SPRINGS   Home  
Notes:  springs.pdf




The Basics

There are 3 things that control the properties of a spring. Wire diameter d, coil diameter D and number of active coils n.  Increase d, spring is stiffer. Increase D, spring is softer. Increase n, spring is softer.

The most basic factor for a spring is k - the stiffness in N/mm. This can be increased several ways - Use thicker wire, less number of coils, or a smaller diameter.

Stress increases with an increase in force F, a larger coil diameter D or reduced wire diameter d.

The Formulas  http://www.efunda.com

Spring Constant 

The spring constant k is a function of the spring geometry and the spring material's shear modulus G,

 where G is found from the material's elastic modulus E and Poisson ratio n,
and D is the mean diameter of the spring (measured from the centers of the wire cross-sections),


Spring Geometry
The distance between adjacent spring coils (defined as the coil pitch) is found by dividing the spring free length by the number of active coils,

The rise angle of the spring coils (the angle between the coils and the base of the spring) is found from the arctangent of the coil-pitch divided by the spring circumference,

The solid height of the spring is found by summing the widths of all the spring coils. The total number of spring coils is equal to the active coils in the spring interior plus the 2 coils at the spring ends,

The length of wire needed to make the spring is found from,



Spring Force and Stress
The maximum force the spring can take occurs when the spring is deformed all the way to its solid height,

The maximum shear stress in the spring associated with the maximum force is given by,

 

where W is the Wahl correction factor (accounting for spring curvature stress) and C is the spring index (essentially an aspect ratio of the spring cross-section),



Spring Deflection


For coil springs, deflection is Force / stiffness, so...
Deflection  =    
 
where G is the material shear modulus, na is the number of active coils, D is coild diameter, d is wire diameter. The number of active coils is equal to the total number of coils nt minus the number of end coils n* that do not help carry the load, 

This depends on how the ends of the spring are formed. See the following illustration for different n* values:





Spring Calculator (offsite: www.Efunda.com)

This calculator computes all parameters (spring rate, maximum load, maximum stress, solid height, coil pitch, coil angle, wire length, resonant frequency, shear modulus, and spring mass) related to a compression spring from basic geometry and material data input.
http://www.efunda.com/DesignStandards/springs/calc_comp_designer.cfm




Assignment Questions.
(You must show all working)

QUESTION 1. 
Calculate the stress in a spring with wire diameter 5mm, outside diameter 49.2mm, a load of 350N. If there are 8 active coils, determine the deflection.

QUESTION 2. A counterbalanced coupler arm mechanism needs an extension spring with a travel of 200mm. The lowest force must be 300N, and the highest force 380N.  Determine D,d & n. The maximum stress must be in the range 350 to 400MPa.