# Torque Characteristic Analysis of a Transverse Flux Motor Using a Combined-Type Stator Core
## 6 Discussion  
Based on the analysis results in Section 5, an optimized CS-TFM is designed and analyzed by 3D FEM, and the comparison between initial model and optimized model is listed in Table 2. It should be mentioned that the parameters of the optimized model in this section are preliminary optimization results based on the forgoing 3D FEM analysis. A more accurate optimization result can be obtained by  
Figure 14: The influence of rotor teeth ratio \(k_{\text{rt}}\) on average torque and torque ripple.  
Figure 13: The influence of air-gap length \(\delta\) on average torque and torque ripple.  
using some optimization methods in the motor design process--for example, numerical optimization algorithms or approximate models [22; 23].  
According to the 3D FEM data, when the volume and ampere-turn are kept the same as that of the initial model, the electromagnetic performance of optimized CS-TFM is improved: the amplitude of no-load BMF is increased by 32.84%, the THD of no-load BMF is decreased by 38.09%, the cogging torque is decreased by 56.49%, and the average torque is increased by 29.48%. Meanwhile, the torque ripple is increased from 4.14% to 4.84%.  
The torque densities are calculated and compared among various types of direct-drive motors, as shown in Table 3. The torque density per volume of proposed CS-TFM is higher than BLDC in [2], TFRM in [13], and lower than ISDW-PMV in [5] and TFPM in [16]. The torque density per permanent magnet volume of CS-TFM is the largest among those motors.  
What should be noticed is that the results of torque density are not calculated under similar conditions (air-gap length, rated speed and current density are different from each other). Thus, it is difficult to evaluate the proposed motor simply.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Initial** & **Optimized** \\ \hline Rotor out Diameter \(D_{\text{out}}\) & 248 mm & 248 mm \\ Air-gap Diameter \(D_{\text{a}}\) & 226 mm & 226 mm \\ Stator inner Diameter \(D_{\text{in}}\) & 140 mm & 140 mm \\ Height of Axial bridge \(h_{\text{b}}\) & 10 mm & 10 mm \\ Axial length of single-phase \(l_{\text{a}}\) & 45 mm & 45 mm \\ Air-gap length \(\delta\) & 1 mm & 1 mm \\ rotor teeth ratio \(k_{\text{rt}}\) & 1 & 0.7 \\ PM thickness \(l_{\text{m}}\) & 2 mm & 2 mm \\ Axial length of PM \(l_{\text{m}}\) & 11 mm & 11 mm \\ Pole-pitch \(\tau_{\text{m}}\) & 11.83 mm & 7.07 mm \\ Pole pair number \(p\) & 30 & 50 \\ Armature winding turns \(N\) & 150 & 90 \\ Rated current \(I\) & 12.73 A & 21.22 A \\ Rated current density \(J\) & 4.5 A/mm\({}^{2}\) & 4.5 A/mm\({}^{2}\) \\ Rated speed \(n\) & 100 r/min & 100 r/min \\ Amplitude of fundamental no-load BMF & 56.55 V & 75.12 V \\ THD of no-load BMF & 12.39\% & 7.67\% \\ Amplitude of cogging torque & 7.63 N.m & 3.32 N.m \\ Average torque & 145.63 N.m & 188.56 N.m \\ Torque ripple & 4.14\% & 4.84\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Initial and optimized parameters of the CS-TFM.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **CS-TFM** & **BLDC [2]** & **ISDW-PMV [5]** & **TFRM [13]** & **TFPM [16]** \\ \hline Air-gap length (mm) & 1 & 1 & 0.5 & 0.25 & 1 \\ Volume of motor (mm\({}^{3}\)) & \(6.5\times 10^{6}\) & \(4.3\times 10^{5}\) & \(9.2\times 10^{5}\) & \(3.3\times 10^{6}\) & \(8.8\times 10^{6}\) \\ Volume of PM (mm\({}^{3}\)) & \(9.4\times 10^{4}\) & - & \(8.0\times 10^{4}\) & - & \(7.7\times 10^{5}\) \\ Rated speed \(n\) (r/min) & 100 & 250 & 600 & - & 66 \\ Current density \(J\) (A/mm\({}^{2}\)) & 4.5 & 5.8 & 6.6 & 5.6 & 9.96 \\ Average torque (N m) & 188.6 & 10.1 & 61.7 & 30.0 & 360.0 \\ Torque density per volume & 28.9 & 23.5 & 67.1 & 9.2 & 40.8 \\ (kN m/m\({}^{3}\)) & 2006.4 & - & 771.3 & - & 467.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of torque density.