Tension in timing-belt drives

A urethane timing belt moves samples into position in this CAD simulation of an automated blood sampling machine. Timing-belt drives transmit torque and motion from a driving to a driven pulley or force to a linear actuator. They may also convey a load placed on the belt surface. A drive under load develops a difference in belt tension between the entering (tight) and leaving (slack) sides of the driver pulley. This effective tension, , is the force transmitted from the driver pulley to the belt and to the driven pulley or load: = tight and slackside tensions. The effective tension or working force generated at the driver pulley overcomes the driven pulley's resistance to motion. The driving torque, , is related to the driven torque (load), = pitch diameter of the driver pulley, = power required at the driven pulley, = angular speeds of the driver and driven pulleys of pitch diameters d , respectively, and = efficiency (typically about 0.94 to 0.96). A force equilibrium at the driver or driven pulley relates tight and slack-side tensions and the shaft reaction forces . In powertransmission drives, forces on both shafts are equal in magnitude: = belt wrap angle around the driver pulley. , is the tension set by an adjustable idler pulley. Pretension prevents belt slack-side sagging and ensures proper tooth meshing. In most cases, timing belts perform best when the magnitude of slackside tension is about 10 to 30% that of the effective tension. Although generally not recommended, belt drives can work without an adjustment mechanism. This is possible because, after initial tensioning and straightening, belts tend not to elongate or creep. Overall belt length remains constant during operation regardless of loading conditions, provided belt sag and some other minor influences are neglected. However, reaction forces vary under load. And