A Rational Design of Helical Spring

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In order to rationalyze the helical spring design, it is essential to take the effects of the pitch angle and end conditons into account in the analysis of the dynamic characteristics and stress characteristics. Recently, the authors showed that the analytical approach based on the finite element method proves effective for evaluating various kinds of spring characteristics. However, when applying the finite elemnt method to the helical spring design, cumbersome caluculations for obtaining the shape function for the spring element, abundant store of knowledge about numerical analysis and skillful programming techniques are reqired. In the present report, therefore, in order to avoid the above mentioned difficulties and simplify programming, the symbolic mathematic system REDUCE is used in computational processing reqired for obtaining the shape function and deriving spring element matrices. As symbolic manipulation reclaims large amounts of computer memory, careful programming for memory savings is required in the symbolic integration obtaining spring element matrices. New algorithm for symbolic integraton is developed and element matrices are obtained successfully.The pressent report also deals with the effect of natural frequencies of coil spring on lateral stability as an application of the above calculation method. Analysis shows that lateral instability apperars clearly, when natural freqency ,corresponding to translational mode, equals twice natural frequency, corresponding to transverse mode.