Motor Thermal Model

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Description

The Motor Thermal Model is a specialized Thermal Model for DC motor components. It calculates heat generation from electrical losses (copper losses) and mechanical losses (friction), and can optionally model temperature-dependent resistance effects and thermal protection. This model can only be attached to components inheriting from Motor Base.

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Example Use Cases

• Motor Thermal Analysis: Predict motor temperature rise during continuous or cyclic operation.
• Thermal Protection Simulation: Test overtemperature shutdown logic and thermal derating strategies.
• Loss Budget Analysis: Evaluate the contribution of different loss mechanisms to total heat dissipation.

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Module Implementation

The thermal model calculates power dissipation from multiple loss mechanisms and uses this as the heat input for thermal calculations.

Copper Losses

Joule heating in the armature windings due to current flow:

$$P_{\text{copper}}=I^2{R}_{\text{eff}}$$

where $I$ is the armature current and $R_{\text{eff}}$ is the effective armature resistance.

Friction Losses

Mechanical power dissipated due to viscous friction:

$$P_{\text{friction}}=B{\omega }^2$$

where $B$ is the viscous friction coefficient and $\omega$ is the motor speed in rad/s.

Iron Losses

Optional losses from eddy currents and magnetic hysteresis in the motor core:

$$P_{\text{iron}}=k_h|\omega |+k_e{\omega }^2$$

where $k_h$ is the hysteresis loss coefficient and $k_e$ is the eddy current loss coefficient.

Brush Losses

Power dissipated across the brush-commutator interface for brushed motors:

$$P_{\text{brush}}=V_b|I|$$

where $V_b$ is the brush voltage drop.

Total Losses

The total power dissipation is the sum of all loss components:

$$P_{\text{total}}=P_{\text{copper}}+P_{\text{friction}}+P_{\text{iron}}+P_{\text{brush}}$$

Temperature-Dependent Resistance

When enabled, the effective armature resistance increases with temperature:

$$R_{\text{eff}}=R_{\text{ref}}\left(1+\alpha (T-T_{\text{ref}})\right)$$

where $R_{\text{ref}}$ is the resistance at reference temperature $T_{\text{ref}}$, $\alpha$ is the temperature coefficient (typically 0.00393 for copper), and $T$ is the current motor temperature.

Thermal Protection

The model monitors temperature against a configurable overtemperature threshold with hysteresis to prevent rapid on/off cycling of protection states.

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Assumptions/Limitations

• The model assumes a lumped thermal mass for the motor; spatial temperature gradients are not modeled.
• Iron losses and brush losses are optional and disabled by default.
• The temperature coefficient is clamped to prevent unrealistic resistance values at extreme temperatures.