Radial pin for shaft-hub connection

The easiest and oldest way joints. It is a joint with a shape contact. The pin serves primarily to ensure the mutual positioning of the two parts. They are cylindrical or conical. The pins are dimensioned under simplified assumptions without will and without the pressing effect. When designing a pin, the cross section of the pin in the shear area must be the nominal cross-section of the pin.

Fig.1 Radial pin for shaft-hub connection

Torsion stress in the shaft:

τs=16MTπD3*JtubesJnetsτall
JtubesJnets=1/JnetsJtubes

τs - torsion stress in the shaft - [MPa]

MT - torque - [Nm]

D - diameter of the shaft - [mm]

τall - allowable shear stress - [MPa]


Allowable shear stress:

τall=0,4Rp0,2TSF*Cc

τall - allowable shear stress - [MPa]

Rp0,2T - the minimum yield strength or 0,2% proof strength at calculation temperature - [MPa]

SF - safety factor - []

Cc - coefficient of use of joints according to load - []


Coefficient of use of joints according to load:

load[]
Unidirectional load, non-impact load0,8
Unidirectional load, with a small impact load0,7
Unidirectional load, with a big impact load0,6
Alternating load, with a small impact load0,45
Alternating load, with a big impact load0,25

Shear stress in the pin:

τp=4MTπ*d2*D+2FAπ*d2τall

τp - shear stress in the pin - [MPa]

MT - torque - [Nm]

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]

FA - axial force - [N]

τall - allowable shear stress - [MPa]


Bearing stress in the pin and shaft:

p1=6MTD2*d+FAD*dσall

p1 - bearing stress in the pin and shaft - [MPa]

MT - torque - [Nm]

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]

FA - axial force - [N]

σall - allowable bearing stress - [MPa]


Allowable bearing stress:

σall=0,9Rp0,2TSF*Cc

σall - allowable bearing stress - [MPa]

Rp0,2T - the minimum yield strength or 0,2% proof strength at calculation temperature - [MPa]

SF - safety factor - []

Cc - coefficient of use of joints according to load - []


Bearing stress in the pin and hub:

p2=4MTd*Dh2-D2+FAd*Dh-D σall

p2 - bearing stress in the pin and hub - [MPa]

MT - torque - [Nm]

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]

Dh - diameter of the hub - [mm]

FA - axial force - [N]

σall - allowable bearing stress - [MPa]


Torsion stress in the hub:

τh=16MTDhπDh4-D4*JtubehJnethτall
JtubehJneth=1/JnethJtubeh

τh - torsion stress in the hub - [MPa]

MT - torque - [Nm]

D - diameter of the shaft - [mm]

Dh - diameter of the hub - [mm]

d - diameter of the pin - [mm]

τall - allowable shear stress - [MPa]

If the shaft and hub is loaded with the bending moment in the joint, the bending stress must be checked. If the shaft and hub is loaded with a shear force in the joint, the shear stress must be checked. The shaft and hub may be load in the joint by axial force. The shaft and hub must be checked for axial stresses. When calculating the different load types, it is necessary to calculate the combined stress.


Bending stress in the shaft:

σBs=32MBπD3*ZtubesZnetsσBall
ZtubesZnets=1/ZnetsZtubes

σB(s) - bending stress in the shaft - [MPa]

MB - bending moment - [Nm]

D - diameter of the shaft - [mm]

σBall - allowable bending stress - [MPa]


Allowable bending stress:

σBall=0,6Rp0,2TSF*Cc

σBall - allowable bending stress - [MPa]

Rp0,2T - the minimum yield strength or 0,2% proof strength at calculation temperature - [MPa]

SF - safety factor - []

Cc - coefficient of use of joints according to load - []


Bending stress in the hub:

σBh=32MBDhπDh4-D4*ZtubehZnethσBall
ZtubehZneth=1/ZnethZtubeh

σB(h) - bending stress in the hub - [MPa]

MB - bending moment - [Nm]

D - diameter of the shaft - [mm]

Dh - diameter of the hub - [mm]

σBall - allowable bending stress - [MPa]


Shear stress in the shaft:

τss=4FRπD2*AtubesAnetsτall
AtubesAnets=1/AnetsAtubes

τs(s) - shear stress in the shaft - [MPa]

FR - shear force - [N]

D - diameter of the shaft - [mm]

τall - allowable shear stress - [MPa]


Shear stress in the hub:

τsh=4FRπDh2-D2*AtubehAnethτall
AtubehAneth=1/AnethAtubeh

τs(h) - shear stress in the hub - [MPa]

FR - shear force - [N]

D - diameter of the shaft - [mm]

Dh - diameter of the hub - [mm]

τall - allowable shear stress - [MPa]


Axial stress in the shaft:

σAs=4FAπD2*AtubesAnetsσAall
AtubesAnets=1/AnetsAtubes

σA(s) - axial stress in the shaft - [MPa]

FA - axial force - [N]

D - diameter of the shaft - [mm]

σAall - allowable axial stress - [MPa]


Allowable axial stress:

σAall=0,45Rp0,2TSF*Cc

σAall - allowable axial stress - [MPa]

Rp0,2T - the minimum yield strength or 0,2% proof strength at calculation temperature - [MPa]

SF - safety factor - []

Cc - coefficient of use of joints according to load - []


Axial stress in the hub:

σAh=4FAπDh2-D2*AtubehAnethσAall
AtubehAneth=1/AnethAtubeh

σA(h) - axial stress in the hub - [MPa]

FA - axial force - [N]

D - diameter of the shaft - [mm]

Dh - diameter of the hub - [mm]

σAall - allowable axial stress - [MPa]


Combined stress in the shaft:

σtrescas =ZnetsZtubes*KtBs*σBs2+AnetsAtubes*KtAs*σAs2+4JnetsJtubes*Kts*τs2+τss2 σCall
ZnetsZtubes=1-16/3/πd/D
AnetsAtubes=1-4/πd/D
JnetsJtubes=1-8/3/πd/D1+d/D2

σtresca(s) - combined stress in the shaft - [MPa]

KtB(s) - concentration factor shaft in bending stress - []

σB(s) - bending stress in the shaft - [MPa]

KtA(s) - concentration factor shaft in axial stress - []

σA(s) - axial stress in the shaft - [MPa]

Kts - concentration factor shaft in torsion stress - []

τs - torsion stress in the shaft - [MPa]

τs(s) - shear stress in the shaft - [MPa]

σCall - allowable combined stress - [MPa]

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]


Concentration factor shaft in bending stress:

KtBs=3,000-6,250dD +41,000dD2-45,000dD3

KtB(s) - concentration factor shaft in bending stress - []

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]


Concentration factor shaft in axial stress:

0d/D0,7
KtAs=12,806-42,602dD +58,333dD2

KtA(s) - concentration factor shaft in axial stress - []

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]


Concentration factor shaft in torsion stress:

Kts=4,000-6,055dD +32,764dD2-38,330dD3

Kts - concentration factor shaft in torsion stress - []

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]


Allowable combined stress:

σCall=Rp0,2TSF*Cc

σCall - allowable combined stress - [MPa]

Rp0,2T - the minimum yield strength or 0,2% proof strength at calculation temperature - [MPa]

SF - safety factor - []

Cc - coefficient of use of joints according to load - []


Combined stress in the hub:

σtrescah =ZnethZtubeh*KtBh*σBh2+AnethAtubeh*KtAh*σAh2+4JnethJtubeh*Kth*τh2+τsh2 σCall
ZnethZtubeh=1-11-D/Dh4 *16/3/πd/Dh1-D/Dh3
AnethAtubeh=1-11-D/Dh2 *4/πd/Dh1-D/Dh
JnethJtubeh=1-11-D/Dh4 *8/3/πd/Dh1-D/Dh3+d/Dh21-D/Dh

σtresca(h) - combined stress in the hub - [MPa]

KtB(h) - concentration factor hub in bending stress - []

σB(h) - bending stress in the hub - [MPa]

KtA(h) - concentration factor hub in axial stress - []

σA(h) - axial stress in the hub - [MPa]

Kth - concentration factor hub in torsion stress - []

τh - torsion stress in the hub - [MPa]

τs(h) - shear stress in the hub - [MPa]

σCall - allowable combined stress - [MPa]

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]

Dh - diameter of the hub - [mm]


Concentration factor hub in bending stress:

d/Dh0,4;D/Dh0,9
KtBh=C1Bh+C2BhdDh +C3BhdDh2+C4BhdDh3
C1Bh=3,000
C2Bh=-6,250-0,585D/Dh +3,115D/Dh2
C3Bh=41,000-1,071D/Dh -6,746D/Dh2
C4Bh=-45,000+1,389D/Dh +13,889D/Dh2

KtB(h) - concentration factor hub in bending stress - []

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]

Dh - diameter of the hub - [mm]

C1B(h) - coefficient - []

C2B(h) - coefficient - []

C3B(h) - coefficient - []

C4B(h) - coefficient - []


Concentration factor hub in axial stress:

0<D/Dh0,9;d/Dh0,45
KtAh=C1Ah+C2AhdDh +C3AhdDh2
C1Ah=3,000
C2Ah=0,427-6,770D/Dh +22,698D/Dh2-16,670D/Dh3
C3Ah=11,357+15,665D/Dh -60,929D/Dh2+41,501D/Dh3

KtA(h) - concentration factor hub in axial stress - []

D - diameter of the shaft - [mm]

d - diameter of the pin - [mm]

Dh - diameter of the hub - [mm]

C1A(h) - coefficient - []

C2A(h) - coefficient - []

C3A(h) - coefficient - []


Concentration factor hub in torsion stress:

d/Dh0,4;D/Dh0,8
Kth=C1h+C2hdDh +C3hdDh2+C4hdDh3
C1h=4,000
C2h=-6,055+3,184D/Dh -3,461D/Dh2
C3h=32,764-30,121D/Dh +39,887D/Dh2
C4h=-38,330+51,542D/Dh -27,483D/Dh


Literature:

AISC: Specification for structural steel buildings: Allowable Stress design and plastic design 1989

Walter D. Pilkey, Deborah F. Pilkey: Peterson’s stress concentration factors. 2008

Joseph E. Shigley, Charles R. Mischke, Richard G. Budynas: Konstruování strojních součástí 2010.

MET-Calc: Allowable stress

A. Bolek, J. Kochman a kol.: Části a mechanismy strojů I. 1989.

K. Kříž a kol.: Strojní součásti 1. 1984.


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Radial pin for shaft-hub connection.pdf


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