Gear selection We are looking for a gearhead with a maximum continuous torque of at least 0.486 Nm and a short-term torque of at least 1.028 Nm. This re- quirement can be fulfilled by the ceramic version of the configurable GPX 22 gearhead with 2 or 3 stages. With 2 stages, the maximum gearhead input speed of 10000 rpm permits a maximum ratio of

Alternative solutions GPX 19 ceramic gearhead 3 stages (138:1 reduction)

with motor type DCX 16 S (graphite brushes) GPX 22 gearhead, standard configuration 3 stages (111:1 reduction) with motor type DCX 19 S (graphite brushes)

n max, G n L

= 10000 100

= 100:1

i max =

Three-stage gearheads permit higher input speeds, and the maximum ratio is 120:1. Because of the shorter design, we decide to use the 2-stage gearhead. To keep the motor torque as small as possible, we select the highest possible ratio of 44:1. The 2-stage gearhead has an efficiency of 81%. Motor type selection Speed and torque are calculated to the motor shaft n mot = i · n L = 44 · 100 = 4400 rpm M RMS M mot, RMS = i � η = 486 44 � 0.81 ≈ 13.6 mNm M max M mot, max = i � η = 1028 44 � 0.81 ≈ 28.8 mNm The possible motors, which match the selected gears in accordance with the maxon modular system, are summarized in the table opposite. The table shows only motors with graphite commutation because they are better suited for stop-and-go operation. We select the DCX 22 S, which has sufficient continuous torque. The motor should have a torque reserve so that it will be able to function in slightly less favorable conditions. The additional torque requirement during acceleration is no problem for the motor. The short-term peak torque is only slightly less than twice as high as the permissible continuous torque of the motor. Selection of the winding The DCX 22 S motor has a mean characteristic gradient of about 110 rpm/mNm. The desired idle speed is calculated as follows: Δ n n 0 , theor = n mot + Δ M � M max = 4400 + 110 � 28.8 = 7570 rpm The extreme operating point should of course be used in the calculation (max. speed and max. torque), since the speed-torque line of the winding must run above all operating points in the speed / torque diagram. This target no load speed must be achieved with the maximum voltage U = 24 V supplied by the control (ESCON 36/2), which defines the mini- mum target speed constant k n, theor of the motor. n 0 , theor k n, theor = U mot = = 315 7570 24 rpm V If one considers the speed constant of the windings, then the first choice would be the motor with a nominal speed of 36 V. At a speed constant of 342 rpm V -1 however, it has only a small speed control reserve. If the tolerances are insufficient, then the winding with the next higher speed constant (24 V nominal voltage) offers better safety. The higher speed constant of the winding compared to the calculated value means that the motor runs faster at 24 V than required, which can be compensated with the speed controller. The motor can be equipped with an encoder to record the speed. The speed constant of the selected 24 V winding is 18.4 mNm/A. The maximum torque therefore corresponds to a peak current of M max I max = k M + I 0 = + 0.036 = 1.6 A 28.8 18.4 This current is smaller than the maximum current (4 A) of the controller and the power supply unit (3 A). Thus, a gear motor has been found that fulfils the requirements (torque and speed) and can be operated by the controller provided.

Suitability

Motor DCX 22 S DCX 22 L

M N

≈ 15 mNm ≈ 30 mNm ≈ 11 mNm

good

too strong, builds long

DC-max 22 S

too weak

n [rpm]

20000

15000

10000

5000

20 25 30

5

10 15

M [mNm]

75

maxon

March 2021 edition / subject to change

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