Time-dependent constitutive modeling of drive belts – I. The effect of geometry and number of loading cycles

This paper presents constitutive modeling of dynamically loaded elastomeric products such as power transmission belts. During the normal operation of the belts certain segments of the belt structure are loaded with a tooth-like periodic (cyclic) loading. When the time-dependent properties of the elastomeric material “match” the time-scale of the dynamic loading a strain accumulation process occurs. The critical angular velocity is proportional to the ratio of the belt length to the common diameters of the pulleys. The magnitude of the strain accumulated in each loading cycle decreases with an increase in belt length. For a given belt geometry the critical angular velocity increases with the number of loading cycles. At the same time the magnitude of the accumulated strain decreases non-linearly as the number of loading cycles increases. However if the belt operates at or in the close vicinity of its critical angular velocity it will almost certainly fail! The critical angular velocity depends on the material retardation time (location in the frequency spectrum), while the magnitude of the accumulated strain is dictated by the strength of the corresponding discrete spectrum lines. Thus, the mechanical spectrum of the elastomeric material from which the belt is constructed is the most important material function for predicting the durability of drive belts and similarly dynamically loaded elastomeric products.