**5. Results**

The linear static analysis of the front swingarm is based on the previously mentioned modelling of forces, materials, connections and constraints and the solver calculates the stresses (Von Misses) and the displacements. Two loading scenarios are conducted and discussed related to the forces applied. The first scenario includes the weight distribution of the forces (weight) resembling a vertical bending scenario, while the second investigates the effect of maximum braking forces. For the representation of the results, META post-processor was used. The first part of results shows the initial swingarm design under the two loading scenarios (Sections 5.1 and 5.2). In Section 5.3, details of the redesign process towards the final swingarm design are presented, based on topology optimization results and

alternative designs evaluation. Finally, in Section 5.4 simulation results of the final swingarm design are shown and a detailed comparison to the initial design is discussed.

#### *5.1. Initial Swingarm Design—First Loading Scenario*

In this part, the force applied is *Nf* = 786.45 N, which corresponds to weight distribution on the front wheel (Section 3.2). Stress results and related displacements for the swingarm are shown in Figure 9.

**Figure 9.** Stress (**a**) and displacement (**b**) results in 1st loading scenario.

A normal stress distribution is observed on the swingarm, where a maximum stress of 23.78 MPa occurs on one of the constrained points that connects it to the chassis. This result has a low magnitude that needs no further evaluation. The displacement results show a maximum value of 0.32 mm for the swingarm.

#### *5.2. Initial Swingarm Design—Second Loading Scenario*

Considering the case of braking, the forces applied are calculated in Section 3.3. As mentioned, the highest braking forces occur at deceleration of *d* = 0.8 g when using only the front brakes. According to this, the forces applied in the simulation are *Nf* = 1210 N and *Mbr* = 400.5 Nm. The results of stresses and displacements obtained are presented in Figure 10.

**Figure 10.** Stress (**a**) and displacement (**b**) results in 2nd loading scenario.

The maximum stress is 98.6 MPa placed on the right rear bracket, far lower than the material yield stress (503 MPa), corresponding to a safety factor *N* = 5.1. This yields that excess of material should be removed. Another important observation is that on the rest of the part stresses distribution are less than 60 MPa, while displacement results show a maximum value of 1.27 mm. According to these insights, certain modifications can be made on swingarm design in order to reduce weight. Additionally, a change of material could be recommended in order to cut down raw material and production costs.

### *5.3. Final Swingarm Design*

Considering the forces applied on the di fferent loading scenarios, we mostly depend on results obtained for the worst-case scenario which is under emergency braking conditions. A swingarm redesign and material replacement is decided, targeting lower weight and production cost. It is clear that stress and displacements will be raised, but the objective is a safety factor close to *N* = 2 and at the same time to keep displacements as low as possible. A topology optimization procedure was used at first, so as to assist on redesign of the swingarm and obtain valuable results regarding specific areas of material removal (Figure 11). Modelling and simulation were conducted based on parameters referred in Section 4.4. The finite element model was solved using the second (worst) loadcase scenario for various topology optimization parameters and the new form obtained was again validated (solved) in a static analysis. In this way it was possible to fine tune certain parameters such as the percentage of mass removed from the swingarm, which was finally set to 40% reduction compared to the original mass. It must be noted that we also experimented with higher reduction percentages, but the results indicated: a) even more complex swingarm forms, which were di fficult to manufacture with our production capabilities (CNC machining) and b) similar stresses and displacements. For these reasons, the specific percentage of mass reduction (40%) was chosen. As seen in Figure 11, material was mostly removed on the front part of the swingarm as well as in the middle, indicating that hollow parts should exist at these points. Most of the features of the form obtained through this procedure were incorporated in the new design.

**Figure 11.** Topology optimization results for the swingarm.

Various designs were considered and evaluated and two new alternatives are shown in Figure 12a,b. Their analysis was based on loads of the first loading scenario and the material used was aluminum 7075-T6. The results obtained are presented in Figure 12c,d, respectively.

**Figure 12.** Different swingarm versions and results: (**a**) 1st alternative swingarm design; (**b**) 2nd alternative swingarm design; (**c**) results of stresses and displacements for 1st alternative swingarm; (**d**) results of stresses and displacements for 2nd alternative swingarm.

The first alternative design showed a weight reduction of 13% (4.94 kg), while the second alternative provided even higher weight reduction of 18.5% (4.62 kg). Considering the results of analysis, the first one presented higher maximum stress (37.2 MPa—first, 25.63 MPa—second) while both had almost the same displacements (0.38 mm—first, 0.37 mm—second). It is evident that the second design alternative was the type of design we should focus on for the final version. The final form was slightly changed, mostly affected by our production capabilities, where CNC machining manufacturing was chosen. According to the redesign procedure followed, the final swingarm design is presented in Figure 13.

**Figure 13.** The final redesigned single-sided front swingarm.

As mentioned, low stress distribution and a high safety factor of the initial design gave us the flexibility to choose a new aluminum alloy (5083-H116) for the swingarm, targeting lower production cost. The modelling of the isotropic material properties used for the new swingarm assembly can be found in Table 5. Four different materials are used: (a) Aluminum 5083-H116 (swingarm and link), (b) Stainless steel 304 (suspension), (c) Stainless steel SS-A4-80 (swingarm axle), (d) Steel AISI4130 (bearings). The required properties used by the pre-processor are: (a) Elastic modulus, (b) Poisson ratio, (c) Shear modulus, (d) Density and (e) Yield strength.


**Table 5.** Materials properties used in the final modelling.

#### *5.4. Final Swingarm Design Results*

An identical modelling process is followed for the new materials applied, as in the initial design. Only the worst-case scenario (second loading scenario) is used for the evaluation and comparison to the initial version. The forces applied are again *Nf* = 1210 N and *Mbr* = 400.5 Nm and the results of stresses and displacements are presented in Figure 14.

**Figure 14.** Stress (**a**) and displacement (**b**) results in 2nd loading scenario for the final swingarm design.

The maximum stress calculated on the swingarm has a magnitude of 117.2 MPa, resulting in a safety factor *N* = 1.95 (yield strength is 228 MPa). As expected, maximum stress is once more observed on one of the constrained points that connects the swingarm to the chassis, as was the case in the simulation results of the first design. It must be also noted that stress distribution on the rest of the swingarm is below 70 MPa. The maximum displacement results in a value of 1.59 mm. Even though there are no comparative results for front swingarms on the literature, these displacements under heavy braking conditions are evaluated as acceptable. That means that no driving or handling problems would be noticed by the driver in braking conditions. A comparison of results from the simulations conducted for the initial and final swingarm design, can be found in Table 6, including maximum stresses, displacements, weight and safety factor.


**Table 6.** Results comparison of the initial and final swingarm design.

As shown, the maximum stresses are 19% higher in the final design, as also displacements are raised by 25%. These results were expected but at the same time do not raise any concerns, since they are lower than the material yield strength. Safety factor is reduced, which is normal for this kind of structure and ensures structural rigidity safety levels. The main target was of course to lower weight, which is accomplished, considering that a 23.2% reduction was achieved. Finally, the change of materials decided had minimum overall e ffects on our results, but on the other hand will help the most on reducing production costs.

The development procedure presented and decisions taken towards the final design, were based on finite element analysis simulations that were modeled based on our knowledge and experience. Due to the lack of relevant research on front single-sided swingarms, no real comparison can be made to similar research or tests in order to validate our results. One engineering parameter found from rear swingarm analysis (as referred to in Table 2 and used for validation in our case), is the safety factor. In rear swingarms it ranges from 1.53 to 2.39 with a mean value of 1.95, which is an important parameter that we successfully met on our new design. The next step would be to set up an experimental testing procedure on a custom test rig, which would provide additional strain and displacement data for the validation and tuning of our finite element model. We should also mention that since the suspension and tire e ffects are not considered in our model, the results of stresses and displacements are higher, providing additional certainty that we can further reduce the weight. According to the above, we are confident that the proposed design will provide the needed safety during driving and braking.
