Worm gear (simplified)#

block — Block appearance in REPEAT VISION#

In a simplified worm gear, two drive axes are connected - the worm (w) and the worm wheel (ww), so that they rotate with a fixed gear ratio.

It is possible to select the direction of rotation of the wheel:

if you install a right-hand thread, the angular velocities of the worm and worm wheel have the same sign;
with left-hand thread - opposite.

The worm gear imposes a kinematic constraint (1) :

(1)#\[\omega_{ч} = R_{чк} \cdot \omega_{к}\]

where:

\(R_{чк}\) - specified gear ratio;

\(\omega_{w}\) – angular velocity of the worm;

\(\omega_{ww}\) – angular velocity of the worm wheel.

Thus, two degrees of freedom are reduced to one.

The torque transfer is given by the equation (2):

(2)#\[R_{чк} \cdot M_{ч} - M_{к} - M_{потери} = 0\]

where:

\(M_{w}\) – moment on the worm;

\(M_{ww}\) – moment on the worm wheel;

\(M_{losses}\) – losses during power transmission. Under ideal conditions, there are no losses, \(M_{losses}\) = 0.

1. Accounting for losses#

When the Calculate losses \(M_{losses} eq\) 0 property is enabled, losses are calculated relative to Efficiency. For a more detailed description of loss calculation, please refer to the Loss Calculation page.

Given Efficiency:

In the variant with constant values Efficiency \(\eta_{чк}\) and \(\eta_{кч}\) are specified by the user regardless of the thread geometry.

Calculation of Efficiency depending on the geometric characteristics of the gearing:

When contact engagement is taken into account, the coefficients \(η_{чк}\), \(\eta_{кч}\) are determined relative to:

Thread geometry - through the rise angle (λ) and the normal pressure angle (α);
Coefficient of friction of surfaces k (3) :

(3)#\[\begin{split}\eta_{чк} = \frac{cos \alpha - k \cdot tan \lambda}{cos \alpha +k / tan \lambda},\\\eta_{кч} = \frac{cos \alpha - k / tan \lambda}{cos \alpha +k \cdot tan \lambda}.\end{split}\]

Note

The full calculation of the coupling Efficiency occurs if the transmitted power exceeds the specified threshold value \(p_{прг}\). Otherwise, for numerical stability, the efficiency is assumed to be equal to unity.

Restrictions:

• The inertia of the components is negligible;

• The components are considered absolutely rigid.

2. Properties#

Property	Default Value	Description	Units of measurement
Gear ratio	20.0	-	-
On - right-hand type thread; Off - left-hand	Off	Gear rotation direction for positive worm rotation: Left-Hand: Opposite (–); Right-Hand: Same (+)	-
Calculate losses	Off	-	-
Torque transfer Efficiency from worm to gear, available when `Calculate losses` - `On` and `Calculate losses by friction coefficient and geometrical parameters` - `Off`	0.45	-	-
Torque transfer Efficiency from gear to worm, available when `Calculate losses` - `On` and `Calculate losses by friction coefficient and geometrical parameters` - `Off`	0.75	-	-
Power threshold, available when `Calculate losses` - `On`	0.001	-	W
Calculate losses by friction coefficient and geometrical parameters, available when `Calculate losses` - `On`	Off	-	-
Normal pressure angle, available when `Calculate losses` - `On` and `Calculate losses by friction coefficient and geometrical parameters` - `On`	15	-	degrees
Lead angle, available when `Calculate losses` - `On` and `Calculate losses by friction coefficient and geometrical parameters` - `On`	17.5	-	degrees
Friction coefficient, available when `Calculate losses` - `On` and `Calculate losses by friction coefficient and geometrical parameters` - `On`	0.08	-	-

3. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Worm	Input	-	-	Rotational motion
Gear	Output	-	-	Rotational motion

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