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Spring Calculations Using Noonan’s XymT Method and an Eccentric Force

Journal Article
ISSN: 1946-3936, e-ISSN: 1946-3944
Published October 14, 2019 by SAE International in United States
Spring Calculations Using Noonan’s XymT Method and an Eccentric Force
Citation: Noonan, M., "Spring Calculations Using Noonan’s XymT Method and an Eccentric Force," SAE Int. J. Engines 13(1):93-100, 2020,
Language: English


The usual method of calculating spring deflection is to assume the end force acts through the central axis of the spring. The author takes a different approach where he calculates the eccentricity of the end force and from this calculates the spring deflection due to combined bending and torsion using a completely new model which he names the Noonan XymT Method. Also, the usual method widely used, where a strain energy approach is used, is proven to be in error. That statement is proven using a special example. Rough measurements have shown that the displacements calculated using the Strain Energy Method, can have errors as high as 40%, at a position up 0.6 coils from the bottom of the spring, and 10% at the top of the spring. The reason for this error has been identified, and calculations using Noonan’s XymT Method greatly reduces, if not eliminates, this error. This is particularly relevant in calculating individual coil stiffness and binding. With the displacement calculated, the combined complex stress due to bending tensile stress and torsional shear stress is calculated. An unusual observation was found, where 3° bending of the valve stem results in a 48% higher spring stress.