CALCS PROC072
Pressure between two Bodies in Contact 190317

CONTENTS

GUIDANCE
NOTATION
INPUT DATA FORMAT
PROJECT EXAMPLE - INPUT FOR GENERAL CASE
PROJECT EXAMPLE - OUTPUT FOR GENERAL CASE
PROJECT EXAMPLE - CYLINDER ON FLAT SURFACE

GUIDANCE


APPLICATION
General case of contact between two bodies. This allows the specification of two mutually orthogonal principle axes of curvature 1/radius for each body.
That is, the specification of 2x2=4 radii, continuous in the area of contact.
There are then limits to the scope of contacting surfaces shapes. Even so, it should be possible to obtain reasonable results for a wide variety of contacting shapes.
Important Special Cases Include:
Wheel-Rail with wheel crown & rail head radii;
Contact between cylinder & flat surface;
Contact between convex & concave cylindrical surfaces (rotating bearing);
Contact between sphere & flat surface;
Contact between convex & concave spherical surfaces (spherical bearing);
Contact between two spheres.
See also: PROC033

INPUT TO PROCEDURE
Generally, all four radii are dissimilar: R11<>R12<>R21<>R22.
Curvatures 1/R are used, then input iR=0 for a flat surface (infinite radius)
Consider the Wheel-Rail with wheel crown & rail head radii.
The radii may then be specified as follows: R11 wheel radius, R12 wheel crown radius (R12<>0 or R12=0 for flat crown), R21 rail head radius (R21<>0 or R12=0 for flat head).
Example of psi angle: wheel cylindrical rim radius R11 & rail head radius R21 then psi=90
Contact between two spheres. The radii may then be specified as follows: R11=R12 & R21=R22.

Analysis for a cylinder is invoked by the following radii: R11=0 for flat OR R11>0 convex OR R11<0 concave contacting surface; R22=0; R21 cylinder and R22=0.

OUTPUT FROM PROCEDURE
Plot showing:
Elliptic shape of contact zone;
Lengths of ellipse principle axes;
Orientation angle of ellipse;
Rotated edges of continuous surfaces.
Calculations solving the contact problem with results:
Orientation angle of contact ellipse;
Semi-axis lengths of contact ellipse;
Maximum contact stress;
Strength assessment.
THEORETICAL BASIS
S.P.Timoshenko. Theory of Elasticity Ed.3. McGraw-Hill (1970). 'Pressure between two bodies in contact - More General Case'.
R.J.Roark & W.C.Young. Formulas for Stress & Strain Ed.5. McGraw-Hill (1975). Table33 Item2 Cylinder & Item4 'General case of two bodies in contact'.
BS EN 13001-3-3:2014 Cl. 5.3.

NOTATION

limiting width of surface (bodies 1 & 2)
A Bf(R11,R12,R21,R22) geometric functions
bwidth of contact line (cylinder analysis)
b1 b2
c dlengths of contact semi-axes
dh1 dh2depth of hardening from contact surface (bodies 1 & 2)
iRcurvature (ex. iR11=1/R11)
k1 k2f(E,v) material constants
m nf(A,B) geometric functions
OceOrientation angle of contact ellipse
Pcontact force
psiAngle (deg) between pr. axes (parallel to curvatures 1/R11 & 1/R21) of bodies 1 &
psi1 psi2Orientation angles of both bodies (pr. axes 1/R11 & 1/R21)
q0max contact pressure
R11Body 1 Principal Radius 1 Minumum (+ve for convex curvature)
R12Body 1 Principal Radius 2 Maximum
R21Body 2 Principal Radius 1 Minumum
R22Body 2 Principal Radius 2 Maximum
thetageometric constant

INPUT DATA FORMAT

LET E1=:nu1=:Fy1=:dh1=0:E2=:nu2=:Fy2=:dh2=0
LET P=:b1=:b2=
LET R11=:R12=0:R21=:R22=0
LET psi1=RAD(0):psi2=RAD(0)
PROC072

PROJECT INPUT


Twelve related test cases are presented.
Each group of four cases considers Body2 being orientated 0, 30, 60 & 90deg from Body1 which is not rotated.
The first group has equal min & max radii for the two bodies. That is: R11=R21 & R12=R22.
The second group (4 cases) has R11 less than R21 & R12=R22.
The third group (4 cases) has R11 greater than R21 & R12=R22.

PROCtitle("1000mm Wheel Test","","Pmax=500t")
LET E1=2070:nu1=.3:Fy1=8:dh1=0:E2=2070:nu2=.3:Fy2=8:dh2=0:REM 180727
LET P=500:b1=50:b2=60
LET R11=100:R12=20000:R21=100:R22=20000:REM 180725
LET psi1=RAD(0):psi2=RAD(0):PROC072
LET psi1=RAD(0):psi2=RAD(30):PROC072
LET psi1=RAD(0):psi2=RAD(60):PROC072
LET psi1=RAD(0):psi2=RAD(90):PROC072
LET R11=100:R12=20000:R21=1000:R22=20000
LET psi1=RAD(0):psi2=RAD(0):PROC072
LET psi1=RAD(0):psi2=RAD(30):PROC072
LET psi1=RAD(0):psi2=RAD(60):PROC072
LET psi1=RAD(0):psi2=RAD(90):PROC072
LET R11=1000:R12=20000:R21=100:R22=20000
LET psi1=RAD(0):psi2=RAD(0):PROC072
LET psi1=RAD(0):psi2=RAD(30):PROC072
LET psi1=RAD(0):psi2=RAD(60):PROC072
LET psi1=RAD(0):psi2=RAD(90):PROC072

PROJECT OUTPUT

The calculated results & plots allow interesting comparisions to be made between these cases.
For example, for the three radii groups and four orentation set, note the variation in aspect ratio, stresses & orientation of the contact ellipse.
These are intuitively correct and confirm the importance of radii & orientation specification on shape & area of contact zone and stress magnitude.

1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 0deg

LET iR11=1/R11:iR12=1/R12:iR21=1/R21:iR22=1/R22
LET iR11=0.01:iR12=5E-5:iR21=0.01:iR22=5E-5
psi=ABS(psi2-psi1)=0
psi=ABS(0-0)=0
XiR=iR11*COS(psi1)-iR12*SIN(psi1)+iR21*COS(psi2)-iR22*SIN(psi2)=0.02
XiR=0.01*COS(0)-5E-5*SIN(0)+0.01*COS(0)-5E-5*SIN(0)=0.02
YiR=iR11*SIN(psi1)+iR12*COS(psi1)+iR21*SIN(psi2)+iR22*COS(psi2)=1E-4
YiR=0.01*SIN(0)+5E-5*COS(0)+0.01*SIN(0)+5E-5*COS(0)=1E-4
Oce=atn_YiRdivXiR=5E-3
Oce=5E-3=5E-3
CE=(1-nu1^2)/E1+(1-nu2^2)/E2=8.792E-4
CE=(1-0.3^2)/2070+(1-0.3^2)/2070=8.792E-4
KD=1.5/(iR11+iR12+iR21+iR22)=74.63
KD=1.5/(0.01+5E-5+0.01+5E-5)=74.63
Ctheta=(KD/1.5)*SQR((iR11-iR12)^2+(iR21-iR22)^2+2*(iR11-iR12)*(iR21-iR22)*COS(2*psi))=0.99
Ctheta=(74.63/1.5)*SQR((0.01-5E-5)^2+(0.01-5E-5)^2+2*(0.01-5E-5)*(0.01-5E-5)*COS(2*0))=0.9901
LET theta=ACS(Ctheta):thetaD=DEG(theta)
LET theta=0.1412:thetaD=8.089
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c=alpha*(P*KD*CE)^(1/3)=24.89
c=7.774*(500*74.63*8.792E-4)^(1/3)=24.89
d=beta*(P*KD*CE)^(1/3)=0.9188
d=0.287*(500*74.63*8.792E-4)^(1/3)=0.9188
fc=1.5*P/(3.142*c*d)=10.44
fc=1.5*500/(3.142*24.89*0.9188)=10.44
RF_001=(3*Fy1)/(fc)=2.299
RF_001=(3*8)/(10.44)=2.299
RF_002=(3*Fy2)/(fc)=2.299
RF_002=(3*8)/(10.44)=2.299
END072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 30deg


LET iR11=0.01:iR12=5E-5:iR21=0.01:iR22=5E-5
psi= ABS(0.5236-0)= 0.5236
XiR= 0.01*COS(0)-5E-5*SIN(0)+0.01*COS(0.5236)-5E-5*SIN(0.5236)= 0.01864
YiR= 0.01*SIN(0)+5E-5*COS(0)+0.01*SIN(0.5236)+5E-5*COS(0.5236)= 5.093E-3
Oce= 0.2668= 0.2668
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(0.01+5E-5+0.01+5E-5)= 74.63
Ctheta= (74.63/1.5)*SQR((0.01-5E-5)^2+(0.01-5E-5)^2+2*(0.01-5E-5)*(0.01-5E-5)*COS(2*0.5236))= 0.8574
LET theta=0.5406:thetaD=30.97
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 2.673*(500*74.63*8.792E-4)^(1/3)= 8.557
d= 0.5002*(500*74.63*8.792E-4)^(1/3)= 1.601
fc= 1.5*500/(3.142*8.557*1.601)= 17.42
RF_003= (3*8)/(17.42)= 1.378
RF_004= (3*8)/(17.42)= 1.378
END072
LET psi1=0:psi2=1.047
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 60deg

LET iR11=0.01:iR12=5E-5:iR21=0.01:iR22=5E-5
psi= ABS(1.047-0)= 1.047
XiR= 0.01*COS(0)-5E-5*SIN(0)+0.01*COS(1.047)-5E-5*SIN(1.047)= 0.01496
YiR= 0.01*SIN(0)+5E-5*COS(0)+0.01*SIN(1.047)+5E-5*COS(1.047)= 8.734E-3
Oce= 0.5286= 0.5286
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(0.01+5E-5+0.01+5E-5)= 74.63
Ctheta= (74.63/1.5)*SQR((0.01-5E-5)^2+(0.01-5E-5)^2+2*(0.01-5E-5)*(0.01-5E-5)*COS(2*1.047))= 0.4952
LET theta=1.053:thetaD=60.33
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 1.479*(500*74.63*8.792E-4)^(1/3)= 4.735
d= 0.7196*(500*74.63*8.792E-4)^(1/3)= 2.304
fc= 1.5*500/(3.142*4.736*2.304)= 21.88
RF_005= (3*8)/(21.88)= 1.097
RF_006= (3*8)/(21.88)= 1.097
END072
LET psi1=0:psi2=1.571
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 90deg

LET iR11=0.01:iR12=5E-5:iR21=0.01:iR22=5E-5
psi= ABS(1.571-0)= 1.571
XiR= 0.01*COS(0)-5E-5*SIN(0)+0.01*COS(1.571)-5E-5*SIN(1.571)= 9.948E-3
YiR= 0.01*SIN(0)+5E-5*COS(0)+0.01*SIN(1.571)+5E-5*COS(1.571)= 0.01005
Oce= 0.7904= 0.7904
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(0.01+5E-5+0.01+5E-5)= 74.63
Ctheta= (74.63/1.5)*SQR((0.01-5E-5)^2+(0.01-5E-5)^2+2*(0.01-5E-5)*(0.01-5E-5)*COS(2*1.571))= 2.017E-4
LET theta=1.571:thetaD=90
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 1*(500*74.63*8.792E-4)^(1/3)= 3.201
d= 1*(500*74.63*8.792E-4)^(1/3)= 3.201
fc= 1.5*500/(3.142*3.201*3.201)= 23.3
RF_007= (3*8)/(23.29)= 1.03
RF_008= (3*8)/(23.29)= 1.03
END072
LET R11=100:R12=2E4:R21=1000:R22=2E4
LET psi1=0:psi2=0
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 0deg

LET iR11=0.01:iR12=5E-5:iR21=1E-3:iR22=5E-5
psi= ABS(0-0)= 0
XiR= 0.01*COS(0)-5E-5*SIN(0)+1E-3*COS(0)-5E-5*SIN(0)= 0.011
YiR= 0.01*SIN(0)+5E-5*COS(0)+1E-3*SIN(0)+5E-5*COS(0)= 1E-4
Oce= 9.091E-3= 9.091E-3
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(0.01+5E-5+1E-3+5E-5)= 135.1
Ctheta= (135.1/1.5)*SQR((0.01-5E-5)^2+(1E-3-5E-5)^2+2*(0.01-5E-5)*(1E-3-5E-5)*COS(2*0))= 0.9817
LET theta=0.1901:thetaD=10.89
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 6.301*(500*135.1*8.792E-4)^(1/3)= 24.58
d= 0.3199*(500*135.1*8.792E-4)^(1/3)= 1.248
fc= 1.5*500/(3.142*24.59*1.248)= 7.778
RF_009= (3*8)/(7.779)= 3.085
RF_010= (3*8)/(7.779)= 3.085
END072
LET psi1=0:psi2=0.5236
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 30deg

LET iR11=0.01:iR12=5E-5:iR21=1E-3:iR22=5E-5
psi= ABS(0.5236-0)= 0.5236
XiR= 0.01*COS(0)-5E-5*SIN(0)+1E-3*COS(0.5236)-5E-5*SIN(0.5236)= 0.01084
YiR= 0.01*SIN(0)+5E-5*COS(0)+1E-3*SIN(0.5236)+5E-5*COS(0.5236)= 5.933E-4
Oce= 0.05467= 0.05467
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(0.01+5E-5+1E-3+5E-5)= 135.1
Ctheta= (135.1/1.5)*SQR((0.01-5E-5)^2+(1E-3-5E-5)^2+2*(0.01-5E-5)*(1E-3-5E-5)*COS(2*0.5236))= 0.9419
LET theta=0.3419:thetaD=19.59
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 3.896*(500*135.1*8.792E-4)^(1/3)= 15.2
d= 0.4084*(500*135.1*8.792E-4)^(1/3)= 1.593
fc= 1.5*500/(3.142*15.2*1.594)= 9.852
RF_011= (3*8)/(9.853)= 2.436
RF_012= (3*8)/(9.853)= 2.436
END072
LET psi1=0:psi2=1.047
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 60deg

LET iR11=0.01:iR12=5E-5:iR21=1E-3:iR22=5E-5
psi= ABS(1.047-0)= 1.047
XiR= 0.01*COS(0)-5E-5*SIN(0)+1E-3*COS(1.047)-5E-5*SIN(1.047)= 0.01046
YiR= 0.01*SIN(0)+5E-5*COS(0)+1E-3*SIN(1.047)+5E-5*COS(1.047)= 9.409E-4
Oce= 0.08975= 0.08975
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(0.01+5E-5+1E-3+5E-5)= 135.1
Ctheta= (135.1/1.5)*SQR((0.01-5E-5)^2+(1E-3-5E-5)^2+2*(0.01-5E-5)*(1E-3-5E-5)*COS(2*1.047))= 0.8566
LET theta=0.5417:thetaD=31.04
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 2.667*(500*135.1*8.792E-4)^(1/3)= 10.41
d= 0.5007*(500*135.1*8.792E-4)^(1/3)= 1.954
fc= 1.5*500/(3.142*10.41*1.954)= 11.73
RF_013= (3*8)/(11.74)= 2.044
RF_014= (3*8)/(11.74)= 2.044
END072
LET psi1=0:psi2=1.571
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 90deg

LET iR11=0.01:iR12=5E-5:iR21=1E-3:iR22=5E-5
psi= ABS(1.571-0)= 1.571
XiR= 0.01*COS(0)-5E-5*SIN(0)+1E-3*COS(1.571)-5E-5*SIN(1.571)= 9.95E-3
YiR= 0.01*SIN(0)+5E-5*COS(0)+1E-3*SIN(1.571)+5E-5*COS(1.571)= 1.05E-3
Oce= 0.1051= 0.1051
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(0.01+5E-5+1E-3+5E-5)= 135.1
Ctheta= (135.1/1.5)*SQR((0.01-5E-5)^2+(1E-3-5E-5)^2+2*(0.01-5E-5)*(1E-3-5E-5)*COS(2*1.571))= 0.8106
LET theta=0.6253:thetaD=35.82
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 2.359*(500*135.1*8.792E-4)^(1/3)= 9.204
d= 0.536*(500*135.1*8.792E-4)^(1/3)= 2.091
fc= 1.5*500/(3.142*9.203*2.091)= 12.4
RF_015= (3*8)/(12.4)= 1.935
RF_016= (3*8)/(12.4)= 1.935
END072
LET R11=1000:R12=2E4:R21=100:R22=2E4
LET psi1=0:psi2=0
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 0deg

LET iR11=1E-3:iR12=5E-5:iR21=0.01:iR22=5E-5
psi= ABS(0-0)= 0
XiR= 1E-3*COS(0)-5E-5*SIN(0)+0.01*COS(0)-5E-5*SIN(0)= 0.011
YiR= 1E-3*SIN(0)+5E-5*COS(0)+0.01*SIN(0)+5E-5*COS(0)= 1E-4
Oce= 9.091E-3= 9.091E-3
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(1E-3+5E-5+0.01+5E-5)= 135.1
Ctheta= (135.1/1.5)*SQR((1E-3-5E-5)^2+(0.01-5E-5)^2+2*(1E-3-5E-5)*(0.01-5E-5)*COS(2*0))= 0.9817
LET theta=0.1901:thetaD=10.89
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 6.301*(500*135.1*8.792E-4)^(1/3)= 24.58
d= 0.3199*(500*135.1*8.792E-4)^(1/3)= 1.248
fc= 1.5*500/(3.142*24.59*1.248)= 7.778
RF_017= (3*8)/(7.779)= 3.085
RF_018= (3*8)/(7.779)= 3.085
END072
LET psi1=0:psi2=0.5236
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 30deg

LET iR11=1E-3:iR12=5E-5:iR21=0.01:iR22=5E-5
psi= ABS(0.5236-0)= 0.5236
XiR= 1E-3*COS(0)-5E-5*SIN(0)+0.01*COS(0.5236)-5E-5*SIN(0.5236)= 9.635E-3
YiR= 1E-3*SIN(0)+5E-5*COS(0)+0.01*SIN(0.5236)+5E-5*COS(0.5236)= 5.093E-3
Oce= 0.4863= 0.4863
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(1E-3+5E-5+0.01+5E-5)= 135.1
Ctheta= (135.1/1.5)*SQR((1E-3-5E-5)^2+(0.01-5E-5)^2+2*(1E-3-5E-5)*(0.01-5E-5)*COS(2*0.5236))= 0.9419
LET theta=0.3419:thetaD=19.59
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 3.896*(500*135.1*8.792E-4)^(1/3)= 15.2
d= 0.4084*(500*135.1*8.792E-4)^(1/3)= 1.593
fc= 1.5*500/(3.142*15.2*1.594)= 9.852
RF_019= (3*8)/(9.853)= 2.436
RF_020= (3*8)/(9.853)= 2.436
END072
LET psi1=0:psi2=1.047
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 60deg

LET iR11=1E-3:iR12=5E-5:iR21=0.01:iR22=5E-5
psi= ABS(1.047-0)= 1.047
XiR= 1E-3*COS(0)-5E-5*SIN(0)+0.01*COS(1.047)-5E-5*SIN(1.047)= 5.958E-3
YiR= 1E-3*SIN(0)+5E-5*COS(0)+0.01*SIN(1.047)+5E-5*COS(1.047)= 8.734E-3
Oce= 0.9723= 0.9723
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(1E-3+5E-5+0.01+5E-5)= 135.1
Ctheta= (135.1/1.5)*SQR((1E-3-5E-5)^2+(0.01-5E-5)^2+2*(1E-3-5E-5)*(0.01-5E-5)*COS(2*1.047))= 0.8566
LET theta=0.5417:thetaD=31.04
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 2.667*(500*135.1*8.792E-4)^(1/3)= 10.41
d= 0.5007*(500*135.1*8.792E-4)^(1/3)= 1.954
fc= 1.5*500/(3.142*10.41*1.954)= 11.73
RF_021= (3*8)/(11.74)= 2.044
RF_022= (3*8)/(11.74)= 2.044
END072
LET psi1=0:psi2=1.571
PROC072


1000mm Wheel - PROC072 Contact General Case - Pmax=500t - Relative Orientation 90deg

LET iR11=1E-3:iR12=5E-5:iR21=0.01:iR22=5E-5
psi= ABS(1.571-0)= 1.571
XiR= 1E-3*COS(0)-5E-5*SIN(0)+0.01*COS(1.571)-5E-5*SIN(1.571)= 9.48E-4
YiR= 1E-3*SIN(0)+5E-5*COS(0)+0.01*SIN(1.571)+5E-5*COS(1.571)= 0.01005
Oce= 1.477= 1.477
CE= (1-0.3^2)/2070+(1-0.3^2)/2070= 8.792E-4
KD= 1.5/(1E-3+5E-5+0.01+5E-5)= 135.1
Ctheta= (135.1/1.5)*SQR((1E-3-5E-5)^2+(0.01-5E-5)^2+2*(1E-3-5E-5)*(0.01-5E-5)*COS(2*1.571))= 0.8106
LET theta=0.6253:thetaD=35.82
alpha=FN_LIP(Ctheta,alpha())
beta=FN_LIP(Ctheta,beta())
c= 2.359*(500*135.1*8.792E-4)^(1/3)= 9.204
d= 0.536*(500*135.1*8.792E-4)^(1/3)= 2.091
fc= 1.5*500/(3.142*9.203*2.091)= 12.4
RF_023= (3*8)/(12.4)= 1.935
RF_024= (3*8)/(12.4)= 1.935
END072


60x120 Cyl Wheel - PROC072b input for contact stress - Fref=sigmaHu

LET E1=.207E6:nu1=.3:Fy1=900:dh1=5:E2=.207E6:nu2=.3:Fy2=900:dh2=0
LET E1=2.07E5:nu1=0.3:Fy1=900:dh1=5:E2=2.07E5:nu2=0.3:Fy2=900:dh2=0
LET b1=150:b2=120
LET b1=150:b2=120
LET R11=0:R12=0:R21=60/2:R22=0
LET R11=0:R12=0:R21=30:R22=0
LET psi1=RAD(0):psi2=RAD(0)
LET psi1=0:psi2=0
LET PRo=0:Fref=1500:Pu=30*9810
LET PRo=0:Fref=1500:Pu=2.943E5

60x120 Cyl Wheel - PROC072b Contact by Cylinder 180906 - Fref=sigmaHu

CE=(1-nu1^2)/E1+(1-nu2^2)/E2=8.792E-6
CE=(1-0.3^2)/2.07E5+(1-0.3^2)/2.07E5=8.792E-6
LET D1=2*R11:D2=2*R21
LET D1=0:D2=60
KD=D2=60
KD=60=60
function was = .798*SQR((PRo/b2)/(KD*CE))-Fref
Bisection Method - 24 iterations to find soluton 2.237E5
p=PRo/b2=1864
p=2.237E5/120=1864
fHz=.798*SQR(p/(KD*CE))=1500
fHz=.798*SQR(1864/(60*8.792E-6))=1500
b=1.6*SQR(p*KD*CE)=1.587
b=1.6*SQR(1864*60*8.792E-6)=1.587
Afl=b2*b=190.4
Afl=120*1.587=190.4
tau=.3*fHz=450
tau=.3*1500=450
ENDPROC


PROJECT END

END072