Simple Gear with Variable Efficiency
Simple spur gearbox with adjustable meshing efficiency.
Description
The Simple Gear with Variable Efficiency unit is a simple gear train with variable meshing efficiency. The gear transmits torque with a specified ratio between the driving and driven gears, which are arranged in parallel planes. The gears can rotate in the same or opposite directions. In the non-ideal case, losses in the gear include losses in the meshing and viscous bearings. To set the variable meshing efficiency, the unit has a control port that can be used to input a time-varying signal. The effects of inertia and pliability are ignored.
Ideal gears and gear ratios
The Simple Gear with Variable Efficiency block imposes one kinematic constraint on two linked axes:
where
-
- is the radius of the idler gear;
-
- angular velocity of the driven pinion;
-
- radius of the drive pinion;
-
- angular velocity of the drive pinion.
The gear ratio for the meshing of the idler gear and the master gear is equal:
where
-
- is the number of teeth of the driving gear;
-
- the number of teeth of the idler gear.
The two degrees of freedom are reduced to one independent gear.
Torque transmission is realised as follows:
where
-
- inlet torque;
-
- output torque;
-
- torque transmission losses.
For the ideal case .
Non-ideal constraints and losses in gears
For the non-ideal case . For more details see Modelling of mechanical gears with losses.
In a non-ideal gear pair angular velocity, gear ratio and tooth count limits remain unchanged. But the transmitted torque and power are reduced due to:
-
Coulomb friction between the tooth surfaces on the gears and , which is determined by the efficiency, ;
-
Viscous friction of the drive shaft coupling with the bearings, which is determined by the viscous friction coefficients, .
Thermal model
You can model the effects of heat flow and temperature change by enabling the optional H heat port. To use the H thermal port, select the check box for the Enable thermal port parameters.
Enabling the thermal model:
-
Opens the non-directional H port.
-
Enables the Thermal mass parameter, which allows you to specify the component’s ability to resist temperature changes.
-
Enables the Initial Temperature parameter, which allows you to specify the initial temperature.
Ports
Input
#
E
—
meshing efficiency
scalar
Details
Input port associated with the gear meshing efficiency. The efficiency is set in the range ].
| Data types |
|
| Complex numbers support |
No |
Conserving
#
B
—
drive pinion
`rotational mechanics
Details
A non-directional port associated with the drive gear.
| Program usage name |
|
#
F
—
idler gear
`rotational mechanics
Details
A non-directional port associated with the driven gear.
| Program usage name |
|
#
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, select the Enable thermal port check box.
| Program usage name |
|
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 >0.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Output shaft rotates —
direction of rotation of idler gear
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 |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
Meshing Losses
# Minimum efficiency — minimum efficiency
Details
The lowest efficiency value allowed for a given gear. The efficiency is the ratio of the output shaft power to the input shaft power. The signal at the E port is maintained above the minimum efficiency and below . The lowest value of efficiency should be >0.
| Default value |
|
| Program usage name |
|
| 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 the full torque transmission efficiency values apply, . For values below these values, the efficiency is smoothed using a hyperbolic tangent function between 0 when the motor is running and the specified efficiency value.
| Units |
|
| Default value |
|
| Program usage name |
|
| 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 |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Thermal Port
# Enable thermal port — switching on the heat port
Details
Checking this box displays the H heat port, which allows the transmission to be connected to the thermal network. Checking this box also enables the Thermal mass parameters and adds the Temperature variable to the Initial Targets section.
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
#
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, select the Enable thermal port checkbox for the Enable thermal port parameters.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |