joint_press_fit.xlsBy Alex Slocum

Last modified 12/10/04 by Xue'en Yang and Alex Slocum, with thanks to Stephen Jarman and Richard Blakelock Clearance and pressure in shrink-fit bodies

LoadsTorque to be transmitted (N-mm) torque 2Axial force to be transmitted (N) force 400

Coefficient of friction mu 0.15ot 20

Stress concentration factor at interface edge scf 2Rotation speed (rpm) rpm 3600

Outer body input parameteresOutside diameter (mm) obod 330.000

Interface diameter (mm) obid 20.000Plus tolerance (mm) obptol 0.005

Minus tolerance (mm) obmtol 0.005obe 2.00E+05obsy 50

Poisson's ratio obn 0.27obcte 1.17E-05obrho 7.827

Inner body input parametersEngagement length (mm) L 10.000

Intended outside diameter (mm) ibod 20.020Dimensioned outside diameter (mm) 20.017

Plus tolerance (mm) ibptol 0.005Minus tolerance (mm) ibmtol 0.005Inside diameter (mm) ibid 2

ibe 2.00E+05ibsy 50

Poisson's ratio ibn 0.27ibcte 1.17E-05ibrho 7

Shrink-fit designDesired assembly clearance at deltaT (mm) ddt 0

robdt 1.17E+02ribdt 1.17E+02

Press-fit designMaximum assembly force to press fit (N) Fpfmax 1.28E+04Minimum assembly force to press fit (N) Fpfmin 3.48E+03

Enter numbers in BOLD, Results in RED

Operating temperature (oC)

Modulus of elasticity (N/mm2)Yield strength (N/mm2)

Coefficient of thermal expansion (1/oC)Density (g/cm3)

Modulus of elasticity (N/mm2)Yield strength, obsy (N/mm2)

Coefficient of thermal expansion (1/oC)Density (g/cm3)

Required differential temperature if heating outer body (oC)Required differential temperature if cooling inner body (oC)

joint_press_fit.xlsBy Alex Slocum

Last modified 12/10/04 by Xue'en Yang and Alex Slocum, with thanks to Stephen Jarman and Richard Blakelock Clearance and pressure in shrink-fit bodies

Interference parametersrPI 4.24E+00

Differential Poisson radial interference due to axial force (mm) ddp -1.73E-05Differential thermal radial expansion (mm) ted 0.00E+00

Outer body rotating inner diameter radial displacement (mm) robd 1.24E-03Inner body rotating outer diameter radial displacement (mm) ribd 9.51E-07

Total additional diametrical interference amount to be added (to ibod) (mm) addi -2.51E-03Interference fit calculations (assumes addi has been added to ibod)

Maximum diametrical interference (mm) maxdelta 2.75E-02maxip 1.36E+02

Minimum diametrical interference (mm) mindelta 7.49E-03minip 3.69E+01

Minimum safety margin (min obtained pressure/required pressure) 8.70E+00Maximum sustainable torque (N-mm) maxt 1.28E+05Minimum sustainable Torque (N-mm) mint 3.48E+04

Minimum safety margin (min obtained torque/required torque) 17400.686Outer body material stresses at maximum interface pressure

Radial displacement of inner surface (mm) 8.66E-03obsr -1.36E+02obsc 1.37E+02obsz 4.69E-03obtau 1.72E-08

Max radial centrifugal stress (N/mm2) obrc 1.09E+01obcc 2.48E+01obvm 2.57E+02

Resulting safety factor (Yield stress)/(scf*Von Mises stress) 0.097Inner body material stresses at maximum interface pressure

Radial displacement of outer surface (mm) -5.09E-03ibsr -1.36E+02ibsc -1.38E+02ibsz 1.28E+00ibtau 1.27E-03ibrc 3.30E-02ibcc 8.17E-02ibvm 2.74E+02

Resulting safety factor (Yield stress)/(scf*Von Mises stress) 0.091

Enter numbers in BOLD, Results in RED

Minimum required interface pressure (N/mm2)

Maximum resulting interface pressure (N/mm2)

Minimum resulting interface pressure (N/mm2)

Radial press-fit stress at ID (N/mm2)Circumferential press-fit stress at ID (N/mm2)Axial stress from applied axial Force (N/mm2)

Shear stress from applied Torque (N/mm2)

Max circumferential centrifugal stress (N/mm2)Max Von Mises stress (N/mm2)

Radial press-fit stress (N/mm2)Circumferential press-fit stress (N/mm2)

Axial stress from applied axial Force (N/mm2)Shear stress from applied Torque (N/mm2)

Max radial centrifugal stress (N/mm2)Max circumferential centrifugal stress at ID (N/mm2)

Von Mises stress at ID (N/mm2)

Equations Ref

1234

(See diagrams)5

(See diagrams)5

6 Evaluate the stresses at inside, outside and sqrt(DiDo) diameters7 For the outer body8 case 1: stresses at inner radius 10.0000009 -135.530890

10 136.5301960.004694

11 0.00000012 Radial centrifugal stress (N/mm2) 0.000000

24.778168257.392998

13 For the inner body14 case 1: stresses at inner radius 1.00000015 -0.00002716 -273.79422717 1.283506

0.00012718 Radial centrifugal stress (N/mm2) 0.00000019 0.081674

274.356545

Radial press-fit stress (N/mm2)Circumferential press-fit stress (N/mm2)

Axial stress from applied axial Force (N/mm2)Shear stress from applied Torque (N/mm2)

Circumferential centrifugal stress at ID (N/mm2)Von Mises stress at ID (N/mm2)

Radial press-fit stress (N/mm2)Circumferential press-fit stress (N/mm2)

Axial stress from applied axial Force (N/mm2)Shear stress from applied Torque (N/mm2)

Circumferential centrifugal stress at ID (N/mm2)Von Mises stress at ID (N/mm2)

Evaluate the stresses at inside, outside and sqrt(DiDo) diametersFor the outer body

case 2: stresses at outer radius 165.000000 case 3: stresses sqrt(DiDo)/20.0000000.9993060.0046940.0000000.0000005.6179246.614884

For the inner bodycase 2: stresses at outer radius 10.010000 case 3: stresses sqrt(DiDo)/2

-135.530890-138.263365

1.2835060.001270

0.0000000.019006

138.191113

Evaluate the stresses at inside, outside and sqrt(DiDo) diametersFor the outer body

40.6201920-7.74462238.74392840.00469400.000000010.92392612.75937120.100212

For the inner body3.1638585

-123.2210912-150.5731637

1.28350630.00020060.0330120.042970

140.157351

From Slocum, A. H., Precision Machine Design, © 1995, Society of Manufacturing Engineers, Dearborn, MI. (first published by Prentice Hall in 1992), pp 387-399

Radial displacements due to Poisson effect, thermal expansion and rotationInner body Poisson radial displacement

Thermal radial mismatch

, use Dint erface=DI , outerOuter body radial displacement caused by rotation

ucentri , outer=ρω2

8 E¿ {−(D I , outer

2 )3

+(3+ηouter)[ (DO, outer2+D

I , outer2)

4(1+ηouter)⋅

D I , outer

2+

DO ,outer

2 D I , outer

8(1−ηouter) ]}(3)

Inner body radial displacement caused by rotation

ucentri , outer=ρω2

8 E¿ {−(DO , inner

2 )3

+(3+ηinner )[ (DO, inner2+D

I , inner2)

4 (1+ηinner)⋅

DO ,inner

2+

DO, inner DI , inner

2

8 (1−ηinner ) ]}(4)

Interface pressure as a result of diametrical interference

P= Δ

DI , outer

Eouter ( DO ,outer2+D

I , outer2

DO, outer

2−DI , outer

2

+ηouter)+ DO, inner

E inner ( DO, inner2+D

I , inner2

DO, inner

2−DI , inner

2

−η inner)For the outer body subjected to internal pressure, axial force, torque and rotation

The radial displacement of the inner surface caused by internal pressure

Radial stress caused by internal pressure

σ r , pressure=D

I , outer2 P

DO, outer2−D

I , outer 2 (1−D

O, outer2

DI , outer2 )

Circumferential stress caused by internal pressure

σ θ, pressure=D

I , outer2 P

DO ,outer2−D

I , outer2 (1+D

O, outer2

DI , outer2 )

Axial stress caused by axial force

σ z=4 F

π ( DO, outer

2−DI , outer

2 )

Radial displacements due to Poisson effect, thermal expansion and rotationInner body Poisson radial displacement

Thermal radial mismatch

, use Dint erface=DI , outerOuter body radial displacement caused by rotation

ucentri , outer=ρω2

8 E¿ {−(D I , outer

2 )3

+(3+ηouter)[ (DO, outer2+D

I , outer2)

4(1+ηouter)⋅

D I , outer

2+

DO ,outer

2 D I , outer

8(1−ηouter) ]}(3)

Inner body radial displacement caused by rotation

ucentri , outer=ρω2

8 E¿ {−(DO , inner

2 )3

+(3+ηinner )[ (DO, inner2+D

I , inner2)

4 (1+ηinner)⋅

DO ,inner

2+

DO, inner DI , inner

2

8 (1−ηinner ) ]}(4)

Interface pressure as a result of diametrical interference

P= Δ

DI , outer

Eouter ( DO ,outer2+D

I , outer2

DO, outer

2−DI , outer

2

+ηouter)+ DO, inner

E inner ( DO, inner2+D

I , inner2

DO, inner

2−DI , inner

2

−η inner)For the outer body subjected to internal pressure, axial force, torque and rotation

The radial displacement of the inner surface caused by internal pressure

Radial stress caused by internal pressure

σ r , pressure=D

I , outer2 P

DO, outer2−D

I , outer 2 (1−D

O, outer2

DI , outer2 )

Circumferential stress caused by internal pressure

σ θ, pressure=D

I , outer2 P

DO ,outer2−D

I , outer2 (1+D

O, outer2

DI , outer2 )

Axial stress caused by axial force

σ z=4 F

π ( DO, outer

2−DI , outer

2 )

Circumferential centrifugal stress at the inner surface

σ θ, centrifugal=ρω2 (3+ηouter)

8 (DI , outer2

4+

DO, outer2

2−

(1+3ηouter)(3+ηouter)

DI , outer2

4 )Von Mises stress at the inner surface

For the inner body subjected to external pressure, axial force, torque and rotationThe radial displacement of the outer surface caused by internal pressure

uouter=−DO, inner P

2 Eouter ( DO, inner2−D

I , inner2

DO, inner2−D

I , inner2

−ηinner)Radial stress caused by internal pressure

σ r , pressure=−D

O , inner2 P

DO , inner2−D

I , inner2 (1−D

I , inner2

DO ,inner 2 )

Circumferential stress caused by internal pressure

σ θ, pressure=D

O, inner2 P

DO , inner2−D

I , inner2 (1+D

I , inner2

DO, inner2 )

Axial stress caused by axial force

σ z=4 F

π ( DO, inner

2−DI , inner

2 )Shear stress caused by torque

τ=16 ΤDO, inner

π ( DO ,inner 4−D

I , inner 4 )Circumferential centrifugal stress at the outer surface

σ θ, centrifugal=ρω2 (3+ηinner )

8 ( DI ,inner 2

2+

DO, inner2

4−

(1+3η inner)(3+ηinner)

DO, inner2

4 )Von Mises stress at the outer surface

Circumferential centrifugal stress at the inner surface

σ θ, centrifugal=ρω2 (3+ηouter)

8 (DI , outer2

4+

DO, outer2

2−

(1+3ηouter)(3+ηouter)

DI , outer2

4 )Von Mises stress at the inner surface

For the inner body subjected to external pressure, axial force, torque and rotationThe radial displacement of the outer surface caused by internal pressure

uouter=−DO, inner P

2 Eouter ( DO, inner2−D

I , inner2

DO, inner2−D

I , inner2

−ηinner)Radial stress caused by internal pressure

σ r , pressure=−D

O , inner2 P

DO , inner2−D

I , inner2 (1−D

I , inner2

DO ,inner 2 )

Circumferential stress caused by internal pressure

σ θ, pressure=D

O, inner2 P

DO , inner2−D

I , inner2 (1+D

I , inner2

DO, inner2 )

Axial stress caused by axial force

σ z=4 F

π ( DO, inner

2−DI , inner

2 )Shear stress caused by torque

τ=16 ΤDO, inner

π ( DO ,inner 4−D

I , inner 4 )Circumferential centrifugal stress at the outer surface

σ θ, centrifugal=ρω2 (3+ηinner )

8 ( DI ,inner 2

2+

DO, inner2

4−

(1+3η inner)(3+ηinner)

DO, inner2

4 )Von Mises stress at the outer surface

Interference Diagrams

From Slocum, A. H., Precision Machine Design, © 1995, Society of Manufacturing Engineers, Dearborn, MI.

Radial displacements due to Poisson effect, thermal expansion and rotationInner body Poisson radial displacement

Thermal radial mismatch

, use Dint erface=DI , outerOuter body radial displacement caused by rotation

ucentri , outer=ρω2

8 E¿ {−(D I , outer

2 )3

+(3+ηouter)[ (DO, outer2+D

I , outer2)

4(1+ηouter)⋅

D I , outer

2+

DO ,outer

2 D I , outer

8(1−ηouter) ]}(3)

Inner body radial displacement caused by rotation

ucentri , outer=ρω2

8 E¿ {−(DO , inner

2 )3

+(3+ηinner )[ (DO, inner2+D

I , inner2)

4 (1+ηinner)⋅

DO ,inner

2+

DO, inner DI , inner

2

8 (1−ηinner ) ]}(4)

Interface pressure as a result of diametrical interference

P= Δ

DI , outer

Eouter ( DO ,outer2+D

I , outer2

DO, outer

2−DI , outer

2

+ηouter)+ DO, inner

E inner ( DO, inner2+D

I , inner2

DO, inner

2−DI , inner

2

−η inner)For the outer body subjected to internal pressure, axial force, torque and rotation

The radial displacement of the inner surface caused by internal pressure

Radial stress caused by internal pressure

σ r , pressure=D

I , outer2 P

DO, outer2−D

I , outer 2 (1−D

O, outer2

DI , outer2 )

Circumferential stress caused by internal pressure

σ θ, pressure=D

I , outer2 P

DO ,outer2−D

I , outer2 (1+D

O, outer2

DI , outer2 )

Axial stress caused by axial force

σ z=4 F

π ( DO, outer

2−DI , outer

2 )

Inner body outside diameter

Outer body inside diameter

Diametrical Interference = (obid-ibod)

Ideal case

Inner body outside diameter

Outer body inside diameter

Worst case for loose fit:Joint may not be able to transmit desired force or torque

Inner body outside diameter

Outer body inside diameter

Diametrical Interference = [(obid-obmtol-(ibod+ibptol)]

Worst case for tight fit:Yield stresses may be exceeded and outer body may rupture

Diametrical Interference = [(obid+obptol-(ibod-ibmtol)]

Radial displacements due to Poisson effect, thermal expansion and rotationInner body Poisson radial displacement

Thermal radial mismatch

, use Dint erface=DI , outerOuter body radial displacement caused by rotation

ucentri , outer=ρω2

8 E¿ {−(D I , outer

2 )3

+(3+ηouter)[ (DO, outer2+D

I , outer2)

4(1+ηouter)⋅

D I , outer

2+

DO ,outer

2 D I , outer

8(1−ηouter) ]}(3)

Inner body radial displacement caused by rotation

ucentri , outer=ρω2

8 E¿ {−(DO , inner

2 )3

+(3+ηinner )[ (DO, inner2+D

I , inner2)

4 (1+ηinner)⋅

DO ,inner

2+

DO, inner DI , inner

2

8 (1−ηinner ) ]}(4)

Interface pressure as a result of diametrical interference

P= Δ

DI , outer

Eouter ( DO ,outer2+D

I , outer2

DO, outer

2−DI , outer

2

+ηouter)+ DO, inner

E inner ( DO, inner2+D

I , inner2

DO, inner

2−DI , inner

2

−η inner)For the outer body subjected to internal pressure, axial force, torque and rotation

The radial displacement of the inner surface caused by internal pressure

Radial stress caused by internal pressure

σ r , pressure=D

I , outer2 P

DO, outer2−D

I , outer 2 (1−D

O, outer2

DI , outer2 )

Circumferential stress caused by internal pressure

σ θ, pressure=D

I , outer2 P

DO ,outer2−D

I , outer2 (1+D

O, outer2

DI , outer2 )

Axial stress caused by axial force

σ z=4 F

π ( DO, outer

2−DI , outer

2 )

Circumferential centrifugal stress at the inner surface

σ θ, centrifugal=ρω2 (3+ηouter)

8 (DI , outer2

4+

DO, outer2

2−

(1+3ηouter)(3+ηouter)

DI , outer2

4 )Von Mises stress at the inner surface

For the inner body subjected to external pressure, axial force, torque and rotationThe radial displacement of the outer surface caused by internal pressure

uouter=−DO, inner P

2 Eouter ( DO, inner2−D

I , inner2

DO, inner2−D

I , inner2

−ηinner)Radial stress caused by internal pressure

σ r , pressure=−D

O , inner2 P

DO , inner2−D

I , inner2 (1−D

I , inner2

DO ,inner 2 )

Circumferential stress caused by internal pressure

σ θ, pressure=D

O, inner2 P

DO , inner2−D

I , inner2 (1+D

I , inner2

DO, inner2 )

Axial stress caused by axial force

σ z=4 F

π ( DO, inner

2−DI , inner

2 )Shear stress caused by torque

τ=16 ΤDO, inner

π ( DO ,inner 4−D

I , inner 4 )Circumferential centrifugal stress at the outer surface

σ θ, centrifugal=ρω2 (3+ηinner )

8 ( DI ,inner 2

2+

DO, inner2

4−

(1+3η inner)(3+ηinner)

DO, inner2

4 )Von Mises stress at the outer surface

Circumferential centrifugal stress at the inner surface

σ θ, centrifugal=ρω2 (3+ηouter)

8 (DI , outer2

4+

DO, outer2

2−

(1+3ηouter)(3+ηouter)

DI , outer2

4 )Von Mises stress at the inner surface

For the inner body subjected to external pressure, axial force, torque and rotationThe radial displacement of the outer surface caused by internal pressure

uouter=−DO, inner P

2 Eouter ( DO, inner2−D

I , inner2

DO, inner2−D

I , inner2

−ηinner)Radial stress caused by internal pressure

σ r , pressure=−D

O , inner2 P

DO , inner2−D

I , inner2 (1−D

I , inner2

DO ,inner 2 )

Circumferential stress caused by internal pressure

σ θ, pressure=D

O, inner2 P

DO , inner2−D

I , inner2 (1+D

I , inner2

DO, inner2 )

Axial stress caused by axial force

σ z=4 F

π ( DO, inner

2−DI , inner

2 )Shear stress caused by torque

τ=16 ΤDO, inner

π ( DO ,inner 4−D

I , inner 4 )Circumferential centrifugal stress at the outer surface

σ θ, centrifugal=ρω2 (3+ηinner )

8 ( DI ,inner 2

2+

DO, inner2

4−

(1+3η inner)(3+ηinner)

DO, inner2

4 )Von Mises stress at the outer surface