When trying to understand the phenomenon of heating of coreless dc motors, its helpful to express it as a simple thermal model and to draw an analogy with an electrical system. Looking at Fig. 1, you can see the power dissipated (heat) is the difference between electrical input power and the mechanical power (speed & torque) generated by motor shaft. With this basic understanding , let’s next examine the thermal model of a DC coreless motor.

**Thermal Model :** There are only two basic building blocks for a thermal system; namely, thermal resistance & thermal capacitance. A simple thermal model describing heating of the coreless dc motor and its analogy to the electric circuit is shown in Fig.2. The model consists of the two components, namely coil & stator, each of which act as thermal capacitance (analogous to capacitance in electrical circuit) and separated by thermal resistances (analogous to resistance in electrical circuit). Heat is generated in the self-supporting coil in a DC coreless motor due to resistive heating (I2R losses). Some heat will be taken up for heating the self-supporting coil itself, which is termed as thermal capacitance of the coil Cth(c) and some heat will be dissipated to the stator through the air gap. The air gap can be thought of as a thermal resistance Rth1 between coil & stator. Next, the stator will start heating up based on thermal capacitance of the stator Cth(s) & dissipate some heat to the ambient (analogous to ground in electrical circuit). The thermal resistance between the stator and ambient is termed as Rth2. Note that there are many other small components in the motor like brushes, magnet, ball bearing etc., made of different materials and having different mass. But we have considered only the coil and stator in this thermal model. Suitable assumptions are made in terms of material and mass in the calculations for thermal capacitance, to bring the thermal model to this simplified form.

**Thermal Resistance (Rth)** is one single parameter combining the cumulative effects of the different modes of heat transfer viz. conduction, convection and radiation which take place for the motor. The higher the thermal resistance, the slower the heat transfer. It is usually estimated experimentally. With reference to the thermal model above , the total thermal resistance of the motor Rth = Rth1 + Rth2.

**Thermal Capacitance or Heat Capacity (Cth)** is mass multiplied by specific heat capacity of the material. In Fig 2., we have a copper material for the coil and steel material for the stator. The higher the thermal capacitance value, the more heat that can be stored by the body. In the above model, the stator can store more heat and hence it will take much longer time to get saturated or complete its heat storage capacity.

Thermal equilibrium or Steady State: As long as the input electrical power or electric current is constant, after the initial transient period of heating of the motor , a steady state or thermal equilibrium is reached , in which the parts of the motor achieve respective stable temperatures. In this state, the individual thermal capacitances are full and there will be only heat dissipation and no storing of heat.

**Thermal Unbalance or Transient State:** This indicates the temperature rise period of the motor, when the thermal capacitances are active.

**Thermal Time Constant:** The heating up and cooling down follow an exponential behavior. Thermal time constant is the time taken by a body to reach ~63% of its steady state temperature. It is calculated by multiplying the Cth & Rth. The stator takes much more time to heat up than the coil due to its larger thermal capacitance Cth(s) and higher thermal resistance Rth2 and hence has a comparatively much higher thermal time constant value. For the coil, the thermal time constant is in the range of seconds to minutes depending on motor size and for the stator it ranges from few minutes to several minutes depending on the motor size.

**Thermal Limit of Motor:** The** maximum continuous torque** in continuous application will draw the **max continuous current** which is limited by the thermal limit of the motor. Exceeding the maximum continuous current specified in the catalogue for a continuous operation will lead to exceeding the thermal limit of the coil. So, for continuous application, the motor selection is typically done so that the application torque is 70% – 80 % of the max continuous torque, to keep a margin of safety on the thermal limit of the coil. The thermal limit of the coil, as stated in coreless motor manufacturers catalogs is typically about 100 deg C or up to 125 deg C. The maximum continuous current may be exceeded in applications with short term operation followed by sufficient ‘off time’ which will allow the coil to cool down during this period and prevent exceeding thermal limit of the coil. It is advisable to consult motor manufacturers while making such a motor selection.

**Motor Regulation (R/k2): **The motor regulation parameter R/k2 is directly related to the motors capability of converting electrical power to mechanical power. A lower value of R/k2 means better power conversion. R/k2 values are usually in the same range for a motor family and are very good indicators of motor performance across different motor sizes. To take into consideration thermal properties of the motor, we can compare the values for R/k2 x Rth which reflect the ability of the motor to convert electrical power to mechanical power and dissipate joule losses for a given job. The lower the R/k2 x Rth value, the better the efficiency of the motor and the better the heat dissipation for the motor. Higher efficiency is a desired critical parameter in some applications, such as battery-operated devices.

Careful consideration of these parameters are necessary to assist in selecting the proper DC motion solution. Give Portescap a call today and speak with an engineer who can help you in optimizing and sizing the best motor for your needs. Or head straight to our e-Store to purchase a sample.

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