Complex model of the dynamics of a multi-axle wheeled amphibious vehicle to improve stability and handling in transient and extreme conditions

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Abstract

BACKGROUND: The dynamics of multi-axle amphibious wheeled transport and technological vehicles (AWTTV) remain poorly understood, especially under variable grip and extreme driving conditions. Existing studies focus primarily on two- and four-axle vehicles, ignoring complex nonlinear effects of tire slip and interaction between axles, which limit control accuracy for heavy multi-axle vehicles.

AIM: Development of a complex mathematical model of AWTTV dynamics that combines torque distribution between axles, real-time correction of wheel steering angles, and consideration of nonlinear effects of slip, to improve stability and handling in transient and extreme conditions.

METHODS: The following methods are used in the research: theoretical and analytical study based on the equations of vehicle dynamics, simulation modeling of the motion of an AWTTV with an 8x8 wheel arrangement, comparative analysis of two steering schemes (1-2-0-0 and 1-2-3-4), assessment of the influence of velocity, acceleration and steer angles on stability, verification of the model by means of the analysis of steady-state and transient modes.

RESULTS: It was found that the difference in the slip angles of the outer axles increases proportionally to the velocity and the steer angle, reaching 10 degrees at a velocity of 40 km/h. Deviation from the specified path for the 1-2-0-0 scheme reaches 40%, which is 1.6 times higher than for the 1-2-3-4 scheme. In transient modes, an increase in the difference in slip angles by 15-20% was observed compared to the steady-state mode.

CONCLUSION: The proposed model demonstrates that the integration of torque distribution and active steering reduces the path deviation and improves the stability of the AWTTV. The results highlight the need for adaptive algorithms for multi-axle vehicles, especially in transient conditions.

About the authors

Mikhail M. Zhilejkin

Moscow Polytechnic University

Email: jileykin_m@mail.ru
ORCID iD: 0000-0002-8851-959X
SPIN-code: 6561-3300

Dr. Sci. (Engineering), professor, Senior researcher at the Scientific and Technical Center for Automated Technical Systems

Russian Federation, Moscow

Oleg A. Kozelkov

Moscow Polytechnic University

Email: kozelkow@mail.ru
ORCID iD: 0009-0009-4163-3721
SPIN-code: 8140-1200

Dr. Sci. (Engineering), professor, Head of the Scientific and Technical Center for Automated Technical Systems

Russian Federation, Moscow

Vsevolod A. Neverov

Moscow Polytechnic University

Author for correspondence.
Email: sevasxp@mail.ru
ORCID iD: 0000-0003-0515-9785
SPIN-code: 4896-2213

Cand. Sci. (Engineering), Senior researcher at the Scientific and Technical Center for Automated Technical Systems

Russian Federation, Moscow

References

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Supplementary files

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2. Fig. 1. Diagram of forces acting on the amphibious wheeled transport and technological vehicle: L, the wheelbase; li , distance from the front to the i-th axle of the vehicle; X, Y, the longitudinal and transverse axes, respectively; δi лев, δi пр, the slip angles of the left and right wheels of the i-th axle of the vehicle, respectively; δi the average slip angle of the wheels of the i-th axle; ϴi лев, ϴi пр the steer angles of the left and right wheels of the i-th axle of the vehicle, respectively; ϴi the average steer angle of the wheels of the i-th axle; the projections of the acceleration of the center of gravity of the vehicle onto the longitudinal and transverse axes, respectively; Px, Py the total external longitudinal and lateral forces applied to the center of mass of the vehicle, respectively; MZ the total external moment acting on the vehicle relative to the vertical axis Z, passing through the center of mass of the vehicle; Xi лев, Xi пр the longitudinal force acting on the wheels of the i-th axle from the road, for the left and right wheels, respectively; Yi лев, Yi пр lateral force acting on the wheels of the i-th axle from the road, for the left and right wheels, respectively; C, center of gravity of the vehicle; O, turning center; P, projection of the turning center onto the longitudinal axis; Xp , distance from the projection of the center of rotation onto the longitudinal axis to the rear axle.

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3. Fig. 2. Dependence of the difference in the steer angles of the wheels of the outer axles on the angle of the steered wheels of the master axle for the amphibious wheeled transport and technological vehicle with the steering formula 1-2-0-0 (a) and 1-2-3-4 (b). Constant velocity cornering. a: 1–4–Va=10, 20, 30, 40 km/h respectively; b: 1–4–Va=5, 10, 15, 20 km/h respectively.

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4. Fig. 3. Dependence of path following accuracy on the motion velocity in a turn for an amphibious wheeled transport and technological vehicle with steering schemes 1-2-0-0 (a) and 1-2-3-4 (b).

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5. Fig. 4. Dependence of the difference in the slip angles of the wheels of the outer axles on the steer angle of the steered wheels of the master axle for the amphibious wheeled transport and technological vehicle with steering schemes 1-2-0-0 (a) and 1-2-3-4 (b) (accelerating in a turn): 1–4–ja is equal to 0.5; 1.0; 1.5 and 2.0 m/s2, respectively.

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6. Fig. 5. Difference in wheel slip angles of the outer axles for an amphibious wheeled transport and technological vehicle with a 1-2-0-0 steering scheme: a, turn-in; b, turn-out.

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7. Fig. 6. Difference in wheel slip angles of the outer axles for an amphibious wheeled transport and technological vehicle with a 1-2-3-4 steering scheme: a, turn-in; b, turn-out.

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8. Fig. 7. Time-domain cyclogram of the action of the specific lateral force depending on time.

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9. Fig. 8. Dependence of the turning angle βa of the longitudinal axis of the machine on the motion velocity and the specific lateral force at rectilinear uniform motion: 1, Py /Ga=0.1; 2, Py /Ga=0.2; 3, Py /Ga=0.3; 4, Py /Ga=0.4.

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10. Fig. 9. View of the time-domain transient process of the turning angle βа at Va=40 km/h and Py /Ga=0.1.

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