Measuring the Rolling Resistance of Heavy Vehicle Tyres
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Abstract The objective of this project is to consider alternative methods for measuring tyre rolling resistance. This project focuses particularly on testing heavy vehicle tyres under heavy load conditions in the region of 4 tonne. Chapter 1 presents a background to the rolling resistance phenomenon and explains the importance of measuring it, particularly for tyre design. A review of the standard methods for measuring rolling resistance is given, and a laboratory method for testing small tyres is presented which lends itself to being extended for use with larger tyres under higher load. The design problem is defined in more detail in Chapter 2, and four conceptual solutions for the problem are introduced. Chapter 3 analyses the case of a rolling axle pendulum, which is one of the considered solutions. A dynamic model is suggested, and several aspects such as angular velocity and contact forces are simulated for certain design choices. Chapter 4 draws conclusions of the project and gives suggestions for future work, which include further investigation of the candidate solutions, and designing and building a prototype of a measuring rig. iii Table of contents Nomenclature .......................................................................................................................................... v Chapter 1 - Introduction .......................................................................................................................... 8 1.1. Background.............................................................................................................................. 8 1.2. Standard methods for measuring rolling resistance ................................................................. 9 1.3. Previous work ........................................................................................................................ 10 1.4. Project objective .................................................................................................................... 12 1.5. Conclusions ........................................................................................................................... 13 1.6. Figures ................................................................................................................................... 13 Chapter 2 - Conceptual design of a rolling resistance measuring rig .................................................... 17 2.1. Introduction ........................................................................................................................... 17 2.2. Specification .......................................................................................................................... 17 2.3. Embodiment design ............................................................................................................... 17 2.4. Suggested concepts ................................................................................................................ 18 2.5. Summary and conclusions ..................................................................................................... 20 2.6. Figures ................................................................................................................................... 20 Chapter 3 - Dynamics of a rolling axle pendulum ................................................................................ 23 3.1. Introduction ................................................................................................................................ 23 3.2. Mass distribution along the axle ................................................................................................ 23 3.3. 2D dynamic model of rigid eccentric pendulum ........................................................................ 24 3.4. 3D dynamic model of rigid eccentric pendulum ........................................................................ 29 3.5. Conclusions ................................................................................................................................ 35 3.6. Figures........................................................................................................................................ 35 Chapter 4 - Conclusions and future work ............................................................................................. 43 4.1. Conclusions ................................................................................................................................ 43 4.2. Future work ................................................................................................................................ 43 Appendix A ........................................................................................................................................... 44 Appendix B ........................................................................................................................................... 46 References ............................................................................................................................................. 47 iv Nomenclature Fr : Rolling resistance force Cr : Rolling resistance coefficient : Rotation angle. Zero angle is defined when the centre of gravity is aligned under the axle. And positive value is defined in Figure 3.4 mini ,maxi ,maxi 1 : Rotation angle, see Figure 1.5 cp : A rolling angle which is account for travel of contact patch length. R1 : external radius of tyre R2 : radius of dead weight cylinder e : distance between axle and centre of gravity, radius of eccentricity J cm. : moment of inertia of the whole system about the centre of mass I yy g : earth gravity coefficient eDW : distance between centre of gravity of dead weight and the axle, see Figure 3.3 mm12, : mass of concentric parts and mass of eccentric part of a pendulum. see Figure 3.3 UU12, : velocity of mass m1 and m2 JJ12, : moment of inertia of concentric and eccentric part of a pendulum. see Figure 3.3 L1 : distance along y axis between centre of gravity and test tyre L2 : distance along y axis between centre of gravity and rigid wheel XX12, : longitudinal contact forces acting on tyre and on rigid wheel, respectively YY12, : lateral contact forces acting on tyre and on rigid wheel, respectively ZZ12, : vertical contact forces acting on tyre and on rigid wheel, respectively X : total contact forces acting on the system in x direction Z : total contact forces acting on the system in y direction x,, y z : inertial coordination frame Ω : vector of rotational velocity about c.g, described in body frame I : tensor of inertia of the whole system about c.g, described in body frame IIxy, zy : tensor of inertia components v x : vector of unknown forces C r1 : steady-state rolling resistance coefficient C r 2 : transient rolling resistance coefficient F 11Frr dx Z1 C dx C r r, fitted ZZZ: Rollingdx resistance dx coefficient as affected from both transient and steady-state 1 1 1 factors E : mechanical energy (gravitational and kinetic) m : total mass of the system d : distance travelled Lcp : contact patch length dd, 12 : distance between the tyre and the outer weight and of the inner weight respectively (see Figure 3.1) Ltotal : total length of the axle La : distance between the test tyre and the outer weight (see Figure 3.1) Lb : distance between the inner weight and the outer weight (see Figure 3.1) Lc : distance between the solid wheel and outer weight (see Figure 3.1) aa12, : width of the outer weight and of the inner weight respectively (see Figure 3.1) WW12, : gravity force of the outer weight and the inner weight respectively (see Figure 3.1) F : total force on the systes in Figure 3.4 and in Figure 3.10 FF xz, : components x and z of the total force on the system in Figure 3.4, : total mass on the system in Figure 3.4 W : system total weight, equal to mg rcg. : location of the centre of gravity rrequ,, x, equ z : 2D location vector of centre of gravity when the system is in equilibrium 0 X requ,,,, x, r equ y r equ z : 3D location vector of centre of gravity when the system is in equilibrium Z : normal force acting on the wheel at the contact area with the floor (see Figure 3.4) : longitudinal force acting on the wheel at the contact with the floor (see Figure 3.4) y : total torque about y axis τcg. : total torque vector about the centre of gravity vi H y : momentum about y axis Hcg. : momentum vector about the centre of gravity AB, : expressions of the differential equation in the 2D approach AB, : matrixes expressing the linear equation system in the 3D force calculation t : time from motion initiation 0 : initial rotation angle T kin,max : maximal kinetic energy throughout a cycle T grav,max : maximal gravitational potential energy throughout a cycle s,max : maximal static friction coefficient Ffr : static friction force Z1stasic : vertical load in the test wheel when the system is stationary f : motion frequency vii Chapter 1 - IntroductionFr 1.1.Cr Background Fuel cost is one of the major expenditures for heavy goods vehicle operators. Fuel consumption is also the direct cause of vehicle carbon emission. Accordingly there is continuous pressure to improve vehicle fuel economy and at the same time to reduce their environmental damage per freight task [1]. Fuel is the vehicle energy source, whereas several factors serve as the vehicle energy sinks. The major energy consumers on a vehicle are engine thermodynamic loss, braking losses, rolling resistance of the drive