Calculation dimensions for drive by key(s) ISO 5211

The feather key are used to transfer the torque between the shaft and the hub. The feather key are inserted into shaft and hub grooves. The torque is transmitted only by the flanks of the feather key. Therefore, the grooves of the grooves and the feather key must be parallel. The feather key are standardized most commonly used, which are listed in DIN 6885A.

The material is usually C45+C steel. For alternating or impact torque loads, the feather key is not suitable because changing the load direction and the impact of the wall, which can lead to loosening of the connection.

Fig.1 Stress, keyway
Fig.2 Key DIN 6885

force on the shaft surface:

F=2MTd

F - perimeter force on the shaft surface - [N]

MT - torque - [Nm]

d - diameter of the shaft - [mm]


key under shear stress:

τ=Fi*l-b-lt*b+πb24τall

τ - key under shear stress - [MPa

F - perimeter force on the shaft surface - [N]

i - number of key - []

l - key length - [mm]

b - key width - [mm]

lt - tolerance of key length - [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

Key/shaft under bearing stress:

ps=Fi*l-b-lt *1hs-t1t-t+t1-h-r1 σall

ps - key/shaft under bearing stress - [MPa]

F - perimeter force on the shaft surface - [N]

i - number of key - []

l - key length - [mm]

b - key width - [mm]

lt - tolerance of key length - [mm]

hs - the height of the key in the shaft - [mm]

t1t - tolerance of the groove height in the hub - [mm]

t - depth in the shaft - [mm]

t1 - depth in the hub - [mm]

r1 - max. rounding the key - [mm]

σall - allowable bearing stress - [MPa]


The height of the key in the shaft:

hs=t-d2+d2cossin-1bd

hs - the height of the key in the shaft - [mm]

t - depth in the shaft - [mm]

d - diameter of the shaft - [mm]

b - key width - [mm]


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 - []


Key/hub under bearing stress:

ph=Fi*l-b-lt *1hh-tt-t+t1-h-r1 σall

ph - key/hub under bearing stress - [MPa]

F - perimeter force on the shaft surface - [N]

i - number of key - []

l - key length - [mm]

b - key width - [mm]

lt - tolerance of key length - [mm]

hh - the height of the key in the hub - [mm]

tt - tolerance of the groove height in the shaft - [mm]

t - depth in the shaft - [mm]

t1 - depth in the hub - [mm]

h - key height - [mm]

r1 - max. rounding the key - [mm]

σall - allowable bearing stress - [MPa]


The height of the key in the hub:

hh=t+t1-hs

hh - the height of the key in the hub - [mm]

t - depth in the shaft - [mm]

t1 - depth in the hub - [mm]

hs - the height of the key in the shaft - [mm]


Example:

We should determine safety factor the keys, for shear stress and bearing stress, material the keys is C45+C. Key size according to DIN6885.

Values for the calculation will be from the standard EN ISO 5211. MT=8000Nm; d=72mm; Rp0,2T=305MPa; l=110mm; i=1; b=20mm; h=12mm; t=7,5mm; lt=0,5mm; t1t=0,2mm; t1=4,9mm; tt=0,2mm; r1=0,8mm.

Perimeter force on the shaft surface:

F=2MTd=2*800000072=222222,2N

Shear the key:

τ=Fi*l-b-lt*b+πb24 =222222,21*110-20-0,5*20+π*2024 =105,6MPa

Shear safety factor:

SF=0,4Rp0,2Tτ*Cc=0,4*305105,6*0,8 =0,92does not suit

The height of the key in the shaft:

hs=t-d2+d2cossin-1bd =7,5-722+722cossin-12072 =6,08mm

Key/shaft under bearing stress:

ps=Fi*l-b-lt *1hs-t1t-t+t1-h-r1
ps=222222,21*110-20-0,5 *1(6,08-0,2-7,5+4,9-12-0,8) =530,5MPa

Key/shaft safety factor under bearing stress:

SF=0,9Rp0,2Tps*Cc=0,9*305530,5*0,8 =0,41does not suit

The height of the key in the hub:

hh=t+t1-hs=7,5+4,9-6,08 =6,32mm

Key/hub under bearing stress:

ph=Fi*l-b-lt *1hh-tt-t+t1-h-r1
ph=222222,21*110-20-0,5 *1(6,32-0,2-7,5+4,9-12-0,8) =504,7MPa

Key/hub safety factor under bearing stress:

SF=0,9Rp0,2Tσall*Cc=0,9*305504,7*0,8 =0,44does not suit

Value safety factor key for shear stress and bearing stress is lower than 1. The key does not meet any safety of the connection.

As an engineer, we always provide the reliability and integrity of the drive and its components. However as far as stem components are concerned we either give little attention to mechanical integrity of stem or sometimes we leave it to valve vendor and assume stem design is sufficient enough to withstand actuator torque, this is not always true.

No table in standard or catalog can in any way replace the expert opinion of the technician. The maximum torque allowed is calculated during the engineering stage with sufficient safety to operate load and it must be ensured that the torque delivered by the drive is always less than the maximum torque allowed.


Literature:

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

František Boháček: Části a mechanismy strojů I. 1984.

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

R. Kříž: Strojní součásti I pro SPŠ strojnické 1984.


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Calculation dimensions for drive by key(s) ISO 5211.pdf


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