Resistive Forces, Acceleration, Gear Ratio, Braking Forces and FEA analysis of Brake Rotor

AIM: To find the Resistive forces, Acceleration, Gear ratio, Braking forces and FEA brake analysis for an urban hybrid vehicle.

Formulas and concepts

Resistive Forces:

• Rolling Resistance
• It is defined as the force resisting a body rolling on a surface. It opposes the motion of the body.

         Fr =rolling resistance (N)

         Crr=coefficient of rolling resistance

         m=mass of the vehicle

         g=gravitational acceleration    

• Aerodynamic Resistance:
• It is the resistance created by the fluid surrounding the body which is in motion relative to the fluid.

          Fa= drag force (N)

          ρ  = destiny of air

          v = velocity

          Cd = drag coefficient

          A=cross sectional area 

• Gradient Forces:
• When the vehicle travels uphill, a component of weight works in the direction opposite to the motion.

         Fg= Gradient resistive forces (N)

          m= mass of the vehicle

          g= gravitational acceleration

          `theta`= slope of the hill.

RPM at wheel

• According to the velocity the wheel RPM can be calculated by using the following formula.

       RPM=  (v∗60)/(π∗d)

       v=velocity of the vehicle (m/s)

       d=rolling diameter of the tire (m)

Load Distribution and Transfer:

• Load Ditribution:
• Rear Axle Load is given by W_R=W∗ l_m/L

  W= Total weight of car

  l_m= Horizontal Distance of CG

  L= Wheel base

• Front Axle Load is given by W_F=W-W_r

Traction force

• It is given by F=(W_R∗μ)/(1-(h_m∗μ)/L)

  W_R=static load on rear axle

  μ = Coefficient of friction

  h_m= vertical distance of CG

Load Transfer:

• It is given by ∆W=±(Fh_m)/L

Braking:

• Deceleration is given by a=(V^2-U^2)/(2∗s)

             v = Final Velocity(m/s)

             u = Initial Velocity (m/s)

             s = stopping distance(m)

Braking Torque

• It is given by τ_B= W_F∗μ∗d/2

      μ= coefficient of friction

      d= rolling diameter of tire (m)

Caliper force: F_B= τ_B/(d_B∗μ_B )

      dB=Rotor Diameter(m)

      μ_B=Coefficient of friction of brakes

Procedure

• All the resistive forces are calculated using the given parameter.
• Add all resistive forces to get the total resistive forces.
• RPM of the wheels is calculated.
• Load Distribution and Load Transfer is calculated.
• Accelerative force is calculated.
• Gear ratios are calculated based on available torque, required torque and RPM is also considered.
• Braking forces are calculated like Braking Torque, caliper force

Input

• here are two motors are being used.

Calculations         

• Gradient forces are zero as the vehicle is considered to be traveling on a flat road.

Total Resistive Forces:

Total tractive Effort:

 Gear Ratio:

Graphs

FEA Analysis on Brake Rotor:

For the FEA analysis of a Brake Rotor

• The rotor is 285 mm in diameter.
• The material used is cast iron which has a friction coefficient of 0.4.
• For the analysis the condition consider is the vehicle is moving at top speed and the brakes are applied with max braking force and the Rotor is applied with high caliper force and the wheels are locked.

Design of the Rotor:

Load case:

Factor of Safety:

Stress:

Displacement:

Summary: