# Dynamic Balance Simulation and Optimization of Electric Vehicle Scroll Compressor Rotor System
## 4 Scroll Compressor Rotor System Model
### Loading Gas Forces  
In this article, we will focus on the normal operation of the scroll compressor. When the compressor operates at a speed of 4500 r/min, it experiences an inlet pressure of 0.377 Mpa and an exhaust pressure of 1.463 Mpa. Using the data provided in Table 2, we will calculate the radial gas force, axial gas force and tangential gas force parameters acting on the movable scroll disc.  
The axial pneumatic force \(F_{a}\) acts perpendicular to the bottom surface of the rotating scroll plate along the axis of the eccentric crankshaft. If this force is too large, it will affect the efficiency and stability of the compressor. The axial pneumatic force is as follows.  
\[F_{a}=\begin{cases}\pi p_{s}P^{2}\bigg{[}\dfrac{A_{1}}{\pi p^{2}}\rho_{1}+\sum \limits_{i=2}^{N}\bigg{(}2i-1-\dfrac{\theta}{\pi}\bigg{)}\rho_{i}\bigg{]}&0 \leq\theta<\theta^{*}\\ \pi p_{s}P^{2}\bigg{[}\dfrac{A_{1}}{\pi p^{2}}\rho_{1}+\sum\limits_{i=3}^{N} \bigg{(}2i-1-\dfrac{\theta}{\pi}\bigg{)}\rho_{i}\bigg{]}&\theta^{*}\leq\theta< 2\pi\end{cases} \tag{3}\]  
According to Equation (3), \(F_{a}=375\) N.  
The tangential gas force acting at the midpoint of the center base ring connection between the dynamic and static scroll discs of the scroll compressor has a direction perpendicular to the center base ring connection line. The tangential gas force not only is a function of the number of compression chambers but also has a bearing on the overall force acting on the scroll compressor. Specifically, when the scroll compressor has \(N\) compression chambers, the combined force of the tangential gas force is as follows:  
\[F_{t}=\sum\limits_{i=1}^{N}F_{ti}=p_{s}p_{t}h\sum\limits_{i=1}^{N}\bigg{(}2i- \dfrac{\theta}{\pi}\bigg{)}(\varepsilon_{i}-\varepsilon_{i+1}), \tag{4}\]  
where \(\varepsilon_{i}\) is the pressure ratio, calculated as follows:  
\[\varepsilon_{i}=\dfrac{p_{i}}{p_{s}}=\bigg{(}\dfrac{V_{s}}{V_{i}}\bigg{)}^{k}= \bigg{(}\dfrac{2N-1-\theta_{s}/\pi}{2i-1-\theta/\pi}\bigg{)}^{k}, \tag{5}\]  
where \(P_{s}\) is the suction pressure, MPa; \(p_{t}\) is the pitch of the scroll teeth, mm; \(h\) is the tooth height, mm; \(\theta\) is the crankshaft angle, rad; \(p\) is the compression chamber pressure, MPa; \(V\) is the compression chamber volume, mm\({}^{3}\); \(i\) is the compression chamber number; and \(i=1,2,3,\ldots,n\).  
According to the Equation (4), the tangential pneumatic force \(F_{t}\) is 214.5 N.  
Radial gas force \(F_{r}\) refers to a force in the radial direction generated by compression of the gas when the compressor is working. It acts on the connection between the center of the base circle of the dynamic and static roller discs and is applied to the dynamic roller. The direction is directed from the dynamic scroll disk to the static scroll disk. When the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Title** & **Notation** & **Numerical Value** \\ \hline Base circle radius & \(r_{a}\) & 1.65 mm \\ Involute start angle & \(\alpha\) & 51.6\({}^{\circ}\) \\ Turning radius & \(R_{or}\) & 3.77 mm \\ Pitch of vortex ring & \(p_{t}\) & 10.3 mm \\ Vortex ring wall thickness & \(t\) & 2.8 mm \\ Vortex ring height & \(h\) & 19 mm \\ Number of swirl rings & \(n\) & 2.5 \\ Maximum spread angle & \(\phi_{E}\) & 5.5\(\pi\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Scroll compressor parameters.  
scroll compressor has \(N\) compression chambers, the combined force of the radial gas force is as follows:  
\[F_{r}=\sum_{i=1}^{N}F_{ri}=\sum_{i=1}^{N}2 ah(p_{i}-p_{i+1}), \tag{6}\]  
where \(a\) is the radius of the base circle, mm.  
According to Equation (6), the radial pneumatic force \(F_{r}\) is 520 N.