Torque Converter

Torque Converter component

The Torque Converter component models a torque converter acting between the two connector ports (Pump and Turbine) as a function of the speed ratio.  Directionality is determined on which port is receiving power. Forward power flow means power flowing from pump to turbine. Reverse power flow means power flowing from turbine to pump.

A torque converter is a hydrodynamic connector between the engine and the rest of the driveline. It is comprised of a pump impeller on the driven side, a turbine on the transmission side and hydraulic fluid within a sealed case. When driven, the pump drives the fluid into the turbine, causing it to rotate, thus transmitting the power smoothly from the engine to the driveline. It also has the advantage of “multiplying” the torque to the driveline at low speeds, maximizing the torque to the wheels at start-up.

Due to the complex nature of the torque converter dynamics, tables of measured data are used. This component uses the following characteristics:

Torque Ratio $\frac{{\mathrm{\tau }}_t}{{\mathrm{\tau }}_p}$ vs Speed Ratio $\frac{{\mathrm{\omega }}_t}{{\mathrm{\omega }}_p}$

Load Capacity $C$ vs Speed Ratio $\frac{{\mathrm{\omega }}_t}{{\mathrm{\omega }}_p}$

Load capacity may be defined as:

$C \= \frac{{\mathrm{\τ}}_p}{{\mathrm{\ω}}_p^2}\left[\frac{N · m}{{\mathrm{rpm}}^2}\right]$                or             $C \= \frac{{\mathrm{\ω}}_p}{\sqrt{{\mathrm{\tau }}_p}}\left[\frac{{\left(\frac{\mathrm{rad}}{s}\right)}^{\frac{1}{2}}}{N · m}\right]$

Note:  It is possible for the power flow to be reversed. For example, during deceleration of the vehicle, inertial energy is transmitted back through the transmission to the engine. In this situation, the turbine is pumping and the pump is acting as a turbine. Since they were not designed to work optimally this way, the torque converter has very different characteristics. This is accommodated in the lookup table by providing torque ratio and capacity data for speed ratios $\> 1$, typically up to about 5.

Equations

Hydrodynamic Equations

${\mathrm{\varphi }}_x \= {\mathrm{\ϕ}}_{\mathrm{fx}}$$-\left\{\begin{array}{cc}{\mathrm{\varphi }}_{\mathrm{support}}& \mathit{use}\mathit{ }\mathrm{Support} \= \mathbf{true}\\ 0& \mathrm{otherwise}\end{array}\right.$  ,   $x$ ∈ $\left\{p\,t\right\}$

Where ${\mathrm{\ϕ}}_{\mathrm{fp}}$  and ${\mathrm{\varphi }}_{\mathrm{ft}}$  are the absolute rotation angles of the $\mathrm{pump}$ and $\mathrm{turbine}$ flanges, respectively, and

${\mathrm{\omega }}_p \= \frac{\ⅆ}{\ⅆ t} {\mathrm{\varphi }}_p \={\stackrel{·}{\mathrm{\ϕ}}}_p$

${\mathrm{\omega }}_t \= \frac{\ⅆ}{\ⅆ t} {\mathrm{\varphi }}_t \={\stackrel{·}{\mathrm{\varphi }}}_t$

$r_{\mathrm{\omega } } \= \frac{{\mathrm{\omega }}_t}{{\mathrm{\omega }}_p}$     , ${\mathrm{\omega }}_p \>0$

${\stackrel{\^}{\mathrm{\omega }}}_P \=$$\left\{\begin{array}{cc}{\mathrm{\omega }}_p& {\mathrm{\ω}}_p \ge {\mathrm{\omega }}_t\\ {\mathrm{\omega }}_t& {\mathrm{\ω}}_t \> {\mathrm{\omega }}_p\end{array}\right.$     and    ${\stackrel{\^}{\mathrm{\omega }}}_T \=$$\left\{\begin{array}{cc}{\mathrm{\omega }}_t& {\mathrm{\ω}}_p \ge {\mathrm{\omega }}_t\\ {\mathrm{\omega }}_p& {\mathrm{\ω}}_t \> {\mathrm{\omega }}_p\end{array}\right.$

${\stackrel{\^}{\mathrm{\τ}}}_{\mathrm{te}} \+$${\mathrm{K}}_{\mathrm{\τ}}$$\left(r_{\mathrm{\omega } }\right) · {\stackrel{\^}{\mathrm{\tau }}}_{\mathrm{pe}} \= 0$

${\stackrel{\^}{\mathrm{\tau }}}_{\mathrm{pe}} \=$$\left\{\begin{array}{cc}\frac{{\stackrel{\^}{\mathrm{\omega }}}_p^2}{C{\left(r_{\mathrm{\omega } }\right)}^2}& \mathrm{mode} \= \mathbf{mode}\mathbf{ }\mathbf{1}\\ \frac{\[\(\frac{2 \mathrm{\π}}{60}\){\stackrel{\^}{\mathrm{\omega }}}_p{\]}^2}{C\left(r_{\mathrm{\omega } }\right)}& \mathrm{mode} \= \mathbf{mode}\mathbf{ }\mathbf{2}\end{array}\right.$

${\mathrm{\τ}}_{\mathrm{pe}} \=$$\left\{\begin{array}{cc}{\stackrel{\^}{\mathrm{\tau }}}_{\mathrm{pe}}& {\mathrm{\ω}}_p \ge {\mathrm{\ω}}_t\\ {\stackrel{\^}{\mathrm{\tau }}}_{\mathrm{te}}& {\mathrm{\ω}}_t \> {\mathrm{\ω}}_p\end{array}\right.$     and    ${\mathrm{\tau }}_{\mathrm{Te}} \=$$\left\{\begin{array}{cc}{\stackrel{\^}{\mathrm{\tau }}}_{\mathrm{te}}& {\mathrm{\omega }}_p \ge {\mathrm{\ω}}_t\\ {\stackrel{\^}{\mathrm{\tau }}}_{\mathrm{pe}}& {\mathrm{\omega }}_t \> {\mathrm{\ω}}_p\end{array}\right.$

${\mathrm{\τ}}_{\mathrm{te}} \+$${\mathrm{\τ}}_{\mathrm{pe} }$$\+ {\mathrm{\tau }}_{\mathrm{se}} \= 0$

Torque Converter Equations

$J_t · {\stackrel{·}{\mathrm{\ω}}}_t \+\frac{1}{2}d · {\mathrm{\omega }}_t \+ {\mathrm{\tau }}_{\mathrm{te}} \+ {\mathrm{\tau }}_t\= 0$

$J_p · {\stackrel{·}{\mathrm{\ω}}}_p \+\frac{1}{2}d · {\mathrm{\omega }}_p \+ {\mathrm{\tau }}_{\mathrm{pe}} \+ {\mathrm{\tau }}_p\= 0$

${\mathrm{\tau }}_{\mathrm{support}} \= {\mathrm{\tau }}_{\mathrm{te}}\+{\mathrm{\tau }}_{\mathrm{pe}} \+ \frac{1}{2}d · {\mathrm{\omega }}_p \+ \frac{1}{2}d · {\mathrm{\omega }}_t$

Power Loss:

The power loss ($P_{\mathrm{loss}}$ ) is calculated as:

$P_{\mathrm{loss}} \= \mid$${\mathrm{\τ}}_p ·$${\mathrm{\omega }}_p$$\+ {\mathrm{\tau }}_t · {\mathrm{\omega }}_t \mid$

Connections 

Parameters

Initial Conditions 

Note: The pump angular velocity, ${\mathrm{\omega }}_P$ , must be greater than zero.

See Also

Driveline Library Overview

MapleSim Library Overview

1-D Mechanical Overview

CVT and Torque Converter

References

D. Hrovat and W.E. Tobler. “Bond graph modeling and computer simulation of automotive torque converters,” Journal of the Franklin Institute. Volume 319, Issues 1-2, January-February 1985, pp 93-114.