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https://hdl.handle.net/2142/68510
Description
Title
Large Deflections of Helical Springs
Author(s)
Morehead, Hubert Lane
Issue Date
1980
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
Abstract
The problem analyzed is that of a helical spring subjected to end couples and forces which produce large deflections of the spring. These deflections are such that the angle of rotation of one end of the spring centerline with respect to the other end of the spring centerline exceeds the range within which small angle approximations are possible and may be as large as (pi) radians. The spring is treated as a prismatic bar with known compressive, bending, and shear rigidities. These rigidities are functions of the pitch of the spring and therefore change as the spring is deformed. Furthermore, the spring rigidities assume different values along the length of the deformed spring as the pitch varies from point to point along the deformed spring centerline.
Equations are developed which will predict the deflections of any number of points along the spring centerline. From these, the deformed shape of the spring is determined. The equations developed employ elliptic integrals of the first, second, and third kinds. To facilitate the use of the equations, therefore, a computer program has been included in the analysis.
Flow charts are presented which assist in the explanation of iterative procedures necessary in the initial stages of the solution, and numerical examples are considered which illustrate the procedures. The analytic solutions developed are compared with the results of laboratory tests using representative springs and loading combinations.
The tests confirm the accuracy of the equations developed for all but very long and heavy springs which experience appreciable deformation due to their own weights.
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