# Impact of Thermal Limits on Motor Performance

For semiconductor equipment, motors are essential components, and are used in various systems such as indexing (theta) tables and wafer-handling robots. Motor torque is extremely important, but to get higher torque, you need to apply higher current. As current increases, motor winding temperature increases and causes heat to dissipate to other components in the system. This temperature rise can cause thermal expansion and introduce inaccuracy to the system which is detrimental for semiconductor applications that require extremely high accuracy.

High torque enables faster throughput, but it also introduces inaccuracy. Integrators must balance temperature rise and torque output. The question stands: How much torque can be achieved when thermal limitations are applied to the motor.

To answer this, we need to understand the relationship between thermal resistance and the motor constant (K_{m}).

Thermal Resistance (R_{th}): thermal resistance is the measure of a motor’s ability to dissipate the heat generated during operation. It represents the resistance encountered by heat flow through the motor’s components, including the stator, rotor, and housing. It is represented by the equation:

\(R_{th}=\ ∆T/Pd\)

where ΔT is the motor’s maximum winding temperature minus the ambient temperature (°C) and P_{d} is the allowable power dissipated (W).

Motor Constant (K_{m}): motor constant shows how efficiently the motor generates torque. It is represented by the equation:

\(K_m=\ \frac{T_{cont.}}{\sqrt{P_d}}\)

Where T_{cont} is the continuous torque (Nm) and P_{d} is the allowable power dissipated (W) by the motor.

If the temperature of the motor must be reduced to avoid thermal expansion, we can use the equation for thermal resistance to solve for power dissipated, which can then be used, along with the motor constant, to determine the continuous torque that can be achieved at the reduced winding temperature.

We make a few assumptions beforehand.

- The motor housing in our system has the same surface area and thermal properties as that which was used to rate the motor’s thermal resistance.
- The maximum winding temperature of the motor has been determined through measurement or modeling.

Use thermal resistance equation to solve for power dissipated:

\(P_d=\ \frac{T_{\max{winding}}-\ T_{ambient}}{R_{th}}\)

Use the calculated power dissipated to solve for the continuous torque of the motor:

\(T_{cont.}=\ K_m\ast\ \sqrt{P_d}\)

Here is an example using Genesis Motion Solutions’ LDX frameless motor (LDX 160-013B)

R_{th} = 0.575 °C/W

K_{m} = 0.87 Nm/√W

Ambient temperature = 20°C

Maximum allowable winding temperature = 50°C

First, solve for the allowable power dissipated:

\(P_d=\ \frac{T_{\max{winding}}-\ T_{ambient}}{R_{th}}\)

\(P_d=\ 50°C- 20°C0.575 °C/W= 52.2 W\)

Next, solve for the continuous torque:

\(T_{cont.}=\ K_m\ast\ \sqrt{P_d}\)

\(T_{cont.}=\ 0.87\frac{Nm}{\sqrt W}\ast\ \sqrt{52.2\ W}=6.3\ Nm\)

Therefore, when the motor temperature rise is limited to 30°C, the motor can achieve up to 6.3 Nm of continuous torque.

These calculations provide an estimate and may vary depending on the motor’s specific characteristics, operating conditions, and the accuracy of the thermal resistance and motor constant values used.

The relationship between thermal resistance and motor constant allows us to estimate the torque a motor can generate based on the temperature rise it experiences during operation. By using the equations for thermal resistance and motor constant, you can assess motor performance, optimize thermal management, and design more efficient and reliable motor systems. Understanding this relationship provides valuable insights into motor behavior and facilitates informed decision-making in various industries where motors play a critical role.