| name | brake-system |
| description | Brake system design — disc and drum brakes, pedal ratio, master cylinder, clamping force, brake torque, pad wear, heat dissipation, brake bias, fade, ABS. |
| metadata | {"priority":7,"promptSignals":{"phrases":["brake design","disc brake","drum brake","brake torque","brake fade","braking force","master cylinder"],"minScore":3}} |
Brake System Design — Complete Skill
Braking Fundamentals
Deceleration: a = μ_road × g (tire-road adhesion limit; μ = 0.7–1.1 for tires)
Stopping distance: s = v²/(2μg) [m; v in m/s]
Total braking force: F_brake = m × a = m × μ_road × g
Braking torque required at wheel:
T_brake = F_brake × r_wheel [N·m]
Brake force distribution (front/rear):
Ideal: F_front/F_total = (l_r + h × a/g) / L (dynamic weight transfer)
l_r = CG to rear axle; h = CG height; L = wheelbase
Disc Brake Analysis
Pad Clamping Force
F_clamp = P_hydraulic × A_piston [N]
N_pistons calipers: F_clamp = N × P × A_piston
Brake torque (disc brake):
T_brake = μ_pad × F_clamp × R_eff × N_friction_faces
R_eff = effective radius = mean of pad inner/outer radius ≈ 0.7–0.75 × R_disc
μ_pad = pad friction coefficient (0.30–0.50 typical; 0.40 standard; 0.50 racing)
N_friction_faces = 2 for floating caliper; depends on design
Pedal Force → Line Pressure
Mechanical advantage:
F_line = F_pedal × r_pedal × η_servo / A_MC
r_pedal = pedal ratio (force amplification): typically 4–6:1
η_servo = brake booster ratio (2.5–3.5:1 for vacuum booster)
A_MC = master cylinder bore area: e.g., 25.4 mm bore → A = 506 mm²
Line pressure:
P_line = F_line / A_MC [Pa → convert to bar or MPa]
Maximum: ~100–160 bar (passenger car with ABS)
Disc Thermal Analysis
Energy to heat: KE = ½mv² (all converted to heat in worst case)
Temperature rise (simplified lumped):
ΔT = KE / (m_disc × c_p,disc)
m_disc = disc mass [kg]; c_p,cast iron = 460 J/kg·K
Peak disc temperature (emergency stop from v):
ΔT ≈ ½mv² / (n_discs × m_disc × c_p)
Fade temperature limits:
Organic/NAO pad: starts fading ~250°C; severe >400°C
Semi-metallic: fade >450°C; racing: to 600°C+
Cast iron disc: max operating 700°C
Ventilated disc: forced convection through vanes; cooling critical for repeated stops (mountain descent)
Thermal resistance reduced by: more vanes, larger disc, better airflow
Drum Brake Analysis (Leading-Trailing)
Self-energizing brake: leading shoe wraps toward rotation → amplified clamping
Self-energizing factor:
a_L = μ_d × a / (c - μ_d × b) (leading shoe factor)
Net braking torque: T = μ_d × (F_L + F_T) × r_drum
F_L > F_T (leading shoe generates more torque)
Brake Fade
Thermal fade (friction fade): pad material degrades at high temperature → μ decreases
Vapor lock: brake fluid boils → compressible gas → loss of pedal feel
Brake fluid DOT specifications:
DOT 3: dry boiling ≥ 205°C; wet ≥ 140°C
DOT 4: dry ≥ 230°C; wet ≥ 155°C
DOT 5.1: dry ≥ 260°C; wet ≥ 180°C
Pad wear: wear rate proportional to PV = contact pressure × velocity
PV limit: semi-metallic ~1.5 MPa·m/s; organic ~0.75 MPa·m/s
ABS (Anti-lock Braking System)
Prevents wheel lockup; maintains μ near peak (slip ~15–20%)
Slip: λ = (v_vehicle - v_wheel) / v_vehicle
Peak μ at λ ≈ 0.15–0.20
ABS cycles: 10–15 Hz pressure modulation to keep λ at optimum
Stopping distance with ABS:
~5–10% shorter than skilled driver; significantly better for inexperienced
Bias and Proportioning
Front brakes: 60–70% of total braking (weight transfers forward)
Rear bias: leads to rear lockup → spin (understeer avoided by design)
Proportioning valve: limits rear brake pressure at high deceleration levels
Electronic brake bias (EBD): part of ABS module; continuously adjusts front/rear split
Brake Sizing Procedure
- Determine maximum deceleration (a = 0.8–1.0g for normal; 1.0–1.3g for sports)
- Calculate total brake force F_total = m × a
- Distribute front/rear (ideal or regulatory minimum front bias)
- Calculate required brake torque per axle from F × r_wheel
- Size disc: R_disc from packaging; check μ_pad × F_clamp × R_eff × 2 ≥ T_required
- Size caliper pistons for required F_clamp at max line pressure
- Check thermal capacity for repeat stop scenario
- Verify pedal force ≤ 500 N at maximum deceleration (EU regulation)
Output
Provide: disc diameter [mm], pad μ, F_clamp [kN], T_brake [N·m], line pressure [bar], pedal force [N], ΔT_disc [°C] per stop, fade margin, ABS slip target [%], bias front/rear [%].
