Date of Graduation


Document Type


Degree Name

Master of Science in Mechanical Engineering (MSME)

Degree Level



Mechanical Engineering


Uche Wejinya

Committee Member

Larry Roe

Second Committee Member

Roy McCann


Applied sciences, Continuously, Controls, Transmission, Variable


A numerical algorithm for modeling the dynamic response of a rubber-belt Continuously Variable Transmission (CVT) belt is recreated. The numerical attributes applied to the algorithm and difficulties with numerical stability are discussed in detail. The degrees of freedom of the system have been expanded to include the dynamics of the engine torque output and vehicle loads such as rolling resistance and aerodynamic drag. This was done to emphasize the use of the model as an analysis tool for simulating CVT/engine/vehicle response. The increased degrees of freedom require the addition of a linear dampening element between belt nodes to dampen resonance between the input and output pulley. This value of damping was computed based on node mass and node natural frequency.

The material properties of the belt greatly influence the model dynamics, but few methods for measuring these properties has ever been outlined in previous works. Different techniques for measuring axial stiffness, longitudinal stiffness, and bending stiffness are described in detail. The range of forces applied during testing were deduced from previous experimental tests to ensure material properties were measured under ideal conditions seen in CVT application. The methods for applying the forces are also designed around re-creating loading conditions seen in application. The material properties are then compared to values used by other researchers. The values for stiffness tend to agree, within an order of magnitude, while material damping was not compared due to testing equipment limitations.

The results of the simulations with a linear PI-controller with a feed-forward gain

generating the axial force on the primary are analyzed. The axial force on the secondary is fixed to simplify the simulation. These results may aid in future work and study of electronically controlled CVT simulation.