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Information about Steering forces on undriven, angled wheels

Steering forces on undriven, angled wheels

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CONTENT Introduction Dimensional analysis Experimental procedure Results Modelling of the results Conclusions References

INTRODUCTION • Measurements of the soil forces acting on a driven or undriven are required for two main purposes: 1) To investigate stability both when working on level ground and on side-slopes 2) To investigate handling characteristics • Only three attempts have been made to model these forces Taylor and Birtwhistle Schwanghart Krick • With the exception of Schwanghart's model, none of these models is sufficiently general to be of widespread use.

Contd… • So requirement is a model of the tyre-soil interaction which will allow the forces on a steered wheel to be readily predicted from a knowledge of the wheel parameters and soil condition.

DIMENSIONAL ANALYSIS Parameters required to describe the system 18 parameters --- 15 non-dimensional groups

Analysis contd… Freitag:

Analysis contd… Turnage:

EXPERIMENTAL PROCEDURE • Research done at the Deere Technical Centre, Moline, Illinois

Experimental procedure contd… • All runs were carried out at a forward speed of 0.5 m/s • The soil used contained 43.8% sand, 34.2 % silt and 22.0 % clay which is a loam soil & Moisture content was 12% • soil was processed by cultivating blades, a scraper and roller • Measurement of the cone penetrometer resistance was made for every soil sample • the aligning torque was extremely small so it was taken to be zero

Experimental procedure contd…

RESULTS Coefficient of rolling resistance at zero slip angle

Results cont… The effect of tyre size, load and inflation pressure at constant slip angle

Results cont… The effect of slip angle at constant load

Results cont… The effect of slip angle at constant load in different soil conditions

Results cont… The effect of "bulldozing" in very soft soils

Results cont… The effect of load and inflation pressure at varying slip angles in the same soil

MODELLING OF THE RESULTS Fig. 8: Coefficient of side force at 10 ° slip angle against the four different mobility numbers

Modelling cont… Fig. 8: Coefficient of side force at 10 ° slip angle against the four different mobility numbers

Modelling cont… Fig. 9: Measured values of (CRR)w plotted against the four versions of mobility number

Modelling cont… Fig. 9: Measured values of (CRR)w plotted against the four versions of mobility number

Modelling cont… • Requirements for modelling: a. The effects of slip angle, tyre size, load, inflation pressure and soil condition on the tyre side force were all able to be predicted satisfactorily using the tyre mobility number and the relationship. b. The effect of these parameters on tyre rolling resistance was not predicted so satisfactorily, particularly at high values of slip angle and mobility number. c. information on tyre steering forces will be for stability and handling calculations.

Modelling cont…

Modelling cont…

Modelling cont… Relationship between (Csf)w /(CRR)w and mobility number

Modelling cont…

Modelling cont…

Modelling cont…

Modelling cont…

CONCLUSIONS • For zero camber angle and low speed, the dimensional analysis indicated that the performance parameters should be functions of tyre mobility number, soil internal friction angle and slip angle. • The wheel aligning torque was negligibly small in all the experiments. • The coefficient of side force relative to the wheel, (Csf)w, was related to the slip angle α, by an exponential relationship of the form in all the experiments except that in the weakest soil (cone index value150 kPa) • The coefficient of rolling resistance relative to the wheel, (CaR)w, was an irregular function of α. However, a linear relationship was found between (CRR) w and α at slip angles between 0 and 20°.

Conclusions cont… • (Csf) w at a slip angle of 10 ° could be adequately modelled using the mobility numbers EMOB and AMOB so long as soil cone index value was a measure of soil cohesion and soil internal friction. The mobility number φMOB, using both cohesion and internal friction angle, gave the best correlation with (Csf)w. angle did not vary. • (CRR)w at a slip angle of 10 ° was modelled equally well by all four versions of mobility number. • As mobility number increased the ratio (Csv)w/(CRR) w also increased and for slip angles greater than 20 °, (CsF)w was always at least 5 times as large as (CRR) w. • The product k{(Csf)w}max increased as mobility number increased and a statistically significant relationship was established.

REFERENCES • D. GF.E-CLOuGH, M. McALLIS'rER, G. PEARSON and D. W. EVERNDEN, The empirical prediction of tractor-implement field performance, J. Terramechanies 15(2), (1978). • R. D. WISMER and H. J. Ltrrn, Off-road traction prediction for wheeled vehicles. J. Terramechanics 10(2), (1973). • G. KNICK, Bchaviour of tyres driven in soft ground with side slip. J. Terramechanics, 9(4), (1973). • H. SCHWANGHART, Lateral forces on steered tyres in loose soil. J. Terramechanics 5(1), (1968).

Modelling • Scientific activity the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate 1. 2. 3. 4. Conceptual models Operational Model Mathematical models Graphical models

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