"Teach a man to fish, and you will feed him for a lifetime" - English proverb
Project Summary:
The purpose of my project is to produce a realistic model for the calculation and assembly of a composite driveshaft. This project will specifically produce a mathematical and visual model, based on real world and experimentally based calculations, that is scalable to both current and future engine and vehicle specifications. In essence, the goal is to create a 'user's manual' on how to make driveshafts out of composite materials, so that future car team members will be able to produce lighter, stronger composite shafts.
I. Intro:
The main Formula SAE race in Detroit provides the motivation behind this project. Every year, Brown sends a team to compete against 140+ international universities and tech institutions. The rules limit engine type and power, and include many safety stipulations, therefore one of the main methods of improving your performance is to lose weight. The latter aspect is where this project comes in.
The composite driveshafts shall accomplish the following key goals
Lighter - The each shaft should be considerably lighter than its steel counterpart. This can be on the order of half the weight.
Cheaper - The ultimate assembly of the materials should cost less than our current $900/ea. steel shafts. This is possible because less work is done through expensive outsourcing. (ex - no annealing or heat treating)
Cooler - Another way to improve a team's score is to perform well in the static design competition, in which the design judges scrutinize your vehicle and assign a score based on engineering accuracy, innovation and optimization. Having any composite parts improves a team's score, and a composite engine or drivetrain component, like a driveshaft, sends the score soaring.
Background:
You can observe below what the car's rear bay looked like in 2007:
The two tubes extending between the differential(center) and the wheels are the half-shafts (a.k.a. driveshafts).
As you can clearly see, there is nothing but the half-shafts to transmit all the engine power and torque into the wheels. This segues into the next section...
II. Challenges:
Toughness(yield strength) - These shafts must be ablet to withstand a 100hp engine with a mechanical advantage. Each shaft must withstand roughly 700ft-lbs of force.
Stiffness - Every pascal of stiffness that the shaft loses in its design (beyond what is required not to break) introduces uncertainty and delay in the acceleration of the car. This must be minimized.
Systemization - The right fiber must be matched to the correct resin, which must fit the correct hardener, metal endlink, etc.
This will be like solving a system of equations, but in design form. The following diagram helps with visualization.
Environmental resistance - This composite shaft will be exposed to wind, rain, prolonged sunlight, and temperatures from 30-100 degrees F.
Repeatability - The repeatability of any characteristic resulting from this experiment must be assessed.
Design Complexity - Considering the design involves analyzing stresses on an anisotropic material with various constants and properties under various conditions, the time and effort involved may counteract the benefit of using the part. While this will not be a specific goal of this project, future designers must ask themselves if their time would be spent better designing other drivetrain components or training peers, etc
**An anisotropic material is one where the material strength is not uniform in all directions. In other words, pulling it from one direction is easier than pulling it from another direction.
III. Components:
The entire assembly will be composed of a shaft and two end-links.
The Shaft
image courtesy of: Rastogi, Naveen. "Design of Composite Driveshafts for Automotive Applications." SAE International. 3/8/04.
The Endlink
The purpose of the endlink will be to mate the composite shaft with a metal spline. The design has undergone several revisions, the most recent of which is the following picture.
End Link Model 1.
Real World Application
Note: In this picture the endlink is integrated into the steel shaft, and is not visible. You can, however, see the assembly into which the endlink design has to fit.
IV. Testing:
Current data on this project's carbon shaft testing can be found here. Objects of note are the ultimate yielding torque of each lamination, as well as the calculated shear modulus at the bottom of the data table.
Objectives
Twist -- In order to be able to prevent, and even cancel out, torque steer**, it becomes necessary to test the twisting characteristics of the carbon fiber tube under torsional loads. The object here is to produce a model that is able to predict the angle of twist as the applied torque and the shaft dimensions vary.
Shear Modulus -- While many of the mathematical methods used in these calculations are based on isotropic models, it might be interesting to see how they can apply to analysis of anisotropic materials.
Approximate Shear Strength -- It is important to know just how much can be expected from the half-shafts, based on several predetermined design inputs like # of plies.
Fabrication Methods -- Small differences in fabrication were noted during testing to document which techniques were effective, and which mistake could lead to critical weaknesses in the part.
Familiarity -- While the physical data is very important, there is an immeasurable benefit to understanding how the material works under the conditions of fabrication. The future car team student needs to understand which sounds and visual indicators are harmless, and which of those should not be ignored.
**Torque steer is the phenomenon where the engine transfers more power through one driveshaft than it does through the other, causing the car to steer in the direction opposite the side with the greater power application.
Assembly - The first testing prototype
The first attempt at fabricating a test-ready tube was not successful for a few reasons.
The tube was not properly mounted in a curing position. As a result, the tube to be used for testing was contaminated with the cardboard flooring. The solution to this was to use a plastic film covering on the fabrication table that would not bond to epoxy. Also, as you will see in later pictures, the carbon fiber was mounted on tubes such that it would not contact any outer surface while curing.
A secondary reason that the first testing prototype did not work was due to the end links. They were designed to fit in a collet-styled grip in a torsional testing machine. When this machine turned out to be unavailable, the tube was rendered useless. The solution to this was to devise a testing method that did not require external testing machinery.
The contamination of the tube is clearly visible along the tube. (above)
Assembly - The Second Testing Prototype
Materials
The materials used during testing were available in Prince Lab, and in the FSAE team garage in the basement. Aside from basic hand tools and measuring devices, the following objects are vital to testing under this model.
Lever Bar to Apply Torsional Load
Vise
Laser Pointer
Tape
Weight
4' Section thin rope
pvc pipe
testing sample of CF tube with T-section endlinks (see below)
Left: Vise grip end of the testing assembly. The laser pointer is necessary to measure the minute changes in angle of such a stiff material. Note how the laser pointer is connected directly to the endlink, negating the effect of bending the lever bar.
Right: Here you can see the assembly with a 5' aluminum lever bar attached.
The bar is marked with measured tick marks, which were used to reference the position of the attached weight. (Below)
The Testing Samples
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The above testing samples were built using 1" diameter, welded t-sections of 0.035" 4130 Steel tubing. This material was chosen for availability and cost for the purposes of testing. The mold for the carbon layup was a tubular section of PVC pipe machined down for a press fit into the steel tubing. The carbon fiber would then be laid up over the whole setup.
Results
Success! As shown below, the material characteristics are predictable and repeatable. Furthermore, even the testing shafts were shown to have remarkable torsional load capacities. Finally, all these results were obtained without expensive curing ovens for the epoxy, or weaving facilities for the fiber.
Bonding Strength - The epoxy used in testing was not known to bond well to steel. On two of the five testing samples, the shaft failed at a point other than at the endlink surface. This is very promising, as it suggests that the bonding strengths needed to hold the large shear forces can be achieved, potentially, without the use of an expensive curing oven.
As you can see on the left, the failure of the shaft was along the small diameter tubing, not on the endlink bond, or at the adjacent knuckle.
Failure Patterns
Below: Bond Failue Pattern
The various carbon tubes failed in specific and repeatable patterns.
Bond Yielding - The most expected (but not always observed) yielding pattern was for the epoxy-to-steel bond to fail in shear.
With this failure pattern it was observed in three cases that the bond failed at the very end of the tube. The bond most commonly broke in two places, and the second breaking point was always diagonal from the first breaking point.
Main tube yielding - Conventional literature states that the failure method for a composite starts at the filament level. Ideally speaking, a single filament breaks, and the adjacent filaments must shoulder a greater burden. As you approach the yielding stress, this set of events occurs all over the composite, and eventually the adjacent fibers also break. What follows is a propagating tear which destroys the composite assembly.
What was observed during testing matched the theory above. The tearing started at a point, and propagated along two fiber seams such that the final yielding pattern approached the shape of a triangle, whose point was oriented along the axis of the tube.
What was also observed was that in this failure method, there was a great degree of warning before catastrophic failure. As the load was applied to the tube, intermittent cracking was audible. This cracking continued periodically and, if left for long enough, led to the tube breaking. Because the tube is strongest while all the fibers are intact, what this phenomenon suggests is that one the cracking starts, the tube has already past it's load limit. In other words, it is only a matter of time until the tube breaks, using the same load.
Below: Main tube yielding failure pattern
Physical Results
The graph to the left relates the reported yield stress as a function of the number of layers, or plies, in the material. The plies were calculated using the length of carbon fiber cut, divided by the circumference of the small PVC mold tube.
As you can see from this graph, the measured yield stress remains above the trend line beyond 3 plies, and remains level and predictable beyond 4. What this suggests is that the results are repeatable and regular, using the hand layup methods in this model.
In the interpretation of the graphical results, it must also be noted that the fabrication method for the final three shafts (plies 4, 5 and 6), was different that for the first two. These differences, which will be detailed in the fabrication lessons section, might account for the fluctuation in yield stress.
The graph to the right relates three parameters: the decimal number of plies, the angle of twist (in radians), and the Applied torque.What this graph shows is a predictable connection between the angle of twist and the number of plies.
By adding more testing sample results in the same manner as was done here, one could produce a 3D plot that more precisely models the twisting properties of the composite tube, making it far easier to design a set of torque-balanced half-shafts. In the fabrication phase, any car team member with knowledge of the vehicles torque steer characteristics could simply look on the chart and see which shaft variations will transmit a certain torque relative to the others.
V. Fabrication tips
In this section, several fabrication tips specific to composite tubes will be detailed. This will not include general layup tips, such as proper surface preparation or curing instructions, which can be found in nearly every composite book out there.
Take your time! It is very difficult to unattach even un-gelled carbon and epoxy without weakening the fabric. The less you move the material around, the better.
The fiber sheet has a very visible sort of poisson's behavior. If you stretch one direction, the other axis will shrink, and vice versa. In pre-fabrication, you must be careful to measure out the fabric without stretching or skewing it.
Once the fabric is on the tube, this property can be quite helpful. It will shrink radially when stretched axially, and as such the fabric itself can be used to squeeze out excess epoxy.
In the future it might be helpful to use carbon fiber sleeving instead of flat fabric. The load transfer of the carbon fiber tube happens as each filament, oriented along the principle loading direction, undergoes tension. If the filament does not reach completely from one side of the tube to the other, then the load transfer onto that filament is determined by the physical properties of the epoxy matrix that surrounds the fiber. By using carbon fiber sleeving whose fibers are already oriented at 45 degrees, each filament will be long enough to bond directly to either side of the tube.
Cost Report
Total Material Cost w/ shipping & taxes: $142.75
Total Machining Time: 275 minutes
Total Welding Time: 100 minutes
Detailed Breakdown
Materials
50”x36” CF Fabric: $60
Epoxy Resin: $40
Epoxy Hardener: $20
Other Epoxy tools: $12
Steel Tube, PVC, Aluminum Bar: free! (Trash and reusable scrap)
Note: In this picture the endlink is integrated into the steel shaft, and is not visible. You can, however, see the assembly into which the endlink design has to fit.
The graph to the left relates the reported yield stress as a function of the number of layers, or plies, in the material. The plies were calculated using the length of carbon fiber cut, divided by the circumference of the small PVC mold tube.
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