Screw - nut gear#

The Screw - nut gear block models a system in which rotational motion is converted to translational motion. The left port transmits the angular speed in [rad/s] and the right port transmits the linear velocity in [m/s].

The input port receives the angular velocity signal in [rad/s], the output port receives the velocity, [m/s] (see Fig. 1 below). Output port transmits force, [N].

The stiffness and damping of the contact surface are necessary to calculate the normal force acting on the threads. Static friction and sliding friction factors shall be specified to account for friction.

In this unit, the “Integrator with reset” friction model is implemented, in which the magnitude of the static friction force depends on the boundary distance of static friction, which is specified in the unit properties.

The resultant force consists of normal and tangent components. Normal force depends on relative speed and distance traveled (1) :

(1)#\[ F_{норм.} = d \cdot v_{отн}+k \cdot \int v_{отн}dt \]

where:

k - hardness, [N/m];

d - damping, [N \(\cdot\) s/m];

v\(_{rel}\) - relative linear velocity of bodies, [m/s] (2) :

(2)#\[ v_{отн}=R \cdot \omega_1 \cdot sin(\alpha ) - v_2 \cdot cos(\alpha )\]

where:

\(\alpha\) - lifting angle, [rad];

R - screw radius, [m].

Hint

If one wants to simulate co-directional rotation of mechanical objects, one shall supply a negative speed value to the output port of the unit.

Important

A negative value for the lead angle models the right screw thread.

forces_on_surface — Fig. 2 Forces on the thread surface#

Initially, the transmission is in rest mode, a static friction force is formed at a non-zero relative speed (3) :

(3)#\[F_{статич.}=c_{статич.}\cdot F_{норм.}\]

In static friction, the tangential force depends on the distance boundary s\(_{boundary}\) (4) :

(4)#\[F_{кас.}=\frac {F_{статич.}}{s_{граница}}\cdot s + k_{статич.} \cdot v_{отн.кас.}\]

where:

\(k_{static.}\) - stiffness at static friction, [r.u.];

\(s_{boundary}\) - boundary distance, at overcoming of which sliding mode occurs, [m];

\(c_{static.}\) - coefficient of static friction, [r.u.];

\(v_{rel.tang.}\) - relative speed parallel to screw thread turn surface, [m/s].

In sliding mode, friction is calculated relative to the normal force using the expression (5) :

(5)#\[F_{скольж.}=c_{скольж.}\cdot F_{норм.}\]

The Stribeck effect allows a smooth transition between static and dynamic friction. Turn on the Account Stribeck effect toggle switch to take this effect into account. With this configuration, the friction force becomes exponential and is determined by the expression (6) :

(6)#\[Ф=(F_{скольж.}+(F_{статич.}-F_{скольж.})\cdot e^{(-3\cdot |v_{отн.кас.}|/ c_{Штрибек})})\]

The force acting on the nut F\(_{but}\) and the moment acting on the screw М\(_{screw}\) are calculated using the formulas (3) :

(7)#\[F_{гайка}=F_{норм.}\cdot cos(\alpha)-F_{кас.}\cdot sin(\alpha)\]

(8)#\[ М_{винт}= D/2 \cdot (F_{норм.} \cdot sin(\alpha ) + F_{кас.}\cdot cos(\alpha )) \]

Hint

Also, translational motion is converted to rotational using the toggle switch Reverse motion dircetion.

1. Properties#

Property	Default value	Description	Units of measurement
Mean diameter	0.01	-	m
Lead angle	2.0	-	deg
Contact stiffness	1000.0	-	N/m
Contact damping	1000.0	-	N/(m/s)
Coulumb friciton coefficient	0.01	-	r.u.
Stiction coefficient	0.02	-	-
Stiction stiffnes	1000.0	-	N/(m/s)
Stiction displacement threshold	0.001	-	-
Account Stribeck effect	Off	-	-
Stribeck effect transfer velocity, available when select `Account Stribeck effect` - `On`	0.001	-	m/s
Reverse motion dircetion	Off	On - conversion of rotational motion into translational motion; Off - conversion of translational motion into rotational motion.	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Angular velocity	Input	Available when `Reverse motion dircetion property` - `Off`	rad/s	Rotational motion
Speed	Input	Available when `Reverse motion dircetion property` - `On`	m/s	Translational motion
Force	Output	Available when `Reverse motion dircetion property` - `Off`	N	Translational motion
Torque	Output	Available when `Reverse motion dircetion property` - `On`	N\(\cdot\) m	Rotational motion

In order to see the connection capabilities of the block, you need to go to page Description of block ports