Gerald W. Brown
Manager, New Motor Development

George H. Ellis Jr.
Senior Scientist
Kollmorgen Motion Technologies Group
Radford, Va.

Neodynium-iron-boron alloys have been the biggest breakthrough ever in magnetic materials for motor designers. They allow building servomotors with as little as one-seventh the inertia of older ferrite-magnet models. What’s more, the latest designs have the same continuous torque as ferrites, and only 40% of the peak-to-peak cogging torque of standard, high-energy-magnet servomotors. Machine-tool builders use these low-inertia motors to increase acceleration, and take advantage of the lower cogging torque to reduce position error and surface-finish roughness. Also, the lower inertia improves the accuracy of motion trajectories with faster axis accelerations.

First things first
Cogging torque is the primary cause of uncompensated position error, although perturbations also come from fluted cutters, ball-screw variations, debris-cover friction, and belt imperfections. Reducing these disturbances let controllers generate the final touch necessary to machine smooth surfaces.

Ball-screw variations and debris-cover friction are commonly compensated for in the software, while the servomotor and ball screws in each axis can be directly coupled thereby eliminating the belts. Controllers often compensate for cogging torque, but the method is not a panacea because software cannot correct for effects such as variations in motor-to-motor cogging torque for a given model, or higher frequency components. A better solution starts with a low-cogging-torque motor. Then machine builders benefit in two ways. One way simply takes advantage of the lower cogging torque to improve the surface finish. The second trades off the reduced cogging torque for lower inertia to reduce the motor’s peak torque and size.

The accompanying block diagram, Motor and load model, with a stiff mechanical coupling between motor and load shows how the system works. It depicts a single free-body servomotor drive and load combination with a proportional position loop and a unity-gain, feed-forward path. The current-loop is shown as a low-pass filter with sufficient bandwidth to handle most frequencies encountered. The velocity-loop gain, feed-forward and position-loop gains, and the other velocity-loop gains are set to values typical for the machine-tool industry.

The servomotor is modeled in three blocks. It has been found that the total inertia, both servomotor and reflected load inertia of the axis, are major factors in servomotor sizing. Thus, motors are sized to peak torque, rather than continuous torque. Common practice is to match the servomotor inertia to the reflected inertia of the load. This keeps the motor’s peak-torque requirement high. The cogging torque (Tcog) summed with the torque command becomes the motor torque. Parameters for the motor, inertia, and cogging torque in the example are taken from a Kollmorgen servomotor specification.

The closed-loop transfer function for torque disturbance is represented as the position-error response to cogging torque. The open-loop transfer function for velocity is determined after setting the position-loop gain to zero, effectively removing the position loop. This is done to evaluate resonance as a function of the velocity loop. A trajectory generator in the model evaluates the time-domain response.

System stability becomes a concern when reducing motor inertia. The model then includes torsional resonance and damping as shown in the illustration, System model with compliant mechanical coupling. The spring constant and damping factors are consistent with typical machine-tool applications.

Standard motors serving the machine-tool industry typically have peak-to-peak cogging torques ranging from 1.0 to 1.5% of continuous ratings. They are usually sized to match the reflected inertia of the axis load, about 0.001 kgm-m2 for midsize machines.

To examine the effects of reduced cogging, five different cases were analyzed. The analysis began with Case 1 using typical motor and controller parameters obtained from a recently modeled system. Cogging torque is injected as a disturbance of 27 cycles/rev. Using these parameters in the system model, and evaluating a transfer function for the closed loop response of the position loop finds the worst-case frequency for cogging torque — which also generates the maximum position error. The resulting worst-case frequency for Case 1 is 45 Hz, shown in the table of Position-error analyses.

The position error is baselined at 7 µm for Case 1, a typical value from a recently deployed control system. Reducing the Case 1 cogging torque drops position error to about 3 µm. This lets the motor inertia be reduced. However, Case 3 shows that cutting motor inertia in half increases the position error, and it gets even worse by reducing the gains (Case 4) to hold susceptibility to resonance constant. Error returns to original levels in Case 5 when the system is driven by the worst-case frequency of 40 Hz, a value that dropped from 45 Hz when system gains were reduced.

These examples show that taking advantage of the reduced cogging in the servomotor by using a motor with only one-half the inertia improves the the position-error envelope which includes allowance for increased peaking and gain-margin loss due to resonance. The 50% reduction in servomotor inertia implies a 25% reduction in the total system inertia (the original Case 1 was with matched inertias). This means that an application based on peak torque can use a 25% smaller motor and benefit from less drive current. Both reductions — motor and drive size — can substantially reduce the machine builder’s cost.

Occasionally, it’s possible to improve this position error even more. Because the motor size can be reduced by 25%, cogging decreases proportionally so the analysis can be repeated until the effort no longer produces a worthwhile benefit. Even when choosing not to further reduce the size of the motor, lowered cogging can provide substantially more gain margin, or allow dropping the gain to further improve the robustness of the system.

Low ripple means high-quality finishes
Cogging is a periodic variation or a ripple in motor torque produced by variations in the permeance of the motor’s magnetic circuit. Cogging torque easily can be felt as a variable-force ripple when a servomotor is turned by hand in the absence of stator current. Most servomotors have slotted stators to facilitate their construction, and it’s this slotting that causes the variations in permeance. Well-designed servomotors have cogging torques from 1.25 to 2.0% of their continuous torque, but in some cases, it can be even higher.

But these relatively low levels of cogging torque can become a problem in some control systems. The disturbance can propagate through a servosystem and produce excessive deviations in position and velocity at low speeds. The position deviations degrade surface finish in machine tools and grinders, reduce uniformity in coating for the film industry, and lower the accuracy of other supposedly high-performance systems.

Often, to compensate for these higher levels of cogging in existing systems, designers use higher inertia motors and higher than typical servosystem gains in the controllers. But these solutions can increase costs or lower overall performance. However, the cogging torque of the Goldline XT Series motors is as low as 0.5% of continuous torque which avoids compromising the system performance.

© 2010 Penton Media, Inc.