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V012024 • © 2024 Portescap. Specifications subject to change without notice.At steady state, the final coil temperature calculated is 118°C which is above the 100°C limit. In theory this motor coil insulation would burn and create a short-circuit in the coil. However, the thermal resistance Rth body– ambient is usually overestimated. It is measured when the motor is placed in air with no contact with another part. In reality, the motor is always fixed in the application (fixed by the front flange, clamped on the outside diameter, etc.). These fixations usually act as heat sinks and allow the motor to dissipate more heat. Therefore a real value for Rth body–ambient in the application is usually closer to half of the value given in the datasheet. Doing the math with Rth body– ambient = 11°C/W (Rth = 17 °C/W) will give you a final coil temperature of 73°C, providing enough security compared to the 100°C limit.Let’s now take into account the impact of the 73° C coil temperature :RT Final = R0 × (1 + α × (TFinal – 22 °C)) = 4.3 Ω × (1 + 0.0039 °C × (73° C – 22° C)) = 5.14 ΩIn our case, the resistance has increased and therefore the joule losses have also increased. To keep the same mechanical power output, we need to provide more electrical input:U = RT Final × I + k × ϖ = 5.14 Ω × 0.76 A + (8.48 × 10-3 Nm/A) × 209.44 rad/s = 5.7 VThus, to achieve the requested speed at 73° C coil temperature, the voltage has to be increased at 5.7 V. Pmech = 6 mNm × 2,000 rpm × 2π/60 rad-s-1/rpm = 1.25 WPelec = 5.7 V × 0.76 A = 4.33 W Pjoule = 5.14 Ω × (0.76 A)2 = 2.97 WEfficiency = Pmech / Pelec = 29%Note: The above model is only valid for continuous operation. For intermittent duty, a time step model is necessary to estimate the final temperatures.In conclusion, the 22DCP will be an appropriate choice if the mountings will help dissipate heat. But to achieve better efficiency, another stronger motor can be selected. The below example takes efficiency into consideration for the same working point.Selecting a DC Brush Motor for better efficiency and temperature regulation:Let’s consider the fundamental equation of DC motors:U = R × I + k × ϖMultiplying both sides of the equation by the current: U × I = R × I2 + k × I × ϖFrom τ = k × I we know that I = τ/k. Substituting into the previous equation and simplifying gives:U × I = R/k2 × τ2 + τ × ϖBy examining this equation we can identify the key parameters.U × I = Pelec is the electrical power suppliedτ × ϖ = Pmech is the mechanical power converted by the motorR/k2 × τ2 = joule losses226Engineer’s Appendix