## 2 Structure and Principle
### A New DHPM Vernier Motor Using Saddle Coil and Salient Pole
On the other hand, for a typical cylindrical motor, the height status of the coils in the interval between \(Z=0\) and \(Z=\mathsf{x}\), which are wound in the slot, when observed in the direction of length, is always the same. The maximum external diameter of the newly proposed motor is the same as that of the comparison model. Therefore, the outer diameter of the stator's end, which is designed to be sloped, is reduced compared to the comparison model. Thus, the width of the coil wound here will be reduced. The coil's width can be decrease while its height will increase, which will resemble a saddle shape as a whole. As shown in Figure 2, the magnetic path of the proposed motor is reduced. It causes to reduce the magnetic resistance and improve motor performance. A slot fill factor will be decreased by inserting an additional salient pole. In other words, a model with a salient pole will have a lower slot fill factor than a model without a salient pole. We developed a saddle-type model with an angle to reduce the resistance. In this case, the wound coil's height is slightly higher, but additional space is obtained. It causes that the slot fill factor of the proposed model is increased compared to the model without a salient pole. Predecessor models are arranged in a stator electromagnet with a PM (the magnetic pole is fixed), but in the structure of the proposed model, the PMs are replaced by a salient pole using the motor's iron core. The salient pole can be various magnetized magnets, unlike PMs, contributing to the reduction in PMs and the improvement in the torque. Thus, the effect of reducing the magnetic resistance on the change in the shape of the slot core of the proposed model guarantees the increase in the number of magnetic field lines derived from that side of the slot core facing the rotor. As a result, the torque performance is improved significantly. The proposed model presented better performance, even though it has fewer PMs than the other counterparts. The winding factor is vital as an indicator of the magnetic flux utilization. When the electrical angle is 180 degrees, the magnetic pitch and winding pitch are the same. The short pitch factors are 1 and 0.866 when the electrical angle is 180 degrees and 120 degrees, respectively. We can increase the magnetic flux utilization using PMs and magnetic substances for the salient pole without increasing the magnetic flux density. This result is caused by the winding factor with a change in the electrical angle. Therefore, a vernier motor of 12S10P for pole pairs in the analytical model has a smaller winding factor. We considered how to increase the magnetic flux density using other factors instead of the winding factor in the motor. Figure 2 depicts the proposed model, which replaces the PM with a magnetic substance (salient pole) and a saddle coil. Additionally, Figure 4 illustrates the deployment chart. The stator structure consists of salient poles without coil windings, and the coils are wound around the center of the slot. In the proposed rotor structure, several PMs and salient poles are installed sequentially in the circumference to rotate facing the stator teeth. It is essential to increase the energy density, which is the ratio of output to the motor volume, to reduce the motor size and increase the output. As presented in Figure 5, the displacement value at a distance of \(x\) from the origin (0, 0) is a function of \(x,f(x)\). The area of space, \(S(x)\), generated when rotating along the \(x\)-axis is obtained from Equation (3). \[S(x)=2\pi\times[f(x)] \tag{3}\]  
Next, the value of \(f(x)\) indicates the distance from the origin (0, 0) of the proposed motor model at the angle of \"theta\" in Figure 5. This value is obtained from Equation (4), and the motor volume is calculated using Equation (5).