A method for determining the power and kinematic parameters of a tire and a wheel for free and driving modes of rolling is given. The displacement of the center of normal reactions of the road support surface was taken into account. The amount of displacement is presented as a linear func-tion of the longitudinal force coefficient. The analytical description of the dependence reflects the relationship between the longitudinal force coefficient and the asymmetry coefficient of the diagram of normal reactions of the bearing surface and determines the displacement of the center of normal reactions towards the front edge of the contact area of the tire. The calculated asymmetry of the epure of relative normal reactions can be obtained by choosing the appropriate value of the asymmetry coefficient in the range from 1 to 0. Based on a numerical example, a graphical-analytical display of the force and kinematic parame-ters of rolling of a wheel with a 15.5-R38 model F-2A tractor tire is presented when using the epure of relative normal reactions described by a parabolic dependence of the fourth degree. The longitu-dinal force coefficient is determined taking into account the formation of the resulting longitudinal reaction by two components - in the slip section and in the rest section of the tire contact pad ele-ments. It was found that the maximum value of the longitudinal force coefficient for an asymmetric epure of relative normal reactions is observed with a larger value of the wheel slip coefficient com-pared to a symmetric epure, but remains practically unchanged for both compared diagrams of rela-tive normal reactions. The presented method for determining the power and kinematic parameters, taking into account the asymmetry of the epure of normal reactions of the supporting surface, can find practical applica-tion in the selection and substantiation of rational modes of operation of wheel propellers of tractor transport and technological units in various road conditions.
The technique of determination of weight ratio longitudinal force, weight ratio traction moment, coefficient of slipping of the wheel and their analysis is given at variation of the central angle of the contact area of the tire. Longitudinal force consists of two components − on the site of slipping and on the site of rest of the contact area of the tire. The first component is defined by normal reaction of seating on the site of slipping and dynamic coefficient of traction of the tire, which is expressed by the function from relative normal reaction on the site of slipping and is in interval of two boundary values. The maximum and minimum values are equal according to the tire static friction coefficient without slipping of the wheel and to tire sliding friction coefficient at full slipping of the wheel. The second component is defined by normal reaction of seating on the site of rest and static coefficient of traction of the tire, which is expressed by the function from relative normal reaction on the site of rest and is limited to two limits -zero value and value of the coefficient of static friction of the tire. The traction moment on the wheel is defined by the work of longitudinal force on the radius of its rolling. The optimum value of the coefficient of slipping of the wheel is defined by functions of the weight ratio traction moment on the wheel to the maximum. Settlement assessment for the wheel with the Goodyear OPTITRAC DT812 tire of standard size 520/70R38 of the BELARUS 82.1 tractor is executed. The central angle of the contact area of the tire is equal to 0.881 radian. The maximum values of the weight ratio longitudinal force and the weight ratio traction moment are respectively to 0.722 and 0.634. Coefficients of slipping of the wheel make at the same time respectively 0.15 and 0.107. These values do not exceed the slipping coefficient size limited under operating conditions to values 0.18 and 0.15 for tractors according to one and two leading bridges.
The expediency of use of analogy of wheel and track movers interaction with the supporting surface is established. The research aim is to implement the possibility of simulation of power parameters of a track mover with rubber-covered caterpillars using the positions designed for movers of wheeled vehicles. It is suggested to determine an axial force in plane of contact area of track mover through the sum of products of normal responses and adhesion coefficients on slipping and idling sections of elements of contact area. The normal response in each section should be determined taking into account the variable diagram of specific normal responses. Without slipping of elements, a rectangular diagram is assumed; with full slipping, a triangle one with right angle on the rear part of contact area is assumed. A diagram is a trapezoidal in case of the intermediate slipping. It is recommended to calculate the adhesion coefficient of elements of contact area in the sliding section through the descending elliptical dependence as a function of the relative normal response on slipping section of contact area. The low value is equal to the static friction coefficient of elements without slipping, the high value is equal to the coefficient of sliding friction with full slipping. It is recommended to calculate adhesion coefficient of the idling section through the ascending elliptical dependence as a function of the relative normal response on slipping section of contact area. The low value is equal to zero without slipping, the high value is equal to the static friction coefficient in the transition to full slipping of extreme rear element. The calculated values of the axial force coefficient for track mover of John Deere 8300RT tractor with 1.91 radians of central angle of contact area are well coherent with the actual data of drawbar tests of John Deere 8310RT, 8335RT and 8360RT tractors carried out in the University of Nebraska-Lincoln. The proposed simulation algorithm of power parameters of track mover could be useful when choosing the rational traction modes of tractors operation in different operating conditions.
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