# The formula for the effec­tive torque

### When selecting the most suit­able motor for dynamic appli­ca­tions, the effec­tive torque is a crucial quan­tity.

Jörg Horn­berger, Devel­op­ment Specialist for Indus­trial Drives and Markus Flaig, Head of Devel­op­ment for Indus­trial Drives

In many appli­ca­tions, a motor’s contin­uous output is limited by its thermal budget. Optimum design is crucial to keep a motor from over­heating in an appli­ca­tion. The rated torque is usually used during design. However, that is based on a motor running in contin­uous oper­a­tion at a clearly defined oper­ating point with constant speed and constant torque. In this case, a state of thermal equi­lib­rium will be reached after a certain period.

But in many appli­ca­tions, espe­cially in dynamic oper­a­tion, the oper­ating points change constantly. An example is a shuttle in a high-bay ware­house. As soon as it receives an order to retrieve stored goods, it accel­er­ates from its starting point to the required speed. Then it moves at constant speed toward its desti­na­tion and decel­er­ates to come to a stop at the required posi­tion. Different torques are required for the accel­er­a­tion, constant speed and decel­er­a­tion phases. This example illus­trates that for dynamic appli­ca­tions, more para­me­ters need to be taken into account during design than for the simple case of contin­uous oper­a­tion: torques for accel­er­a­tion, constant speed and decel­er­a­tion, and times at rest.

Example cycle for effec­tive torque

The formula for effec­tive torque shown above is an ideal­iza­tion of such cyclical oper­a­tion. MA and tA repre­sent the starting torque and the start-up time; staying with our example, the accel­er­a­tion phase for the shuttle. ML and tL repre­sent the load torque and the travel time to the desti­na­tion, while MBr and tBr account for the decel­er­a­tion phase. With tSt , the time at rest (without torque) is also accounted for. The formula can be expanded as needed depending on the actual cycle, making it possible to deter­mine the corre­sponding effec­tive torque for contin­uous oper­a­tion. That allows an assess­ment of whether the selected motor is suit­able for the appli­ca­tion. The effec­tive torque for the appli­ca­tion has to be less than or equal to the rated torque of the selected motor.

The effec­tive torque is an aid in the selec­tion of a suit­able motor. In motor devel­op­ment, we use repre­sen­ta­tive oper­ating points (contin­uous oper­a­tion) for the design and char­ac­ter­is­tics of the various motor sizes. They are based on empir­ical values from actual ­appli­ca­tions.