After playing around with various kinds of hole cutters, mills, angle vises, and so on, I’ve settled on the best method for cutting fishmouths in tube ends so they fit together properly when building a tube frame with round tubing. Since the tubes will be welded they don’t have to be perfect as you would get by using a milling machine. Also, the typical joint has several tubes meeting which need to accomodate each other, and on a milling machine this would take a separate setup for each tube at each joint, taking an inordinate amount of time. Forcing Solidworks to show the correct shape of the ends of each tube requires some real work, an explanation of which I found over on the LoCost website. I’m going to provide a modified and updated tutorial here.
The first thing to understand is that each tube must be fully welded before adding the next tube. This makes the finished structure much stronger than if you tacked all the tubes in place and simply welded around the remaining visible joints. Here’s an example:
Although the following tutorial may look long and complicated, once you understand what’s going on each step will only take seconds. And believe me, it’s much faster than grinding a tube to fit using trial and error. More accurate, too.
It’s time to finalize my parts order, which means I have to pick all the rod ends and spherical bearings for the suspension. Up to now I’ve relied on rules of thumb, which isn’t good enough for a state-of-the-art race car. So I simply opened up one of my higher-level chassis models in Solidworks, one with most of the suspension attached, and created a 3D sketch of the upper and lower left front suspension A-arms, constraining the endpoints of the lines to the centers of the rod ends and spherical bearings. Then another line to simulate the upright and tire, and I’m done with the sketch. Then I created a structural member along each line and opened a static simulation study. In the study I constrained the inboard ends of the A-arms to zero translation and applied a 1400 pound load toward the rear of the car to simulate 4-G braking. Run the study, and voila! axial loads on each member.
Upper Front: 785 pounds
Upper Rear: 1211 pounds
Lower Front: 2639 pounds
Lower Rear: 3096 pounds
This allows me settle on 1/4″ rod ends for the inner upper attachments, 3/8″ for the inner lowers, a 7/16″ spherical bearing for the upper ball joint, and a 5/8″ one for the lower ball joint. All chrome moly alloy. Even these are far stronger than indicated necessary by this analysis, but I don’t want to deviate too far from standard practice on this design. Maybe transitory loads can be far higher?
Calculating the Loads, Round II
At the urging of a poster on ApexSpeed.com who insisted my calculations were inaccurate due to the non-zero joint stiffnesses, I re-ran the analysis with the suspension a-arms modeled as trusses. A truss model allows only axial loads on a member, using hinges at both ends to zero the moments. This gave me results that were the same +/- 2%, which makes no difference given the uncertainty in estimating the operating loads.
However, I also refined my model to include the suspension pushrod and that did indeed give me a different result. With the pushrod in place I could model the vertical load due to the weight of the car and the aerodynamic downforce. I’m now working with a braking force of 1600 pounds and a vertical load of 1230 pounds, which assumes a coefficient of friction of 1.3 for the tire on the surface of the track. This gives me the following axial forces:
Upper Front: 1103 pounds
Upper Rear: 1258
Lower Front: 4432
Lower Rear: 2366
Note that including the vertical load and increasing the braking load shifted the most highly-loaded member from the lower rear to the lower front, and increased the maximum load from 3096 to 4432 pounds, or 43%. The chrome-moly 3/8″ rod ends I’ve specified for the lower a-arm inboard joints still have a safety factor of 2.14 under these conditions. The posters on ApexSpeed have strongly warned me against using 1/4″ rod ends in the suspension, so existing inventory will be used in a different application and the upper rod ends will be upgraded to 8mm. It appears that only metric rod ends are available locally. Under these assumptions the pushrod rod ends will have to be further upgraded to 10mm, although I hate to have a whole separate part for just the pushrods, so I’ll have to re-examine the assumptions.
Now it’s time to test one of the big unknowns of this project: can the top rails be formed in the shape of a complex 3D spline, and can the left and right sides be made to match? The CAD software won’t even allow a structural member in the shape of a spline, requiring them to be composed of straight sections and arc sections. Other exoskeleton cars have been built, but as far as I know always with a single curve in the main frame members. And of course a tubing bender is designed with the assumption that it will be used to form constant-radius segments. I believe this is the first car to be done this way, so I’ve put a lot of effort into the chassis jigs to get it right. The top rail spline is a key to the beauty of this design. To make a long story short, it is in fact possible to bend a 3D spline on a tubing bender. It just takes a lot of trial and error, patience, and about a day of work per rail. And luckily, overbending can be corrected by running the tube back through the bender, clocked 180 degrees.
“The pricking of my thumbs” is not entirely rhetorical. In fact I almost cut off my left thumb while building the top rails, so a word about safety. A tubing bender is a SERIOUS PIECE OF EQUIPMENT. It won’t even notice bones and flesh being fed into its’ rollers. I had already turned off the bender and reached to grab the tube as it was twisting on the way into the bender. The bender caught my glove and started pulling my thumb in, stopping at the last possible millisecond before inflicting permanent damage. It hurt and left a mark, but I was insanely lucky. So, 1.) Never wear gloves while using a tube bender. They protect you about as much as Saran Wrap, and it’s better to have your fleshy appendages dangling about unprotected to remind you of the danger. 2.) NEVER, NEVER touch the tube on the side being fed into the bender. Always handle the side being fed out. and 3.) Before pushing the “on” switch, stop, think, and say to yourself “I’m not going to become an amputee on this bend.”
To get optimal suspension geometry and aerodynamics I’ve designed the car with a front keel under a raised nose. This gives the longest possible lower front A-arms, minimizing the angle changes of the front suspension as it goes through bump and jounce motions. The raised nose clear airflow around the front wing. My computational fluid dynamics (CFD) studies show airflow around the front wing is extremely important as the wing operates in ground effect and generates downforce all out of proportion to its size. I spent a considerable amount of time trying to increase the downforce generated by the underbody and rear wing to match that of the front wing, even though those elements are far larger.
The front keel will use a stressed skin of aluminum formed to shape and riveted to tabs welded onto the frame tubes. This is the highest-stress area of the entire chassis, as under braking something like 2800 pounds of force will be transmitted through these members. You can visualize the car supported vertically on the front keel, with two more cars stacked on top of it, so this needs to be really strong.
After more than a year and a half of design and several months of tool preparation, that long-awaited day has finally arrived: the day I touch saw to metal on an actual car part. The first step is to build the front subframe that sell sit horizontally at the bottom of the nose of the car. The chassis table already has holes drilled and tapped for 3/8″ bolts locating the subframe members precisely. Here’s the first tube in place among the pins on the chassis table.