Engee documentation

Variable Ratio Transmission

Dynamic model of gearbox with variable and adjustable gear ratio, transmission elasticity and friction losses.

variable ratio transmission

Description

The Variable Ratio Transmission unit is a gearbox that dynamically transmits motion and torque between two coupled drive shaft axes: a drive shaft and a driven shaft.

If the dynamic pliability of the transmission is ignored in the unit, the drive shafts are constrained so that they rotate at a variable gear ratio that can be controlled. It can be selected whether the driven axle rotates in the same or opposite direction as the drive axle. If the slave and master axes rotate in the same direction, their angular velocities and have the same sign. If the driven axis and the master axis rotate in opposite directions, and have opposite signs.

The elasticity of the transmission introduces an internal time delay between axis movements. Unlike gearing, a variable ratio gearbox has no kinematic constraints. Torque losses due to friction and transmission losses can also be controlled.

Ideal transmission of motion and torque

The Variable Ratio Transmission unit dynamically transmits motion and torque between the drive and driven shafts.

If there is no relative offset between the axes, the block is equivalent to a variable ratio transmission . This transmission imposes a time-dependent kinematic constraint on the movement of the two drive shafts:

However, the Variable Ratio Transmission unit incorporates elastic coupling between the axles. The dynamic motion and torque transmission replace the kinematic constraint with a non-zero , which responds dynamically via the basic pliability parameters and :

where

  • - is the torque of the drive shaft;

  • - torque of the driven shaft;

  • - torque transmission losses. In the ideal case .

*Estimation of the pliability parameters

  • It is possible to estimate the basic angular pliability from the transmission time constant and the moment of inertia :

  • It is possible to estimate the basic angular velocity pliability based on the transmission time constant с , moment of inertia and damping coefficient :

Non-ideal torque transmission and losses

For non-ideal torque transmission losses . The Variable Ratio Transmission block models losses in a similar way to losses in non-ideal gears. For more information on modelling non-ideal gears, see Modelling of mechanical gears with losses.

In a non-ideal gearbox, the angular velocity and pliability dynamics remain the same as in the ideal case. The transmitted torque and power are reduced due to:

  • Coulomb friction (e.g. friction between belt and wheel or internal losses due to belt stretching), characterised by efficiency ;

  • viscous coupling of the drive shafts with the bearings, parameterised by viscous friction coefficients .

When the angular velocity changes sign, the hyperbolic tangent function smooths out the change in torque from Coulomb friction.

Power flow Power loss condition PTO shaft output,

Straight

Slave,

Reverse

Leading,

Clutch efficiency

This block fully accounts for friction losses characterised by the efficiency , only if the absolute value of the angular speed of the driven shaft is greater than the threshold speed .

If the value of is less than , the block smooths the efficiency to unity at zero speed.

Ports

Conserving

# B — drive PTO shaft
`rotational mechanics

Details

A non-directional port associated with the drive shaft.

Program usage name

base_flange

# F — driven PTO shaft
rotational mechanics

Details

A non-directional port associated with the driven shaft.

Program usage name

follower_flange

Input

# r — ratio of input shaft speed to output speed
scalar

Details

Dimensionless ratio of input shaft speed to output shaft speed.

Data types

Float64.
Complex numbers support

No

Parameters

Main

# Output shaft rotates — direction of rotation of the output shaft in relation to the direction of rotation of the input shaft
In same direction as input shaft | In opposite direction to input shaft

Details

Direction of rotation of the output shaft in relation to the direction of rotation of the input shaft.

Values

In same direction as input shaft | In opposite direction to input shaft
Default value

In same direction as input shaft
Program usage name

rotation_direction_type
Evaluatable

No

Compliance

# Transmission stiffness at base (B) — drive shaft stiffness factor
HP_DIN/rpm | N*m/rad | W*s/rad | m*mN/rad | HP_DIN*s/rad | ft*lbf/rad

Details

The inverse of the angular pliability , measured at the drive shaft.

Values

HP_DIN/rpm | N*m/rad | W*s/rad | m*mN/rad | HP_DIN*s/rad | ft*lbf/rad
Default value

3e5 N*m/rad
Program usage name

k_base
Evaluatable

Yes

# Transmission damping at base (B) — drive shaft damping factor
N*m/(rad/s) | ft*lbf/(rad/s)

Details

The inverse of the angular pliability of the damping , measured at the drive shaft.

Values

N*m/(rad/s) | ft*lbf/(rad/s)
Default value

0.05 N*m/(rad/s)
Program usage name

C_base
Evaluatable

Yes

# Initial input torque at base (B) — initial torque of the drive shaft
N*m | mN*m | lbf*ft

Details

Torque applied to the drive shaft at the beginning of the simulation.

Values

N*m | mN*m | lbf*ft
Default value

0.0 N*m
Program usage name

T_start
Evaluatable

Yes

Transmission Losses

# Losses model — loss modelling

Details

If this checkbox is unchecked, the block calculates the ideal torque transmission.

If this checkbox is selected, the unit calculates friction losses for non-ideal torque transmission: it reduces the gearbox torque transmission by a constant efficiency value , satisfying the condition .

Default value

false (switched off)
Program usage name

enable_loss_modeling
Evaluatable

No

# Efficiency — Efficiency of torque transmission from the drive shaft to the driven shaft

Details

Efficiency of torque transmission between the drive and driven shafts.

Dependencies

To use this parameter, select the Losses model checkbox.

Default value

0.8
Program usage name

efficiency
Evaluatable

Yes

# Follower angular velocity threshold — threshold value of the angular speed of the driven shaft
rpm | deg/s | rad/s

Details

Absolute angular velocity threshold , above which the full efficiency loss is taken into account for the output shaft speed .

Dependencies

To use this parameter, select the Losses model checkbox.

Values

rpm | deg/s | rad/s
Default value

0.01 rad/s
Program usage name

w_threshold
Evaluatable

Yes

Viscous Losses

# Viscous friction coefficients at base (B) and follower (F) — vector of viscous friction coefficients of the driving and driven shafts
N*m/(rad/s) | ft*lbf/(rad/s)

Details

Vector of viscous friction coefficients μ for the drive shaft and the driven shaft respectively.

Values

N*m/(rad/s) | ft*lbf/(rad/s)
Default value

[0.0, 0.0] N*m/(rad/s)
Program usage name

viscous_coefficient_vector
Evaluatable

Yes