How to Predict Dynamic Behavior of a Continuously Variable Transmission Assignment Using MATLAB

Alex Thompson

Australia

Matlab

Alex Thompson has over 8 years of experience in automotive system modeling and simulation. He earned his Master’s degree in Mechanical Engineering from Curtin University, Australia.

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CVTs are especially popular in lightweight vehicles and are widely used in applications such as motorcycles, snowmobiles, and Baja SAE cars due to their simplicity and adaptability compared to conventional clutches and multi-gear transmissions.

Challenges in CVT Design and Testing

Traditionally, CVT design and tuning rely heavily on experimental testing, which involves manually adjusting mechanical components such as flyweights and springs, followed by repeated field tests. This process can be both time-consuming and costly.

Flyweights respond to engine rotation by exerting centrifugal force, which in turn adjusts the axial forces on the pulleys, changing the belt position and thus the transmission ratio. Springs provide resistance that helps control the position of the flyweights, affecting the balance of forces in the system. Small variations in flyweight mass, spring stiffness, and other parameters can significantly impact vehicle performance.

Without proper predictive tools, optimizing these parameters involves a lot of trial and error.

Why Use MATLAB for CVT Simulation?

MATLAB offers powerful numerical computing capabilities, especially suited for solving complex dynamic systems. It supports matrix computations, numerical integration, and simulation techniques essential for modeling mechanical systems like CVTs.

By building a MATLAB model of a CVT, it's possible to simulate the transmission’s dynamic response to changes in design parameters—such as flyweight mass or spring stiffness—without needing costly physical prototypes.

This also allows for testing multiple configurations quickly, identifying the optimal setup for desired vehicle performance.

Modeling the CVT System in MATLAB

To capture the full behavior of the CVT, the system is divided into two main components for modeling:

1. The Belt Model: The belt is discretized into small segments or nodes connected by springs and dampers, representing its elastic and damping properties. The positions and forces on each node are calculated dynamically over time.
2. The Drive Mechanism Model: This includes the flyweights and springs controlling the axial forces applied on the pulleys, which influence the belt’s position and therefore the transmission ratio.

Belt Discretization and Dynamics

The belt in the CVT is not just a simple, rigid connection; it stretches and slips slightly under load. To model this accurately, the belt is broken down into discrete nodes connected by spring-damper elements. This allows the model to capture variations in tension and position along the belt length.

For each node, the sum of forces is calculated considering axial forces from the pulleys, belt tension, and inertial effects. Using Newton’s second law, the acceleration of each node is obtained by dividing the net force by the node mass. By integrating acceleration twice over time, MATLAB calculates the node’s position dynamically.

This detailed model allows the simulation of phenomena like belt slip and slack during gear ratio changes, which are critical to understanding transmission efficiency and durability.

Drive Mechanism and Control Model

The drive mechanism controls the axial forces on the pulleys that adjust their effective diameters. It consists primarily of flyweights attached to the primary pulley, which move outward due to centrifugal force when the engine spins. This outward movement compresses springs, balancing the forces and determining the axial force applied.

This axial force affects the tension distribution on the belt, influencing how torque is transmitted to the secondary pulley and ultimately the wheels.

In MATLAB, this control mechanism is modeled by calculating the centrifugal force on flyweights based on their mass and rotation speed, then balancing it with spring forces. This interaction feeds into the belt model as an input axial force.

Combining the Models

With both models built, they are coupled in MATLAB to simulate the CVT’s overall behavior. Input parameters include:

• Primary pulley rotation speed (from the engine)
• Flyweight mass and inertia
• Spring stiffness
• Resistive torque (load on the system)

The model then iteratively calculates:

• Node positions along the belt over time
• Resulting tension forces
• Rotation and torque on the secondary pulley
• Transmission ratio changes

A numerical integration method such as the Runge-Kutta algorithm solves the system’s differential equations step-by-step, ensuring accurate dynamic simulation.

Benefits of This MATLAB Model

This approach offers several significant advantages:

• Reduced Testing Time and Costs: By simulating different configurations and parameters, engineers can avoid costly physical experiments for initial testing.
• Insight into Dynamic Behavior: The discretized belt model reveals detailed tension variations and slack behavior impossible to see in static models.
• Optimization Potential: Designers can quickly test how changes in flyweight mass or spring stiffness affect acceleration and torque, enabling data-driven tuning.
• Theoretical Understanding: It deepens knowledge of how mechanical parameters influence transmission efficiency and vehicle longitudinal dynamics.

Example Results from Simulation

When running the complete MATLAB model, you can visualize key aspects such as:

• Shift Ratio Variation Over Time: Showing how the transmission ratio smoothly changes as pulley diameters adjust.
• Torque Transmission: Analysis of torque output on the secondary pulley, indicating how power is delivered to the wheels.
• Belt Tension Distribution: Nodes under the primary pulley experience high tension (tight side), while the secondary pulley side sees less tension (loose side). This tension difference drives torque transmission.
• Slack and Slip Behavior: The model captures moments where the belt slips or loses tension, which affects transmission efficiency.

These insights allow engineers and students to correlate mechanical design changes with vehicle performance outcomes, optimizing for acceleration, fuel economy, or durability.

Using the Model for Vehicle Dynamics

The CVT transmission ratio curve generated by the MATLAB simulation feeds into higher-level vehicle dynamic models. For example, it provides input for longitudinal acceleration models that predict how quickly a vehicle can accelerate based on engine torque and transmission ratio.

This integration allows simulation of complete vehicle performance, linking mechanical design to on-road behavior.

Future Directions for CVT Simulation with MATLAB

The model described here represents a crucial step in simulating CVTs, but many enhancements are possible:

• Integration with Full Vehicle Models: Combining the CVT simulation with models of suspension, tires, and aerodynamics for complete vehicle analysis.
• Optimization Algorithms: Using MATLAB’s optimization toolbox to automatically find the best flyweight and spring configurations based on performance goals.
• Thermal Effects: Modeling how heat generated by belt slip affects material properties and efficiency.
• Control System Simulation: Incorporating electronic control units (ECUs) to simulate closed-loop control of transmission parameters.

Advancements like these would allow engineers to design and test custom CVTs with greater confidence, reducing the need for costly prototypes.

Why This Matters for Students and Engineers

For university students working on automotive or mechanical engineering projects, mastering MATLAB for dynamic system simulation is an invaluable skill. Building and testing models like this CVT simulation project not only enhances programming and modeling proficiency but also deepens understanding of real-world engineering problems.

For anyone dealing with MATLAB assignments, developing a simulation that links mechanical theory with numerical methods is a great learning experience. It also prepares students for professional work where simulation-driven design is increasingly standard.

Final Thoughts

This project shows how MATLAB can be a powerful ally for engineering students working on complex systems like CVTs. Not only does it provide a platform to simulate and predict real-world performance, but it also helps students build a deeper theoretical understanding of the mechanics at play. For anyone involved in similar student engineering projects—or for those looking to learn MATLAB by working on practical applications—this CVT modeling approach is a great case study. By combining force analysis, differential equations, and dynamic simulations, it’s possible to reduce costs, increase accuracy, and speed up development time. If you're a student working on vehicle dynamics, CVT systems, or just want to gain more hands-on experience with MATLAB, building this type of model could be the perfect learning opportunity.