Worm gear
 |
 |
| C | |
| in the palette | on the schematic |
The block is designed to simulate a worm gearbox with a constant gear ratio and friction in bearings and with gear meshing. The block is described by the following formulas:
where:
- sC and sR – turn angles of bodies at ports "C" and "R", respectively, rad
- ωC and ωR – angular speeds at ports "C" and "R", respectively, rad/s
- εC and εR – angular accelerations at ports "C" and "R", respectively, rad/s2
- TC and TR – torques at ports "C" and "R", respectively, Nm
- BW and BG – coefficients of bearing friction on the worm and gear shafts, Nm·s/rad
- U – gear ratio
- dir – value indicating the matching of the directions of rotation of the worm and gear shafts, has a value of 1 or -1
- ν – gearbox efficiency, depending on the direction of power transmission: worm-to-gear or vice versa
The calculation of the gearbox efficiency is carried out depending on the gearing geometric characteristics:
where:
- νWG – efficiency when transmitting power from the worm gear to the gear
- νGW – efficiency when transmitting power from the gear to the worm gear
- α – normal pressure angle, °
- γ – lead angle of the worm, °
- k – friction factor
A detailed description of the calculation methods for the variable efficiency in the gear meshing is given on page Gearbox efficiency simulation.
The block allows you to change the direction of the "W" and "G" ports for easy connection to other blocks of the model. If the block has both input ports, then the coupling equation is solved. A detailed description of the simulation approach for the gear ratios is given on the page Simulating transmission.
The gear ratio value U is displayed next to the block.
Ports
| Name | Description | Connection line type |
|---|---|---|
| W | Port for connecting the worm gear shaft. The port is input if specified in the "Input port" property, otherwise this port is output | Rotary mechanics |
| G | Port for connecting the gear. The port is input if specified in the "Input port" property, otherwise this port is output | Rotary mechanics |
Outputs
| Name | Description | Connection line type |
|---|---|---|
| Q | Power losses due to bearing friction and gear meshing (efficiency) | Mathematical |
Properties
| Title | Parameter | Description | By default | Data type |
|---|---|---|---|---|
| Input port | Mod_Type | Allows you to specify the input ports. The possible values are: "W", "G", "W and G" | "W and G" | Перечисление |
| Time constant for solving the nonlinear algebraic equation, s | Tau | The time constant for solving the nonlinear algebraic equation. Used to solve the coupling equation. The property is available when selecting the input ports "W and G" | 0.1 | Вещественное |
| Kinematics | A group of properties that set the kinematic parameters of the rotary motion | |||
| Gear ratio (Ww/Wg) | U | Gear ratio | 25 | Вещественное |
| Direction of rotation of the worm gear and the gear | Dir | Allows you to set the direction of rotation of the driving and driven shafts. The possible values are: "Same direction", "Opposite direction" | In the same direction | Перечисление |
| Losses | A group of properties that define loss parameters | |||
| Coefficient of the worm bearing friction, Nm·s/rad | B_W | Coefficient of the worm bearing friction | 0 | Вещественное |
| Coefficient of the gear bearing friction, Nm·s/rad | B_G | Coefficient of the gear bearing friction | 0 | Вещественное |
| Friction model | FrType | Allows you to define the friction model. The possible values are: "No loss", "Set efficiency manually", "Calculate efficiency by geometry", "Table data efficiency on load", "Table data efficiency on temperature" | No loss | Перечисление |
| Power threshold, W | Q_th | The value of the power transmitted through the block, below which the efficiency is increased to achieve the stability of the numerical solution. The property is available when selecting the following friction models "Set efficiency manually", "Calculate efficiency by geometry", "Table data efficiency on load", "Table data efficiency on temperature" | 0.1 | Вещественное |
| Worm-to-gear transmission efficiency | Nu_wg_m | Worm-to-gear transmission efficiency. The property is available when selecting the friction model "Set efficiency manually" | 0.74 | Вещественное |
| Gear-to-worm transmission efficiency | Nu_gw_m | Gear-to-worm transmission efficiency. The property is available when selecting the friction model "Set efficiency manually" | 0.65 | Вещественное |
| Normal pressure angle, deg. | alfa | Normal pressure angle. The property is available when selecting the friction model "Calculate efficiency by geometry" | 18 | Вещественное |
| Worm lead angle, deg. | lam | Worm lead angle. The property is available when selecting the friction model "Calculate efficiency by geometry" | 20 | Вещественное |
| Friction factor | Mu | Friction factor. The property is available when selecting the friction model "Calculate efficiency by geometry" | 0.08 | Вещественное |
| Worm-to-gear transmission efficiency | Nu_wg_g | Worm-to-gear transmission efficiency. The property is available when selecting the friction model "Calculate efficiency by geometry" and is displayed in the "Read-only" mode, is for reference only | 0.787407 | Вещественное |
| Gear-to-worm transmission efficiency | Nu_gw_g | Gear-to-worm transmission efficiency. The property is available when selecting the friction model "Calculate efficiency by geometry" and is displayed in the "Read-only" mode, is for reference only | 0.746049 | Вещественное |
| Temperature, °C | Temp | Temperature. The property is available when selecting the friction model "Table data efficiency on temperature" | 20 | Вещественное |
| Array of temperatures, °С | Temp_Arr | Array of temperatures The property is available when selecting the friction model "Table data efficiency on temperature" | [0 , 20 , 100] | Массив |
| Array of torques on the gear, Nm | T_Arr | Array of torques on the gear. The property is available when selecting the friction model "Table data efficiency on load" | [0 , 10 , 20] | Массив |
| Array of the worm-to-gear transmission efficiency values | Nu_wg_Arr | Array of the worm-to-gear transmission efficiency values. Efficiency values are calculated by linear interpolation depending on the load or temperature values. The property is available when selecting the following friction models: "Table data efficiency on load" or "Table data efficiency on temperature" | [0.75 , 0.7 , 0.65] | Массив |
| Array of the gear-to-worm transmission efficiency values | Nu_gw_Arr | Array of the gear-to-worm transmission efficiency values. Efficiency values are calculated by linear interpolation depending on the load or temperature values. The property is available when selecting the following friction models: "Table data efficiency on load" or "Table data efficiency on temperature" | [0.5 , 0.45 , 0.4] | Массив |
Parameters
| Name | Parameter | Description | Data type |
|---|---|---|---|
| Power losses, W | Q | Power losses due to bearing friction and gear meshing (efficiency) | Вещественное |
| Worm gear | A group of parameters displaying the parameters of the worm gear | ||
| Angular speed, rad/s | Ww | Angular speed value at the port "W" | Вещественное |
| Torque, Nm | Tw | Torque transmitted from the worm gear shaft to the gearbox | Вещественное |
| Power, W | Qw | Power transmitted from the worm gear shaft to the gearbox | Вещественное |
| Gear | A group of parameters displaying the parameters of the gear | ||
| Angular speed, rad/s | Wg | Angular speed value at the port "G" | Вещественное |
| Torque, Nm | Tg | Torque transmitted from the gearbox to the gear shaft | Вещественное |
| Power, W | Qg | Power transmitted from the gearbox to the gear shaft | Вещественное |
Examples
Examples of block application: