Brakes & Clutches

Brakes & Clutches (brakes-clutches)

Purpose

Calculate friction torque capacity, energy dissipated per stop or engagement, and thermal screening for disk and drum brakes and clutches. Supports single-plate and multi-plate configurations.

Physics & theory

Friction devices transmit torque through normal force $F_n$ and coefficient of friction $\mu$: $T=n\mu F_n{r}_{\mathrm{eff}}$, where $n$ is number of friction surfaces and $r_{\mathrm{eff}}$ is effective radius (mean radius for uniform pressure assumption).

Energy per engagement is $E=T\Delta \theta$ for angular displacement $\Delta \theta$, or $E=\frac{1}{2}I{\omega }^2$ for full stop from speed $\omega$. Repeated engagements heat friction surfaces; average power dissipation $P=E\cdot f_{\mathrm{cycle}}$ must not exceed material and coolant limits.

Governing equations

Numerical method

Closed-form friction torque and energy relations. Safety factor applied to required vs available torque. Thermal screening compares energy per cycle to allowable surface temperature rise (simplified lumped model).

Inputs

Outputs

• Friction torque capacity, torque utilization, energy per stop, average dissipated power, thermal warning flags.

Design codes & checks

• Indicative: Friction torque capacity, energy per stop screening

Assumptions & limitations

• Uniform pressure or uniform wear assumption — user selects model.
• Dry or wet friction $\mu$ from tables; no dynamic $\mu$ vs speed/temperature.
• No detailed transient thermal FEA of friction surfaces.
• Vibration, chatter, and fade not modeled.

References

1. Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 16.
2. SAE J2681. Brake Effectiveness — Vehicle Analysis.
3. Newcomb, T. P., & Spurr, R. T. A Technical History of the Motor Car. (Brake fundamentals)
4. ISO 7649:1988. Brakes — Friction materials — Classification.
5. PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
6. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.