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It is well-known that double-mass torsional rubber dampers which have two masses and springs in parallel are effective for controlling torsional vibration characteristics over a wide range of engine speed. On the occasion of reliability estimation of the rubber dampers, it is important to consider generation of heat in the rubber due to torsional vibration. By predicting generation of heat at the designing stage, optimum design of the torsional rubber dampers can be achieved. By development and application of this prediction method, a new type double-mass damper was developed. It provided higher vibration control characteristics and reliability than conventional viscous dampers, and also it provided advantages in terms of noise, productivity and weight.