The gear box represents an important mechanical sub system. In machine tools, the propose of a gear box is to provide a series of useful output speeds so that the machining operation can be carried out at its most optimum operating conditions high spindle speeds with low feed rate for roughing operations. An important aspect in the design of machine tool transmission is to keep the cost and volume of the gear box to a minimum. The probabilistic approach to design has been considered to be more rational compared to the conventional design approach based on the factor of safety. The existence of uncertainties in either engineering simulations or manufacturing processes calls for a reliability-based design optimization (RBDO) model for robust and cost-effective designs. In the present work a three shaft four speed gear box is designed using reliability principles. For the specified reliability of the system (Gear box), component reliability (Gear pair) is calculated by considering the system as a series system. Design is considered to be safe and adequate if the probability of failure of gear box is less than or equal to a specified quantity in each of the two failure modes. A FORTRAN program has been developed to calculate the mean values of face widths of gears for the minimum mass of gear box. By changing the probability of failure of system variations in the face widths are studied. The reliability based optimum design results are compared with those obtained by deterministic optimum design. The minimum mass of the gear box is increase as the specified values of the reliability is increased.
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