journal of Sound and Vibration, vol 308, no 3–5, pp 632–646, Dec 2007 [5] Z Jamaludin, H Van, G Pipeleers, and J Swevers, “Accurate motion control of xy high-speed linear drives using friction model feedforward and cutting forces estimation,” CIRP Annals- Manufacturing Technology, vol 57, pp 403–406, 2008 717 [6] V Lampaert, J Swevers, and F Al-Bender, “Comparison of model and non-model based friction compensation techniques in the neighbourhood of pre-sliding friction,” in Proceeding of the 2004 American Control Conference, 2004, pp 1121–1126 [7] V Lampaert, F Al-Bender, and J Swevers, “A generalized Maxwell-slip friction model appropriate for control purposes,” Physics and Control, 2003 [8] B Armstrong-Hélouvry, P Dupont, and C C De Wit, “A survey of models, analysis tools and compensation methods for the control of machines with friction,” Automatica, vol 30, no 7, pp 1083–1138, Jul 1994 [9] X.-C Xi, A.-N Poo, and G.-S Hong, “Tracking error-based static friction compensation for a bi-axial CNC machine,” Precision Engineering, vol 34, no 3, pp 480–488, Jul 2010 [10] F Al-Bender, V Lampaert, and J Swevers, “The generalized Maxwellslip model: a novel model for friction simulation and compensation,” Automatic Control, vol 50, no 11, pp 1883–1887, 2005 [11] C Canudas de Wit, H Olsson, K J Astrom, and P Lischinsky, “A new model for control of systems with friction,” Automatic Control, IEEE Transactions on, vol 40, no 3, pp 419–425, 1995 [12] T Piatkowski, “Dahl and LuGre dynamic friction models — The analysis of selected properties,” Mechanism and Machine Theory, vol 73, pp 91–100, Mar 2014 [13] J Swevers, F Al-Bender, C G Ganseman, and T Projogo, “An integrated friction model structure with improved presliding behavior for accurate friction compensation,” IEEE Transactions on Automatic Control, vol 45, no 4, pp 675–686, Apr 2000 [14] V Lampaert, J Swevers, and F Al-Bender, “Modification of the Leuven integrated friction model structure,” IEEE Transactions on Automatic Control, vol 47, no 4, pp 683–687, Apr 2002 [15] M Boegli, T De Laet, J De Schutter, and J Swevers, “A Smoothed GMS friction model for Moving Horizon friction state and parameter estimation,” in 2012 12th IEEE International Workshop on Advanced Motion Control (AMC), 2012, pp 1–6 [16] T Piatkowski, “GMS friction model approximation,” Mechanism and Machine Theory, vol 75, pp 1–11, May 2014 [17] Z Jamaludin, H Van Brussel, and J Swevers, “Friction Compensation of an XY Feed Table Using Friction-Model-Based Feedforward and an Inverse-Model-Based DIsturbance Observer,” IEEE Transactions on Industrial Electronics, vol 56, no 10, pp 3848–3853, 2009  ... static friction model, GMS model and combination of static and GMS model Table compares experimental data in term of contour error and tracking error Table RMS Error and tracking error of quadrant... effective implementation of PID and friction feedforward compensation model is when velocity is mm/s Fig shows XY plot and radial error of circular motion for a different condition of model implementation... result of applied friction compensation model onto ball screw driven positioning stage Section concludes the finding and gives recommendation for future works Friction compensation model This section