## Mechanical Models

### Mechanical Shaft Block

The Mechanical Shaft block is used to simulate a shaft interconnecting mechanically a motor drive block to a mechanical load block. Hence the Mechanical Shaft block allows decoupling of the mechanical parameters of the load from the ones of the motor. The mechanical shaft is represented by its stiffness coefficient Ksh and damping coefficient Dsh. The shaft transmitted torque Tsh is computed with

`${T}_{sh}={K}_{sh}\int \left({\omega }_{m}-{\omega }_{l}\right)dt+{D}_{sh}\left({\omega }_{m}-{\omega }_{l}\right)$`

where ωm and ωl are the speeds of the motor and the load, respectively.

The following figure shows the interconnections between the Motor Drive block, the Mechanical Shaft block, and the Mechanical Load block. The Mechanical Shaft block 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 the Mechanical Load block, which can be modeled by

`${T}_{sh}={J}_{l}\frac{d{\omega }_{l}}{dt}+{B}_{l}\cdot {\omega }_{l}$`

where Jl and Bl are the inertia coefficient and the viscous friction coefficient, respectively.

Interconnection Diagram of the Transmission Shaft ### Speed Reducer Block

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. The Speed Reducer block is composed of a high-speed shaft and a low-speed shaft connected by a speed reduction device, as shown in the following figure. The Speed Reducer block 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 the Speed Reducer block are the motor speed (high speed) and the load speed (low speed) while the outputs are the high-speed shaft torque Th and the low-speed shaft torque 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 the Mechanical Load block.

Interconnection Diagram of the Three Internal Blocks of the Speed Reducer Block 