©Hal Gurgenci 2003
FUNCTION OF THE CAR STRUCTURE
The structure is the framework to which everything is attached in the vehicle. In a modern vehicle, it is expected to fulfill the following functions:
While fulfilling these functions, the modern car structure should be light enough to reduce inertia and offer satisfactory performance and tough enough to resist fatigue loads that are produced due to the interaction between the driver, the engine and the power transmission, and the road.
The structural form has changed substantially since the early days of the automotive era. Probably the most striking change is the disapperance of the chassis. The first "horseless carriages" were built on a clearly visible and identifiable chassis frame. Today chassis, as a robust horizontal box frame usually in the shape of an H, has been designed out of almost all cars. If you are wondering what a chassis is look under a truck and compare it with what is supporting your automobile. None of the current car models come with a chassis. Each element on the body is a load-carrying member in modern cars. This referred to as a shell-type design also called as a integral, unitary, chassisles, monocoque (reflecting the French origin of this design approach) or "stressed-skin" approaches. On the other hand, trucks would still have their solid chassis frames. On the left below is a 4WD chassis (Mitsubishi Pajero):
Mitsubishi Pajero Chassis
The F-SAE car design by the UQ team (2001)
Having said this, it would probably be easier for you to use a chassis to provide structural strength as opposed to a monocoque design. Use tubular hollow sections to keep the weight down. This was the approach adopted by the University of Queensland team in 2001. Their design is shown on the right. The body does not have a significant structural purpose in this design and the strength and rigidity are provided by the tubular frame.
STARTING YOUR DESIGN
THE STRUCTURAL LAY-OUT
The strength and the rigidity of your structure will be provided by major transverse members or "bulkheads". You will probably have one on each wheel axle and more in between as you see fit. Your racing car may, for example, a three-chamber topology as suggested by my poor chassis design attempt on the left. On the right is a chassis design copied from the Mitsubishi web page, where other components and their mountings can also be seen. This is an experimental vehicle that is equipped with an all-wheel active control system.
Detailed designs of the mounings on the bulkheads and longerons (structural members oriented along the length of the car) are important. The "bulkheads" may be real plate bulkheads as in the ship structures or they can be triangulated frame sections. In either case, you must provide sufficient clearance if the driver's body is supposed to go through the bulkhead, eg between the central and rear bays in the above figure on the left.
The above figures are given to demonstrate the concept of the bulkheads. In your design, try to use triangulated frames rather than rectangular box structures. The difference is given by the following two figures:
The triangulated structure on the left can be analysed as a pin-jointed structure even when the members are welded together. On the other hand, the joints in the rectangular structure on the right will carry bending moments.
The chassis has to be stiff enough to be safely ignored when you are doing your suspension calculations. A flexible chassis would result in a car, that is
The chassis is typically designed for stiffness rather than strength. Your chassis design would have to be trade-off between stiffness and weight. You obviously would not want to increase the mass of the chassis beyond what is necesary.
Use the following stiffness specifications :
Bending deflections at mid-span : Less than 2 mm under static loads
Torsional stiffness : More than 5000 N-m/degree (Milliken & Milliken, Race Car Vehicle Dynamics)
The torsional stiffness is more important for handling properties. The purpose of torsional stiffness is to allow the lateral loads to be distributed from from front to rear in proportion to the suspension roll stiffnesses. The torsional stiffness is usually expresses in terms of the twist produced under torsion as shown in the following figure. This figure shows the twist in a rectangular chassis frame. The deflections are exaggerated to demonstrate the twist action.
Monocoque designs typically provide the highest torisonal stiffness. In a frame-based design, you may want to use the following to increase the torsional stiffness of the chassis:
You may consider using the engine as part of your structure. You have to make sure that the loads are not high enough to distort the engine block. This may be difficult to assess in your case since most of you do not have adequate information in the structural properties of the engine block.
The easiest way of assessing the strength and stiffness of your chosen design configuration is through finite-element analysis. I am expecting that this is what you will do. Use beam elements in your finite-element model and generate the following information
In order to carry out the above analysis, you should know the following:
Let us now try to address these issues.
In any complicated design like this that is subject to multi-modal loading, you should first generate a load case table. This table should cover all significant modes of loading for this application. For some industrial machinery, there are relevant standards that specify the load cases that need to be considered for the design of a given class of machinery, eg cranes or pressure vessels.
Static Load Cases
In this instance, I suggest you assess the static strength of your frame against the five primary and two combination load cases defined in the following table.
|No||Load case title||Description||Safety Factor|
|1||Bending||Static weight of the components on a flat road||3|
|2||Torsion 1||One of the front wheels is off the road||3|
|3||Torsion 2||One of the rear wheels is off the road||3|
|4||Lateral||Car cornering a 50-m radius bend at 100 km/h||3|
|5||Longitudinal||Straight Line Braking at maximum deceleration||3|
|6||Bending + Torsion 1 + Lateral + Longitudinal||While cornering & braking we hit a bump and one front wheel lifts off||3|
|7||Bending + Torsion 2 + Lateral + Longitudinal||While cornering & braking we hit a bump and one front wheel lifts off||3|
Fatigue Load Cases
When you are designing in real cars, the determination of dynamic loads for fatigue strength assessment is usually done by multi-axial testing in the laboratory and by instrumenting the prototypes on different road surfaces.
For this project, I suggest that you base your fatigue design on the stresses produced while the car is travelling on a straight line over a road surface which characterised by the following roughness profile:
where x represents the distance along the road and h is the roughness as seen in the following chart:
Base your calculations on the assumption that the car travels
Note that the above road profile is uni-directional, ie all undulations are in the travel path. Therefore, it is probably a good assumption that the road interaction will not introduce any unequal dynamic forces betwen the two sides of the cars. However, the load sharing between front and rear wheels will unequal as the car is traveling over these peaks and troughs.
For the purpose of this exercise, the following procedure shall be used to estimate the stresses on the structure under this loading scenario:
1. First treat the sprung mass as one rigid mass distributed over the four wheels, which are travelling on the road described by the above profile and calculate the loads that are generated in the suspensions as a result of this travel. In the following figure, m is the total mass and k is the total suspension stiffness.
2. Since the loading (the road profile) is sinusoidal, these loads will also have a sinusoidal structure. Model is as a dynamic system and generate the maximum and minimum loads on the chassis (the lumped mass in the model).
3. Applying these loads onto your structure, generate the stress ranges applying on your structure
4. Apply Miner's rule to calculate the effective stress
The fatigue load cases are then given as follows:
|8||Fatigue Load Case #1 - Vertical||+/- a where a is the vertical acceleration due to vibrations (see below)||n.a.|
|9||Fatigue Load Case #2 - Lateral||+/- 0.5a||n.a.|
|10||Combination Fatigue Load Case||Load Case 8 + Load Case 9||n.a.|
This table will be constructed for both design speeds given above and the two results will be combined into an effective stres range using Miner's rule.
Use Section 11 of the Australian Structural Design Code. This section applied to fatigue strength assessment of welded structures. The Section is included in the compilation entitled "SAA HB6 - 1999 : Design Standards for Mechanical Engineers".
Your summarised results in the report should include
The following is a numerical example that shows the fatigue strength assessment of a welded structure according to the Australian standard, SAA HB6 - 1999. This is the Standard that replaced AS4100 in 1999. The main application area considered in this standard is the design of stationary civil engineering structures such as bridges and building structures. It is also intended for application to cranes.
A more relevant standard for the fatigue strength assessment of a car chassis is AS3990, the intended application areas of which include design, fabrication, erection, repair and alteration of steelwork associated with boilers and pressure vessels, lifts, cranes, mining equipment, gas and liquid petroleum piping systems, bulk handling equipment and the like, in accordance with the working stress design method.
I chose SAA HB6 because it was included in the SAA Compilation entitled "Design Standards for Mechanical Engineers". I thought this would make it more accessible compared to online access to AS3990 from a library computer. I also would like to encourage you to acquire a personal copy of this compilation. It is a useful document for a Mechanical Engineer.
Both SAAHB6 and AS3990 state that they do not apply to structures with steel elements less thn 3 mm thick, with the exception of sections complying with AS1163 and packers. The AS1163 tables includes sections less than 3-mm thick. For your design, you should pick an AS1163-compliant section.
EXAMPLE - Constant Amplitude Loading
The structure shown on the left is a structural joint found in a mining machine. Strain gauges are placed around this joint to determine stresses that are experienced by the joint during normal operation. The measured stresses are found to be oriented along the axis of the connecting member as shown. A typical stress trace is plotted on the right.
Please note that the section sizes in the figures were selected to demonstrate certain points about the use of SAA HB6. The stresses are real measurements recorded in one of our projects but the amplitudes were scaled down for this example.
A welded joint
Stresses measured on the welded joint
This operation corresponds to a mining cycle (e.g. spot, dig, lift, swing, dump, and return) that takes 40-45 seconds to complete. The cycle duration is clearly visible from the stress traces. The stress amplitudes and the cycle durations vary slightly but for the purpose of this exercise let us assume the following values:
Stress Range = smax - smin=35 MPa
Cycle duration = 40 seconds
The steel is Grade 350 structural steel with a yield strength of sy = 350 MPa.
Estimate the fatigue life for this joint in hours according to the standard SAA HB6. The welds are full-penetration butt welds.
The wall thickness for the lacing is 2.6 mm. This is less than 3 mm, which is the limit specified in the SAA HB6 1.1.1. If you check AS1163, you will see that this is a standard section. At this point, you have to contact the steel supplier to get it confirmed that this section does comply with AS1163. Let us assume that this is done and we get the confirmation. SAA HB6 covers those sections that comply with AS1163, even if their wall thicknesses are less than 3 mm. So we proceed.
In the standard reference is made to the "design stress". This is the stress against which the joint strength is checked. In this example, the maximum design stress (in absolute value) is -35 MPa and the design stress range is f* = 35 MPa (it is equal to the maximum stress because the minimum stress is zero).
11.1.5 Weld Category
Finding the right weld category is a problem. SAA HB6 lists welded detail alternatives in Table 11.5.1(4) but there is only a limited choice. Other standards such as the British Standard BS7608 : Code of Practice for Fatigue Design and Assessment of Steel Structures offers a larger choice. But we are assessing this joint according to SAA HB6.
The Article 11.5.1 of SAA HB6 states that details not classified in the tables are to be treated as the lowest detail category of a similar detail, unless a superior fatigue strength is proven by analysis and testing. We do not have access to such data. Therefore, after examining Table 11.1.1(4), we decide to use Detail Category 41. This is for for circular hollow sections fillet-welded by using an intermediate plate. We suspect our joint should do better than this because it is butt-welded. Nevertheless, #41 it is.
It should be noted that SAA HB6 assumes that this joint is welded properly and the weld quality conforms with Category SP as defined in AS/NZS 1554.1. You may want to check this standard and establish some quality control measures to confirm this conformance.
Assume that this is on a non-redundant path. Since we believe that the weld category choice was conservative, we will not be too generous with the capacity factor and allow the maximum value recommended for a joint on a non-redundant path, so f = 0.70.
11.1.7 Thickness Effect
11.6 Fatigue Strength
The modified design stress = 35/0.7 = 50 MPa.
From Figure 11.6.1 and for weld category #41, we read that the life is around 1.1 x 106 cycles. One can also use the equation given to get the same number:
Since each cycle takes 40 seconds, the estimated fatigue life is then 12200 hours.
EXAMPLE - Variable Amplitude Loading
It is a rare load history that includes only one form of stress cycle. Usually machines perform different operations and the stress histories for these operations can be dramatically different.
Usually, by examining and analysing the stresses during operation, one can group and list the operating stress ranges as in the following table:
Stress Range, MPa
% of the cycles
You can use Article 11.8.2 of the SAA HBB to deal with this situation. The Equation in 11.8.2 is written for a situation where we want to know if the joint is safe for a given number of cycles. If the question is to estimate the life when the stresses as given in the above table, then we can rearrange that equation to get the following:
where for the above table, i = 1...3 and b values are 0.30, 0.60 and 0.10. The denominator fc is the corrected fatigue strength and
where f3c and f5c are read from Figure 11.6.1 of SAA HBB.
Another way of preparing a stress spectrum table as given above is by analysing the experimental stress traces. Different methods have been proposed but presently the common method of generating a stress spectrum is by using a rainflow counting approach. This approach is standardised by the ASTM. Several Rainflow counting algorithms are included in the ASTM publications.
To understand how rainflow counting works, first redraw the stress-time history by making the time the vertical axis. The stress peaks and troughs will then appear as some sort of roof structure (you need a bit of imagination). The method was first proposed by Matsuishi and Endo who described it as rain drops falling down the pagoda roofs. A number of rules are imposed to identify the strain cycles.
For example, there are four stress ranges in the above trace: A-D, B-C, E-F and G-H.
In your project, you do not need to use the rainflow counting appraoach because you do not have experimental strain data.