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.

Critical Speed of Vehicle: Calculation and other important considerations

CRITICAL SPEED OF A VEHICLE

"One of our user Mr Manoj Nain asked us about critical velocity and its calculation. In this article, we have included fundamentals of critical velocity and its calculation in the practical context. We hope that you all will enjoy the article and will let us know in case you want more information. We love receiving queries from our users and answer them to help you evolve .So here is the article......".

Critical speed of a vehicle is the speed at which the vehicle will lose lateral control on the roadway. There are different methods to calculate the critical speed. It depends on friction force, elevation and radius of turn. Calculation of critical speed of a vehicle plays a vital role in the field of accident reconstruction.

Calculation of Critical speed

According to Newton’s 1^st Law of motion, a body moving in a straight line will continue in a straight line unless acted on by an external force. A body moving on a circular path with constant speed will have a changing velocity (directional speed) due to the body's changing direction. This velocity change with time, called centripetal acceleration, has a radial direction toward the center of the circular movement and is given by the following equation:

_­ 

                                                                    a= V² /R.............................................1

V: velocity (m/s)

            R = Radius of Turn (m)

                    a = Centripetal acceleration

Since Newton's second law tells us that a force has to act on the body to produce an acceleration. Therefore,

                                                                          F = m a................................................2

m = mass of vehicle

              a = centripetal acceleration

   F = Centripetal Force

Therefore,

                                                                         F = m v²/R...................................................3

Now, the lateral force on a vehicle moving in a circular motion on a pavement surface is produced by the frictional force between the tires and the roadway as follows :

                                                                         
                                                                         F = µN.................................................4

Where, N=Normal Reaction

Therefore,

                                                                        F = µmg.........................................................5

Condition for a vehicle to not to slip: Centripetal force should not exceed the Frictional force. Therefore, equating both the forces will give the critical velocity which should not be exceeded.

                               m v²/R = µmg..............................................6

 Solving the equation will give, critical velocity v,

                                   V _critical = (µgR) ^0.5    .............................7

Equal sign is important. g = 15 is used for practical design (accident reconstruction).The formula is not valid for low radial speeds. To calculate critical speed, equal sign is important. Converting the above Equation to allow for the velocity, v, in mph, and accounting for the roadway curve super-elevation, e, yields the familiar form of the centripetal acceleration equation.

It is important to understand here, that above equation can be applied on the basis of following assumptions and they are:

• Vehicle should be at its friction limit so that the slipping starts
• Vehicle follow a circular arc
• Vehicle  should be within the tyre marks
• Speed of the vehicle is constant

   

     Application of the above equation: 

• Highway curve design
• Elevations
• Speed limit elevations
• Emergency turns by vehicle

From the above equation derived, we can conclude many  characteristics.They are:

  

Characteristics of Critical speed 

• It depends on the friction between the road surface and tyre. Higher is the coefficient of friction, more is the critical velocity. But it is proportional to square root of the coefficient friction and value of coefficient of friction is not very high relative to other values (g, R) hence effect will not be more than the other parameters.
• It depends on the elevation or the banking of the road, as the normal reaction changes accordingly.
• It depends on the Turning Radius. Radius can hold any value hence it can have large values too thus, it will have higher influence on critical velocity. Thus, it is critical to design turns carefully or design vehicle for higher radius of turn.
• It is not affected by the position of CG. However, it affects Yaw, Pitch and Roll which is a different concept and seems to clash with this phenomenon. 
•  Does not depend on the vehicle geometry.
•  CSF is valid for the assumptions described earlier in the article
•  CSF is not applicable for low values of coefficient of friction.
•  CSF does not take care of quantities such as steer angle, temperature effects, suspension etc.
• CSF should be calculated using the radius derived from earliest possible part of the tire marks as possible. Use curvature traced out by leading front tire for better results.

 ·      There is always uncertainty in using CSF formula and hence uncertainty or standard deviation    should be taken care of while designing using CSF.

In this article, we have tried to give brief idea of the concept called as critical velocity. We can work to give more detailed calculation and theories developed for measuring critical velocity in practical context. We hope that this information will be useful for our users. Please let us know whether this was useful or not. Thanks for believing in us...and yes don't forget to like..for our efforts...