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Definition of a Chassis and Required Properties





Introduction

 

Luego Sports Cars Ltd

 

Luego Sports Cars Ltd has been involved in the motor sports industry for a number of years. They have produced work for Champion Motor Company (CMC) Spain, Tiger Racing, CMC USA, Ron Champion, and Locost ltd.

Aims of Project

 

The purpose of this thesis is:

- To perform a torsion test on the prototype chassis to determine its torsional stiffness;

- To create a finite element model of the chassis;

- To incorporate a design improvement study and note the effects on the global torsional stiffness of the chassis;

- To attempt an optimisation for maximum efficiency.

The following limitations are given for this project:

- The body shape is fixed and therefore the overall external shape of the chassis must not be altered;

- The engine bay must remain as open as possible to allow a variety of engines to be fitted;

- Complex assemblies are to be avoided, as Luego is a small manufacturer.


Definition of a Chassis and Required Properties

 

Definition of a Chassis

 

The chassis is the framework to which everything is attached in a vehicle. In a modern vehicle, it is expected to fulfil the following functions:

· Provide mounting points for the suspensions, the steering mechanism, the engine and gearbox, the final drive, the fuel tank and the seating for the occupants;

· Provide rigidity for accurate handling;

· Protect the occupants against external impact.

 

While fulfilling these functions, the chassis should be light enough to reduce inertia and offer satisfactory performance. It should also be tough enough to resist fatigue loads that are produced due to the interaction between the driver, the engine and power transmission and the road.

Calculation of the Global Torsional Stiffness

 

 

The torsional stiffness of a chassis is determined from the twist angle between the front and rear axles under a torsional load, either static or dynamic.

The static load occurs when the chassis is stationary and one corner is elevated, for example under jacking conditions. The forces on the four corners impose a twist torque on the chassis.

The dynamic load occurs when the chassis is moving, for example, when a wheel travels over a bump. The force applied by the bump travels through the wheel and tyre into the coil-over and is applied to the coil-over mounting points. This also causes the chassis to twist.

The static load has been chosen for this project as it can be easily replicated for the testing and modelling of the chassis. A load is applied to the coil-over mounting points and the torsional stiffness of the chassis can be easily determined.

The torque applied to the chassis is a function of the force acting on the coil-over mounting points and the distance between the two front or rear coil-over mounting points.

 
 

 

 


Fig. 18

 

The global twist angle of the chassis is the function of the vertical displacement between the two involved coil-over mounting points and their distance.

 

 


Fig. 19

 

qtwist = arc tan {(DL - DR) / Lwidth} deg

 

The torsional stiffness of the chassis can be obtained:

 

MT = ¦ dMT = KT x qtwist

 

Ю KT = MT / qtwist [Nm/deg]

 

The equation above describes the torsional stiffness of the chassis as ‘the torque required to generate one degree of chassis twist angle.’

 


FE Modelling Description and Validation of Baseline Model

 

FE Model

 

To begin the Finite Element analysis a model of the chassis must be created. This was achieved using the universities Patran/Nastran FE modeller/solver software. It was decided to create a line model of the prototype chassis. This type of model is not a dimensionally or geometrically perfect copy of the prototype but a simple representation of it. This was chosen to facilitate relatively simple modification of the baseline model for the improvement study. The results are not intended to be 100% accurate but are intended to give an indication of the stiffness achievable and the effects each of the modifications has.

Patran/Nastran

 

The finite element analysis software used is the Patran/Nastran geometric and solver package developed by MSC [Ref. 6]. Patran is the geometric section where a line model representative of the chassis is created. The geometry (cross sectional area A; 2nd moment of inertia Ix, Iy; torsion constant J), element type, load cases and application regions, material properties (Young’s modulus E; shear modulus G; Poisson’s ratio m; density kg/m3) and basic analysis are selected and created. The Nastran solver can then be employed for the full analysis of the structure. The output file is then read back into Patran for viewing the results.

The geometry is modelled in 3D with point-to-point lines representing the beams and tubes and their intersections. Surfaces are also created in this way with either points or lines representing surface vertices or edges. The element type can then be selected and a mesh applied to all beams and surfaces. The element types selected were the Beam element for all beams and tubes, and the shell element for all surfaces.

Bar element

 

The RBAR element is a beam element that supports tension, compression, torsion, bending and shear in two perpendicular planes. It connects two nodes and provides stiffness to all six degrees of freedom in each end. Its gravity axis, elastic axis and its shear centre are all coincident [Ref. 6].

 

Shell element

 

The shell element chosen for modelling surfaces and panels was the QUAD4 element. This is a 2-dimensional shell element that can represent in-plane bending and transverse shear behaviour. This means it only has five degrees of freedom at the nodes, the rotational degree of freedom perpendicular to the element is unconnected and must be given an artificial stiffness. This is performed in Patran by setting the K6ROT – parameter to a greater than zero value [Ref. 6].

Model correction

 

A number of models were created, as the stiffness value necessary was not being obtained. Upon analysis of these models, it was found that some of the geometry of the engine bay was incorrect. This was modified but the stiffness value was still not in the region of the physical test result further analysis of the model was required. After thorough examination of the model, it was discovered that the main engine bay top rails were not connected to the front suspension box. With this corrected the model achieved a stiffness value of 1352.33 Nm/deg.

 

The model should not be expected to give completely accurate results when comparing with a torsion test of the real chassis, as certain simplifications may be influential:

- Offset connection of two tubes, leading to local bending is not included in the model.

- Varying material thickness due to welds, etc. has not been taken into consideration.

- A finite element model assumes that joints are infinitely stiff, which is incorrect.

- The suspension mounts are approximate to the actual shape and exact location.

These factors should lead to the model being slightly stiffer than the test result as has been found with this model.

 

7.4 Final Validation of Baseline Model

 

 

Fig. 28

 

 

Table 2

 

This model [Fig. 28] represents the prototype chassis as supplied by Luego for physical testing.

All modifications were made to this model to ensure as accurate a stiffness value as possible. The areas highlighted in green are mild steel panels. The engine plates, gearbox plates, roll bar plates and rear side plates are all 3mm thick with the remaining floor panels and footwells 1.6mm thick.

The mass of the model is higher than the physical chassis due to a number of factors. The modelling software does not take into account that material is removed from each beam where it joins another, i.e. at every joint the software assumes that the material from each beam is present so for a joint with four connecting beams there will be material from each beam at the same point. The software also extends the material of angled beams past their end-points on the chassis. As previously mentioned the model is also not an exact geometrical copy. This material will add up to give the excess mass. These phenomena can be seen in Fig. 29 below.

 

 

Fig. 29


Design Improvement Study

One- piece floor

Fig. 30

 

Table 3

As mentioned in chapter 5 the transmission tunnel is an open section. As a first step, the floor can be made from one continuous panel, strengthening the backbone feature of the transmission tunnel by closing this section.

 

8.1.2 Transmission tunnel panelled

 

 
 

 

 


Fig 32

 

 

Table 4

 

 

With the replacement of the two-piece floor with a one-piece item and the panelling of the transmission tunnel [Fig. 32] a backbone is formed. With this now being closed along the majority of its length it acts as a torque tube. The improvement to the torsional stiffness can clearly be seen in table 4 with a 37.82 % increase. These panels are mild steel of 1.6mm thickness.

 

Addition of rear firewall

 
 

 

 


Fig. 34

 

Table 5

 

As shown in Fig.34 and Table 5 the rear firewall forms a large shear panel across the rear bulkhead. The torsional stiffness is increased once again by almost 20% over the previous model. The efficiency has also improved by approximately 7% over the previous model. This shows that the some of the loads are being taken up by this rear firewall. This is to be expected, as the framework to which it is attached is a major load-carrying bulkhead taking the load of the rear suspension mounts. The panel helps prevent lozenging of this bulkhead. This firewall is a mild steel panel of 1.6mm thickness.

 


Stage 4-Optimisation Study

 

Now that a significant increase in torsional stiffness has been achieved, an optimisation study can be performed. This involves keeping the stiffness as high as possible but removing as much mass as possible. This can be achieved by conversion of mild steel panels to aluminium, by reduction in section size of beams that are not highly stressed or conversely increasing the section size of highly stressed beams. The optimisation has been aimed at achieving a minimum of 6000Nm/deg torsional stiffness with the minimum mass. It should be remembered at this stage that the baseline validation model was measured by the software as being 8Kg heavier than the original chassis. This means that the efficiency of the chassis will be even higher than the results suggest if a physical chassis with these modifications were to be constructed and it matched the predicted stiffness values. This is unlikely however and the efficiency is more likely to be as predicted due to the drop in mass and torsional stiffness that a physical chassis would have.

 

Conclusions

 

 

The purpose of this thesis was to:

  • Perform a torsion test on the prototype chassis to determine its torsional stiffness
  • Create a finite element model of the chassis
  • Incorporate a design improvement study and note the effects on the global torsional stiffness
  • To attempt an optimisation for maximum efficiency.

 

Physical Testing

 

The physical testing supplied an empirical value of global torsional stiffness for the prototype chassis. This gave a basis with which to validate the results of the Finite Element baseline model. By using only the restraints necessary to satisfy all six equilibrium equations, an accurate and viable value was achieved. This value of 1330Nm/deg was slightly unexpected as a similar but somewhat smaller and stiffer looking chassis recorded a lower value of stiffness.

 

Design Improvement Study

 

Discussed Modifications

 

These modifications and panel modelling showed how the ‘cosmetic’ covering panels and some minor modifications in fact increase the torsional stiffness by up to 128%.

The basic panelling of the passenger compartment contributing up to 85% by acting as shear panels on untriangulated areas, with the addition of the dash bar and dash panelling contributing the remainder. The effect of converting the mild steel panels to aluminium showed the benefits achievable in mass reduction while still offering up to 81% more torsional stiffness and up to 54% more efficiency over the baseline model.

 

Optimisation Study

 

With the torsional stiffness increased sufficiently the optimisation study aimed to keep the stiffness over 6000Nm/deg whilst minimising mass and maximising efficiency. An optimum combination will be a compromise as are most areas of design of a sports car. The optimum was reached in model 8.4.4 with a torsional stiffness of 6474.9Nm/deg, an increase of 378% over the baseline model. A mass of 135.9Kg for the fully panelled chassis was achieved with an efficiency of 20.99g/Nm/deg, an increase of 323% over the baseline model.

 

 


References

 

  1. Forbes, Aird. (1997). Race Car Chassis, Design and Construction. MBI Publishing Company, Wisconsin, USA.

 

  1. Brown, J.C. (2002). Structural Design for Motorsport. Lecture Notes, Cranfield University.

 

  1. Pawlowski, J. (1969). Vehicle Body Engineering. Business Books, London.

 

  1. Brown, J.C., Robertson, A.J. and Serpents, S.J. (2002). Motor Vehicle Structures: Concepts and Fundamentals. Butterworth-Heinemann, Oxford.

 

  1. C hampion, Ron. (2000). Build Your Own Sports Car for as Little as Ј250-and Race It!, 2nd ed. Haynes Publishing, Somerset.

 

  1. MSC/NASTRAN Quick Reference Guide. (1998). MacNeal-Schwendler Corporation.

 

  1. www.daxcars.co.uk. Company Information Website. Accessed 24th July 2002.

 

 

  1. www.caterhamcars.co.uk. Company Information Website. Accessed 2nd August 2002.

 

  1. www.westfield.co.uk. Company Information Website. Accessed 2nd August 2002.

 

  1. www.quantumcars.co.uk.. Company Information Website. Accessed 4th August 2002.

 

  1. www.robinhoodengineering.co.uk. Company Information Website. Accessed 7th August 2002.

 

 

Introduction

 

Luego Sports Cars Ltd

 

Luego Sports Cars Ltd has been involved in the motor sports industry for a number of years. They have produced work for Champion Motor Company (CMC) Spain, Tiger Racing, CMC USA, Ron Champion, and Locost ltd.

Aims of Project

 

The purpose of this thesis is:

- To perform a torsion test on the prototype chassis to determine its torsional stiffness;

- To create a finite element model of the chassis;

- To incorporate a design improvement study and note the effects on the global torsional stiffness of the chassis;

- To attempt an optimisation for maximum efficiency.

The following limitations are given for this project:

- The body shape is fixed and therefore the overall external shape of the chassis must not be altered;

- The engine bay must remain as open as possible to allow a variety of engines to be fitted;

- Complex assemblies are to be avoided, as Luego is a small manufacturer.


Definition of a Chassis and Required Properties

 

Definition of a Chassis

 

The chassis is the framework to which everything is attached in a vehicle. In a modern vehicle, it is expected to fulfil the following functions:

· Provide mounting points for the suspensions, the steering mechanism, the engine and gearbox, the final drive, the fuel tank and the seating for the occupants;

· Provide rigidity for accurate handling;

· Protect the occupants against external impact.

 

While fulfilling these functions, the chassis should be light enough to reduce inertia and offer satisfactory performance. It should also be tough enough to resist fatigue loads that are produced due to the interaction between the driver, the engine and power transmission and the road.







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