Page 225 - Demo

V012024 • © 2024 Portescap. Specifications subject to change without notice.Thermal considerations while selecting a motor:When torque is applied to a motor, joule losses are created (PJoule = R × I2) and the rotor temperature increases. The motor dissipates the heat generated at two levels:1. From the coil to the motor body (Rth rotor–body)2. From the motor body to the ambient environment (Rth body–ambient)The ability for a motor to dissipate heat is determined by these thermal resistances. Moreover, the coil resistance value increases with temperature. Therefore PJoule increases until it reaches a steady state value. In this exercise we would like to check whether at a given continuous operating point the coil temperature stays below the maximum rated coil temperature.The 22DCP 32G1 213P.1 requires 0.76 A and 5.0 V at a working point 6.45 mNm and 2,000 RPM. The given catalogue parameters are:Maximum rated coil temperature: 100 [°C]Thermal resistance Rth rotor–body: 6 [°C/W]Thermal resistance Rth body–ambient: 22 [°C/W]Terminal resistance R0*: 4.3 [Ω]Thermal coefficient of resistance for Copper α: 0.0039 [°C-1]*The terminal resistance in the catalog is always given at room temperature (22 °C).The resistance increase with temperature is given by the following equation: RT Final = R0 × (1 + α × (TFinal – 22 °C))According to the Thermal La ∆T = Pdissipated × RthIn our case, we consider the following thermal law between the coil and the ambient environment. ∆T [°C] is the temperature difference between the coil and the ambient temperature Tcoil – Tamb. Pdissipated = PJoule = R × I2 = R0 × (1 + α × (Tcoil – 22 °C)) × I2 [W] Rth = Rth rotor–body + Rth body–ambient = 28 °C/W (total thermal resistance between the coil and ambient) Thus: Tcoil – Tamb = Rth × R0 × (1 + α × (Tcoil – 22 °C)) × I2 [°C]Finally, isolating Tcoil gives:Tamb + Rth x R0 x (1-α x 22° C) x I2 1 - R0 x I2 x Rth x α22° C + 28° C/W x 4.3Ω x (1 - 0.0039° C-1 x 22° C) x (0.76 A)21 - 4.3Ω x (0.76 A)2 x 28° C/W x 0.0039° C-1Tcoil = = = 118° C225