Engee documentation

Simple Gear

Simple transmission of driving and driven gears with adjustable gear ratio, friction losses.

blockType: Engee1DMechanical.Transmission.Gears.Simple

simple gear

Path in the library:

/Physical Modeling/1D Mechanical/Gears/Simple Gear

Description

Block Simple Gear It is a gearbox in which the axes of the drive gear are connected ( ) and the driven gear ( ) rotate with a fixed gear ratio that you specify. You also choose whether the axis of the driven gear rotates in the same or opposite direction as the axis of the driving gear.

  • If they rotate in the same direction, the angular velocity of the driven gear ( ) and the angular velocity of the driving gear ( ) have the same sign.

  • If they rotate in opposite directions, and they have opposite signs.

You can add and remove backlash and thermal effects.

The thermal model

You can simulate the effects of heat flow and temperature changes by turning on an additional heat port H. To use the H thermal port, set the Friction model parameter to `Temperature-dependent efficiency'.

In addition, you can select an efficiency model that varies depending on load and temperature by setting the Friction model parameter to `Temperature and load-dependent efficiency'. Enabling the thermal model:

  • Opens the non-directional port H.

  • Includes the Thermal mass parameter, which allows you to specify the ability of a component to resist temperature changes.

  • Enables the Initial Temperature parameter, which allows you to set the initial temperature.

Ideal gears and transmission ratios

Block Simple Gear imposes two kinematic constraints on two connected axes:

where

  • — radius of the driven gear;

  • — angular velocity of the driven gear;

  • — radius of the driving gear;

  • — angular velocity of the driving gear.

The gear ratio for engagement of the driven and driving gears is:

where

  • — the number of teeth of the driving gear;

  • — the number of teeth of the driven gear.

Two degrees of freedom are reduced to one independent gear.

The transmission of torque is carried out as follows:

where

  • — input torque;

  • — output torque;

  • — losses during transmission of torque.

For the perfect occasion .

Imperfect limitations and losses in gears

In an imperfect case . For more information, see the article Modeling of mechanical gears with losses.

In an imperfect gear pair The angular velocity, gear ratio, and restrictions on the number of teeth remain unchanged. But the transmitted torque and power are reduced by:

  • Coulomb friction between tooth surfaces on gears and , which is determined by the efficiency, .

  • Viscous friction of the coupling of drive shafts with bearings, which is determined by the coefficients of viscous friction, .

Constant EFFICIENCY

In the case of constant efficiency, It is a constant value that does not depend on the load or the transmitted power.

Load-dependent efficiency

EFFICIENCY ( ) depends on the load or power transmitted through the gears. For any of the power streams:

where

  • — a torque that depends on Coulomb friction;

  • — proportionality coefficient;

  • — the torque acting on the input shaft in idle mode.

EFFICIENCY ( ) is associated with in the standard form, but becomes load-dependent:

The backlash effect

You can include the backlash effect in your model.

A luft is an excess space between a gear tooth and the teeth of another gear mated to it. The increased backlash compensates for the decrease in manufacturing tolerances and ensures the free movement of lubricants in the gears to prevent jamming. However, excessive backlash can lead to premature wear of system components and affect measurements that depend on the gear position. This block applies backlash to launch and reverse using the block implementation Translational Hard Stop.

If you enable the Enable backlash option, the unit correlates gear rotation with linear backlash as:

where

  • — the relative linear speed of the gear tooth;

  • — corresponds to the value of the Base (B) gear radius parameter;

  • — the radius of the driven gear, where , and the parameter Follower (F) to base (B) teeth ratio (NF/NB) corresponds to the ratio ;

  • and — angular velocities of the driving and driven gears, respectively;

  • — the sign of the direction of rotation of the gear. If the Output shaft rotates parameter is set to:

    • `In the same direction as input shaft', then .

    • `In opposite direction as input shaft', then .

The block considers the teeth engagement as a position, , in relation to linear backlash, , where . corresponds to the Linear backlash parameter. The initial value of the Backlash position variable corresponds to the initial position .

The rigid stop simulates static contact at the borders. The gear is locked in a collision and when . As soon as the gear is locked, . As soon as the condition is met , the gear is unlocked where:

  • — the value of the Static contact release force threshold parameter.

  • — the value of the Static contact speed threshold parameter.

  • — this is the engagement force between the teeth of the gear, such that .

Assumptions and limitations

  • The inertia of the gears is negligible.

  • Gears are treated as solids.

  • Coulomb friction slows down the simulation. (for more information, see here)

Ports

Conserving

# B — drive pinion
`rotational mechanics

Details

A non-directional port associated with the drive gear.

Program usage name

base_flange

# F — idler gear
`rotational mechanics

Details

A non-directional port associated with the driven gear.

Program usage name

follower_flange

# H — heat flux
`heat

Details

A non-directional port associated with heat flow.

The heat port allows modelling the heat flow between the unit and the connected network.

Dependencies

To use this port, set Friction model to `Temperature-dependent efficiency' or `Temperature and load-dependent efficiency'.

Program usage name

thermal_port

Parameters

Main

# Follower (F) to base (B) teeth ratio (NF/NB) — gear ratio from driven pinion to driving pinion

Details

Constant gear ratio, , revolutions of the driven pinion to revolutions of the driving pinion. The gear ratio must be strictly >0.

Default value

2.0
Program usage name

ratio
Evaluatable

Yes

# Output shaft rotates — direction of rotation of the drive pinion
In same direction as input shaft | In opposite direction to input shaft

Details

The direction of movement of the idler gear in relation to the movement of the drive gear.

Values

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

In opposite direction to input shaft
Program usage name

rotation_direction_type
Evaluatable

No

Meshing Losses

# Friction model — friction model
No meshing losses - Suitable for HIL simulation | Constant efficiency | Load-dependent efficiency | Temperature-dependent efficiency | Temperature and load-dependent efficiency

Details

A model of friction in a transmission. Defined as:

  • No meshing losses - Suitable for HIL simulation - the gearing is assumed to be perfect.

  • Constant efficiency - torque transmission between gear pairs is reduced by a constant efficiency value, , such that .

  • Load-dependent efficiency - torque transmission is reduced by a variable efficiency factor. This coefficient is in the range of and is load-dependent.

  • Temperature-dependent efficiency - torque transmission between gear pairs is determined from an interpolation table of temperature and torque efficiency correspondence.

  • Temperature and load-dependent efficiency - the reduction in torque transmission by the temperature and load-dependent efficiency. This coefficient is in the range of and varies with load. The torque transmission efficiency is determined based on user supplied data on gearbox load and temperature.

Values

No meshing losses - Suitable for HIL simulation | Constant efficiency | Load-dependent efficiency | Temperature-dependent efficiency | Temperature and load-dependent efficiency
Default value

No meshing losses - Suitable for HIL simulation
Program usage name

friction_model
Evaluatable

No

# Input shaft torque at no load — idling torque
N*m | mN*m | lbf*ft

Details

Torque, , acting on the drive pinion at idle speed, i.e. when the torque transmission to the driven pinion is zero. At non-zero values, the input power in the idle mode is completely dissipated due to losses in the meshing.

Dependencies

To use this parameter, set Friction model to `Load-dependent efficiency'.

Units

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

0.1 N*m
Program usage name

T_no_load
Evaluatable

Yes

# Nominal output torque — nominal torque
N*m | mN*m | lbf*ft

Details

Torque at the driven pinion, , at which the efficiency is normalised depending on the load.

Dependencies

To use this parameter, set Friction model to `Load-dependent efficiency'.

Units

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

5.0 N*m
Program usage name

T_nominal
Evaluatable

Yes

# Efficiency at nominal output torque — nominal efficiency

Details

The efficiency of torque transmission, , at nominal torque on the driven pinion. Higher efficiency values correspond to greater torque transmission between the drive and idler gears.

Dependencies

To use this parameter, set Friction model to `Load-dependent efficiency'.

Default value

0.8
Program usage name

nominal_efficiency
Evaluatable

Yes

# Efficiency — Torque transmission efficiency

Details

The efficiency of torque transmission between the drive and driven gears. The efficiency value is inversely proportional to the power loss in the meshing.

Dependencies

To use this parameter, set the Friction model parameter to `Constant efficiency'.

Default value

0.8
Program usage name

efficiency_const
Evaluatable

Yes

# Temperature — vector of temperature values
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

A vector of temperature values used to construct an interpolation table of temperature and torque transmission efficiency. The elements of the vector should be monotonically increasing.

Dependencies

To use this parameter, set Friction model to `Temperature-dependent efficiency' or `Temperature and load-dependent efficiency'.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

[280.0, 300.0, 320.0] K
Program usage name

temperature_vector
Evaluatable

Yes

# Load at base gear — vector of loads on the base gear
N*m | mN*m | lbf*ft

Details

A vector of base gear loads used to construct a two-dimensional interpolation table of efficiency versus temperature and load values. The elements of the vector should be monotonically increasing. The load vector must be the same size as one column of the efficiency matrix.

Dependencies

To use this parameter, set the Friction model parameter to `Temperature and load-dependent efficiency'.

Units

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

[1.0, 5.0, 10.0] N*m
Program usage name

load_vector
Evaluatable

Yes

# Efficiency — vector of torque transmission efficiency values

Details

Vector of torque transmission efficiency values for the gear meshing of the driving and driven gears.

The unit uses these values to build an interpolation table of temperature and efficiency correspondence.

Each element is the efficiency related to the corresponding temperature value in the vector of Temperature parameter values. The length of the vector must be equal to the length of the Temperature parameter vector.

Dependencies

To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.

Default value

[0.95, 0.90, 0.85]
Program usage name

efficiency_vector
Evaluatable

Yes

# Efficiency matrix — matrix of torque transmission efficiency values

Details

Matrix of torque transmission efficiency values for the gear meshing of the driving and driven gears.

The unit uses these values to build a two-dimensional interpolation table of the efficiency versus temperature and load values.

Each element is the efficiency related to the corresponding temperature value in the Temperature parameter value vector and at the loads specified in the Load at base gear parameter value vector.

The number of rows shall be the same as the number of elements in the Temperature parameter vector. The number of columns must be equal to the number of elements in the Load at base gear vector.

Dependencies

To use this parameter, set the Friction model parameter to `Temperature and load-dependent efficiency'.

Default value

[0.85 0.80 0.75; 0.95 0.90 0.85; 0.85 0.80 0.70]
Program usage name

efficiency_matrix
Evaluatable

Yes

# Follower angular velocity threshold — angular speed of the driven gear at which the maximum efficiency value is applied
rpm | deg/s | rad/s

Details

The absolute value of the idler angular speed at which the maximum torque transmission efficiency value is achieved is . For values below this value, the efficiency is smoothed using a hyperbolic tangent function to 1, reducing the loss to 0.

The angular velocity threshold value should be lower than the expected angular velocity during simulation. Higher values may cause the block to underestimate the efficiency loss. Very low values increase the computational cost of the simulation.

Dependencies

To use this parameter, set the Friction model parameter to `Temperature and load-dependent efficiency'.

Units

rpm | deg/s | rad/s
Default value

0.01 rad/s
Program usage name

w_threshold
Evaluatable

Yes

# Follower power threshold — minimum threshold power value
W | GW | MW | kW | mW | uW | HP_DIN

Details

The absolute value of the driven pinion power above which full torque transmission efficiency values apply, . For values below these values, the efficiency is smoothed using a hyperbolic tangent function to 1, reducing losses to 0.

The power threshold value should be lower than the expected power transmitted during the simulation. Higher values may cause the block to underestimate the efficiency loss. Very low values increase the computational cost of the simulation.

Dependencies

To use this parameter, set the Friction model parameter to `Constant efficiency'.

Units

W | GW | MW | kW | mW | uW | HP_DIN
Default value

0.001 W
Program usage name

power_threshold
Evaluatable

Yes

Backlash

# Enable backlash — backlash activation

Details

Select this checkbox to take backlash into account.

Default value

false (switched off)
Program usage name

enable_backlash
Evaluatable

No

# Hard stop model — behaviour during the transition to a hard stop
Stiffness and damping applied smoothly through transition region, damped rebound | Full stiffness and damping applied at bounds, undamped rebound | Full stiffness and damping applied at bounds, damped rebound | Based on coefficient of restitution

Details

Stiffness and rebound parameter for the rigid stop model. Defined as:

  • `Stiffness and damping applied smoothly through transition region, damped rebound';

  • `Full stiffness and damping applied at bounds, undamped rebound';

  • `Full stiffness and damping applied at bounds, damped rebound'.

For more information, see Translational Hard Stop.

Dependencies

To use this option, enable the Enable backlash checkbox.

Values

Stiffness and damping applied smoothly through transition region, damped rebound | Full stiffness and damping applied at bounds, undamped rebound | Full stiffness and damping applied at bounds, damped rebound | Based on coefficient of restitution
Default value

Stiffness and damping applied smoothly through transition region, damped rebound
Program usage name

hardstop_model
Evaluatable

No

# Linear backlash — tooth free distance
m | cm | ft | in | km | mi | mm | um | yd

Details

The distance that a gear tooth can travel between the meshing teeth.

Dependencies

To use this parameter, select the Enable backlash checkbox.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

1e-3 mm
Program usage name

backlash_distance
Evaluatable

Yes

# Base (B) gear radius — drive pinion radius
m | cm | ft | in | km | mi | mm | um | yd

Details

Distance from the centre of the pinion to the point of tooth engagement.

Dependencies

To use this parameter, select the Enable backlash check box.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.1 m
Program usage name

base_tooth_radius
Evaluatable

Yes

# Transition region — the area of gradual impact of hard stop
m | cm | ft | in | km | mi | mm | um | yd

Details

The distance over which the unit gradually applies stiffness and damping effects.

If you set the Hard stop model to `Stiffness and damping applied smoothly through transition region, damped rebound', the block transitions smoothly from one stiffness to another as the hard stop approaches full stiffness.

Dependencies

To use this parameter, select the Enable backlash checkbox and set the Hard stop model to `Stiffness and damping applied smoothly through transition region, damped rebound'.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

1e-4 mm
Program usage name

transition_region
Evaluatable

Yes

# Linear stiffness — translational rigidity
N/m | lbf/ft | lbf/in

Details

The reciprocating stiffness of the spring when the gears collide.

Dependencies

To use this parameter, check the Enable backlash checkbox and Hard stop model one of the following values:

  • `Stiffness and damping applied smoothly through transition region, damped rebound';

  • `Full stiffness and damping applied at bounds, undamped rebound';

  • `Full stiffness and damping applied at bounds, damped rebound'.

Units

N/m | lbf/ft | lbf/in
Default value

1e6 N/m
Program usage name

k_backlash
Evaluatable

Yes

# Linear damping — progressive damping
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Damping of translational energy when gears collide.

Dependencies

To use this parameter, select the Enable backlash check box and one of the following values for Hard stop model:

  • `Stiffness and damping applied smoothly through transition region, damped rebound';

  • `Full stiffness and damping applied at bounds, undamped rebound';

  • `Full stiffness and damping applied at bounds, damped rebound'.

Units

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

1e3 N*s/m
Program usage name

C_backlash
Evaluatable

Yes

Viscous Losses

# Viscous friction coefficients at base (B) and follower (F) — viscous friction coefficients between gears
N*m/(rad/s) | ft*lbf/(rad/s)

Details

Vector of values of viscous friction coefficients for the movement of the drive and driven gears respectively. To neglect viscous losses, use the default value [0.0, 0.0].

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

Thermal Port

# Thermal mass — heat capacity
J/K | kJ/K

Details

The heat energy required to change the temperature of a component by one degree. The greater the heat capacity, the more resistant the component is to temperature change.

Dependencies

To use this parameter, set Friction model to one of the following values:

  • Temperature-dependent efficiency;

  • `Temperature and load-dependent efficiency'.

Units

J/K | kJ/K
Default value

50.0 J/K
Program usage name

thermal_mass
Evaluatable

Yes