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# Variable Pitch Conical Spring

## Variable Pitch Conical Spring

(OP)
In the above thread it is suggested that the mean diameter of the conical spring be used for a variable pitch conical spring "linear".  I have found when I do this the calculated number of active coils is greater than using the iterative process also discussed in the above thread (I divide the spring into a series of springs each with a different diameter but the same number of active coils, the number of active coils was adjusted to get the needed spring rate).  Is using the average diameter an "exact" calculation or just an approximation?

### RE: Variable Pitch Conical Spring

All formulations for spring design are approximations. For example: the load is never apply in the center of the coil, etc. The formulations are good approximations and with the tolerances on the spring dimensions and the spring properties (+/-10%) it gives the spring manufacturer enough freedom to "play" with the dimensions to get the designed properties.

### RE: Variable Pitch Conical Spring

(OP)
Thanks for the reply I did some more research and found an equation for spring rate of a conical spring.  The 8*Dm^3 in the standard rate equation is replaced by 2*(D1^2+D2^2)*(D1+D2).  Timoshenko derives it in Strength of Materials Part I Elementary theory and problems.  I also belive it is posted in one of the older threads for conical springs.  The equation would be valid for any spring with equal horizontal space between each coil.

For a given spring rate the number of active coils given by this equation is equal to the number of coils calculated by the iterative process.  It is much niceer to have a closed form solution.

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