Abstract
This paper presents a novel nonlinear dynamic model of a multi-axle steering vehicle to estimate the lateral wear amount of tires. Firstly, a 3DOF nonlinear vehicle dynamic model is developed, including dynamic models of the hydropneumatic suspension, tire, steering system and toe angle. The tire lateral wear model is then built and integrated into the developed vehicle model. Based on the comparison of experimental and simulation results, the nonlinear model is proved to be better than a linear model for the tire wear calculation. In addition, the effects of different initial toe angles on tire wear are analyzed. As simulation results shown, the impact of the dynamic toe angle on the tire wear is significant. The tire wear amount will be much larger than that caused by normal wear if the initial toe angle increases to 1° - 1.5°. The results also suggest that the proposed nonlinear model is of great importance in the design and optimazation of vehicle parameters in order to reduce the tire wear.
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Abbreviations
- m b :
-
vehicle body mass
- m i :
-
vehicle unsprung mass of ith axle
- I 11 :
-
moment of vehicle body inertia about X-axis
- I 33 :
-
moment of vehicle body inertia about Z-axis
- I 13 :
-
product of vehicle body inertia about XZ plane
- I zzi :
-
moment of inertia about Z-axis (unsprung mass of ith axle)
- X i :
-
signed distance from i th axle to CG (the center of gravity)
- h b :
-
distance from roll center to sprung CG
- h ao :
-
height of the roll center
- h ai :
-
height of the roll center at ith axle
- Δ:
-
distance from mass center to steering center
- B w :
-
vehicle wheelspan
- B K :
-
distance around two springs of the same axle
- B C :
-
distance around two dampers of the same axle
- R 0 :
-
free radius of the tire
- R iL :
-
load radius of the left tire of ith axle
- R iR :
-
load radius of the right tire of ith axle
- k z :
-
vertical stiffness of the tire
- K i :
-
cornering stiffness of ith axle tire
- F s :
-
force of the hydro-pneumatic spring
- k s :
-
stiffness of the hydro-pneumatic spring
- C eq :
-
equivalent damping of the hydro-pneumatic spring
- K φ :
-
vehicle body roll stiffness
- C φ :
-
vehicle body roll damping
- K iL :
-
stiffness of the left hydro-pneumatic spring of ith axle
- K iR :
-
stiffness of the right hydro-pneumatic spring of ith axle
- C iL :
-
damping of the left hydro-pneumatic spring of ith axle
- C iR :
-
damping of the right hydro-pneumatic spring of ith axle
- E i :
-
wheel roll steer angle per unit roll angle
- u :
-
vehicle longtitude velocity
- δ i :
-
steering angle of ith axle
- δ iL :
-
steering angle of left tire of ith axle
- δ iR :
-
steering angle of right tire of ith axle
- α i :
-
sideslip angle of ith axle
- α iL :
-
sideslip angle of left tire of ith axle
- α iR :
-
sideslip angle of right tire of ith axle
- γ iL :
-
toe angle of left tire of ith axle
- γ iR :
-
toe angle of right tire of ith axle
- v :
-
vehicle lateral velocity
- ψ :
-
vehicle yaw angle
- r :
-
vehicle yaw rate
- φ :
-
vehicle roll angle
- β :
-
sideslip angle of CG
- v i :
-
lateral velocity of ith axle
- E T :
-
kinetic energy of the vehicle
- E V :
-
potential energy of the vehicle
- E Ti :
-
kinetic energy of ith axle
- E Tbt :
-
vehicle body kinetic energy of translational
- E Tbr :
-
vehicle body kinetic energy of rotational
- E Ti :
-
kinetic energy of ith axle
- E D :
-
dissipative energy of the vehicle
- F Qv :
-
lateral generalized force
- F Qr :
-
yaw generalized force
- F Qφ :
-
roll generalized force
- F YiL:
-
lateral force of left tire of ith axle
- F YiR :
-
lateral force of right tire of ith axle
- F ZiL :
-
vertical force of left tire of ith axle
- F ZiR :
-
vertical force of right tire of ith axle
- S y :
-
lateral slip ratio
- μ y :
-
lateral friction coefficient
- K y :
-
tire cornering stiffness
- F z0 :
-
nominal vertical load of the tire
- F z :
-
vertical load of the tire
- F zn :
-
normalized vertical load
- F y :
-
lateral force of the tire
- \({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\phi } _y}\) :
-
normalized slip ratio
- F y :
-
normalized lateral force
- E y :
-
curvature of the lateral force
- V sym :
-
friction characteristic parameters
- V sy :
-
slip speed between the road and tire
- R wear :
-
wear mass per unit time and unit area
- P f :
-
wear power per unit area
- F f :
-
friction force
- V s :
-
sliding speed of friction
- η :
-
proportion of the tire tread pattern
- D patch :
-
width of the tire grounding mark
- A patch :
-
contact area of friction
- A patch_iL :
-
area of the left tire grounding of ith axle
- A patch_iR :
-
area of the right tire grounding of ith axle
- Δh iL :
-
wear height of left tire of ith axle
- Δh iR :
-
wear height of right tire of ith axle
- Δh i :
-
average wear height of ith axle
- ρ :
-
rubber density of the tire tread
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Chen, X., Xu, N. & Guo, K. Tire wear estimation based on nonlinear lateral dynamic of multi-axle steering vehicle. Int.J Automot. Technol. 19, 63–75 (2018). https://doi.org/10.1007/s12239-018-0007-2
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DOI: https://doi.org/10.1007/s12239-018-0007-2