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Shrink-fitted parts are commonly structured in mechanical systems (e.g., bearing-shaft coupling). This paper is to perform the theoretical study of the stress and displacement fields in multiple shrink-fitted elastic cylinders (tubes) under thermal and mechanical loads. Based on classic elasticity, the problem is reduced to find the interface pressures of neighboring tubes via solving a system of tridiagonal linear algebraic equations with the interface pressures as unknowns. Formal solutions are derived for the entire stress and displacement fields in general multiple shrink-fitted elastic tubes, which can recover the classic solution in the reduced cases. Numerical scaling analysis is conducted to examine the effects of interference, temperature change and mechanical loads on the stress variation in the elastic tubes. A concise computer code is programmed to implement the theoretical formulation for efficient and reliable stress analysis of an arbitrary number of shrink-fitted elastic tubes subject to constant temperature change and/or inner and outer pressures. As examples, numerical results of the radial and circumferential stresses of two, three and five shrink-fitted elastic tubes of different materials are demonstrated and compared. The present study facilitates the theoretical stress and strength analysis of broad shrink-fitting problems for optimal design and manufacturing of various mechanical press and shrink fits.

shrink fit, stress analysis, elastic cylinders, thermomechanical loads, elasticity.