Design of Vehicle Brakes

"Easy Steps to Design Vehicle BRAKES"

Here is again Auto Tech team, presenting article on "Design Of Brakes for automobile application" based on the demand of our users.  We hope that the following article will suffice the requirements of our users. In case of feedback ,please feel free to contact us.

Representative Pictures of brake

 It goes without saying that brakes are one of the most important control components of vehicle. They are required to stop the vehicle within the smallest possible distance and this is done by converting the kinetic energy of the vehicle into the heat energy which is dissipated into the atmosphere.

Design Calculations 

The calculation is followed in following steps:

  1.      Vehicle Dynamics Calculation.   
  2.      Brake requirement calculation. 
  3.      Hardware Calculation.
  4.      Cable operated losses.

1.         Vehicle Dynamics Calculations :

There are two types of calculations involved viz. Static & Dynamic. While calculating brake it is assumed that you have calculated the Basic dimensioning & Weight distribution calculations of the vehicle.

Now, Static Axle Load distribution :

                                  
         _{Mr\ M       =}    φ                                 

                                  

              

Where,

                

 M_r = Static rear Axle Load (kg); 
 M  = Total vehicle Mass (kg)'                                                                                        

 φ   =  Static axle load distribution

Now, calculate Relative Centre of Gravity Height:

H / W_b   =        X    

H         =  Vertical Distance from C of G to ground on the level (m)                                                              

W_b       =     Wheel base (m)                                                                                          

 X          =     relative COG height 

In actual practice when a vehicle is tried to stop, the weight transfers from Rear to Front wheel. Thus, it needs to be considered while designing a brake. Therefore Dynamic Front Axle load is calculated.

[(1-φ) + (X.a)].M = M_fdyn  

Where,

            a    =   decelration (g units)                                                                                          

           M   =   total vehicle mass (kg)                                                                                        

           M_fdyn   =   dynamic front axle load distribution

“a” i.e. deceleration is given in g units and is taken as 0.3g for Normal Automotive Brakes with Handle operated lever.   

The front axle load cannot be greater than the total vehicle mass. The rear axle load is the difference between the vehicle mass and the front axle load and cannot be negative.

2.         Requirements from Brake :

Now we need to calculate the loads which brakes should apply to complete the desired task.

Braking Force required can be simply calculated using Newton’s 2^nd Law of Motion.

                                         B_F  =  M.a.g

 Where,

            

   B_F                 =   Total Braking force (N)                                                                          

   M              =   Total vehicle Mass (kg)                                                                        

   a          =   deceleration (g units)                                                                               

   g          =   acceleration due to gravity (m/sec²)

                        

 Wheel Lock :

The braking force can only be generated if the wheel does not lock because the friction of a sliding wheel is much lower than a rotating one. The maximum braking force possible on any particular axle before wheel lock is given by:

F_A         =      M_Wdyn . g . µ_r

Where,

  F_A                 =  Total possible braking force on the axle(N);

  M_Wdyn              =  dynamic axle Mass (kg)  ;

  g          =  acceleration due to gravity (m/sec²)                                                   

               µ_r         =  Coeff. of friction between Road and tyre

Now we need to calculate the Brake torque:

Having decided which wheels will need braking to generate sufficient braking force the torque requirements of each wheel need to be determined. For some legislation the distribution between front and rear brakes is laid down. This may be achieved by varying the brake size or more likely using a valve to reduce the actuation pressure.

 T =  BF_w R/r

                      

 T                   =  Brake Torque (N-m)                                                                     

 BF_W     =  Braking force for the wheel (N)                                                      

  R          =  Static laden radius of tyre (m)                                                    

  r          =  Speed ratio between the wheel & the brake

3.         Hardware Design :

Disc Effective Radius:The effective radius (torque radius) of a brake disc is the centre of the brake pads by area. 

For dry discs it is assumed to be:

                       r_e     =   (D+d)/4

Where,

r_e                  =  Effective Radius (m)                                            

D         =  disc usable outside dia. (m)                                            

d          =  disc usable inside dia. (m)       

                           

For full circle brakes it is:

                      r_e  =  1/3 * [ (D³  -  d^3)/(D²  -  d² )]

Where,

r_e                  =  Effective Radius (m)                                            

D         =  disc usable outside dia. (m)                                            

d          =  disc usable inside dia. (m)

Clamp Load:

C =   T/ (r_e  * µ_{f  *} n)

Where,

C                    =  Brake Clamp load (N)                                             

T          =  Brake Torque (N-m)                                           

r_e         =  effective radius (m)

µ_f         = Coeff. of friction of lining material on the disc material

n          = no. of friction faces

The clamping load is assumed to act on all friction surfaces equally. For dry disc brakes it doesn’t matter whether the brake is of the sliding type or opposed piston. Newton’s Third Law state every force has an equal and opposite reaction and a reaction force from a sliding calliper is the same as an opposed piston one.

Stopping Distance:

 S =   V²  /  2*g*a _avg

Where,

S                    =  Stopping distance (m)                                            

V          =  test speed (m/s)                                      

a_avg      =  avg deceleration for the whole stop (g units)

g          =  acceleration due to gravity (m/s²)

4.         Cable operated Losses :

Cable losses are not inconsiderable and vary depending on the number and angle of bends. A typical cable supplier uses the following calculation to calculate cable efficiency:

η  =   1000 / (B_a  + 1000)

                                                    B_e  = Total angle of bends (degree)

After this mechnical calculations, thermal caluclations of brake is done and then component is designed in CAD softwares like proE, Solidworks, and then Structural, Thermal & CFD failures are analyzed in ANSYS.