engineering fundamentals Range of Compression Spring Rates
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This calculator allows you to search for a range of spring constant k values when all you have is a range of spring forces and deformed spring lengths. Can a single spring meet the ranges in your design requirements? Furthermore, will spring manufacturing tolerances add any complications? Use this calculator to find out.
Inputs
  Spring free length, Lfree:    
  Max. deformed length, Ldef_max:    
  Min. deformed length, Ldef_min:    
  Maximum spring force, Fmax:    
  Minimum spring force, Fmin:    
  Spring constant tolerance, ktol:     %
Answers
  Spring Constant upper limit, kmax:  4.09  lbf/in
  Spring Constant lower limit, kmin:  3.70  lbf/in
 
Equations Behind the Calculator
The equations used here can be described graphically. The ranges of spring forces and spring deformations D can be plotted on a graph. Where they overlap defines the area where permissible spring rates may pass.

To find the minimum spring rate, draw a line through the graph's origin and the {Dmin, Fmin} point. Likewise, to find the maximum spring rate, draw a line through the graph's origin and the {Dmax, Fmax} point. Both lines are shown on the following figure,

All values of k in between the kmin and kmax lines are permissible, as shown by the shaded region on the graph.

To include the effect of a manufacturing toloerance on the spring rate k, move the kmin and kmax lines together by the tolerance fraction, as shown on this figure,

If we find that kmax is less then kmin, then no solution exists.

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