Belt transmissions

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1. BELT TRANSMISSIONS 1.1 FLAT BELTS Figure 1 shows a belt transmission in which the drive torque is applied to the smaller pulley. Figure 2 shows the isolated driving pulley. The drive torque is denoted Md , while the tensions in the two sides of the belt are denoted 1T and 2T , respectively. The radius of the pulley is 1R , while the component of the reaction force acting at the centre of the pulley, along the straight line passing through the centers of the two pulleys, is denoted Q . Figure 1 Belt transmission Figure 2 Isolated driving pulley Figure 3 Wrap angle and independent variable ϕ The balance of the moments about the axis passing through point O 1, orthogonal to the lateral side of the pulley, gives: ( )121M TTRd = − (1) In accordance with eq.(1) the tension 1T must be higher than the tension 2T . The belt side subjected to the tension 1T is denoted tight side, while the opposite side is denoted slack side. The balance of the forces acting along the straight line passing through the centers of the two pulleys gives: 12T cos T cos Qαα+= (2) where α is the inclination angle of the belt sides with respect to the axis passing through the centers of the pulley (Figure ). In order to study the law with which the tension of the belt changes from the lower value 2T , in the slack side, to the higher value 1T , in the tight side, it is possible to isolate an infinitesimal portion of the belt, which is in contact with the smallest pulley and subtended by an infinitesimal angle dϕ . The independent variable ϕ is measured starting from the first contact point between belt and pulley, on the slack side (Figure 3). Owing to the tension of the belt, a pressure distribution is generated on the contact surface between belt and pulley. As a result, an infinitesimal normal…