Calculation of rubber-metal silent-blocks under quasi-static loading

Abstract

Abstract. In this paper, an algorithm for calculating rubber-metal silent blocks (hinges) under the action of a lateral quasi-static load is presented. Silent blocks of a welded type made of new brands of rubbers, which are widely used in vibration machines of various types as elastic links, are considered. A calculation is given for a very long hinge, for which the length is large compared to its outer diameter. In the calculation, it was assumed that there are no axial displacements, and the angular and radial displacements can be represented as a product of arbitrary functions of the radial coordinate and the sine and cosine of the angular coordinate, respectively. The relationship between these functions is obtained from the condition of rubber incompressibility. From the condition of the minimum total energy of the system, we have a linear inhomogeneous differential equation of the third order for one of these functions. By solving it under known boundary conditions, we obtain final expressions for the radial and angular displacement, and, consequently, for the displacement of the inner cage. With taking these expressions into account, a solution was also obtained for the hinge, the length of which cannot be considered infinite in comparison with its diameter. In this case, axial displacements should also be considered. Besides, it is assumed that the functions of the radial coordinate for the radial and angular displacement can be represented as a linear combination of the corresponding functions for the long hinge. The corresponding function for axial displacement can be found from the condition of volume constancy. The linear combination coefficients are obtained from a system of two linear algebraic equations, to which the minimum condition for the total energy of the system leads. The exact expression for the movement for the short hinge is rather cumbersome. But for the most common sizes of rubber-metal hinges, you can use a series expansion of the expression for displacement and thus get a fairly simple formula. By comparing the resulting expression with the expression for displacement of the long hinge, you can see that the formula for the infinitely long hinge can only be used if a certain condition is met that binds the dimensions of the hinge. At the end of the paper, an example of calculating a rubber-metal element ШРМ-102, which is under the action of a radial load, is given. The rubber layer in it is made of a new medium-filled rubber made of natural rubber. The obtained value of the displacement of the inner cage is in good agreement with the experimental data.