Авіаційно-космічна техніка та технологія (Aug 2020)
EQUATIONS OF SPATIAL MOTION OF A SOLID BODY WITH MOLDABLE FASTENING TO THE FOUNDATION (THE TASK OF DEPRECIATION IN SPACE)
Abstract
The task of fastening equipment, especially ship equipment, is considered important in conditions of vibration and shock. Equipment can be mounted on shock absorbers. These shock absorbers solve the problems of vibration isolation and shock protection. The classic case is the use of rubber-metal shock absorbers. The equipment can be attached to the foundation with bolts and dowels. In this case, the bolts mustn't collapse and the joints do not open during shock. An interesting case is an attachment, the fastening of which should not be destroyed. Attachments are usually attached by bolts, the destruction of which is not permissible. In the case of plastic deformation of the bolts they can be tightened, and then replacing the collapsed shock absorber is not easy. The condition of the fastening devices can be investigated by modeling, using computer technology, the movement of the unit. The use of computer technology is justified by the cumbersomeness of the task, the nonlinear characteristics of rubber-metal shock absorbers, and bolts in the case of plastic deformations. Typically, when modeling the movement of shock-absorbing equipment, they are limited to a flat task or a case of hard keys. To solve the spatial problem, we introduce three coordinate systems. One system is non-mobile and connected to the foundation. Two other coordinate systems have a beginning at the center of gravity of the unit. The axes of one of these systems are parallel to the axes of the system associated with the foundation. And the other of these systems are rigidly connected to the unit. At the initial moment, in case of rest, all three systems coincide. For the general case of motion, Euler angles can be used, but due to the small movements of the equipment, accuracy is lost. Indeed, the intersection line of the planes determining the Euler angles is determined with an error (the case of almost parallel planes). To solve this problem, the authors used the angles between the axes associated with the equipment and the foundation plane. Then, through these angles, Euler angles were expressed and expressions were obtained that allow the use of numerical methods to solve the equations of motion.
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