Tài liệu Machine Considerations pdf

12 Machine Considerations 12.1 MACHINE FEEDBACK DRIVE CONSIDERATIONS Machine Feed Drive Considerations for Resolver Feedback The usual configuration for resolver position feedback is to have the resolver geared to the servo drive motor. Computer-aided design programs for hydraulic drive sizing are based on the fact that the hydraulic resonance is the predominant resonance in the servo loop. With electric drives the mechanical time constant is not of prime consideration since it can be compensated for with the drive compensation. These are two important dynamic considerations with electric and hydraulic servo drives using resolver feedback at the servo motor. Since the position feedback resolver is close-coupled to the drive servo motor, all other mechanical resonances and nonlinearities are excluded from the position servo loop. Recommendations for the required indexes of performance (I.P.) are identical with those given in Section 9.2. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved Machine Feed Drive Considerations for Direct Machine Slide Position Feedback The main reason that direct feedback could be used was the universal use of the ‘‘soft servo’’ with its low position-loop g ain. By definition a soft servo has a low position-loop gain of about 1 ipm/mil with no frequency breaks below the servo bandwidth. The range of gains for the ‘‘soft servo’’ range from 0.5 ipm/mil to 2 ipm/mil. As long as no resonances are within six times the high end of this range (200 rad/sec or 32 Hz, Eq. [9.2-27]), it should be possible to close the position loop and be stable. As previously stated, if the feedback position transducer (resolver) is located at the drive motor, any mechanical resonance in the machine will be outside the servo loop. The effects of these mechanical resonances on the closed-position loop will be reflected load disturbances. However, if direct (e.g., Inductosyn-linear scales) position feedback is to be used, the mechanical resonance in the mechan ical drive components will be inside the position loop. For this situation, some guidelines, recommendations, etc. should be put forth to prevent a situation where direct feedback is used on a feed drive that will not be stable. 12.2 BALL SCREW MECHANICAL RESONANCES AND REFLECTED INERTIAS FOR MACHINE DRIVES As a constraint the lower limit on any resonance (hydraulic or mechanical) inside the velocity loop should not be less than 200 rad/sec (Eq. [9.2-27]). Likewise, the bandwith ðo c Þ of the closed velocity loop should not be greater than one-third the lowest resonance in the servo loop, which is usually the hydraulic resonance, o h , in hydraulic drives (Eq. [9.2-23]). With the position loop, there may be a number of different mechanical resonances. These resonances are outside the velocity loop but inside the position loop. Considering the mechanical feed drive components, the one of greatest concern is the drive screw axial resonance. This resonance will probably be the predominant low mechanical resonance in a ball-screw feed drive. Typical values of ball screw stiffness are shown in the graph of Figure 1 for the variables of screw diameter and length. These values are based on constant end bearing and ball nut stiffnesses. In actual practice, these would be varied according to the screw diameter. In Figures 2 to 5, the ball screw resonances are plotted for various screw diameters, lengths, and applied load weights. Resonances occurring outside the velocity loop and inside the position loop will contribute phase shift to the open-position loop frequency- Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved Fig. 1 Ball screw stiffness. Fig. 2 Ball screw resonance. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved Fig. 3 Ball screw resonance. Fig. 4 Ball screw resonance. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved response characteristics. To maintain the desired 458 phase margin for the position loop, the resonances (such as the ball screw) should be sufficiently high relative to the position-loop velocity constant ðK v Þ that they will not reduce the phase margin. It is recommended practice that the lowest resonance inside the position servo loop should be three times higher than the minimum hydraulic resonance (200 rad/sec). If this practice is followed, the reflected phase shift occurring at the velocity constant ðK v Þ from the position loop resonance will not reduce the overall position-loop phase margin. In actual practice this is somewhat academic because in large machinery mechanical resonances do occur above and below 200 rad/sec. As an index of performance (I.P.) it is recommended that the position loop resonance (usually the ball screw) should be at least six times the position- loop velocity constant ðK v Þ or greater than o h . (Refer to Section 9.2, Eq. [9.2-22] to [9.2-28].) A graph displaying this I.P. can be drawn (Figure 6) showing the relation between position-loop velocity constant ðK v Þ and the lowest allowable resonance in the position servo loop. For numerical controls using the ‘‘soft servo’’ technique, it can be determined from the graph in Figure 6 that resonances inside the position loop should, in general, be large Fig. 5 Ball screw resonance. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved enough (at least 200 rad/sec) such that the resonance will not have a detrimental effect on the drive. For large machines where the velocity constant ðK v Þ usually cannot be larger than 0.5 ipm/mil for reasons of stability, the lowest allowable resonance (from Figure 6) could be as low as 50 rad/sec. For small machines using the ‘‘soft servo’’ with velocity constants of 2 ipm/mil, the lowest resonance in the position servo loop should not be less than 200 rad/sec. Therefore, it is difficult to make an across-the-board recommendation with changing velocity constants ðK v Þ from machine to machine. One possible way to arrive at a recommendation is to assume that all machines being built use position loop gains up to 2 ipm/mil, and therefore, machines with ball screw resonances under 200 rad/sec cannot use direct feedback. Another possibility, which is more practical, is to list the machines with the recommended maximum allowable position servo loop gains ðK v Þ that can be used with direct feedback. Since all axes on a machine must have the same position loop gain, the machine axis with the lowest resonance will be the determining factor in how low the position loop gain or velocity constant ðK v Þ must be set. Other Resonance Considerations Additional mechanical resonances inside the position loop that may cause stability problems should also be considered. Reflected structural resonances Fig. 6 Lowest recommended resonance inside the position loop. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved due to large and sometimes limber machine structures may reflect their resonances into the machine slide as the result of an antinode vibration. Likewise, very large and heavy workpi eces placed on an otherwise stable machine slide can cause stability problems when direct position feedback is used. Additionally, mechanical power transmission devices, such as ‘‘wound up’’ gear trains, can be a source of stability problems when they are included inside the position loop with direct slide position feedback. The gearbox can have two types of problems. First, the amount of windup can vary causing a change in spring rate that can cause instability. Second, any nonlinearity such as backlash that occurs as a result of lost windup will result in an unstable servo drive. Reflected Inertias for Machine Drives An important parameter to consider in sizing a machine servo drive is the total inertia at the servo motor. The definition of inertia is the prop erty of a body, by virtue of which it offers resistance to any change in its motion. For an industrial machine slide the total reflected inertia to the servo motor is made up of the reflected belt and pulley inertia (or gearboxes), the reflected drive screw, and the reflected machine slide with its load weight. Knowing the total inertia at the servo drive motor is a requirement for any form of servo analysis or drive sizing. The reflected inertia at the drive motor can be calculated as J reflected ¼ J load ðD 2 =D 1 Þ 2 (lb-in sec 2 Þ (12.2-1) Where D 1 ¼ diameter of the motor pulley or gear (in.) D 2 ¼ diameter of the load pulley or gear (in.) A very important consideration in applying a drive to a machine axis is the torque to inertia ratio. A mechanical equation for acceleration torque is: T T ¼ J a (lb-in.) (12.2-2) Where J T ¼ total inertia at the motor shaft (lb- in.) a ¼ acceleration at motor shaft (rad=sec 2 ) Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved Equation (12.2-1) can be rearranged as a ¼ T J (rad=sec 2 ) (12.2-3) Equation (12.2-3) is known as the torque to inertia ratio, and has important significance. In a given drive application the machine will have a total inertia (motor inertia plus reflected inertia) that exists by design. For productivity requirements there will be a required acceleration. The question must now be asked: Is there enough acceleration torque to meet these requ irements? Quite often this becomes a critical drive-sizing problem providing enough available current from the servo amplifier to accelerate the load required to meet a productivity requirement? For industrial servos using brushless DC drives there are two types of motors to be considered. The brushless DC motor in general industrial applications uses ceramic magnets. For high-performance applications, low inertia motors are used. These motors use Neodymium-iron-boron (NdFeB) magnet material or Samarium cobalt (SmCo) magnet material. A comparison of torque to inertia ratios ðT/JÞ with various total inertia loads is compared in Figure 7. At small inertia loads the torque to inertia ratios for low inertia motors are significantly higher than standard ceramic motors, which is an indication that the low inertia motors are capable of higher performance (and acceleration) with small total inertia loads. These curves also indicate that the low inertia motors have a significant reduction in performance as total load inertia increases. The standard ceramic magnet-type motors have less reduction in performance with added total load inertia. The low inertia drive is usually more expensive than the standard ceramic-magnet brushless DC motor. For larger total inertia loads it is not economically justifiable to use the low inertia type motor since performance will be compromised. If high performance is a requirement, the reflected inertia load should be reduced with a ratio if possible. To further study the performance of brushless DC drives under various inertial loads, a transient step response test will be made for a velocity servo using a lag/lead compensation in the servo amplifier with a gain of 1000 volts/volt. A more detailed analysis is presented in Chapter 14. A 3-volt/1000 rpm tachometer feedback will be used. The block diagram for this servo drive is shown in Figure 8. A simple velocity servo was chosen for this analysis to minimize complexity. A standard ceramic brushless DC motor and a low inertia brushless DC motor will be used for this analysis. The motor parameters are identified as the following: Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved MOTOR STANDARD MOTOR LOW INERTIA MOTOR (Kollmorgan M607B) (Kollmorgan EB606B) K T ¼ 9.9 lb-in./A 9.9 lb-in./A K e ¼ 0.3734 v-sec/rad 0.3734 v-sec/rad R motðl ÀlÞ ¼ 0.14 ohm 0.14 ohm SR motðl ÀlÞ 0.189 ohm 0.189 ohm SR motðphaseÞ ¼ 0.0945 ohm 0.0945 ohm L lÀl ¼ 0.0038 henry 0.0038 henry J mot ¼ 0.1872 lb-in sec 2 0.02688 lb-in sec 2 t e ¼ L ðl ÀlÞ SR motðl ÀlÞ ¼ 0:0038 0:189 ¼ 0:02 sec 0:02 sec (12.2-4) t m ¼ SR motðphaseÞ J tot K eðphaseÞ K T (12:2-5) J total ¼ J mot þ J reflected (12.2-6) Transient responses for a multiplicity of load inertias are shown in Figures 9 to 16. In this analysis it is assumed that each drive will be analyzed with identical inertia loads as if a machine axis was being tested with a standard brushless DC motor and then tested again with a low inertia motor. Load inertia Standard motor Low inertia motor (lb-in sec 2 ) transient responses transient responses 1 X MOTOR Fig. 9 Fig. 10 0.2 Fig. 11 Fig. 12 0.8 Fig. 13 Fig. 14 2.0 Fig. 15 Fig. 16 A ceramic-magnet brushless DC servo motor will have some reduction in servo bandwidth with added load inertia (Figures 9, 11, 13, and 15), but these drives are tolerant of added load inertia without having to be recompensated. Rare earth brushless DC drives are load inertia sensitive (Figures 10, 12, 14, and 16). For br ushless DC servo drives with ceramic- magnet armatures, a ratio of approximately four times reflected load inert ia to the motor armature can be tolerated. For low-inertia brushless DC motors it is recommend ed that the reflected load inertia matc h the motor inertia. Since these motors are used for high-performance applications, it is advisable not to reduce the servo bandwidth with inertia mismatch ratios larger than one. Reflected load inertias can be computed as follows: Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved Reflected Machine Slide Inertia J slide ¼ W6ðL=NÞ 2 60:0000656 ðlb-in sec 2 Þ (12.2-7) where: W ¼ total machine slide and load weight (lb) L ¼ ball screw lead (in./rev) N ¼ drive ratio Fig. 7 Torque to inertia ratio comparisons. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved [...]... Feedback A mechanical model of a machine feed slide is shown in Figure 24 It is assumed that the drive screw spring rate is represented by GT The machine s slide inertia reflected to the drive screw plus the inertia of the drive screw is represented by JL The load forces acting on the machine slide are reflected to the drive screw as TL The friction forces of the machine slide are reflected to the... places, such as the drive motor shaft, at the drive input to the ball screw, or at the machine slide When the stiffness is measured at the rotary components the units of measurement are lb-in./rad When the stiffness is measured at the machine slide the unit of measurement is lb/in Drive stiffness, measured as the machine slide displacement in inches caused by a displacement force in pounds, increases... for a low inertia No Pulley no Approx diameter 18 19 20 21 84H200 96H200 120H200 156H200 13.21 15.12 18.94 24.67 Inertia 1.9541 3.2206 6.7934 17.3840 In addition to the reflected inertias for a linear machine slide, other configurations are given for a belt drive (Figure 17), a rack drive (Figure 18), a rotary drive (Figure 19), and a rotary drive with a ring gear and pinion (Figure 20) using a ring... Lead ¼ ln=rev N ¼ ratio Radius ¼ in: Copyright 2003 by Marcel Dekker, Inc All Rights Reserved WT6RADIUS2 263866ðRATIO6LEADÞ 2 (lb-in.-sec2 ) Fig 21 Rotary inertia conversion table 12.3 DRIVE STIFFNESS Machine feed drives should have sufficient static stiffness to be insensitive to load disturbances In addition, a feed drive in a contouring numerical control system must remain stationary or clamped when... machine slide are reflected to the drive screw as TL The friction forces of the machine slide are reflected to the drive screw and represented by BL The mechanical drive ratio is represented by N Fig 24 Machine slide free-body diagram Copyright 2003 by Marcel Dekker, Inc All Rights Reserved The equations for the mechanical model of Figure 24 are written in the following steps: y1 ¼ ym N T1 ¼ NTm T1 ¼... Reserved (12.3-67) Substituting Eq (12.3-66) into (12.3-67) yields FL 2p Dm N Kv 2pN 6Dm ð1 þ Kvo Þ ¼ Xo L KL L (12.3-68) The drive stiffness equation for direct position feedback and measured at the machine slide is FL ¼ Xo   2p 2 D2 N 2 Kv ðKvo þ 1Þ m L KL (lb/in.) (12.3-69) As a dimensional check,   2rad2 rev2 in:6 1 V sec lb lb 6 6 3 2 ¼ 6 26 6 6 2 rev sec V in: in: in in: rad Linear Electric . 12 Machine Considerations 12.1 MACHINE FEEDBACK DRIVE CONSIDERATIONS Machine Feed Drive Considerations for Resolver Feedback The. 9.2. Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved Machine Feed Drive Considerations for Direct Machine Slide Position Feedback The main reason that