BikeSim Math Models

Here are some features of the BikeSim mathematical models. More details about the math models are provided in this 4-page PDF file.

Complete Motorcycle Model

BikeSim is delivered with complete two-wheeled motorcycle models with 16 multibody degrees of freedom (DOF):

• The sprung mass is a rigid body with six DOF.
• Each suspension has one DOF for stroke. Other suspension motions, such as spindle pitch and longitudinal position are constrained by configurable functions.
• Each wheel has one spin DOF.
• The steering system has three DOF (twist, bend and steer).
• Rider body has two DOF (upper body lean and lateral translation relative to main frame).
• Drivetrain has one gearbox sprocket spin DOF.

The math model for a two-wheeled motorcycle has 58+ ordinary differential equations (ODEs), whereas each multibody DOF has two equations; other equations represent the dynamics of components:

• Each tire has two DOF for lagged response.
• TNO Delft-Tyre and COSIN FTire add more DOF.
• The brake fluid in each actuator has one DOF.
• The engine crankshaft has one DOF.
• Throttle has a lag with one DOF.
• Clutch torque has a log with one DOF.
• Fuel consumption has one DOF.

The math model has about 100 state variables, needed (along with parameters and configurable function definitions) to fully define the state of the system. These include the ODE variables plus others such as: friction elements, locked states of clutches and wheels and other dynamic mode conditions.

Control Inputs

The four main control inputs involve steering, braking, speed, and riding position. BikeSim has options for open-loop and closed-loop inputs for steering, braking, throttle, and gear shifting (riding position is open-loop input only). There are also options for building complex control sequences as a series of "events," where a new control can be triggered by any output variable reaching a specified value.

Environmental Inputs

BikeSim includes an advanced description of 3D road surfaces. You can quickly build descriptions of roads with arbitrary horizontal, vertical, and cross-elevation geometry. Friction between the tire and the ground is specified as a function of distance along the road and lateral position relative to the centerline. Users can create 3D roads such as banked curves, hills and race tracks with a range of simulated friction coefficients.

Events

Complicated sequences of inputs can be specified as events. For example, open throttle until an engine speed is reached, then engage the clutch to lift the front wheel, etc. Conditions can also be in place for changing vehicle properties. For example, change the tire crown radius in the middle of the maneuver to simulate the stability with a blown tire.

Outputs

The solver programs generate over 800 output variables. Any subset of the list of variables can be specified at run time, to control the size and organization of output files. BikeSim provides a graphical interface for browsing the list of available variables, sorting by several categories. All variables are described in documentation text files.

Extending a BikeSim Model

The BikeSim math models include nearly 200 inputs that you can specify in Simulink, VS Command or with your own C code. These inputs include all control and environmental inputs, and all forces and moments generated by the powertrain, brakes, steering system, tires, and some suspension components. These inputs are used to extend the Bike math models by defining them with MATLAB/Simulink, available from The MathWorks, Inc, or with custom C code.

BikeSim Information