Method and apparatus for measuring or controlling friction
First Claim
1. Method for measuring or controlling friction relationships when a pneumatic rubber wheel and a surface interact during rolling motion under slip conditions between the wheel and the surface, comprisingcontinuous measurement of the linear velocity v of the wheel axle in relation to the surface and continuous measurement of the rotational velocity of the wheel within an acceleration or deceleration time interval during the rolling motion of the wheel in relation to the surface,calculation of a corresponding, varying slip speed Vs from said linear velocity v being measured and said rotational velocity being measured while taking the wheel radius into account, andcalculation of friction relationships occuring during said time interval,characterized in that measurement values or control parameters relating to said friction relationships are calculated as a function of the varying slip speed Vs and the linear velocity v on the basis of the following relation(s):
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space="preserve" listing-type="equation">μ
.sub.max =-f+g·
STDslope-h·
A.sub.r (v,V.sub.s)where μ
max is the maximum friction valueSTDslope is standard deviation of the surface texture slope angles, as measured for example with a known measurement method,A (v,Vs) is the real or total contact area between the wheel and the surface, as a function of the velocities v and Vsand ##EQU11## where D=fractal dimensionG=fractal scaling factorL=upper wave length cut-off limit for a chosen number of sinusoidal wavesL=lower wave length cut-off limit for a chosen number of sinusoidal wavesσ
=stress-factor for the rubber wheelτ
=the rubber wheel relaxation spectraη
=the rubber wheel viscosityδ
=rubber wheel shape-factorb=the length of the contact area between the wheel and the surfacer=the rubber wheel radiusand where f, g and h are constants.
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Abstract
The friction between vehicle wheels provided with rubber tires follows three influence curves (5, 6, 8). The friction between a wheel with rubber tire and a road surface is represented by a measuring result curve (1-4) the shape of which is determined symptotically from the rubber tire influence curve (6). Thus the measuring result curve (1-4) will have a characteristic shape with maximum values (1A-4A). The maximum friction is determined by the influence curve of the rubber tire and the road surface respectively, also denoted the maximum friction influence curve (8). Each influence curve has its mathematical model. In the mathematical model for the maximum friction influence curve (8) there is incorporated a slip speed, properties of the car tire and road surface-to-car tire properties. The car tire properties and the pavement-to-car tire properties can be determined as process parameters by measurement. Then the maximum friction will be a dependent variable of the slip speed alone, as long as the properties of the car tire and the road surface-to-car tire properties are unaltered. The invention can be utilized for measuring car tires or road surfaces and for controlling traction, i.e. braking or propulsions.
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Citations
15 Claims
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1. Method for measuring or controlling friction relationships when a pneumatic rubber wheel and a surface interact during rolling motion under slip conditions between the wheel and the surface, comprising
continuous measurement of the linear velocity v of the wheel axle in relation to the surface and continuous measurement of the rotational velocity of the wheel within an acceleration or deceleration time interval during the rolling motion of the wheel in relation to the surface, calculation of a corresponding, varying slip speed Vs from said linear velocity v being measured and said rotational velocity being measured while taking the wheel radius into account, and calculation of friction relationships occuring during said time interval, characterized in that measurement values or control parameters relating to said friction relationships are calculated as a function of the varying slip speed Vs and the linear velocity v on the basis of the following relation(s): -
space="preserve" listing-type="equation">μ
.sub.max =-f+g·
STDslope-h·
A.sub.r (v,V.sub.s)where μ
max is the maximum friction valueSTDslope is standard deviation of the surface texture slope angles, as measured for example with a known measurement method, A (v,Vs) is the real or total contact area between the wheel and the surface, as a function of the velocities v and Vs and ##EQU11## where D=fractal dimension G=fractal scaling factor L=upper wave length cut-off limit for a chosen number of sinusoidal waves L=lower wave length cut-off limit for a chosen number of sinusoidal waves σ
=stress-factor for the rubber wheelτ
=the rubber wheel relaxation spectraη
=the rubber wheel viscosityδ
=rubber wheel shape-factorb=the length of the contact area between the wheel and the surface r=the rubber wheel radius and where f, g and h are constants. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. Apparatus for measuring or controlling friction relationships when a pneumatic rubber wheel and a surface interact during rolling movement under slip conditions between the wheel and the surface, comprising
means for continuous measurement of the linear velocity v of the wheel axle in relation to the surface and continuous measurement of the rotational velocity of the wheel within an acceleration or deceleration time interval during the rolling motion of the wheel in relation to the surface, means for calculation of a corresponding, varying slip speed Vs from said linear velocity v being measured and said rotational velocity being measured while taking the wheel radius into account, and means for calculation of friction relationships occuring during said time interval, characterized by means for calculating measurement values or control parameters depending on the varying slip speed Vs and the linear velocity v on the basis of the following relations: -
space="preserve" listing-type="equation">μ
.sub.max =-f+g·
STDslope-h·
A.sub.r (v,V.sub.s)where μ
max is the maximum friction valueSTDslope is standard deviation of the surface texture slope angles, measured for example with a. known measuring method, Ar (v,Vs) is the real or total contact area between the wheel and the surface, as a function of the velocities v and Vs, and ##EQU17## where wherein D=fractal dimension G=fractal scaling factor L=upper wave length cut-off limit for a chosen number of sinusoidal waves L=lower wave length cut-off limit for a chosen number of sinusoidal waves σ
=stress-factor for the rubber wheelτ
=the rubber wheel relaxation spectraη
=the rubber wheel viscosityδ
=rubber wheel shape-factorb=the length of the contact area between the wheel and the surface r=the rubber wheel radius, and where f, g and h are constants. - View Dependent Claims (10, 11, 12, 13, 14, 15)
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Specification