## 3 Engine Modifications and Mechanism Design
### Mechanism Design
Moreover, the hydrodynamic lubrication behavior of the lubricant was simulated at the piston pack and cylinder liner interface, as well as the main journal and main bearing interface. Once the oil forces for the piston and main journal were obtained, the dynamic equations of the piston-crank system were developed and validated numerically [31]. The vibration differential equations for the main journal were expressed as  
\[m\ddot{X}+q\dot{X}+kX+F_{ox}-F_{01x}+F_{ex}=0, \tag{5}\]  
\[m\ddot{Y}+q\dot{Y}+kY+F_{oy}-F_{01y}+F_{ey}=0, \tag{6}\]  
Figure 8:0 Modal density comparison of the original vs. modified engine designs [28]. Figure is reprinted with permission from publisher. where \(m\) and \(q\) are the mass and damping coefficient of the main journal, respectively. \(X\) and \(Y\) are the displacements of the main journal, and \(F_{01x}\) and \(F_{01y}\) are the reactions applied by the main journal on an initiated crack. The components of the unbalanced force \(F_{e}\) were computed as  
Figure 8:1  
Figure 8:2  
where \(m_{1}e_{1}\) is the torque exerted by the eccentricity of the unbalanced mass of the crankshaft, with respect to its original center. The \(X\) and \(Y\) displacements of the main journal were then determined from the dynamic equations, at varying connecting-rod length to piston diameter (\(L_{c}/D_{s}\)) ratios. Although the ratios exhibited minimal effect on orbit of the main journal center and \(Y\) displacements, they significantly affected the \(X\) displacements. With increasing \(L_{c}/D_{s}\), the vibration amplitude of the main journal was increased along the \(x\)-direction, while it was dropped with negligible effect on the \(Y\) displacement. Damping coefficient, \(q\), is another parameter that influences the orbit and vibration amplitude of the main journal center. The researchers also investigated the effect of different damping coefficients on the relative difference in vibration displacements and eccentricity ratios of the main journal, in the 1500-3000 N s/m speed range. While the orbits were relatively stabilized (i.e., round loop shape), with increasing the \(q\), a further increase made the relative differences in vibration amplitudes larger and, thus, degraded the hydrodynamic action (vibration attenuation) of the lubricant between the main journal and main bearing. To highlight the contribution of engine lubricating oil quality and condition, [PERSON] et al. [32] remotely measured the surface-borne and airborne acoustic signals caused by piston slap, and studied the effects of load, engine speed, and oil temperature. They reported that a reduction in the oil level and/or the use of poor quality oil can cause an increase in structure-borne acoustic and airborne acoustic signals of certain frequency bands. Figure 8:3 Schematic of the piston–crankshaft system: (**a**) piston-cylinder; (**b**) main bearing–journal system [2]. [PERSON] et al. [33] designed a crank and slider mechanism to enhance the combustion performance of a four-stroke spark ignition (SI) engine. By lowering the ratio of the engine's connecting-rod length to crank radius (\(l/R\)), the isentropic process in the power stroke was desirably resembled, leading to a reduction in the maximal gas temperature after the first spark and increase in the compression ratio. These two factors improved the thermodynamic (heat) efficiency of the engine and increased the linear speed of the piston within the range of combustion. Particularly, with increasing the crank angular velocity, higher friction efficiency and less engine noise were achieved, through removing the piston lateral pressure and providing no contact condition between the piston and cylinder barrel. These improvements in the engine design and thermodynamic performances were accompanied by lower NO\({}_{x}\) pollutions and a longer life service of the engine. However, there were some drawbacks associated with their proposed mechanism, such as increasing the number of the engine components, complexity of the mechanism, and barriers in assembling the engine parts.