Mathcad Leaf Spring

 

LEAF SPRING CALCULATIONS  As shown in the picture, the leaf spring or laminated leaf spring consists of a couple of  full-length leaf and a number of graduated leaves. You can also observe from the picture of the leaf spring that the thickness of the whole spring is maximum at the centre and is gradually decreases towards the ends.

Leaf Spring Design Procedure Let’s start with a leaf spring design problem. We have the following data as input: Where , W  250  N Tb - Maximum bending stress in the leaf spring L  0.445  m W - Applied load on the spring  N  8 t - Thickness of the individual leaves n  2 X - Maximum deflection of the spring due to applied load E  2.1MPa L - Span of the leaf spring n - Number of full-length leaves X  0.13 m

N - Number of graduated-length leaves

 N Sa  60 6000 0000 0000 000 0

2

b - Width of the spring

m

E - Young's modulus of the spring material

 

Sa is Sa is the allowable bending stress for the spring material. You have to find out the width (b)  and the thickness (t)  of the spring. (b) and (t) of

Formula to be used You have to use the following two formulas for the leaf spring design process: Bending stress produced in the whole spring:

Tb 

( 3 W    L)

................................ eqn1.1

 b N  t  2

Maximum deflection in the whole spring:

X 

6W  L3

.................................. eqn 1.2

2   n    E   N   bb   t3    N  

Solution:  Apply the eqn1.1  and you will get the value of: eqn1.1 and

Tb 

( 3 24516    0.445 ) 4091.1075   simplify 

 b8 t2

2

 b t

6

 b  t   6.81 10

2

.............................................. eqn 1.3

Now, apply the eqn1.2  and you will get the value of: eqn1.2 and 3

   0.445 simplify  720.1258335 X  624516 3 2   2    8   bb   t3  b  t   8  



3



8

 b  t   2  63  10

................................................ eqn 1.4

By solving the eqn1.3  and eqn1.4  you will get: eqn1.3 and eqn1.4 you t  0.0038 m  b  0.455  m