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V012024 • © 2024 Portescap. Specifications subject to change without notice.Examples of DC Coreless Gearmotor CalculationsExample: Direct drive with a gearhead attached to the motor.For this application we are looking for a DC Coreless Motor & Gearhead for a continuous duty application. The application requirements are:Available voltage: 15 VdcAvailable current: 1.5 AmpMotor operating point: 30 rpm [n] desired motor speed500 mNm [τ] desired output shaft torque 22°C [Tamb] ambient temperatureContinuous operationMotor dimensions: 80 mm maximum allowable length25 mm maximum allowable diameterThe specification page for the R22 gearhead shows a maximum continuous torque of 600 mNm, so the required 500 mNm can be handled by this planetary gearhead. When choosing the reduction ratio, we should keep in mind that the recommended maximum input speed of the R22 gearhead is 5,000 rpm. We should keep the input speed below this value to assure low wear and low audible noise.i = nmax / nloadi = 5,000 rpm / 30 rpm = 166.7The catalog indicates that the closest ratio to the desired value calculated above is 159:1. The efficiency for this ratio is η = 0.6 (or 60%). We may now calculate the motor speed (nm) and the reflected torque (τm) on the motor shaft. τm = τ / (i × η) [mNm] τm = 500 mNm / (159 × 0.6) = 5.24 mNm nm = nload × i = 30 rpm × 159 = 4,770 rpmThe motor data sheet shows the 22DCP family of motors can deliver a torque up to 6.21 mNm continuously and will be our candidate. The 22DCP is available as a standard combination with the planetary gearhead R22. Based on the available voltage let’s consider the 211P winding (12 V measuring voltage) and calculate the motor current and voltage the same way as in the previous example.The motor is required to be driven at a speed of 4,770 rpm under a load of 5.24 mNm. The ambient temperature (Tamb) is 22 °C and the available voltage in the application is 15 Vdc. The characteristics we are most interested in are the torque constant (k) of 11.63 mNm/A, and the terminal resistance of 7.8 Ω. Neglecting the no-load current (lo), for a torque load of 5.24 mNm the motor current is: I = τ / k = 5.24 mNm / 11.63 mNm/A = 0.45 ANow we can calculate the drive voltage required to run the motor at 22°C, for a desired speed of 4,770 rpm with a load torque of 5.24 mNm:U = R × I + k × ϖ [Vdc] ϖ = 2π/60 × n = 2π/60 rad/rpm-s × 4,770 rpm = 499.51 rad/sU = (7.8 Ω × 0.45 A) + (11.63 × 10−3 Nm/A × 499.51 rad/s) = 9.3 VdcWe note the current of the motor under load is 0.45 A, which is under the rated continuous current of 0.57 A. We therefore can safely assume that the final rotor temperature (Tf) will stay below the maximum rated coil temperature of 100 °C. We can also be sure that the voltage will remain within the 15 Vdc due to raise in coil resistance. The final coil temperature would be 76 °C and the required voltage due to higher coil resistance would be 10 Vdc. Both are well within the limits and our assumptions are justified. The problem is now solved. The gearmotor 22DCP 32P2 211P.5 R22 0 159 would be a good choice for the application. If the application requires particularly long motor life or if this were a battery application, the 22DCT could also be considered to increase efficiency and extend battery life.228Engineer’s Appendix