Modified from problem 10 7 (p 434) from our old textbook. Alciatore & Histand 20

Question

Modified from problem 10 7 (p 434) from our old textbook. Alciatore & Histand 2007 A designer wishes to use a stepper motor coupled to a gearbox to drive an indexed conveyor belt to achieve a linear resolution of 1 mm and a maximum speed of 10 cm/sec The gearbox is a speed reducer with a gear ratio of 3:1. and the conveyor is driven by a 10 cm drum attached to the output shaft of the gearbox What is the minimum resolution required for the stepper motor? The language in this problem is a little confusing The question asks for the largest number of degrees per step (drg/step) that will satisfy the linear resolution requirement Of course you could use a motor with a smaller number of degrees per step if it is fast enough If I use a stepper motor with 1 8 degree per step then what speed (rotation rate in steps/sec) must the motor run at to achieve a belt velocity of 10 em / sec?

Explanation / Answer

a. (stepper resolution / 360) * (belt travel per revolution) = desired linear resolution (x / 360) * ((pi * 10) * (1/3)) = .1 x = 3.438 deg/step b. (v / (pi * d)) * (360 / stepper resolution) * gearbox ratio (10 / (pi * 10) * 360 / 1.8) * 3 = 190.99 steps/sec

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