Some Notes on V-Belt Drives

This paper consists of four separate parts: 1) Radial penetration of a V-belt, 2) Formulas for axial forces, 3) Additional slip in varispeed drives, 4) Arc of contact in belt drives. There is a slight connection between the parts in the way that all the results are applicable to variable speed drives. 1 The penetration of a V-belt into the groove depends on wedge angle, friction, elasticity of the belt and belt design. It is shown that certain combinations of these parameters result in zero penetration i.e., there is a kind of blocking. This is different from the well known self-locking phenomenon, where the belt is prevented to move outwards if the wedge angle is less than the friction angle. 2 The axial forces calculated from the theory of V-belt mechanics are not possible to express in simple formulas. However, approximate formulas can be developed. Previously reported formulas are here completed with the influence of belt design and elastic properties of the belt. It is convenient to use formulas in the computerized analysis of variable speed drives. 3 In variable speed drives consisting of e.g. one spring loaded pulley and one rigid (manually adjustable) pulley there are two kinds of speed loss present. Except the ordinary slip between the belt and the pulleys there is an additional speed loss due to a small axial motion of the spring loaded pulley. The additional speed loss depends on spring load, transmitted torque, drive geometry, friction, elastic properties of the belt and, what is important, the flexural rigidity of the belt. On a spring loaded driver pulley the width between the pulley halves always increases with increasing torques whereas the width of a spring loaded driven pulley can both increase and decrease. This means that in the first case the additional speed loss is always positive but in the second case it can be both positive and negative. If the maximum slip is used as a design criterion it is important to recognize this difference. 4 The arc of contact is included in the formulas presented in part 2. The geometric arc of contact differs from the real one due to the curvature of the belt between the pulleys. Previously ordinary beam theory has been applied to calculate the decrease in contact angle. Here a modified analysis is presented—except flexural rigidity also compressibility of the belt is introduced. It appears that the decrease in contact angle in ordinary belt drives is considerably smaller than that predicted by the beam theory. Sometimes the contact angle can increase. In most cases the change in contact angle is negligible and the geometric arc of contact can be used in the formulas in part 2.