Table 2.

Governing equations of AFPSE.

Modeling of DC motor [12]	$$\mathrm{V}-K_b\frac{d\theta }{dt}=\frac{R_e}{K_T}{T}_m+\frac{L_1}{K_T}\frac{d{T}_m}{dt}$$ (1)
Kinematic relation of slider crank [12]	$$y=R_m\left(1-\cos \theta \right)-\beta +L\text{where}\beta =L\sqrt{1-{\left(\frac{R_m}{L}\sin \theta \right)}^2}$$ (2)
Dynamic relations of slider crank [12]	$$\{\begin{array}{c}{T}_m=I_e\mathrm{Ӫ}\\ I_e=I_m+I_R+I_L{\left(\frac{R\cos \theta }{\beta }\right)}^2+m_L\left[{\left(\frac{R\cos \theta }{2}\right)}^2+{\left(R\sin \theta +\frac{\sigma L}{2}\right)}^2\right]+m_D{\left(R\mathit{sin}\theta +\sigma L\right)}^2\\ \sigma =\frac{R^2\sin \theta \cos \theta }{\beta L}\end{array}$$ (3)
Thermal modeling [12]	$$\{\begin{array}{c}2\pi \frac{h_h}{\omega }{s}_{pe}\left(T_H-T_h\right)=\frac{mr{T}_c{T}_h}{T_c-T_h}\left(\mathit{ln}\frac{T_h{v}_{co}+T_c\left(S_d{y}_0+v_{ho}\right)}{T_h\left(S_d{y}_0+v_{co}\right)+T_c{v}_{ho}}+\mathit{ln}\frac{T_h\left(S_d{y}_0+S_p{x}_0+v_{co}\right){+T}_c{v}_{ho}}{T_h\left(S_p{x}_0+v_{co}\right)+T_c\left(S_d{y}_0+v_{ho}\right)}\right)+\Delta m\frac{r}{{\rm Y}-1}\left(T_h-T_c\right)\left(1-{\eta }_{reg}\right)\\ 2\pi \frac{h_c}{\omega }{s}_{de}\left(T_C-T_c\right)=-\frac{mr{T}_c{T}_h}{T_c-T_h}\left(\mathit{ln}\frac{T_h{v}_{co}+T_c\left(S_d{y}_0+v_{ho}\right)}{T_h\left(S_d{y}_0+v_{co}\right)+T_c{v}_{ho}}+\mathit{ln}\frac{T_h\left(S_d{y}_0+v_{co}\right){+T}_c({S_p{x}_0+v}_{ho}}{T_h{v}_{co}+T_c\left(S_d{y}_0+S_p{x}_0+v_{ho}\right)}\right)+W-\Delta m\frac{r}{{\rm Y}-1}\left(T_h-T_c\right)\left(1-{\eta }_{reg}\right)\end{array}$$ (4)
Estimated heat transfer coefficient in hot and cold chamber [13]	$$\begin{array}{c}{h}_h=\frac{0.0090{Re}_m^{1.4892}\mu c_p}{2D_h\mathit{Pr}}\\ h_c=\frac{0.0035{Re}_m^{2.0048}\mu c_p}{2D_h\mathit{Pr}}\end{array}$$ (5)
Pressure equation [12]	$$p\left(x,y\right)=\frac{mr{T}_h{T}_c}{T_h\left(s_d\left(y_0-y\right)+s_{p}x+v_{h0}\right)+T_c\left(s_{d}y+v_{h0}\right)}$$ (6)
Mass spring damper mechanism [12]	$$m\frac{d^{2}x}{{dt}^2}+c\frac{dx}{dt}+kx=\left(p\left(x,y\right)-p_0\right)s_p$$ (7)
Estimated damping coefficient [13]	$$C\left(\omega \right)=0.0618{\omega }^7-1.56{\omega }^6+15.79{\omega }^5-80.23{\omega }^4+207.11{\omega }^3-212.50{\omega }^2-88.24\omega +270.37$$ (8)