Dog Clutch

Dog Clutch component

The Dog Clutch component models a clutch where the coupling of the two sides is achieved by the engagement of toothed connections between the two shafts (as opposed to friction in normal clutches). A typical usage of dog clutches is in manual transmissions.

Geometry

The Dog Clutch geometry is defined by two parameters; $\mathrm{gap}$ and $\mathrm{\ϵ}$ as shown in the figure below.

Equations

${\mathrm{\ϕ}}_{\mathrm{rel}} \= {\mathrm{\varphi }}_b - {\mathrm{\varphi }}_a$ 

and

${\mathrm{\ω}}_{\mathrm{rel}} \= \frac{\ⅆ}{\ⅆ t} {\mathrm{\ϕ}}_{\mathrm{rel}}$ 

$\stackrel{\&Hat;}{\mathrm{\&varphi;}}{}_{\mathrm{rel} } \&equals; \left\{\begin{array}{cc}0& \mathrm{state}\&equals; 0\\ \mathrm{\varphi }{}_{\mathrm{rel}} - \mathrm{gap} · \mathrm{floor}\left(\frac{\mathrm{\varphi }{}_{\mathrm{rel}}}{\mathrm{gap}}\right)& \mathrm{state} \ne 0 \mathbf{and} {\mathrm{\&varphi;}}_{\mathrm{rel}} \ge 0\\ \mathrm{\varphi }{}_{\mathrm{rel}} - \mathrm{gap} · \mathrm{ceil}\left(\frac{\mathrm{\varphi }{}_{\mathrm{rel}}}{\mathrm{gap}}\right)& \mathrm{state} \ne 0 \mathbf{and} {\mathrm{\&varphi;}}_{\mathrm{rel}} < 0\end{array}\right.$

${\mathrm{\tau }}_a \&plus; {\mathrm{\&tau;}}_b \&equals; 0$

${\mathrm{\tau }}_b \&equals;\left\{\begin{array}{cc}s a& \mathrm{state} \&equals;\mathbf{ }2\\ 0& \mathrm{state} \ne \mathbf{ }2\end{array}\right.$

The contact between the teeth on the two sides of the Dog Clutch is modeled using linear angular springs and dampers: 

$\mathrm{sa} \&equals; \left\{\begin{array}{cc}\&lcub;\begin{array}{cc}\left\{\begin{array}{cc}0& {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c \ge 0\\ {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c & {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c < 0\end{array}\right.& -\mathrm{gap} \le \stackrel{\&Hat;}{\mathrm{\varphi }}{}_{\mathrm{rel}} \le -\mathrm{gap} \&plus; \mathrm{\&varepsilon;} \\ \left\{\begin{array}{cc}0& {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c \le 0\\ {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c & {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c \&gt; 0\end{array}\right.& - \mathrm{ϵ} \le \stackrel{\&Hat;}{\mathrm{\varphi }}{}_{\mathrm{rel} } < 0\\ \left\{\begin{array}{cc}0& {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c \ge 0\\ {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c & {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c < 0\end{array}\right.& 0 \le {\stackrel{\&Hat;}{\mathrm{\varphi }}}_{\mathrm{rel} } \le \mathrm{\&varepsilon;} \\ \left\{\begin{array}{cc}0& {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c \le 0\\ {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c & {\mathrm{\tau }}_k \&plus; {\mathrm{\tau }}_c \&gt;0\end{array}\right.& \mathrm{gap} - \mathrm{ϵ} \le {\stackrel{\&Hat;}{\mathrm{\varphi }}}_{\mathrm{rel}} < \mathrm{gap} \\ 0& \mathrm{otherwise}\end{array}& \mathrm{state} \&equals;\mathbf{ }2\\ 0& \mathrm{otherwise}\end{array}\right.$

where

${\mathrm{\tau }}_k \&equals;\left\{\begin{array}{cc}\left\{\begin{array}{cc}c\mathit{ }\mathit{·}\mathit{ }\left(\stackrel{\&Hat;}{\mathrm{\varphi }}{}_{\mathrm{rel} } \&plus; \mathrm{gap} - \mathrm{ϵ}\right)& -\mathrm{gap} < {\stackrel{\&Hat;}{\mathrm{\varphi }}}_{\mathrm{rel}} \le -\mathrm{gap} \&plus; \mathrm{ϵ} \\ c\mathit{ }\mathit{·}\mathit{ }\left(\stackrel{\&Hat;}{\mathrm{\varphi }}{}_{\mathrm{rel} } \&plus; \mathrm{ϵ}\right)& - \mathrm{ϵ} \le \stackrel{\&Hat;}{\mathrm{\varphi }}{}_{\mathrm{rel} } < 0\\ c · \left(\stackrel{\&Hat;}{\mathrm{\varphi }}{}_{\mathrm{rel} } - \mathrm{ϵ}\right)& 0 \le {\stackrel{\&Hat;}{\mathrm{\varphi }}}_{\mathrm{rel} } \le \mathrm{\&varepsilon;}\\ c · \left(\stackrel{\&Hat;}{\mathrm{\varphi }}{}_{\mathrm{rel} } - \mathrm{gap} \&plus; \mathrm{ϵ}\right)& \mathrm{gap} - \mathrm{ϵ} \le {\stackrel{\&Hat;}{\mathrm{\varphi }}}_{\mathrm{rel}} < \mathrm{gap}\end{array}\right.& \mathrm{state}\&equals;2\\ 0& \mathrm{otherwise}\end{array}\right.$

and

${\mathrm{\tau }}_c \&equals; d · {\mathrm{\&omega;}}_{\mathrm{rel}}$

State Machine Definition

The Dog Clutch has three distinct states as shown in the figure below.

$\mathrm{state} \&equals; \&lcub;\begin{array}{cc}\&lcub;\begin{array}{cc}1& \frac{1}{2} \le \mathrm{s} \le 1 \\ 0& 0 \le \mathrm{s} < \frac{1}{2} \end{array}& \mathrm{pre}\left(\mathrm{state}\right)\&equals; 0\\ \&lcub;\begin{array}{cc}\left\{\begin{array}{cc} 1 & \stackrel{\&Hat;}{\mathrm{\varphi }}{}_{\mathrm{rel} }<-\mathrm{gap}\&plus;\mathrm{\&varepsilon;} \mathbf{or} {\stackrel{\&Hat;}{\mathrm{\varphi }}}_{\mathrm{rel} } \&gt; -\mathrm{\&varepsilon;} \mathbf{and} {\stackrel{\&Hat;}{\mathrm{\varphi }}}_{\mathrm{rel} } < \mathrm{\&varepsilon;} \mathbf{or} {\stackrel{\&Hat;}{\mathrm{\varphi }}}_{\mathrm{rel} }\&gt;\mathrm{gap} - \mathrm{\&varepsilon;}\\ 2& \mathrm{otherwise}\end{array}\right.& \frac{1}{2} \le \mathrm{s} \le 1\\ 0& 0 \le \mathrm{s} < \frac{1}{2}\end{array}& \mathrm{pre}\left(\mathrm{state}\right)\&equals; 1 \\ \left\{\begin{array}{cc}2& \frac{1}{2} \le \mathrm{s} \le 1\\ 0& 0 \le \mathrm{s} < \frac{1}{2}\end{array}\right.& \mathrm{pre}\left(\mathrm{state}\right)\&equals; 2\end{array}$

The boolean output locked is defined as

$\mathrm{locked} \&equals; \left\{\begin{array}{cc}0& \mathrm{state} \ne 2\\ 1& \mathrm{state} \&equals; 2\end{array}\right.$

Connections 

Parameters

See Also

Driveline Library Overview

MapleSim Library Overview

1-D Mechanical Overview

Clutches and Brakes