M.Sc. Thesis Presentation:

An Investigation Into The Kart Hopping Phenomenon

Simon Scott

Supervisor: Mr. A. J. Robertson

11 September 1998

Cranfield I UNIVERSITY

Outline

Introduction

Work carried out

Results

Conclusions

Cranfield I UNIVERSITY

increased grip between road / tyre slower speed / smaller radius of corner reduced torsional chassis stiffness reduced tyre pressures reduced axle stiffness fewer bearing hangers taller, more upright seating position

3

Introduction To Kart Hopping

Kart construction

Hopping phenomenon

Factors increasing the tendency to hop

Work Carried Out

Dynamic Testing

Mass Distribution and Centre of Gravity

Torsional Stiffness Test

Tyre Testing

Finite Element Model

Cranfield I UNIVERSITY

Dynamic Testing 6000

3000

PSD

0 7 14 Frequency (Hz)

Filtered spectral plot for z axis, rear right accelerometer, 201b/in2 tyre pressure, without torsion bar

Confirmed: hopping frequency range effect of decreasing tyre pressures effect of reducing chassis stiffness

Difference in PSD values from each axes: lateral vertical longitudinal

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Cranfield I UNIVERSITY

Mass Distribution and Centre of Gravity

Laden bias: - front / rear - side / side

Centre of gravity: - xy plane position

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Torsional Stiffness Test S t i l l n e s s t e s t fo r l a d e n c a s e i n c l u d i n g t o r s i o n b a r

1 0 0 ,

2 0 4 0 GO C h a s s i s t o r q u e ( N m )

S t i f f n e s s t e s t f o r l a d e n c a s e w i t h o u t t o r s i o n b a r 1 0 0

8 0

6 0

4 0

2 0

2 0 4 0 C h a s s i s t o r q u e ( N m )

6 0

8 0

8 0

•Torsion bar effects: •chassis stiffness for laden / unladen cases •rate of change of chassis stiffness with applied load

•Natural frequencies

7

8 0 r

6 0

4 0 \

20 I

o i

Tyre Testing

Stiffness tests: - radial / lateral / longitudinal

Tyre pressures: - 10,20, 30, 40lb/in2

Normal loads: - 500, 1000, 1500, 2000N

Dynamic results interpretation Natural frequency calculations

Cranfield I UNIVERSITY

Cranfield 1 UNIVERSITY

Finite Element Model

-. l - o ° .

* ft j.4 Kl •'i * rn* V - * * ** t> C si

& 0

- * * a 1

Simulations / chassis configurations Model construction:

elements tyre representation boundary conditions applied loads effective corner masses

Results: stiffness natural frequencies

9

Cranfield I UNIVERSITY

Conclusions Section f n range (Hz) Dynamic Testing 3^9 Torsional Stiffness Tyre Testing 6.6-11.8 Finite Element Model 7-11

Hopping is very slightly damped natural frequency problem, exhibiting self-excitated characteristics Major components of kart have similar natural frequencies in certain configurations Control analogy