ENGR 3399: Olin Baja Front Suspension Analysis FinaL Report

Juan Carlos del Rio

5.04.2017

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Abstract

In this report we will outline the results obtained from a number of simulations performed on the suspension geometry of the 2017 Olin Baja car. These simulations aim to probe the dynamic performance of the vehicle  while providing a platform for exploration into an array of simulation tools. The results from these studies show promising improvements over the performance of the car’s suspension in previous years.

Background

Mini Baja SAE is a competition where students from 100 colleges from the across the US and around the world build and race off-road vehicles in a series of challenges culminating in the  grueling 4hr endurance race. Reportedly, the race organizers design these courses to break half the cars on the first lap and only about a fifth of the cars are able to complete the suspension course. Therefore, as a team we have to ensure our car is not only fast but also reliable and able to tackle any obstacles that may be thrown at us. In previous years Olin Baja has repeatedly suffered from reliability issues, particularly in the front suspension, that reduce our running time and cost the team invaluable points. However, over the past year we have worked tirelessly to build a more robust system that will hopefully see us drive over the finish line when the checkered flag falls sunday afternoon in Kansas. With so much of our time being tied down in improving reliability we have never really had the opportunity to tune and optimize or even characterize our suspension before it drives at competition. Therefore, for this project I used Finite Element Analysis to try to gain some insight into the general dynamic behavior of our system under a number of conditions that we might expect to see on the track come competition. This analysis will help give some insight into what the driver can expect out of our front suspension so that the adjustment process can be sped up and we can begin to test the car at its limit.

The System

For this project we will focus on the analysis of the front suspension geometry as it dictates the steering capabilities of the car as well as taking the highest impacts when going over obstacles.  Olin Baja runs a double wishbone (A-arm) suspension in the front of the car as it provides fine control of wheel position at all times. There are four main components to this system : the coilover, the top A-arm, the bottom A-arm, and the knuckle. Knuckle is the the mounting fixture on which the wheel spins and is steered from, it also holds the brakes in place. It is connected to the chassis via the a-arms which allows it to travel up and down through a  specific path. The shock mount then takes the load from the wheels through the bottom A-arms and it compresses to help the navigate over obstacles.

Front suspension geometry sketch,  Full system render

The picture on the left above shows the geometry sketches used to lay out the general dimensions of the system and the right shows the complete linkage. The suspension can be tuned through camber and toe changes as well as adjusting the preloading on the spring, however, there is no damping control on the current shock absorbers.

Goals for project

The main goal for this project was to obtain a general idea of the motion of the system under different loading conditions. Having a baseline model working we could then tweak the parameters mentioned in the previous section to try to optimize the driving dynamics of the car without having an actual running car. Additionally, I hoped to become better acquainted with the different types of dynamic analysis and learn how to interpret them and how to extract useful design insight from them. As i mentioned in section 2 we have rarely had the opportunity to run any sort of analysis other than static stress on our system and so this project serves as exploration into the Solidworks simulation package and its capabilities. It is important to do the analysis in solidworks as it is the program that is most familiar to our team members so any insight I gain from this project can be easily passed down to future generations without having to learn how to use a new program such as ANSYS.

Simplest MODEL

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Since the spring is perhaps the most important part in a suspension system we can run  less computationally intensive studies on the spring alone. These studies can inform decisions made in more complicated studies to minimize their chance of time consuming failure. The spring used in the front suspension is a part of Polaris  proprietary 19.3 in coilovers. The spring has a 2.06 inch inner diameter and sits at 12.25 at full extension. Beyond these measurements Polaris does not provide any CAD so without the spring at hand all the remaining dimensions were carefully guesstimated from online pictures. The material of the spring is also not provided so I used ANSI 5160 as it is know to be used in car springs and data is readily available.

Modal Analysis

Since the spring is the component that will contribute most to lowest modes of oscillation we can run a modal analysis on just the spring and obtain the first five natural frequencies and modes of oscillations.

Mode   Frequency(Hertz)   Period(Seconds)

       1                                   7.2995                                                   0.137

       2                                  33.759                                               0.029622

       3                                  37.998                                                0.026317

       4                                  41.867                                                0.023885

       5                                 99.584                                                 0.01004

Modes of Oscillation [1,2,3,4,5]

The modal analysis revealed that the first natural frequency (7.3 Hz) and mode are within the operating range of the car. Therefore, under the right circumstances such as a washboard style road or a rock crawl (both of which are present in baja tracks)  the spring could shatter. The low value is not surprising because the 4-10 Hz range is known where cars lose control due to vibrations. The period of oscillation of the first mode is also close to the period of the pulse used in one of my first dynamic simulations so it could explain the uncharacteristic shattering of the spring at very low displacements

Simplified full model

Set up and abstractions

In order to avoid complicated mates, contact sets, and the extremely fine meshes that would be needed to simulate the entire system I abstracted all the complex part geometries and mates to create a model that would behave the same but would take less time to compute. Below we can see the abstracted model labeled like the original diagram in order to highlight the changes to the model. Though the diagram only shows the linkage of the suspension, for the entire analysis I abstracted all the unsprung mass (wheel, hubs, discs, brakes, etc) to be a combined lump of mass with the knuckle, the density of the material was adjusted so that the total unsprung mass mass would be around 20 lbs. The ball joint rod ends and swivel bearings that connected the a-arms to the knuckle were replaced with simple pinned joints that allow the arms to swing only in the geometry path. The a-arms were also replaced by long beams (essentially “H-arms”) in order to avoid having to mesh the tubes. The shock mount position was moved to the top a-arm because there is no longer a gap for it to stick through from the bottom a-arm. The shock was not  simplified as it serves the purpose of constraining the spring axially and can be fixed with a pin. The system was then meshed as seen below, since we are not concerned about accurate displacements on the arms or the ball they are left with a coarse mesh. The spring was meshed using a very fine curvature based mesh. Lastly the entire system is constrained at the correct geometry using a sketch which mimics the angle of the floor on the car (10 degrees). Modal damping was used for all studies and was set at 0.075, this number wash chosen after doing some online research into reasonable coefficients and then playing around with the simulation until the dynamic response seemed qualitatively correct. All displacements are calculated “at the wheel” (unsprung mass).

Simplified Model and Mesh

Modal Analysis

Mode   Frequency(Hertz)   Period(Seconds)

      1                                 7.8679                                                        0.1271

     2                                 23.341                                                     0.042843  

     3                                 43.228                                                     0.023133    

     4                                  44.78                                                       0.022331  

     5                                 68.618                                                      0.014573    

Modes of Oscillation [1,2,3,4,5]

The modal analysis reveals that thought the first natural frequency remains fairly constant with respect to the spring analysis the second and fifth natural frequencies drop significantly. This analysis also revealed a bad fixture in the shock absorber model that allowed the shaft to go outside the main body and the solver appears to allow penetration between the spring and the body. After searching long and hard for the error and trying different fixtures I was not able to solve this issue and concluded the sicrepancy might be down to the exagerated displacement settings in the analysis. 

Dynamic Time Dependent Analysis

Going Over a Log

The first load case that was simulated was the car going over a log. In this case suspension should benefit from the angled mounts (10 deg from the ground plane) to comply with the angled load created by the contact with the log. The forces of the impact with the log were separated into vertical and horizontal components as shown below. The shape of the curve is meant to approximate the force the suspension would experience if it hit the log at some driving speed, started to crawl up and then dropped down on the front wheels again on the other side creating another spike. The analysis was carried out for 2 seconds.

Log Load Case Setup and Unsprung Mass Displacement [Y, Total; Visual]

The displacements plots show that there is some rebounding effects from the spring but they are still reasonable. The maximum displacement we see is about 2 inches which is just under a third of the total travel of the shock. From personal experience these plots do seem to correlate with what the driver feels in the car which suggests there is validity to this simulation despite the abstractions and estimations. The animations of the suspension travel for this load case and the two next can be found in the Youtube link at the bottom of this document.

Rhythm Section

The next obstacle I simulated was the rhythm section which consists of a series of evenly spaced “medium” sized bumps. Front running teams are able to take this obstacle at speed without being bounced off because their damping is properly tuned. The load case for this section assumes a car moving at speed through 4 bumps in  2 seconds, this pattern is represented by sine waves and as with the log the impact of the hills is simulated by two separate vertical and horizontal loads.

Rhythm Load Case Setup and Unsprung Mass Displacement [Y, Total; Visual]

The results from the show that the modal damping is  more effective for this load case than it was for the log climb case as the resultant displacement shows little to no signs of rebound. The magnitude of the displacement also seems reasonable for this load case which indicates that with the current setup we would be able to  move at speed through a fast rhythm section.

Big Air Landing

Lastly, we have the simplest but largest load case for our car, landing from a jump. This landing can be modeled as a short,high amplitude pulse. Due to the momentum of the car the fact that cars typically tend to land on the front wheels the load experienced in this scenario is much greater than the weight of the car. In previous years we would expect the car to reach the end of its travel (4.8 inches) with such a load case.

Landing Load Case and Unsprung Mass Displacement [Y, Total; Visual]

n contrast to last year’s design, due the added travel (4.5 → 6.7) and increased spring stiffness, the shock does not bottom out which means that since the spring still has yield left in it the a-arm is less likely to break. This result also indicates that the coilovers chosen for this year  will allow us to push the car much harder than in years past. The system does see some residual vibrations but their amplitude will be negligible with the roughness of the terrain. Additionally in the total displacement plot the vibrations seem to be damped to a comfortable low frequency.

 

Random vibration

The last analysis that we will run on the front suspension is a random vibration analysis. This analysis sweeps through the system’s operating range of frequencies and outputs the Power Spectral Density which can be used to determine at which frequency the system will have the most energy. The load applied in this study is meant to represent the weight of the wheel being excited by the range of frequencies.

Random Vibration Load Case Setup and Output

The analysis reveals that the PSD over the most probable range of frequencies  for the suspension (1-10 Hz) is high relative to the higher frequencies but is not the most energetic state. The peak of this graph coincides with the second natural frequency of the suspension. While this is a rather low frequency, at 23.34 Hz it is sufficiently removed from our expected range that it will likely not be an issue.

Limitations and Improvements

    Though this model appears to be qualitatively correct there are several improvements that would make this analysis directly applicable to our on-track operations. One of the first immediate improvements that could be made is to create a more accurate model for the spring. As we previously mentioned the springs were made from estimates and guesses an though they behave as expected slight changes in the geometry could and material properties could have significant effects on the behavior of the system. The model seemed to be stiffer than expected by about a factor of 2 which could be down partly to a thicker spring and a stiffer material. Once the model is accurate and properly fixtures we can adjust damping to obtain the desired behavior of the system and replicate these adjustments on track.

    In future iterations I would like to examine the response of the system to more realistic conditions. Preloading the spring could stiffen its response and starting geometry with the car at resting height rather than full extension would provide a more realistic simulation. Simulating the tube a-arms rather than abstracting them under dynamic loads would allow us to determine to a higher fidelity if they would fail even when the abstracted stiffer system performs without issues.

Conclusion

    From these simulations we can see that even though the material models and  loads may not be numerically correct the model is a reasonable approximation of the qualitative behavior of the Baja front suspension. The dynamic simulations also indicate that for the rough models of  we currently have shocks we can expect an increase in vehicle dynamic performance. These performance increases can be seen in the coilovers being able to take higher loads without much rebound and so we can approach obstacles at higher speeds, which in racing is always a good thing. The vibration analysis in the project also will help the drivers know what to expect of the car at obstacles with higher vibration frequencies, such as the first mode present at around 7 Hz. In conclusion, these simulations are a good first attempt at understanding vehicle dynamics with the simulation tools available to Olin Baja and will help inform design decisions for next year’s contender.

 

Reflection

In the process of performing this analysis I learned a lot about dynamic simulations and developed a good intuition for damping coefficients.  Thought these particular models are not yet directly applicable to our track  operations they are good first foray into performance based analysis. In retrospection it would have been interesting to reduce the amount of different analysis and varied geometry parameters instead to be able to get direct performance comparisons. Despite the system and analysis types not being overly complex I think the varied nature of the all the analysis really allowed me to learn more about the different dynamic analysis types.