- Thermal Model Definition: A thermal model of a motor is defined as a simplified representation to calculate heat generation and dissipation in a motor.
- Heat Generation (p1): This is the amount of heat produced inside the motor, measured in watts.
- Heat Dissipation (p2): Heat is transferred to the cooling medium, also measured in watts.
- First Order Differential Equation: This equation calculates temperature rise over time, helping predict motor heating and cooling.
- Heating and Cooling Curve: This curve shows how the motor’s temperature changes during operation, crucial for understanding thermal behavior.
We know that when an electrical motor and drive operates, there is a generation of heat inside the motor. The amount of heat generated inside the motor should be known as accurately as possible. That’s why thermal modeling of motor is necessary. The material of the motors and the shapes and size of the motors are not unique but the generation of heat does not alter very much depending on these characteristics. So, a simple thermal model of any motor can be obtained assuming it to be a homogeneous body. The main aim of this modeling is to choose the appropriate rating of a motor so that the electric motor does not exceed its safe limit during operation.
At time ‘t’, let the motor has following parameters
p1 = Heat developed, Joules/sec or watts
p2 = Heat dissipated to the cooling medium, watts –
W = Weight of the active parts of the machine.
h = Specific heat, Joules per Kg per oC.
A = Cooling Surface, m2
d = Co-efficient of heat transfer, Joules/Sec/m2/oC
θ = Mean temperature rise oC
At time dt, let the temperature rise of the motor be dθ.
Therefore, heat absorbed in the machine = (Heat generated inside the machine – Heat dissipated to the surrounding cooling medicine)
Where, dθ = p1dt – p2dt…………….(i)
Since, p2 = θdA…………….(ii)
Substituting (ii) in (i), we get
Here, C is called the thermal capacity of the machine in watts/oC and D is the heat dissipation constant in watts/oC.
When we acquire the first order differential equation of the equation –
We find the value of K by setting t = 0 in equation (iii) and solving it.
Using the equation, we can determine the temperature rise inside a working motor with good accuracy. By plotting a graph of temperature changes over time during heating and cooling, we complete the thermal modeling of a motor.
