List of Figures
1) Side View of Fairing with Drag Force Acting the Nose
2) Fairing Modeled as ‘I’ beam
3) Compute Total Moment
4) Section of ‘I’ Beam
5) Sandwich Structure
6) Hexagonal Honeycomb
7) Laminate vs. Sandwich Weight Trade Off
8) Mounting Plate
9) Bolt in Wet Composite
10) Butt Joint at the Parting Plane
11) Using a Joggle Joint for a Door Seam
12)HPV 2000 Mounting Locations
13)Cross-section of Bonding Mounting Plate under Front Axles, Post-Process.
14)Attachment at Rider’s Hip
List of Equations
1)Total Drag Resultant Force
2)Calculate Total Moment About Cg
3)Flexural Stress equation
4)Moment of Inertia for an I beam
5)Shear Stress
6)Simplification of Q
7)Deflection of a Simply Supported Beam with a Uniformly Distributed Load
8)Volume Fraction
9)Weight of Resin
Abstract
This paper describes the methodology for optimizing the weight of a fairing for a human powered vehicle. Considerations include using a laminate vs. a sandwich structure, using proper resin amounts, mounting hardware, minimizing amount of stiffeners used in the lay up process, and the utilization of existing reinforcements at the seams to mount points. The first step in this process, however, is a load analysis that considers aerodynamic forces acting on the fairing and impact loads experienced by the fairing due to the bike hitting bumps or running into a curb.
Introduction
This is Colorado State University’s third year participating in the Human Powered Vehicle competition. Since CSU has been involved, there has yet to be seen a technical contribution regarding a weight optimization of an HPV fairing that is not structural in nature. The importance of this technical reference is to lay the groundwork of things to consider when designing a fairing such as this.
Structural analysis should include all of the existing loads acting on the fairing, as well as loads that will be applied in an unpredictable situation (such as hitting a curb). It is imperative that all the possible loads that could act on the fairing are known or estimated as a worst case scenario. The worst case scenario is desired because it will act as a built-in safety factor for all of the structural calculations. Materials to build the fairing can then be chosen which will optimize the weight while still supporting the loads found in the analysis.
Fiber reinforced composites are not isotropic; the do not exhibit the same properties in all directions. The maximum loads are carried best in tension. Carbon and glass fibers are capable of carrying loads in compression, while kevlar is not a good choice for this application.
One main advantage of using composites is the ability to achieve extremely high mechanical properties in very thin sections of material, but thin sections are also more susceptible to buckling than thicker sections. To prevent buckling, a sandwich structure is recommended, which separates the face sheets of fibers to increases the overall stiffness of the structure. This increase in stiffness also makes sandwich structures an applicable solution in bending.
In composite materials, it is not the epoxy that carries the load; it is the fibers. Epoxy is less dense than fiber and displays much lower mechanical properties. The epoxy is designed to transfer loads between the fibers, therefore has very good shear strength, not tensile strength.
Composites are able to carry localized loads, but these loads must be determined before the construction process begins. There are many ways to accommodate for concentrated load areas. Microsphere glass fillers can be used to increase local compressive properties, extra layers of fabric can be applied locally, or higher density cores can be added in the high load areas.
Goal of Fairing Composite Team
Our primary goal is to optimize the weight of the fairing while at the same time having it structurally sound given the loads that will be present. The 2000 HPV fairing is not structural in nature, meaning it does not have to support any loads besides it’s own weight and outside forces that act on the fairing either directly or through the chassis. The outside forces due to aerodynamics are skin friction drag and lift. The forces acting on the fairing through the chassis are impact loads due to hitting bumps or potholes, etc.
How to Achieve this Goal
To minimize the weight of the fairing, a structural analysis should be done. This will provide the requirements for the strength and stiffness that the fairing needs to display which will, in turn, dictate what materials to use. Given the forces acting on the fairing, it will be possible determine the stress on the fairing, the shear stress between the laminate faces and the core, and the deflection of the fairing. The deflection of the fairing will dictate what stiffness of composite is required to minimize that deflection.
Analysis
Stress/strength design
The design of a composite part can be strength limited or stiffness limited. For example, composite pressure vessels are designed with strength in mind where as airplane wing skins are limited by their stiffness. The loads on the 2000 HPV fairing are quite low and the shape is near that of an airfoil, therefore it is stiffness limited design. That is not to say that both types of analysis are not needed, but with such low loads, the fairing would first fail due to lack of stiffness, not lack of strength.
Forces acting on Fairing
In order to minimize the weight of the fairing, it is crucial that the least amount of material is used. Since the fairing is not structural in nature, it should only require a minimal amount of material. To utilize a minimum amount of material to construct the fairing, a knowledge what forces are acting on the fairing is necessary. An analysis using the worst case scenario is desired because it will have a built in factor of safety. Unlike the 1998-1999 CSU monocoque, “Faith in the Fiber”, the 2000 HPV fairing does not have any torsional loads acting on it, therefore the analysis is not as complex. A complete guide to finding the loads on a monocoque fairing can be found in the 1998-99 Human Powered Vehicle Monocoque Chassis Team’s report, “Faith in the Fiber” Appendix A.
Since the chassis and the fairing are two separate entities, the only forces that act on the fairing are as follows:
- Aerodynamic forces such as drag and negative lift
- “Impact” forces due to riding over bumps which will act at points where the fairing is mounted to the chassis and will be modeled as 3G
- The weight of the fairing
The aerodynamic force acting on the 2000 fairing is the total drag force. This force has two components: skin friction drag and lift. The skin friction drag acts as a distributed pressure load over the entire length of the fairing. The lift is due to the airflow around the specific shape of the 2000 fairing and is a downward force that acts at the center of pressure. Because a worst case scenario is desired, these forces will be modeled as acting at the nose of the fairing which will cause a maximum moment about the center of gravity (see figure 1).
Figure 1: Side View of Fairing with Drag Force Acting the Nose
The forces on the fairing due to the bike hitting bumps will be referred to as “impact” loads. This impact load is not what would normally considered impact because two objects are not colliding with one another. Rather, it is the impact the fairing will feel at the mounting positions when the bike is ridden over bumps. After a consultation with Dr. Radford, a conservative estimate of three times the weight of the fairing is used for this force.
Analysis of Forces
The fairing will be modeled as an ‘I’ beam. This approximation is possible due the stiffeners that will be added to the fairing around the perimeter of the parting plane (right and left halves). A side view of the fairing is shown below. From the side view it can be seen that the fairing with stiffeners can be modeled as ‘I’ beam.
Figure2: Fairing Modeled as ‘I’ beam
This approximation will greatly simplify the structural analysis. Analyzing the actual shape of the fairing would make the analysis much more complex without adding much insight.
From CFD analysis of the fairing, the total drag force on the fairing was found. At the worst case, the horizontal component of the total drag force (the skin friction drag) was found to be 4.72 lbs.
The vertical component (lift) was found to be –1.97 lbs. and acts downward (See figure A and B at end of report). However, this lift is calculated for the fairing in free space. Ground effects could increase the negative lift by as much as 38 lbs., therefore a value –40 lbs. will be used in the analysis. The resultant total drag force on the fairing is 40.05 lbs.
Equation 1: Total Drag Resultant Force
This resultant force of total drag will be modeled to act at the nose of the fairing and will exert a maximum moment about the center of mass. The total moment about the center of gravity is the total drag force multiplied by the perpendicular distance to the center of gravity of the fairing.
Assuming that the fairing is 132 inches long (2000 fairing), the center of gravity will be 66 inches from the nose of the fairing. From the two components of the drag force, the angle of the force can be found so that the perpendicular distance (d) to the center of gravity can computed.
Figure 3: Compute Total Moment
Equation 2: Calculate Total Moment about Cg
Once the total moment is calculated from the total drag force, the stress due to bending can be found at the most critical locations on the fairing by the following equation.
Equation 3: Flexural Stress equation
M is the moment computed from the total drag force. I is the moment of inertia for an ‘I’ beam. To calculate the moment of inertia for an I beam, the parallel axis theorem must be used. As suggested in the “Faith in the fiber” report, the moment if inertia will be left in cubic inches. The equation for stress is then non-dimensionalized for any size shell as long as an initial shell thickness of 1 inch is used. The stress will then give units of psi*in, which can pertain to any thickness of shell by dividing the outcome by the desired thickness.
Figure 4: Section of ‘I’ Beam
Equation 4: Moment of Inertia for an I beam
The shear stress between the core material and the face sheets of the composite can also be calculated by the following equation.
Equation 5: Shear Stress
Where the shear force (V) is found from a shear moment diagram from the ‘I’ beam model. The forces on this beam, in addition to the moment due to the drag force, will be the forces acting on the fairing at the various mounting positions to stop rotation. Q for this cross section can be simplified to:
Equation 6: Simplification of Q
Where C is the distance form the neutral axis of the ‘I’ beam (x in Figure 4) to the outer edge of the beam, and y is the distance from the neutral axis to the shear section of concern (between the core and the face sheet for this case).
Weight Reduction Using a Sandwich Structure
Using a sandwich structure in composite materials may help reduce the overall weight of a part. A sandwich structure is a composite structure that has some kind of core like foam or honeycomb between top and bottom face sheets of fabric. Because the core separates the face sheets by the distance of its thickness (thus increasing the moment of inertia) it adds stiffness to the part while being extremely lightweight depending on the density of core used. As the thickness of core increases, the density of core used will also have to increase to maintain the same shear properties; larger moment of inertia will require larger shear strengths. The figure below from Andrew Marshall’s Composite Basics gives a good example of how using a core can drastically increase the stiffness and strength while adding very little weight to the structure. This example considers an aluminum skin sheet with stiffness, strength and weight having a relative value of one.
Figure5: Sandwich Structure [2]
There are many core materials that can be used for composite structures. There are many different types of core material that can be used to make a sandwich structure, but for the purpose of manufacturing a fairing the choices will be limited. The core material is designed to resist shear loads. The core increases the overall stiffness of the material by separating the facings, but also gives continuous support to the facings. This shear strength adds to the face sheets, which are designed to carry tensile or compressive loads.
“Analysis of Flat Rectangular Sandwich Beams” has been put into Excel. This program will allow the user to enter in thickness of the core and face sheets and the physical properties of the possible materials to use. This spreadsheet will compute centroid distance, the bending stress in the facings, the core shear stress, the beam deflection, face dimpling, face wrinkling, and panel stiffness. The highlighted values are ones that would be entered in by the user. Units for this program must be consistent because there is no conversion built in.
Foam Cores
Foam cores are widely used because they are reasonably priced and easy to work with. There are many different families of foam cores, each displaying different mechanical and physical properties as well as working and handling characteristics. There may also be great differences between low and high density foams of the same family. In order to minimize the weight of a composite structure, the core chosen should be the least dense possible while displaying the required mechanical properties for the application for which it is desired.
The first family of foams is polystyrene foam. The material usually used in this family is Styrofoam, originally produced by Dow Chemical Co. Styrofoam is usually a light blue color, and is “quite uniform and reliable in a 2 lb/ft3 density”. [2]
Polyurethane foam is another family that can be used for core materials. This family has a very wide range of densities (2.5-100 lb/ft3), chemical versions, and can be both rigid and flexible. Typical problems with polyurethane foam include brittleness, variable density within a single piece, and possible internal cracks. Some suppliers offer very low-density polyurethane foams, down to 1 or 2 lb/ft3, however, the material at these low densities for this particular material become extremely fragile. Therefor, densities under 4 lb/ft3 should be considered unreliable [2].
Polyvinyl chloride foams (PVC) are of the same chemical family as garbage bags, plastic pipe and plastic films. The most commonly used structural foams from this family are Klegecell and Divinycell. There is a third called Airex, but it is not as common as these other two types. It is more suited for applications like heavier boat hull structures, so would probably never be used for lightweight applications. Klegecell and Divinycell, on the other hand, make very good lightweight structural cores. They have a fairly large cell size compared to other structural cores so are not as sensitive to the type of solvents used as the urethanes. [2] For these two foams, densities down to 2.5 lb/ft3 are available, and the properties are maintained even at this lower density.
Ploymethacrylimide foams are known as a very high performance material called “Rohacell”, characterized by a luminous white color. Rohacell is available in densities as low as 1.9 lb/ft3, has a very fine cell size and is extremely uniform. The mechanical properties of Rohacell surpass those of urethanes and PVC foam at any density. [2] Rohacell will expand during cure at temperatures at or above 350F, which allows for a tight fit between facings and the core. The cost of this particular foam is higher than most other foams, so is generally used in the most weight sensitive applications that are more critical than a Human Powered Vehicle.
Syntactic foam is a type of foam that is made by mixing micro balloons, ceramic spheres or some other kind of lightweight aggregate with resin. Using this mixture gives a density after cure that is the same as the density of the mixture before the resin cure. Most other foams will expand slightly during cure which results in a lower density. Syntactic foam is usually mixed with resin until it has a “peanut butter” constancy or thicker, and displays a very high compressive strength.
The lighter densities of the foams mentioned above (below 6 lb/ft3) are considered to be structural foam. The heavier densities (above 6 lb/ft3) are considered to be tooling foam. The difference is simple. Structural foam would be used as potential core material for sandwich structure, or could also be used at any openings or seams in the final composite part to add stiffness in those areas. Tool foam is too heavy to be used for core material, so is mainly used to make plugs. To make the 2000 HPV plugs, a combination of 15 and 18 lb/ft3 urethane foam was used. The foam was glued together in layers and then machined into the final shape of the fairing.
Honeycomb Core
Similar to foam, there are many different families of honeycombs with different properties. There are variations in the material ranging from material type, cell size, cell shape, as well as densities. For more information is needed on honeycomb cores, a complete guide can be found in Andrew Marshal’s Composite Basics.
There are countless variations is cell shape for honeycomb core, so common variations of the hexagonal honeycomb will be the focus for the 2000 HPV needs. A complete guide to these shapes is found in the Appendix A.