# Coming to grips with compliance

July 26, 2007
Q. The single issue that causes the most discussion during our motor-sizing process is compliance and stiffness. Is there a typical way of allowing for compliance?

A. When properly sizing a motor, we use a very simple equation: Tpk = a X Jt. This equation tells us the amount of peak torque (Tpk; lb-ft) needed to accelerate a load to a given speed, for a specified acceleration rate (a; ft/sec2), for the total inertia (Jt; lb-ft2) of the system. However, this equation will not explain how the load will react or perform during acceleration. And compliance is the real beast that will reduce system performance.

For all practical purposes, compliance results in a momentary disconnection of the motor from the load. At this point the system gains (when tuned for inertia alone) will make the motor oscillate violently. Even at a standstill the system will be noisy.

The system must be detuned to overcome these oscillations. The tuning of the system is what creates the performance, so detuning effectively reduces system performance. Detuning will stop the oscillations, but at this point the system can become unstable, accelerate up to speed more slowly, and take more time to settle to a stop.

One simple fix is to oversize the motor to reduce JL/JM, your motor's load-to-inertia ratio. However, use of larger-than-necessary motors is costly. In compliant systems you should be seeking a JL/JM of ≤ 5:1.

Another option is to directly couple the inertial load to the motor, which will eliminate the vast majority of system compliance. A directly coupled load permits higher system gains which, in turn, lets the system perform better. It takes less time to accelerate, actual velocity tracks commanded velocity more closely, and the system settles out in minimum time. Reducing or eliminating compliance makes JL/JM less important.

— Gordon Ritchie

Gordon Ritchie is a System Engineer with Danaher Motion Corp. Got a question about motion control or mechatronics? Ask Gordon via e-mail at [email protected].

An example of how a low-compliance, directly coupled motion system performs. Note close agreement between commanded and realized velocities.

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