A First-Principles Dynamic Model of a Rubber V-Belt CVT for General Transient Simulation

With Mechanical Actuation and Traction-Limited Torque Transfer

Abstract

Mechanically actuated rubber V-belt continuously variable transmissions (CVTs) couple ratio change, clamping, torque transfer and shaft motion through the same hardware. Predicting their complete transient response therefore requires these interactions to evolve together rather than prescribing part of the CVT motion. To the authors’ knowledge, this is the first mechanically actuated rubber V-belt formulation in which all retained CVT motion is determined by the coupled dynamics, while attached systems enter only through shaft torque and inertia.

Primary flyweight motion and helix-constrained secondary-sheave rotation enter both the axial force and shaft angular-momentum balances, retaining direct inertial coupling through the clamping hardware. A reduced, fixed-length belt retains independent transport motion and the radial and tangential accelerations associated with changing pulley radii, linking the pulleys through closed-loop tension compatibility and traction-limited contact. Contact and support conditions determine engagement, free shifting, ratio-limit support and changes between sticking and sliding, with impulse–momentum balance supplying the velocity changes at finite-speed constraint activation.

Mechanical, energy and numerical checks support internal consistency across the tested regimes. In the nominal 10 s reference acceleration, stored-energy changes and modelled sliding and capture losses account for net shaft work with a final relative remainder of 4.9 ×10−5%. A reconstructed benchmark against a transient model with a more detailed belt representation gives relatively close feedback-controlled shaft-speed histories despite substantially different clamping demand; replaying the published clamp produces a much larger primary-speed discrepancy. Reconstruction differences limit attribution of the mismatch to any single omitted mechanism, and experimental validation remains to be done.

The retained dynamics are strongly motion-dependent. Primary flyweight dynamics alter engagement, but the quasi-static reduction remains close during the tested smooth shifting and engaged torque changes, whereas secondary shaft deceleration can sustain additional clamping during continuous loaded backshift. In the belt, circulation acceleration supplies the main inertial adjustment during gentle shifting; radial inertia becomes appreciable during rapid shift-speed changes, while curvature and moving-radius contributions remain small in the tested conditions.

Coupled engine–CVT–vehicle simulations demonstrate full-transient capability by carrying state continuously through engagement, shifting, ratio-limit support, traction loss and reverse power. Hardware changes consequently propagate through clamping, ratio, traction, engine operating point and vehicle response rather than altering one quantity in isolation. Together with the benchmark, these simulations show that similar external trajectories can coexist with different internal mechanical states; agreement in selected trajectories therefore does not by itself establish agreement in the mechanics that produced them. Resolving those mechanics together with the motion allows responses to be traced to their causes and hardware changes through the operating conditions they create, supporting mechanics-based design and tuning studies.