A geometrical set of closed form trigonometric equations are developed as a simplified alternative to the complex numerical computations required for determining lateral belt tracking locus due to pulley misalignment tolerances. Solutions are validated by a comprehensive statistically designed database. Further, analytical verification is obtained from ABAQUS/Explicit results based on a nonlinear hyperelastic Ogden finite element model.
Three-dimensional geometric equations form the basis of a computer tool developed to predict belt displacement across a flat backside pulley, as well as angles of entering and exiting spans. Predictions are performed for the critical combination of a grooved-flat-grooved pulley arrangement typically found in automatically tensioned front-end automotive serpentine accessory drives.
Excellent correlation is found between the three-dimensional finite element analysis, experimental data, and the simplified geometrical model. Consequently, accessory design engineers can effectively deploy the geometrical model to rapidly determine relationships between belt tracking and numerous critical drive parameters.