Page 236 - Demo

V012024 • © 2024 Portescap. Specifications subject to change without notice.Chopper Driver – With Gearbox – With Ramping AccelerationThe P310 has a holding torque 14 mNm at nominal current and would not be able to directly provide 10 mNm at 477 rpm for accelerating the load. However we could use a gearbox to achieve the work. A first choice consists of matching inertias, and then making sure that with the selected ratio the motor speed remains within a reasonable range and the necessary torque can be delivered. With incremental motion, an inertial match assures the shortest move time, with the motor providing constant torque over the speed range considered. In our example this calls for a desired ratio i0 of: i0 = √(Jload/Jmotor) = √(20 kg-m2/0.86 kg-m2) = 4.82 [no units]From the various gearhead models available for combination with the P310 stepper motor, we select the K24. This gearhead offers a ratio of 5:1 which is close enough to our target 4.82, and has an efficiency of 85%.The load inertia reflected onto the motor shaft is calculated by:Jload at motor = Jload at gearbox / (i2 x 0.85) = 20 × 10-7 / (52 x 0.85) Jload at motor = 0.94 × 10-7 kg-m2.If we now consider the previous values reflected on the motor shaft, the required motor acceleration, angular speed, and step rate are:αat motor = α at gearbox x i = 5,000 rad/s2 x 5 = 25,000 rad/s2ω at motor = ω at gearbox x i = 50 rad/s x 5 = 250 rad/sf = (250 rad/s)/(2π rad/rev) × 60 steps/rev = 2,387 steps/sτ = (Jload at motor + Jmotor) x αat motor = (0.94 + 0.86) x 10-7 kgm2 x 25,000 rad/s2 = .0045 Nm = 4.5 mNmThe pull-out torque curve shows that at around 2,000 steps/s the P310-158-005 with coil in series, chopper drive, 45 V Vdc and a 0.5 A current limit can provide up to 8 mNm. With a safety factor of 75% we have up to 6 mNm available and the motor with gearhead can easily perform the job.Here again, the shortest move time would be: τ max = 6 mNm α max at motor = τ max / (Jload at motor + Jmotor) = .006 Nm / 1.8 x 10-7 kg-m2 = 33,333 rad/s2 α max at gearbox = α max at motor / 5 = 6,666 rad/s2 ∆t = √(2 x θ / α max at gearbox) = √(2 x 0.25 rad / 7,230 rad/s2) = 8.7 msecThe P310 with K24 0 5 is an excellent alternative to the P430 if a smaller diameter is required. DMM motors feature not only a low inertia rotor, but also a very strong magnetic design which enables use at high speed compared to other multi-pole stepper motors.0.01.02.03.04.05.06.07.08.09.00.00.20.40.60.81.01.21.40 400 800 1200 1600 2000 4000 6000 8000 10000120000 400 800 1200 1600 2000 4000 6000 8000 1000012000mNmrpmoz-inppsP310 158 005, P310 158 170 Series Torque vs SpeedP310 158 005 @ 45, 0.5 AP310 158 170 @ 7VP310 158 005 @ 45V, 0.5 AP310 158 170 @ 7VPull-Out Torque Pull-In Torquerpm236Engineer’s Appendix