Engineering:Effective torque

Short description: Measure of torque on geartrains

Not to be confused with Machine torque.

Effective torque (often referred to as wheel torque or torque to the wheels) is a concept primarily associated with automotive tuning. Torque can be measured using a dynamometer. Common units used in automotive applications can include foot-pounds and Newton·meters. Although commonly discussed in automotive contexts, the concept applies to any mechanical system involving torque transmission through intermediate components.

Effective torque represents the torque available at the output of a mechanical system after accounting for both transmission ratios and energy losses. In systems such as vehicle drivetrains, torque is increased through gear reduction, but reduced by inefficiencies due to friction and heat.

Definition

The formula for effective torque to the wheels is:

$T_{\omega }=T_e\cdot N_t{N}_f\cdot {\eta }_t{\eta }_f$

where T_ω is wheel torque, T_e is engine torque, N_t, η_t are, respectively, the gearbox gear ratio and efficiency, and N_f, η_f are, respectively, the differential gear ratio and efficiency. Effective torque is often 5-15% lower than the shaft or crank ratings of an engine due to drivetrain losses.

Cyclic Loading

Illustration of torque variation over a duty cycle, showing how an equivalent (RMS) torque may be defined from time-varying loads

For a system that undergoes cycles (changes in load, speed, efficiency, etc...) a more general formula, not just used for automotive applications, for effective torque is

$M_{eff}=\sqrt{\frac{M_A^2\cdot t_A+M_L^2\cdot t_L+M_{Br}^2\cdot t_{Br}+M_{St}^2\cdot t_{St}+...+M_x^2\cdot t_x}{t_A+t_L+t_{Br}+t_{St}+...+t_x}}$

where M_A, t_A are the starting torque and start-up time respectively, M_L, t_L are the load torque and travel time respectively, M_Br, t_Br are the braking torque and braking time respectively, M_St, t_St are the rest torque and rest time respectively, and M_x, t_x represents any following cycle changes with this form.

A condensed root mean square (RMS) form for M_eff may be written as

$M_{eff}=\sqrt{\frac{\sum _{i=1}^n[M_i^2\cdot t_i]}{\sum _{i=1}^n[t_i]}}$

This formulation is commonly used in engineering to account for thermal and fatigue effects in components subjected to varying torque.

See also

• Machine torque
• Torsion (mechanics)