Leadscrew
 |
 |
| C | |
| in the palette | on the schematic |
The block is designed to simulate a leadscrew block (screw-nut or screw-ball) with a constant gear ratio and friction in bearings and with gear meshing.
The gear ratio U, rad/m, is determined by the formula:
where L – screw pitch, m.
The block is described by the following formulas:
where:
- sN – linear position of the body at the port "N", m
- φS – turn angle at the port "S", rad
- vN – linear speed at the port "N", m/s
- ωS – angular speed of the port "S", rad/s
- aN – linear acceleration at the port "N", m/s2
- εS – angular acceleration at the port "S", rad/s2
- FN – force at the port "N", N
- TS – torque at the port "S", Nm
- BS and BN – coefficients of bearing friction on the screw and the nut, respectively, Nm·s/rad and N·s/m
- dir – the value indicating the matching of the directions of rotation of the screw shaft and the movement of the nut, has a value of 1 or -1. If the motion directions match, an increase in the screw turn angle will correspond to an increase in the linear position of the nut
- ν – transmission efficiency, depending on the direction of power transmission: screw-to-nut or vice versa
The calculation of the block efficiency is carried out depending on the gearing geometric characteristics:
where:
- νSN – efficiency when transmitting power from the screw to the nut
- νNS – efficiency when transmitting power from the nut to the screw
- α – normal pressure angle, °
- γ – lead angle of the screw, °
- 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 "S" and "N" 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 |
|---|---|---|
| S | Port for rotating screw connection. The port is input if specified in the "Input port" property, otherwise this port is output | Rotary mechanics |
| N | Port for connecting the translatory moving nut. 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: "S", "N", "S and N" | "S and N" | 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 "S and N" | 0.1 | Вещественное |
| Kinematics | A group of properties that set the kinematic parameters of motion | |||
| Screw pitch, m | Ls | Screw pitch | 0.015 | Вещественное |
| Gear ratio (Ws/Vn), rad/m | U | Gear ratio | 418.879 | Вещественное |
| Direction of rotation of the screw and the nut | Dir | Allows you to define the mutual rotation direction of the screw and the nut. 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 screw bearing friction, Nm·s/rad | B_S | Coefficient of the screw bearing friction | 0 | Вещественное |
| Coefficient of sliding friction of the nut, N·s/m | B_N | Coefficient of sliding friction of the nut | 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" | 0.01 | Вещественное |
| Screw-to-nut transmission efficiency | Nu_sn_m | Screw-to-nut transmission efficiency. The property is available when selecting the friction model "Set efficiency manually" | 0.74 | Вещественное |
| Nut-to-screw transmission efficiency | Nu_ns_m | Nut-to-screw 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 |
| Screw 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 |
| Screw-to-nut transmission efficiency | Nu_sn_g | Screw-to-nut transmission efficiency. The property is available when selecting the friction model "Calculate efficiency by geometry" | 0.790075 | Вещественное |
| Nut-to-screw transmission efficiency | Nu_ns_g | Nut-to-screw transmission efficiency. The property is available when selecting the friction model "Calculate efficiency by geometry" | 0.748435 | 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 forces on the nut, N | F_Arr | Array of torques on the nut. The property is available when selecting the friction model "Table data efficiency on load" | [0 , 10 , 20] | Массив |
| Array of the screw-to-nut transmission efficiency values | Nu_sn_Arr | Array of the screw-to-nut 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 nut-to-screw transmission efficiency values | Nu_ns_Arr | Array of the nut-to-screw 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 |
| Screw | A group of parameters displaying the parameters of the screw | ||
| Angular speed, rad/s | Ws | Angular speed value at the port "S" | Вещественное |
| Torque, Nm | Ts | Torque taken from the screw | Вещественное |
| Power, W | Qs | Power taken from the screw | Вещественное |
| Nut | A group of parameters displaying the parameters of the nut | ||
| Speed,m/s | Vn | Speed value at the port "N" | Вещественное |
| Force, N | Fn | Force transmitted to the nut | Вещественное |
| Power, W | Qn | Power transmitted to the nut | Вещественное |
Examples
Examples of block application: