A Mechanical Time-Delay Device Sensitive to Centrifugal Fields

JOSEPH RUSSELL BAUMGARTEN, Purdue University

Abstract

Electronic time-delay circuits have wide usage in controlling mechanical and electrical systems. Some mechanical systems do not contain a source of electrical energy as an integral part of the de- sign. The design could be simplified if a suitable mechanical time- delay device were defined. A mechanical device would require no electrical energy, and if properly designed, could be reliable, sturdy, and inexpensive.The purpose of this investigation is to complete an analytical study of a proposed design of a time-delay device which would operate in a centrifugal field. The device consists of two thin co-axial disks, free to rotate relative to each other, with an interconnecting string fastened at the periphery of the outer disk and wound about the inner disk. A small mass is fixed to the string at an intermediate point between the disks. A coil spring of small diameter is connected between the two disks and produces a torque on the disks proportional to the relative rotation. When the device is released in a centrifugal field, the mass moves radially outward under the action of centrifugal force. This radial motion of the mass causes a net relative rotation of the disks. The relative rotation can be used to measure the time that the device has been subjected to the centrifugal field.In this investigation, the equations of motion of this mechanism were derived. The derivations embodied the assumptions that the string (or tension member) is massless and inelastic. The equations of motion were found to be a set of second order non-linear equations which required simultaneous solution.The equations were programmed for digital computation in order that a solution by numerical quadrature could be obtained. A dimensional analysis was performed for the parameters of the device and dimensionless ratios were formed so that a range of design could be covered by the solution.As the dimensionless ratios were varied, the effect on the response of the system was noted. A composite curve comparing the response of systems with various designs was prepared from the numerical solution of each given case.An approximate solution for the equations of motion was found and this solution was compared with the solution of the actual case. It was found that the approximate solution would yield results to within 10% of error for systems having relative rotation of 1250 or less.

Degree

Ph.D.

Subject Area

Mechanical engineering

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