Partial Meshing of Synchronous Belt Teeth
Authors: Johannesson Tomas 
Published: May 2009

Synchronous belts have been used in power transmissions where synchronization is also needed since the 1940’s. In the 1960’s overhead camshaft engines were introduced and synchronous belts were used as cam belts. This made way for a new standard for belts: improvements were made in materials and profile geometry. These new belts had lower noise emissions and, at the same time, greater durability. Often, both wear and noise are generated when a belt tooth seats or unseats a pulley. A tooth is considered to be fully meshed when the whole belt pitch forms a circular arc. This is not the case for teeth in partial mesh, which occurs in seating and unseating zones. In these zones force peaks are often present. These peaks are believed to arise mainly as a result of two phenomena: one is the overlap effect due to the belt geometry not fitting the pulley, and other is the velocity difference effect. The latter is speed-dependent while the former depends on the belt and pulley profile geometries and the belt teeth positions relative to the pulley. Although force peaks of high magnitude occur, they are present at a such small part of the engagement that their contribution to power transmission can be neglected. This indicates that the positions of the belt pitches relative to the pulley pitches can be established by the load distribution from fully meshed conditions. Although the characteristics of partial mesh teeth have been improved by the introduction of new profiles and materials, problems of durability, noise and transmission error, arising from partially meshed teeth, are still present. Therefore it is important to study belt mechanics in seating and unseating zones. This paper describes a method to calculate force peakson seating and unseating. An overlap area (geometrical interference) is formed by giving belt teeth profiles displacement and checking for interference with the pulley profile. Since it is assumed that the seating and unseating force peaks do not influence the load distribution, the positions of the first and last teeth are superimposed on belt teeth profiles using the results from a quasi-static load distribution model covering fully meshed conditions. The superimposed first and last belt teeth profiles are modelled by line segments. A pulley profile is also modelled by line segments and the profiles are checked for interference. Where interference occur an overlap area is formed. The overlap is translated to a force value via correlation with belt tooth force measurements. Results from the model show good agreement with measurements when force peaks are small. This is due to the fact that the quasi-static load distribution model produces correct belt displacements for these cases. For measured force peaks of higher amplitude the seating and unseating effects are under estimated by the method. The semicircular belt geometry in combination with the hyperelastic nature of the elastomer is probably the reason. A solution is to implement a non-linear force-overlap relation. Another effect not included is the velocity difference effect. The results are sensitive to belt tooth height and radial tooth stiffness.