Brake Disc Thermal Stress during Repeated Braking

The problem

Even with regeneration, EVs still need friction brakes for hard stops and low-speed braking, and heavier EVs put more energy into the disc. Repeated stops can overheat a thin disc, causing warping or cracks. Linking braking energy to disc temperature and thermal stress helps choose disc size and shape.

Objectives

• Calculate braking energy and heat flux into the disc for a repeated-stop cycle.
• Run a transient thermal study with convection and radiation to find disc temperatures.
• Use temperatures in a static study to find thermal stress.
• Compare disc thickness, slot and hole patterns.

What you need

Key concepts

Braking energy

Kinetic energy ½mv² removed in a stop. The share that goes into the friction disc depends on brake balance and how much regeneration recovers.

Heat flux

Heat power per unit area entering the disc through the pad contact. It is highest at the start of a stop and falls as speed drops.

Convection coefficient

How quickly air removes heat from a surface. It rises with speed, and choosing it is one of the largest uncertainties in disc models.

Thermal stress

Stress from uneven temperature, as hot regions try to expand but are held by cooler ones.

Step-by-step guide

1. 1

   Define the braking cycle

   Take an example e-scooter of stated mass with rider, a front disc and a stated brake balance. Define a repeated-stop cycle, for example ten stops from 60 km/h at 0.6 g with a fixed interval between them. Assume a share of braking recovered by regeneration, or zero for a worst case. Calculate kinetic energy per stop, the share into the front disc and stop duration.

   Checkpoint: A cycle table with energy per stop into the front disc, stop time and interval, with assumptions stated.

2. 2

   Calculate heat input

   Calculate heat power at the start of a stop as braking force times speed for the front disc share, falling linearly to zero over the stop for constant deceleration. Divide by the pad-swept area of the friction ring for heat flux, noting that the disc rotates so heat spreads over the whole ring on average. State the share of heat to the disc versus the pad, for example 90 per cent, as an assumption.

   Checkpoint: A heat power-versus-time curve for one stop and the full cycle, with the energy under it matching the energy per stop.

3. 3

   Model the disc

   Model the disc with an example outer diameter of 220 mm, friction ring width, thickness and inner carrier with mounting holes. Add drilled holes or slots with a Pattern feature. Create configurations for two thicknesses and plain, drilled and slotted versions. Assign a stainless steel grade suited to brake discs from the material library, and check its thermal conductivity, specific heat and expansion coefficient.

   Checkpoint: Disc configurations that rebuild correctly, with material thermal properties set and checked.

4. 4

   Set up the transient thermal study

   Create a thermal study, transient type, with total time covering the cycle and a time step small enough to resolve each stop. Apply heat power on the friction faces as a time curve from your calculation, split between both faces. Apply convection on all exposed faces with a coefficient you state, and radiation with an emissivity. Set the initial temperature to ambient.

   Checkpoint: The study solves and the temperature at the friction ring rises during stops and falls between them.

5. 5

   Check the energy balance

   Run a single stop with convection and radiation turned off and compare the temperature rise with the hand value: energy into the disc divided by disc mass times specific heat, for the average temperature. Large differences mean a unit or area error. Then turn cooling back on and check that temperatures fall between stops at a believable rate. Use the average temperature of the whole disc body from the results, not the surface peak, for this comparison.

   Checkpoint: The adiabatic single-stop average temperature rise agrees with the hand calculation within a few per cent.

6. 6

   Study convection sensitivity

   Because the convection coefficient is uncertain, run the full cycle with a low, medium and high value, for example derived from a flat-plate correlation at a stated speed. Plot peak friction ring temperature against stop number for each. Report the range of results rather than one number. If you can measure disc temperature on a real vehicle, use it to choose the coefficient.

   Checkpoint: Peak temperature plots for three convection values showing how much the answer depends on this assumption.

7. 7

   Calculate thermal stress

   Create a static study, set the thermal option to use temperatures from the thermal study at the time of peak temperature, and set a reference temperature at zero strain. Fix the disc at the mounting holes in a way that allows radial growth if the real disc is floating. Plot von Mises and hoop stress and compare with the yield strength at the peak temperature.

   Checkpoint: Thermal stress results at peak temperature, with factor of safety computed using yield strength at that temperature.

8. 8

   Compare designs

   Run the thermal and stress studies for each configuration and record disc mass, peak temperature, peak stress and stress near holes or slots. Explain why drilled holes can cut mass and add cooling but raise local stress. Choose a design that keeps temperature and stress within targets, and note the trade-off with mass. Show how temperature and stress concentrate around holes and slots with close-up plots. Note that slots also affect pad wear and noise, which this study does not model.

   Checkpoint: A comparison table across configurations and a justified choice.

9. 9

   Validate and report

   If possible, run the braking cycle on a test vehicle on a safe closed area under supervision and measure disc temperature after the last stop with an infrared thermometer or thermocouple. Compare with the model. Write a report with cycle definition, heat input, energy check, thermal and stress results, sensitivity and design comparison. State limits such as uniform heat flux and assumed convection.

   Checkpoint: A report with an energy-balance check, sensitivity range and, where possible, a measured temperature comparison.

Testing & validation

• Adiabatic temperature rise agrees with the energy-balance hand calculation.
• Sensitivity of peak temperature to convection coefficient reported.
• Thermal stress compared with temperature-dependent yield strength.
• Measured disc temperature compared with the model where possible.

Expected results

A coupled thermal and stress analysis of an EV brake disc under repeated stops, with verified heat input, convection sensitivity, design comparison and a recommendation for disc thickness and pattern.

Take it further

• Model how much regeneration reduces disc temperature on the same cycle.
• Use SOLIDWORKS Flow Simulation to estimate convection on the rotating disc.
• Add a fatigue estimate for thermal cycling.

Viva and review questions

Learn it at DIYguru

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