Nikhil Krishna

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Penn Electric Racing Mechanical Challenge: Brake Pedal Design

a full Formula SAE braking system derived from first principles, in one week

project
03 of 05
event
Penn Electric Racing
credit
Solo design project, completed in one week as the mechanical application challenge for Penn Electric Racing.

01the problem

  • Formula SAE is a student contest to design and build a race car
  • this was the Penn mechanical application challenge, which i did alone
  • the rules demand two independent hydraulic circuits and no brake by wire
  • target pressures of 1200 psi front and 400 psi rear had to be validated, not assumed
the force path, from the driver's foot to each axle

02from deceleration to hydraulic pressure

  • weight transfer under 1.5 g braking moves 740.5 N onto the front axle
  • front axle load rises to 1964.8 N while the rear drops to 585.8 N
  • tire friction sets the torque each axle must absorb, 748.6 and 223.2 newton meters
  • working back through the caliper gives 613 psi front and 183 psi rear required
free body diagram of the car under braking
Load transferred to the front axle under braking, 740.5 N.
Eq. 1. Load transferred to the front axle under braking, 740.5 N.
Required line pressure. The factor of two is because a caliper clamps from both sides.
Eq. 2. Required line pressure. The factor of two is because a caliper clamps from both sides.

03pedal and hydraulics

  • moment balance about the pivot gives a pedal ratio of 6 to 1
  • a 1.0 inch pushrod arm therefore sets a 6.0 inch pedal arm, inside the envelope
  • 70 lbf of foot force becomes 420 lbf at the pushrod
  • one bore serves both circuits at 0.578 inch calculated, rounded to a 9/16 inch Tilton unit
  • balance bar pivot at one quarter length splits that 420 lbf into 315 and 105 lbf
moment balance on the pedal arm about its floor pivot
The pedal ratio is both a force ratio and a length ratio.
Eq. 3. The pedal ratio is both a force ratio and a length ratio.
Bore sizing from the target pressure.
Eq. 4. Bore sizing from the target pressure.
the balance bar, pivoted a quarter of the way along
Balance bar reactions. A three to one split puts the pivot one quarter along the bar.
Eq. 5. Balance bar reactions. A three to one split puts the pivot one quarter along the bar.

04structural sizing

  • structural case uses the rulebook 1500 N foot load, giving 2023 lbf at the pushrod
  • bending stress with a safety factor of 2.5 sizes the aluminum arm to 0.625 inch
  • steel would need only 0.448 inch but weighs more for the stiffness gained, so aluminum wins
  • Euler buckling on the pushrod returns a safety factor of 48.2
  • pin shear and bolt bearing return 3.24 and 54.1
the two checks, arm bending and pushrod buckling
Bending stress in a solid rectangular section.
Eq. 6. Bending stress in a solid rectangular section.
Euler critical buckling load for the pushrod.
Eq. 7. Euler critical buckling load for the pushrod.

05results