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OPTIMIZATION OF A KART CHASSIS
By Andrew Innes

This article is theoretical treatment of the design of a kart racing chassis, and was the basis of an undergraduate final year project undertaken within the Department of Manufacturing Systems Engineering at the Royal Melbourne Institute of Technology (RMIT) in Melbourne, Australia. The aim is to improve the design process using the finite element method. It is proposed to optimize chassis performance using this technique, as significant variability exists in current testing procedures. The following is a summary of how the stiffness and performance of a chassis can be predicted by combining laws of physics with the finite element method.

There are several advantages when using structural analysis or computer simulation software. Firstly, they can predict to a certain degree of accuracy, how a component will perform under different conditions, in this case, a kart chassis. Secondly, by designing a chassis in a three-dimensional CAD (computer-aided design) package, several variations of a design can be analyzed in a day. This allows a designer to experiment with different variations of chassis geometry without producing a chassis, therefore research and development costs are reduced, and a kart design representing something closer to the optimal solution results. Thirdly, variability is eliminated in current testing of prototype chassis up until a designer is confident with how a chassis should perform under varying dynamic conditions.

Most karters can appreciate how difficult it is to maintain consistent lap times in a day to day practice, and with the exception of the driver, the largest variability is the characteristics of the tires. Tires are influenced by several factors governing their road holding performance, thus altering the dynamics of the chassis.

CHASSIS FLEX
The primary function of a vehicle chassis is to join all suspension mounting points, and distribute the load from each mounting point to all other mounting points. The essential difference between a kart and automobile chassis is in its suspension. Karting simplicity demands an un-sprung chassis, but while the kart may not have suspension, it is still subjected to the same forces affecting any automobile. Kart chassis design must take these forces into account. The requirements are for something rigid in bending and torsion moments and without excessive sag or twist.

When people talk of karts not having suspension they are wrong. Karts are a form of springing and shock absorbing, but instead of being recognizable individual units, it is part of the chassis and shows itself as frame flex. As the flex moves back down the frame, members having different main functions can be used to impart more and more restraint to flex continuing.

The placing of cross members drastically alters how much the chassis will flex, and one is usually placed about half way back in the frame and provides the first restriction to further flex. The undertray (floor pan) is left loose so the frame isn’t restricted and remains flexible, thus localizing the stress to the chassis tubing. When the flexure has reached the seat and the outsweeping of the frame, little opportunity for flex is left, so by the time it gets to the engine mount and rear axle, it is finally fully restricted.

The stiffness of a chassis can be measured in several directions simulating different dynamic conditions. For the purpose of this article, only torsional stiffness is reviewed. The torsional stiffness of a chassis is important, as this determines how much a kart chassis flexes during braking into a corner. The relationship of stiffness is linear; i.e. you apply a force and get displacement so by doubling the force the displacement increases by the equivalent margin. In brief, stresses too are linear. Every material has a critical stress (yield strength), and once this critical stress has been reached, the material becomes permanently deformed from the original design.

On some older karts, it is possible to see a wheel slightly raised, most likely caused by driving in the same direction around similar corners, thus localizing the stressing on the frame at the same point. An example of permanent deformation is if a piece of metal is bent and the critical stress is reached, the metal become permanently deformed and the material will not return to its former position.

LOAD TRANSFER
The handling of a kart is influenced by a large number of factors. These include weight distribution, center of gravity, tires, wheelbase, and track dimensions, polar moment of inertia and even the amount of power being applies to the driving (rear) wheels. Because of limitations set by karting legislation, the design scope is predetermined to quite tight limits.

The question arose, how can realistic forces be introduced into the simulation that are comparable to forces found during racing? After a little thinking, the answer is by deriving an equation of motion for deceleration of a kart. In this case, only deceleration is considered, because acceleration forces are minimal in comparison to braking. By applying Newton’s Laws, an expression can be derived allowing for the calculation of the reaction forces on the tires during braking.

A little understanding is required into how weight is transferred during braking, and then turning. When a vehicle is braked, a retarding force is immediately introduced between the tires and the track surface. But the inertia of the vehicle introduces an equal force through the center of gravity in the opposite direction. These two equal and opposite forces constitute an overturning couple tending to lift the rear of the vehicle. Consequently, a proportion of the total load of the vehicle is transferred from the rear to the front wheels so that the magnitude of the load transferred to the static front axle reaction is increased by a small amount, then the static rear axle reaction will be decreased by an equal amount. After braking, the kart is turned into a corner and the weight is transferred to the outer wheels, leaving minimal weight on the inner rear wheel.

After deriving an expression for the reaction forces at the front of the kart, the only missing variable for the equation is deceleration, as this is the subject of obtaining realistic data/forces for the simulation. Braking forces can be measured by using a data logging system such as that available from PI Systems, coupled with an inertial accelerometer. This solves the unknown, and realistic reaction forces for the vertical loading on the front tires can be calculated for varying deceleration conditions. Otherwise, reaction forces can theoretically be calculated by approximating the coefficient of friction (grip), which is dependent on grip conditions and the weight of the driver.

TORSION ANALYSIS
The torsion analysis investigates how different components effect the torsional stiffness of the chassis. Maximum torsional deflection occurs during maximum braking/deceleration and turning into a corner. A chassis with optimal torsional stiffness is important, where the torsional effect is evident. Example: A kart entering a right hand corner – due to weight transfer on the front left wheel, this causes the left front to sag and the diagonal wheel (right rear) to lift.

It is important not just to analyze the performance characteristics with respect to torsional stiffness, but also investigate that maximum stresses on the members don’t exceed the material yield strength (critical stress).

Torsional stiffness is calculated from the formula k=T/O, where k is the chassis torsional stiffness (Nmdeg 1), T is the amount of the torque on the front cross member about the fulcrum (Nm), and O is the angle of deflection of the front cross member, w.r.t. equilibrium position.

The highest reaction forces expected over the front wheels are during maximum braking as the weight is transferred through the center of gravity over the front wheels. After maximum braking, the kart is turned into a corner with the weight still over the front wheels, therefore the outside front wheel is flexed further upwards from the additional reaction force, in comparison to the other wheels. The torsion test is a comparable situation, where the front of the kart at the front cross member is twisted relative to the rest of the chassis.

Several permutations of kart chassis adjustments are available with respect to how a chassis can be adjusted prior to racing. By using the finite element, these changes can be simulated and predicted. The objective of the analysis is to show how a chassis flexes during braking and turning, and secondly that stresses are below the yield strength for each structural member.

The simulation involves analyzing how the torsion bar, side pod bars (Nerf bars) and rear bumper affect the rigidity of the chassis. The first analysis begins with a flexible kart chassis set-up, and after each successive analysis, a component is added to the flexible chassis. A comparison is made to observe how the chassis stiffness changes with respect to each member. The final analysis incorporates all the components (side pod bar, rear bumper, torsion bar, etc.). This makes a comparison with the flexible chassis that has no torsion bars, And how the torsional stiffness has been changed.

Comparison of torsional stiffness for different chassis configurations (Figures are percentage increases over the flexible chassis)

CASE
1 – Flexible Chassis 0%
2 – Rear Bumper       0.8%
3 – Side Pod Bar     15.9%
4 – Torsion Bar         3.4%
5 – Rigid Chassis    19.4%

The simulation analysis (see above) shows what effect certain bars have on the stiffness of a chassis. These representations of a chassis are used in a certain grip conditions, where bars, loosely secured to the chassis by means of a nut and bolt assembly, are assumed not to be acting in any capacity with respect to the rigidity of the chassis. Therefore in these cases, the members have negligible effect on chassis performance, and are not analyzed for that case.

The first case looks at the most flexible option in kart chassis adjustment, which analyzes a chassis with loose side pod bards, rear bumper and no torsion bar. The second analysis of the kart chassis is with the rear bumper firmly secured. The third case looks at the chassis with side pod bars firmly secured. The fourth case analyzes the contribution the mid-mounted torsion bar has on the rigidity of the chassis. The final analysis looks at the most rigid option in kart chassis adjustment; i.e. all the bars previously mentioned are combined and analyzed.

On analyzing all chassis configurations, the least torsionally stiff chassis was the flexible configured chassis (#1), as expected, with the rigid chassis (#5) being the most torsionally stiff. The rear bumper had negligible effect with regards to the stiffness of the chassis, while the torsion bar increased torsional stiffness by 3.4% over the flexible chassis. The most influential components were the side pod bars; these increased the stiffness by 15.9%.

CONCLUSION
On the basis of the results, the most influential components with regard to increasing the torsional stiffness of the chassis were the side pod bars. The material selected for each member should be on the basis of having comparable yield strength with respect to the maximum stress for that member.

Designing a chassis using this design philosophy: i.e. CAD, allows an accurate comparison of how members change the characteristics of the kart under different dynamic conditions. This is important when designing and developing any mechanical component for performance, because developing for optimum performance at the design stage (as with any motorsport) is the objective.

Article courtesy of Karting Magazine (England)

END

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