# Why Speed Matching?

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#### Tom Bullock

BULL!
Why Speed Matching?
By Tom Bullock

A reckless driver is defined as one who passes you when you are exceeding the speed limit. While it may be reckless to size your servo such that it exceeds the mechanical speed limitations of the design, it may also be imprudent not to take the full benefit from what is available. It is understandable that, for cost reasons, one may operate his motor well below its rated speed. This is often done to avoid a gear ratio. But, one should also recognize what he or she is sacrificing by such a choice.

During the servo seminars that my partner, George Younkin, and I teach, we recommend speed matching as the first step in sizing an application. Speed matching means that a gear ratio is selected such that the motor will be running at its rated RPM when the machine is travelling at its maximum rated speed. This will result in the largest safe ratio that can be used. Why do we want the largest ratio possible? To begin with, doesn’t it seem reasonable that to take full advantage of a motor’s capability, it should be used to its capacity? Besides that, there are four good reasons to want to maximize the ratio.

The first reason is because a high ratio reduces the reflected inertia. Ideally, the reflected load inertia should equal the motor rotor inertia, but mismatches as high as four to one can usually be tolerated without a significant loss of performance (usually loss of bandwidth). This is especially important with longer travels that use ball screws. This is because the diameter of the ball screw must be increased as its length is increased to reduce the compliance (spring action). Since inertia is the fourth power of diameter, a 50% increase in diameter is a 400% increase in inertia. Since inertia is reflected by the square of the ratio, even a two to one ratio will reduce the inertia by a factor of four.

The second benefit of a high ratio is an increase in thrust. Remember that a ball screw or similar device converts rotary torque into linear thrust. Torque is increased in direct proportion to the ratio selected. The thrust or torque is needed for three primary purposes. The rate of acceleration is directly proportional to torque, so it is critical when trying to optimize motions. Overcoming friction requires thrust. This can be quite significant with linear motions having metal to metal contacts. Even when roller bearings or hydrostatics are used, other friction forces may be significant. Our Mr. Younkin made a comparison on a machine tool application that showed that friction was cut by only 50% when a machine was converted to antifriction rollers This was despite the fact that the coefficient of friction between the two was a factor of twelve. He found that the way wipers, way covers, end bearings for the screw, nut wiper, etc. made a very significant contribution to the total friction. Thrust is, of course, also required to do the work. Forces of 10,000 pounds and more are very common in machine tools when trying to force a drill into a piece of steel or when hogging off metal with a milling cutter.

The third benefit of a high ratio is an increase in stiffness. You’ll find another of my articles on this web site dealing with stiffness. Basically, stiffness is the spring constant of the system. If one compresses a spring, it requires a certain force for each unit of displacement (i.e. lbs/inch). Similarly, if one exerts force on an axis of motion, the amount by which it moves out of position is proportional to that force. The stiffness of a servo increases in proportion to the square of the ratio. As mentioned in that other article, it is not uncommon for a properly designed machine tool servo to deflect less than .0001 inches with 50,000 pounds of force applied.

Improved drive resolution is the fourth benefit of a high ratio. Again you will find an article at this site on drive resolution. Resolution is the smallest unit to which the axis will respond. It is inversely proportional to the ratio. A high ratio gives a smaller (better) resolution.

Mohandas K. Gandhi said that "There is more to life than increasing its speed". Let the record show that, in respect to selecting the proper motor for your application, Tom Bullock said "There is more to be gained by increasing its speed".

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Tom Bullock can be reached at Industrial Controls Consulting, a division of Bull’s Eye Marketing, Inc. See them at www.bullseyenet.com, or contact Tom at (920) 929-6544 or email: [email protected].