Chapter 16, Problem 26P

When a motor armature inertia, a pinion inertia, and a motor torque reside on a motor shaft, and a gear inertia, a load inertia, and a load torque exist on a second shaft, it is useful to reflect all the torques and inertias to one shaft, say, the armature shaft. We need some rules to make such reflection easy. Consider the pinion and gear as disks of pitch radius.

• A torque on a second shaft is reflected to the motor shaft as the load torque divided by the negative of the stepdown ratio.
• An inertia on a second shaft is reflected to the motor shaft as its inertia divided by the stepdown ratio squared.
• The inertia of a disk gear on a second shaft in mesh with a disk pinion on the motor shaft is reflected to the pinion shaft as the pinion inertia multiplied by the stepdown ratio squared.

(a)    Verify the three rules.

(b)    Using the rules, reduce the two-shaft system in the figure to a motor-shaft shish kebab equivalent. Correctly done, the dynamic response of the shish kebab and the real system are identical.

(c)    For a stepdown ratio of n = 10 compare the shish kebab inertias.

Problem 16–26

Dimensions in millimeters.