CVT Powertrain is described by a Control State Equation (CSE). The inputs to the powertrain are throttle and gearbox input shaft speed. The output is the secondary pulley torque. There are two optional clamping forces inputs to the powertrain. The CVT property file allows to choose between a mechanical CVT or electric/hydraulic CVT. By default, MS models a mechanical CVT and the clamping forces are calculated based on parameters in the CVT property file.

If the CLAMP_MECH value is something other than ‘CENTRIFUGAL’, the clamping force values are not calculated and must be input to the model.
Figure 1. Schematic of CVT Powertrain
The model needs a CVT property file as input. This property files contains the parameters and options which are taken into account while evaluating the state derivatives and outputs. The CVT property file has a ‘.cvt’ extension. It contains the following parameters:
Parameter Details Unit Symbol
BELT_TYPE Type of variator belt (rubber, steel, etc) Currently the belt is considered rigid despite the value of this parameter
CLAMP_MECH Mechanism to generate clamping force. It can be CENTRIFUGAL or user-defined name
RP_MAX Maximum running radius of belt on Primary pulley Length
RP_MIN Minimum running radius of belt on Primary pulley Length
RS_MAX Maximum running radius of belt on Secondary pulley Length
RS_MIN Minimum running radius of belt on Secondary pulley Length
THETA Half of Pulley wedge angle Angle
BELT_LENGTH Length of the belt, it is assumed constant Length
MU_STATIC Friction value between belt and pulley when belt does not shift
MU_DYNAMIC Friction value between belt and pulley when belt slips on pulley
BELT_MASS Mass of the belt Mass
PULLEY_DISTANCE Distance between primary and secondary pulley Length
NO_ROLLERS Number of rollers
ROLLER_MASS Mass of a roller Mass
P_SHEAVE_ANGLE Inner angle of the moving sheave in primary pulley Angle
KP Spring stiffness in primary pulley Force/Length
KP_LOAD Preload of the spring in secondary pulley Length
KS Spring stiffness in secondary pulley Force/Length
KS_LOAD Preload of the spring in secondary pulley Length
KT Torsional spring stiffness Force*Length/Angle
KT_LOAD Preload torsion angle Angle
HELIX_RAD Helix radius Length
HELIX_ANGLE Helix angle Angle
RADIAL_SHIFT_PROFILE The variation of the roller radius from rotating shaft and ramp angle with respect to the axial shift of moving sheave of the primary pulley Length vs Length and Angle vs Length and
CMM CMM coefficient and thrust ratio (dimensionless) variation with respect to radius ratio 1/(Force*Angle)
The outputs from the CVT powertrain are:
Output Name Request ID Elements Component Unit
Throttle position, input throttle, static throttle 1 1 Modified Throttle position 0-1
2 Throttle demand 0-1
5 Throttle modulation indicator
Radius ratio, Radius - Pr. pulley, Radius - Sec. pulley, Alpha, Beta 2 1 Geometric gear ratio/pulley running radius ratio
2 Primary Pulley radius Length
3 Secondary Pulley Radius Length
5 Primary Pulley Wrap Angle Angle
6 Secondary Pulley Wrap Angle Angle
Eng. omega (rad/s), Eng. omega (rpm), Engine trq., [d/dt] Engine trq. 3 1 Engine Speed RPM
2 Engine Speed Rad
3 Engine Torque Force*Length
5 Engine Speed Derivative Rad/Sec
Pr. pulley trq., Sec. pulley trq., Pr. pulley frc., Sec. pulley trq., k_thrust 4 1 Primary Pulley Torque Force*Length
2 Secondary Pulley Torque Force*Length
3 Primary Clamping Force Force
5 Secondary Clamping Force Force
6 Stationary Clamp Force Ratio
7 Belt Slip
CVT pri. pulley [Sh. shft., Rad. shft., Ramp ang., Spr. frc., Fly. wt. frc.] 5 1 Primary pulley sheave axial shift Length
2 Rollers radial shift Length
3 Primary pulley sheave ramp angle Angle
5 Primary pulley spring force Force
6 Centrifugal force by fly weights/rollers Force
7 0
CVT sec. pulley [Sh. shft., Spr. rot., Helix frc., Spr. frc., Spr. trq., Trq. feedback] 6 1 Secondary pulley sheave axial shift Length
2 Secondary pulley spring rotation Angle
3 Helix Force Force
5 Secondary Pulley Spring Linear Force Force
6 Secondary Pulley Spring Torque Force*Length
7 Torque Feedback Force
The Request Id refers to the POWERTRAIN_REQ function used to create the outputs.
Figure 2.

In MotionView these six outputs access the POWERTRAIN_REQ “USER(0,id)” to display the different plots in HyperGraph.

Figure 3.