Finite Element Analysis and Validation of Miata Frame Rail Design
The original Mazda Miata is known to enthusiasts as one of the last true sports cars. A machine built to feel like a race car at the speed limit. The Miata is also known for having the torsional rigidity of a wet noodle compared to traditional sports cars that are able to leverage a permeant roof structures to resist torsional and bending loads. In order to combat this issue with the platform, 3rd party vendors such as Flyin’ Miata have developed multiple chassis brace implementations to reduce chassis flex and improve driving performance. In this writeup, I aim to validate Flyin’ Miata’s claims that their frame rails stiffen the chassis by 17%.
To simulate the chassis of the NA Miata, a uniform thickness shell element with the dimensions of the NA Miata wheelbase is used. The front wheels are translationally fixed and a moment couple is applied at each of the rear wheels of the model and the deflection is measured at each of the rear wheels as shown in figure 1.
Fig 1: Free Body Diagram of Chassis Torsion Test
The appropriate thickness steel plate is determined using equation 1 given chassis width and torsional rigidity from this website. The numbers for the NB2 Miata without the sport package is used as that is what Flyin’ Miata uses for their calculations.
The value for FT is then applied the FEA model on one edge of the chassis while the other two edges are fixed translationally, but not rotationally. By solving equation 2 with a value of 1 degree for theta, the desired deflection for a moment couple load of FT can be found.
On chassis that has the width of an NB2 Miata, this desired deflection is 14.619cm. This number was then used in the FEA simulation to determine the optimal thickness of the plate to simulate the chassis of a Miata.
The next variable is where this calculation becomes a little less scientific. In order to properly determine the effectiveness of the frame rails, the neutral bending axis of the chassis must be known. To determine this value, I used a measuring tape and guessed that the neutral bending axis was around 6 inches above the floor of the car. This is not particularly important as I am more interested in the methods of determination rather than the actual values. The most interesting part about this calculation, however, is that adding a hardtop to a Miata will increase the bending load and effectiveness of floor-mounted chassis bracing. This is because the hardtop will move the neutral bending axis of the Miata up, causing the frame rails to deal with more tensile and compressive stress. The same principle is responsible for the effectiveness of I beams relative to T beams.
To implement this chassis thickness, I made a shell thickness element in ABAQUS with the dimensions of the Miata wheelbase. I found varying sources on the internet claim that the torsional rigidity values are determined from the strut mounts and others that measured from the edge of the body itself. In this case, I will be assuming a uniform plate of material with the wheelbase and width of a Miata. The equations I used earlier will take this into account anyway. The plate was made to be about 20 inches thick, and a material modulus was experimentally applied until the chassis deformed the correct amount under the load from equation 1. This put the unbraced neutral bending axis around the door bushings on a Miata.
To create an FEA model of Flyin’ Miata’s V2 frame rails, a shell thickness extrusion that matched the given dimensions on Flyin’ Miata’s website was created. The shell element is given a thickness of 14 gauge, a Young’s modulus of 200 GPa, and a Poisson ratio of 0.29. Using the images on the website, I made guesses for the size of the triangular cuts in the frame rails. I had a hypothesis going into this simulation that the weight savings of the holes was not worth the lost chassis rigidity, but I will focus on that later in the write-up. The frame rails were placed on the chassis 78 cm apart and fixed to the chassis, locking relative translational and rotational movement.
The model was run in two separate scenarios. The first scenario is the traditional torsion rigidity test that can effectively be performed by putting the car on 4 jack stands and removing one of the corners. The second test is a bending test. These are not traditionally performed as physical tests due to the high difficulty of mounting a car to a wall in a cantilever fashion. The cantilever test can be seen in Figure 2.
Fig. 2: Cantilever Chassis Bending Analysis
After running the model, the simulated frame rails showed to increase torsional rigidity in the chassis by 13% and bending rigidity by 17%. These numbers are slightly lower than Flyin’ Miata’s 17.5% claim, but this is most likely a result FEA error and generalizations made about the chassis, such as modeling the chassis as a block with a homogenous cross-section. Now that the model is mostly complete, we can get to the fun stuff- redesigning the frame rails and seeing if any difference is made.
The first modification I made was to remove the weight reduction cuts in the rails. While I had assumed that this would make a sizeable difference, the simulation showed that removing the triangular holes increased the rigidity by just 0.3%. This difference is so minute that Flyin’ Miata is absolutely justified in their decision to make the cuts.
The next modification is to increase the thickness of stainless steel used in the frame rail. I ran 6 simulations with different steel thicknesses to produce the graph below showing percent stiffness increase over steel thickness in millimeters.
The results speak for themselves. Flyin’ Miata chose a thickness that comes close to perfectly optimizing for stiffness without greatly increasing material cost or weight.
After combing over the data, it becomes clear that Flyin’ Miata employs some really great mechanical engineers as every aspect of the frame rails that I can reasonably test are wisely chosen to optimize performance, weight, and cost. The most alarming part of the test, however, is still that the effectiveness of the frame rails increases with the addition of a hardtop, or high mounted bracing like a full cage.
In the future, I plan to test the butterfly brace in addition to the frame rails, but information on their dimensions is hard to find on the internet. Once I get a hold of a set of plans, I should be able to run the analysis relatively simply.
