Gandhinagar Institute of Technology

Subject :- Theory of Machine (2151902)

MECHANICAL ENGINEERING 5th - B : 2

Braking analysis of four wheels

Prepared By – Malaviya Bhautik [130120119094] Pavan Narkhede [130120119111]

Darshit Panchal [130120119114]

Guided By : Prof. Prananjay Patel

Active Learning Assignment

What is Brake ??

Brake is a device used for slowing ,stopping & controlling the vehicle.

Braking operation based on kinetic energy of vehicle is to converting

into heat, which dissipated into atmosphere.

While driving the vehicle, torque of the engine produces the tractive

effort due to periphery of driving vehicle.

When the brakes are applied it produces negative tractive effort on

wheel.

Types Of Braking system

HYDRAULLIC BRAKING SYSTEM

PNEUMATIC BRAKING SYTEM

MECHANICAL

BRAKING SYSTEM

DISC BRAKE

SYSTEM

ANTI BRAKING SYSTEM(ABS)

Braking Analysis of a Vehicle

In a four wheel moving vehicle, the brakes may be applied to• 1. the rear wheels only,• 2. the front wheels only, and• 3. all the four wheels.

Now, consider a vehicle moving up an inclined plane,

• α = Angle of inclination of the plane to the horizontal,

• m = Mass of the vehicle in kg

• x = Perpendicular distance of C.G. from the rear axle in metres,

• L = Distance between the centres of the rear and front wheels (also called

wheelbase) of the vehicle in metres,

• RA = Total normal reaction between the ground and the front wheels in newtons,

• RB = Total normal reaction between the ground and the rear wheels in newtons,

• µ = Coefficient of friction between the tyres and road surface, and

• a = Retardation of the vehicle in m/s

1. When the brakes are applied to the rear wheels only

It is a common way of braking the vehicle in which the braking force acts at the rear wheels only

Let FB= Total braking force (in newtons) acting at the rear wheels due to the application of the brakes. Its maximum value is µ.RB.

For the equilibrium of the vehicle, the forces acting on the vehicle must be in equilibrium.

Resolving the forces parallel to the plane,

FB + mg sinα = ma Resolving the forces perpendicular to the plane,

RA + RB = mg cosα

• Taking moments about G, the centre of gravity of the vehicle, FB × h + R × x = RA(L – x) • Substituting the value of F in the above expression, we have FB= µ.RB, and RA =

m.g cosα – RB

2. When the brakes are applied to front wheels only

• It is a very rare way of braking the vehicle, in which the braking force acts at the front wheels only.• Let FA= Total braking force (in newton's) acting at the front wheels due to the

application of brakes. Its maximum value is µ.RA.

3. When the brakes are applied to all the four wheels

• This is the most common way of braking the vehicle, in which the braking force

acts on both the rear and front wheels.

• Let FA = Braking force provided by the front wheels = µ.RA

• Let FB = Braking force provided by the front wheels = µ.RB

• A little consideration will show that when the brakes are applied to all the four

wheels, the braking distance (i.e. the distance in which the vehicle is brought to

rest after applying the brakes) will be the least. It is due to this reason that the

brakes are applied to all the four wheels.

•Resolving the forces parallel to the plane,

FA FB m.g sin m.a

•Resolving the forces perpendicular to the plane,

RA RB m.g cos

•Taking moments about G, the centre of gravity of the vehicle,

(FA FB )h RB x RA (L x)

• Substituting the value of FA .RA , FB .RB and RB m.g cos RA in the above expression,

(RA RB )h (m.g cos RA ) x RA (L x) (RA m.g cos RA )h (m.g cos RA )x RA (L x) .m.g cos h m.g cos x RA L

Now from equation (i),

.RA RB m.g sin m.a

(RA RB ) m.g sin m.a

.m.g. cos m.g sin m.a

References:• Wikipedia• A Text book of theory of machine by R.S.KHURMY and J.K.GUPTA• www.sae.org.in

Thank you …