Vehicle Dynamics And Control-Free PDF

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Tapered wheels Tapered wheels Basic motion,Why is the wheels on a train tapered. Consider a wheelset with tapered wheels on a rail In the steady. motion basic motion the wheels are moving on a straight line in the. longitudinal direction, Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 17 43 Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 18 43. Tapered wheels A train taking a turn Tapered wheels Perturbed motion. One reason for using tapered wheels is illustrated in the following figure What will happen if the basic motion is perturbed. showing a wheelset of a train taking a right turn Basic motion is shown to the left and perturbed motion to the right. 2r0 2 y 2r0 2 y Vxl, The longitudinal speed is larger for the outside wheel Vxl than for the w x. inside wheel Vxr but the rotational speed is the same The basic motion. in this case includes a constant drift y in the lateral direction which. compensates for this difference,Vxl r0 y Vxr r0 y, Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 19 43 Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 20 43. Tapered wheels Tapered wheels, Lateral drift causes a difference in the longitudinal.
velocity of the wheels in the same way as before,dx Using Vxl r0 y and Vxr r0 y the. dx Vxl r0 y,angular velocity can be written as,Vxl Vxr r0 y. Vxr Vxl 2 y, The longitudinal velocity of the center of gravity is Differentiating y r0 and using the expression. x t y t now given by w,for the angular velocity above the following. Vxl Vxr differential equation for y is obtained,The approximation gives the lateral velocity Vxr.
Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 21 43 Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 22 43. Tapered wheels Harmonic oscillation Tapered wheels Unstable system. For a wheelset with positive taper angle as in the figure the solution. 2r0 2 For a wheelset with negative taper angle the solutions of the differential. y t y t 0 equation,is a harmonic oscillation y t y t 0. y t cos n t,with natural frequency r, 2r0 which means that the a small perturbation would cause an exponential. w growth of the lateral displacement and the system is clearly unstable. If there is friction in the system then the wheelset will return to the basic. motion asymptotically, Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 23 43 Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 24 43. Tapered wheels Spatial coordinates Tire,The dynamic equation. can be rewritten by using the relations,Figure 1 1 Tire construction.
d 2y x 2 Figure 1 2 Coordinates forces and moments. x t y t dx 2 r02,and the result is the following,y 00 x y x 0. A model that doesn t depend on speed, Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 25 43 Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 26 43. Rolling resistance Hysteresis,Exampel of a hysteresis loop caused by friction. Direction of motion, The rolling resistance of tires is primarily caused by the hysteresis in tire. materials due to the deflection of the carcass while rolling Ffriction. Other less important contributors to the rolling resistance are. Direction of motion, Friction between the tire and the road caused by sliding F Ffriction.
Displacement,Air circulating inside the tire, The energy loss due to hysteresis is equal to the shaded in the figure. 2 d Ffriction, Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 27 43 Jan A slund Linko ping University Vehicle Dynamics and Control Lecture 1 28 43. Rolling resistance Hysteresis Rolling resistance, The center of normal pressure is shifted in the direction of motion due to. the hysteresis The coefficient of rolling resistance fr is defined as the ratio of the rolling. Normal pressure resistance Rr to the normal load W i e fr Rr W. Empirical formulas for calculating the rolling resistance coefficient as a. function of speed V based on experimental data, O Radial ply passenger car tire fr 0 0136 0 40 10 7 V 2. Radial ply truck tire fr 0 006 0 23 10 6 V 2, Fz Other factors that affect the rolling resistance.