Page 238 - Demo

V012024 • © 2024 Portescap. Specifications subject to change without notice.Acceleration also may be accomplished by changing the timing of the input pulses (frequency). For example, the frequency could start at a ¼ rate; go to ½ rate, ¾ rate and finally the running rate.For applications where ramping acceleration or deceleration control time is allowed: τJ = JT × ∆ω/∆t Where JT = rotor inertia (gm2) + load inertia (gm2) ∆f = step rate change ∆t = time allowed for acceleration in seconds λ = steps per revolution (for Portescap Can Stacks this can be 20 steps/rev, 24 steps/rev, or 48 steps/rev) ω = f steps/s × 2π rad/rev × 1/(λ steps/rev) [rad/s]Dividing by ∆t: ∆ω/∆t = ∆f/∆t step/s2 × 2π rad/rev × 1/(λ step/rev) [rad/s2]Plugging this definition of ∆ω/∆t into the equation for τJ yields: τJ = JT × ∆f/∆t step/s2 × 2π rad/rev × 1/(λ step/rev) [mNm]In order to solve an application problem using acceleration ramping, it is usually necessary to make several estimates to avoid needing a procedure similar to the one used in the following example.Example: Frictional torque plus inertial load with acceleration controlFor this application we are looking for Stepper Motor for an intermittent duty application. The application requirements are: Available voltage: 24 Vdc Available current: 3 Amp Motor operating point: 67.5° [θ] - desired motor position 15 mNm [τf] – frictional load < 0.5 [∆t] - desired move time Intermittent operation Motor dimensions: 60 mm maximum allowable length 60 mm maximum allowable diameterAn assembly device must move 4 mm in less than 0.5 seconds. The motor will drive a lead screw through a gear reduction. The lead screw and gear ratio were selected so that 100 steps of a 7.5° per step motor results in 4 mm of linear motion.The total inertial load (rotor + gear + screw) = 25 × 10-4 gm2. The frictional load is 15 mNm.(1) Select a stepper motor pull-out torque curve which allows a torque in excess of 15 mNm at a step rate greater than: f = 100 steps/0.5 sec = 200 steps/s238Engineer’s Appendix