Key Joint Calculation Formulas in English Units

Transferred torque

where:

 

P

power [lb ft]

 

n

speed [rpm]

Calculation of Minimum Shaft Diameter

1. shaft inside diameter d h > 0

a)

b) if d min d h -> d min = 1.1 d h [mm]

c) if d min 1.5 d h -> d min = 1.5 d h [mm]

2. shaft inside diameter d h = 0

where:

 

d min

minimal shaft diameter [in]

 

d h

shaft inside diameter [in]

 

T

torque [Nm]

 

K a

application factor

 

K f

fatigue-life factor

 

S v

desired safety

 

τ A

Allowable Shear Stress

 

s

chamfer

 

p Dmins

minimal allowable pressure (groove, shaft) [MPa]

 

p Dminh

minimal allowable pressure (groove, hub) [MPa]

General calculation

the range of force activity on the shaft

h k = h - h s - 2 s [in]

the range of force activity on the hub

shaft diameter of the range of the force activity

hub diameter of the range of the force activity

force on shaft

force on hub

where:

 
 

T

torque [lbft]

 

F s

force on shaft [lb]

 

F h

force on hub [lb]

 

K a

application factor

 

K f

wear-life factor

 

K w

application factor

 

K m

load distribution factor

 

S v

desired safety

 

d

shaft diameter [in]

 

d s

shaft diameter where force F s actuates [in]

 

d h

shaft diameter where force F d actuates [in]

 

N

number of grooves [-]

 

h

height of groove [in]

 

h s

height of force point of action on shaft [in]

 

h h

height of force point of action on hub [in]

 

b

width of groove [in]

 

t

groove depth in shaft [in]

 

s

chamfer

 

p Dmins

minimal allowable pressure (groove, shaft) [psi]

 

p Dminh

minimal allowable pressure (groove, hub) [psi]

Minimum key length to transfer the torque

1. Fixed connection:

a)

 

b)

 

L min = min(L mins , L minh )

2. Flexible connection:

a)

 

b)

 

L min = min(L mins , L minh )

where:

 
 

F s

force on shaft [lb]

 

F h

force on hub [lb]

 

K a

application factor

 

K f

wear-life factor

 

K w

application factor

 

K m

load distribution factor

 

S v

desired safety

 

d

shaft diameter [in]

 

N

number of grooves [-]

 

h s

height of force point of action on shaft [in]

 

h h

height of force point of action on hub [in]

 

p Dmins

minimal allowable pressure (groove, shaft) [psi]

 

p Dminh

minimal allowable pressure (groove, hub) [psi]

Minimal Allowable pressure

1. Fixed connection:

a)

 

b)

2. Flexible connection:

a)

 

b)

where:

 
 

F s

force on shaft [lb]

 

F h

force on hub [lb]

 

K a

application factor

 

K f

wear-life factor

 

K w

application factor

 

K m

load distribution factor

 

S v

desired safety

 

d

inside diameter of groove section [in]

 

N

number of grooves [-]

 

h s

height of force point of action on shaft [in]

 

h h

height of force point of action on hub [in]

 

l f

active key length [in]

Strength Check

p mins p Ds

p minh p Dh

where:

 

p mins

minimal calculated shear pressure in shaft [psi]

 

p minh

minimal calculated shear pressure in hub [psi]

 

p Ds

allowable pressure in shaft [psi]

 

p Dh

allowable pressure in hub [psi]

Simplified calculation

Minimum key length to transfer the torque

1. Fixed connection:

2. Flexible connection:

where:

 
 

T

torque [lbft]

 

K a

application factor

 

K f

wear-life factor

 

K w

application factor

 

K m

load distribution factor

 

S v

desired safety

 

d

shaft diameter [in]

 

N

number of grooves [-]

 

h

height of groove [in]

 

s

chamfer

 

h st

connection height h st = h - 2 s [in]

 

p Dmin

allowable pressure on supporting surface of shaft, groove, or hub [psi]

Allowable pressure

1. Fixed connection:

2. Flexible connection:

where:

 
 

T

torque [lbft]

 

K a

application factor

 

K f

wear-life factor

 

K w

application factor

 

K m

load distribution factor

 

S v

desired safety

 

d

shaft diameter [in]

 

N

number of grooves [-]

 

h

height of groove [in]

 

s

chamfer [in]

 

h st

connection height h st = h - 2 s [inm]

 

l f

active key length [in]

Strength Check

p min p Ds

p min p Dh

where:

 

p min

minimal calculated h/2 pressure [psi]

 

p Ds

allowable pressure in shaft [psi]

 

p Dh

allowable pressure in hub [psi]