Engee documentation

Variable Ratio Transmission

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

blockType: Engee1DMechanical.Transmission.Gears.VariableRatio

variable ratio transmission

Path in the library:

/Physical Modeling/1D Mechanical/Couplings & Drives/Variable Ratio Transmission

Description

Block Variable Ratio Transmission It is a gearbox that dynamically transmits motion and torque between two connected axes of the drive shafts: the driving and the driven.

If the dynamic ductility of the transmission is ignored in the unit, then the drive shafts are limited so that their rotation is carried out with a variable gear ratio that can be controlled. You can choose whether the driven axis will rotate in the same or opposite direction as the driving axis. If the driven and driving axes rotate in the same direction, then their angular velocities and they have the same sign. If the driven and driving axes rotate in opposite directions, then and they have opposite signs.

The elasticity of the transmission introduces an internal time delay between the movements of the axles. Unlike a gear train, a variable-ratio gearbox has no kinematic limitations. Torque losses caused by friction and transmission losses can also be controlled.

Perfect transmission of motion and torque

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

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

However, the block Variable Ratio Transmission it includes an elastic connection between the axes. Dynamic transmission of motion and torque replace the kinematic limitation with a non-zero one , which dynamically reacts through basic compliance parameters and :

where

  • – torque of the drive shaft;

  • – torque of the driven shaft;

  • – losses during transmission of torque. In the ideal case .

Assessment of compliance parameters

  • The basic angular compliance can be assessed based on a constant transmission time and the moment of inertia :

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

Imperfect transmission of torque and losses

In case of imperfect transmission of torque, losses . Block Variable Ratio Transmission It models losses similarly to losses in non-ideal gears. For more information about modeling imperfect transmissions, see the article Modeling of mechanical gears with losses.

In an imperfect gearbox, the angular velocity and ductility dynamics remain the same as in the ideal case. The transmitted torque and power are reduced due to:

  • Coulomb friction (for example, friction between the belt and the wheel or internal losses due to belt tension), characterized by efficiency ;

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

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

Power flow Power loss condition Driveshaft output,

Straight

The slave,

Reverse

Leader,

Coupling efficiency

This unit fully accounts for friction losses characterized by efficiency , only if the absolute value of the angular velocity of the driven shaft higher than the threshold speed .

If the value is less , then the unit 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.

Units

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.

Units

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.

Units

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.

Units

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.

Units

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