## 3 Engine Modifications and Mechanism Design
### Mechanism Design
Figure 11a represents that the correlation between measured and simulated \(M_{FW}(\varphi)\) had a good agreement at 600 rpm and 4 mm eccentricity. The close agreement between the compensated torque, measured from forces in the connecting rod and values measured directly from the experiments, assured the consistency of the measurements (Figure 11b). In a computer-aided engineering-based (CAE-based) study conducted by [PERSON] and [PERSON] [28], finite element analysis (FEA) and multi-body analysis (MBA) tools were implemented for modeling the dynamics of acoustical components of a six-cylinder 6160 in-line diesel engine, to understand the interaction between excitation mechanisms and noise transmission in the system (see Figure 12). The research was aimed at applying structural modifications to reduce noise and optimize vibrations at the engine, while operating at 400-1000 rpm, under full load, and in low-frequency range of <1 kHz. Whereas the FEA was conducted to analyze the vibrational behavior of the housings and crank train/valve drive of the engine, the MBA was utilized to model the dynamic behavior of rotating components (e.g., transmission shafts, gears, timing drive, etc.) and simulate vibroacoustic responses of the whole system. Forced vibration calculations were performed in the time-domain, under various speed and load conditions. The simulations were carried out in a direction perpendicular to the engine surface, to obtain rpm spectral maps at different vibration levels. Results discern  
Figure 11: (**a**) Numerically simulated non-uniform part of the engine torque \(\Delta M_{Eng}(\varphi)\) and compensation torque \(M_{FW}(\varphi)\) of the synthesized KDF. (**b**) Flywheel angular speed \(\dot{\varphi}_{ideal}\) for complete compensation of \(\Delta M_{Eng}(\varphi)\) and flywheel angular velocity \(\dot{\psi}(\varphi)\) of the synthesized KDF [27]. Figures are reprinted with permission from publisher. Figure 12: Multi-body analysis (MBA) model of a 6160 diesel engine. (**a**) Left and (**b**) right part of the engine [28]. Figures are reprinted with permission from publisher. engine surface vibrations were induced at a range close to the natural frequencies of the crankshaft, and at a speed between 600 to 1000 rpm. To minimize the vibration transferred through the internal paths and enhance the structural stiffness of the engine, two major design modifications were proposed: (i) increasing the local wall thickness of the crankscase, front gear cover, and back flywheel cover; (ii) adding ribs (extra mass of 14.85%) to the drive shaft of the engine which added extra supports for the drive shaft bearing bracket and more stiffness to the oil sum. Figure 13 demonstrates that the modifications reduced the vibration intensity of the original design for the modes between 0 to 1 kHz. [PERSON] and [PERSON] [2] investigated the impact of the geometric and operation parameters of a piston-crankshaft system on the dynamic performance of a single-cylinder four-stroke ICE (Figure 14a). In their proposed analytical model, the coupling between the components and oil film forces of the lubricated components were simultaneously incorporated into the dynamic response of the piston pack. For developing the dynamic equations of the system, an average flow model (Reynolds equation) [29; 30] was adopted, based on classical lubrication theory, to take into account the effect of the oil film forces of the piston rings and piston skirt. The \(x\) and \(y\) components of the oil force, \(F_{o}\), exerted by the main bearing were calculated as  
\[F_{ox}=\int_{0}^{L}\int_{0}^{2\pi}pR_{2}\sin\phi d\phi dz, \tag{3}\]  
\[F_{oy}=\int_{0}^{L}\int_{0}^{2\pi}pR_{2}\cos\phi d\phi dz, \tag{4}\]  
where z is the width direction of the main journal, \(\phi\) is the circumferential angle measure from the negative \(x\)-axis (Figure 14b), and \(L\) is the width of the main bearing with inner radius of \(R_{2}\).