Correction to Design Equation for Spring Diametral Growth Upon Compression

In the textbook by Wahl (1963, Mechanical Springs, 2nd ed., McGraw-Hill, New York, Chap. 20), he derived an equation predicting the diametral growth of a helical spring as the spring is compressed from free to solid height, and the spring's ends are free to rotate. A recent comparison with test data for growth of compression springs revealed that the calculated growth predicted by the Wahl formula did not agree well with measured values. Review of the Wahl derivation uncovered an arithmetic error that, when corrected, brought the calculated and measured diameters into closer agreement. The corrected diametral growth equation presented herein bounds the original data provided by Wahl, better matches an alternate growth equation derived by Ancker and Goodier for most springs evaluated, predicts larger growth than the original Wahl equation, and is a better fit to recent measured data.