Designing a Helical Compression Spring for Maximum Load of 1000N

Introduction:
A helical compression spring is a type of spring that is designed to resist compressive forces. It is made by winding a wire around a cylindrical shape, with the turns of the wire touching each other. When a load is applied to the spring, the wire compresses, and the spring stores energy. Helical compression springs are used in a variety of applications, including automotive suspension systems, industrial machinery, and consumer products.

Design Parameters:
To design a helical compression spring, we need to know the following parameters:

1. Maximum Load: The maximum load that the spring will be subjected to.
2. Deflection: The amount of compression that the spring will undergo when the load is applied.
3. Spring Index: The ratio of the mean coil diameter to the wire diameter.

Design Process:

1. Determine the Wire Diameter:
The wire diameter is calculated using the following formula:

d = (K*F)/(G*sqrt(N))

Where,
d = Wire Diameter
K = Spring Constant
F = Maximum Load
G = Modulus of Rigidity
N = Number of Active Coils

Here, the spring index is 5, so we can use the formula:

K = (4*C-1)/(4*C-4) + 0.615/C

Where,
C = Spring Index

Substituting the values, we get:

C = 5
K = 1.25

Substituting the values in the formula for wire diameter, we get:

d = (1.25*1000)/(84*sqrt(6)) = 2.45 mm

2. Determine the Mean Coil Diameter:
The mean coil diameter is calculated using the following formula:

D = d*(N+2)/C

Where,
D = Mean Coil Diameter
d = Wire Diameter
N = Number of Active Coils
C = Spring Index

Substituting the values, we get:

D = 2.45*(6+2)/5 = 3.68 cm

3. Determine the Number of Active Coils:
The number of active coils is calculated using the following formula:

N = (F*G*(N+2)^3)/(8*d^3*max_shear_stress)

Where,
F = Maximum Load
G = Modulus of Rigidity
d = Wire Diameter
max_shear_stress = Maximum Permissible Shear Stress

Substituting the values, we get:

N = (1000*10^3*84*(6+2)^3)/(8*(2.45*10^-3)^3*420*10^6) = 9.48

Since the number of coils must be an integer, we can round up to 10.

4. Check the Spring for Solid Height and Buckling:
The solid height is the length of the spring when it is fully compressed. It is calculated using the following formula:

H = d*(N-1)

Substituting the values, we get:

H = 2.45*(10-1) = 22.05 mm

The buckling load is the load at which the spring will buckle due to its own weight. It is calculated using the following formula:

F_c = (pi^2*E*d^4)/(8*(N/d)^2)

Where,
E = Modulus of Elasticity