## 4 Results
### Engine Balancing
#### 4.1.2 Influence of an Offset Angle Between the Two Crankshafts  
Introducing an offset angle causes both configurations to become unbalanced. However, they exhibit different behaviors depending on the specific scenario considered. In Scenario 2, where the rotating component of the first-order reciprocating forces remains unbalanced, both configurations exhibit the same behavior, as depicted in Figures 9 and 10. The total moment is represented by a vector with a constant direction and a variable magnitude. This direction is aligned with the y-axis, which is orthogonal to the plane of the cylinder axes. Since the direction remains fixed, an advantage of this configuration (Scenario 2) is the ability to use engine mounts with different stiffness values in different directions. As these unbalanced moments are transmitted to the chassis through the engine mounts, understanding their behavior allows for improved mount design and reduced vibration transmission from the engine to the chassis. However, the orientation of the engine is critical. If the engine is mounted vertically, i.e., with the cylinder axes parallel to the vehicle vertical axis, the vibrations generated by the engine may be decoupled from those transmitted vertically from the ground. However, since the application considered in this contribution addresses an OP engine fueled by hydrogen, it would be more likely mounted horizontally to provide sufficient space for the hydrogen tank above it. In this case, the two vibration sources would have the same direction and could not be decoupled. Figure 8: Resultant moment under zero offset conditions for 4-cylinder configuration; (a) co-rotating shafts with \(M^{\prime}_{rec,r}\) balanced; (b) counter-rotating shafts with \(M^{\prime}_{rec,r}\) balanced; (c) co-rotating shafts with \(M^{\prime}_{rec,r}\) unbalanced; (d) counter-rotating shafts with \(M^{\prime}_{rec,r}\) unbalanced. In Scenario 1 however, the two configurations exhibit completely different behaviors (Figures 11 and 12). As mentioned earlier, the counter-rotating shafts' configuration is already unbalanced without the offset and thus remains unbalanced with the offset introduction. In contrast, the co-rotating configuration presents the unbalanced moment as a rotating vector with a magnitude lower than the one of Scenario 2 addressed before, where the rotating component of the first-order reciprocating forces is not balanced by counter-weights. In this case, the engine mounts must have the same stiffness in all directions, and the engine orientation no longer represents a decoupling option. In conclusion, for both engine architectures (3-cylinder and 4-cylinder), the co-rotating shaft configuration appears to be the most promising. It offers the flexibility to choose between a more conservative setup for bearing reliability (Scenario 1) or a configuration with a resultant moment of constant direction (Scenario 2). In contrast, the counter-rotating shaft configuration can only achieve overall balancing if the rotating component of the first-order reciprocating forces remains unbalanced for each crankshaft. Reducing imbalances is the first step in minimizing vibrations transmitted to the chassis. These cyclic loads can lead to fatigue failure of the engine mounts, and the presence of an offset further increases these loads, exposing chassis components to higher stress. Figure 9: _Cont._  
Figure 10: _Cont._  
Figure 9: Resultant moment of co-rotating and counter-rotating shafts with \(M^{\prime}_{rec,}\) unbalanced (scenario 2) and with different offset angles for 3-cylinder configuration; (a) co-rotating with \(0^{\circ}\) offset; (b) counter-rotating with \(0^{\circ}\) offset; (c) co-rotating with \(5^{\circ}\) offset; (d) counter-rotating with \(5^{\circ}\) offset; (e) co-rotating with \(10^{\circ}\) offset; (f) counter-rotating with \(10^{\circ}\) offset; (g) co-rotating with \(15^{\circ}\) offset; (h) counter-rotating with \(15^{\circ}\) offset.