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Mechanical Models

Mechanical ShaftBlock

TheMechanical Shaftblock is used to simulate a shaft interconnecting mechanically a motor drive block to a mechanical load block. Hence theMechanical Shaftblock allows decoupling of the mechanical parameters of the load from the ones of the motor. The mechanical shaft is represented by its stiffness coefficientKshand damping coefficientDsh. The shaft transmitted torqueTshis computed with

T s h = K s h ∫ ( ω m − ω l ) d t + D s h ( ω m − ω l )

whereωmandωlare the speeds of the motor and the load, respectively.

The following figure shows the interconnections between theMotor Driveblock, theMechanical Shaft块,Mechanical Loadblock. TheMechanical Shaftblock has two inputs, the load and motor speeds, and one output, the shaft transmitted torque. Note that the transmitted torque is applied at the load torque input of the motor. The transmitted torque is also applied at the input of theMechanical Loadblock, which can be modeled by

T s h = J l d ω l d t + B l ⋅ ω l

whereJlandBlare the inertia coefficient and the viscous friction coefficient, respectively.

Interconnection Diagram of the Transmission Shaft

Speed ReducerBlock

In many applications, the mechanical load requires high torque at low speed rather than low torque at high speed. This can be obtained by interconnecting the motor to the mechanical load by a speed reducer. TheSpeed Reducerblock is composed of a high-speed shaft and a low-speed shaft connected by a speed reduction device, as shown in the following figure. TheSpeed Reducerblock has seven parameters: the stiffness and damping coefficients of the high-speed and the low-speed shafts, the reduction ratio, and the speed reduction device inertia and efficiency. The two inputs of theSpeed Reducerblock are the motor speed (high speed) and the load speed (low speed) while the outputs are the high-speed shaft torqueTh和低速轴扭矩Tl. The high-speed shaft torque must be applied to the load torque input of the motor. The low-speed shaft torque must be applied directly to theMechanical Loadblock.

Interconnection Diagram of the Three Internal Blocks of theSpeed ReducerBlock