Related Resources: calculators

### Bolt Torque and Clamping Force Formulas and Calculator per. JIS B 1083

Fastener Relation Between Torque and Clamping Force Formula and Calculator per. JIS B 1083

Relationship between the applied tightening torque and bolt preload Ff

Equation 1
Tf = Ts + Tw = K · Ff · d

Where:

Tf = fastener tightening torque
Tw = bearing surface torque
Ts = shank (threaded) portion torque
K = Torque coefficient (Eq. 2)
d = nominal diameter of the screw thread

Equation 2
K = 1 / ( 2 · d ) ( P / π + µs · d2 · sec α' + µw · Dw )

Where:

µs = coefficient of friction between threads
d2 = pitch diameter of the thread
µw = coefficient of friction between bearing surfaces
Dw = equivalent diameter of the friction torque bearing surfaces
α' = flank angle at the ridge perpendicular section of the thread ridge

Equation 3
tan α' = tan (α) · cos(β)

Where:

α = thread half angle (30°, for example),

Equation 4
β = l / ( 2πr )

Where:

When the bearing surface contact area is circular,

Equation 5
Dw = 2/3 · ( Do3 - Di3 ) / ( Do2 - Di2 )

Where:

Do = outside diameter bearing surface contact area
Di = inside diameter bearing surface contact area

Torques attributable to the threaded portion of a fastener, Ts, and bearing surfaces of a joint, Tw, are as follows:

Equation 6
Ts = Ff / 2 ( P / π + µs · d2 · sec α' )

Equation 7
Tw = ( Ff / 2 ) · µs · Dw

Where:

Ff, P, µ, d2, α′, µs, and Dw are as previously defined.

Equation 8
Tfy = K · Ffy · d

where the yield clamping force Ffy is given by:

Equation 9
Ffy = σy · As / { 1 + 3 [ 2 / dA ( P / π + µs · d2 ·sec(α') ) ]2 }

Where:

σy = yield point or proof stress of the bolt
As = stress area of the thread
dA = diameter of a circle having an area equal to the stress areaof the thread
Other varibles have been identified previously

Equation 10
dA = ( 4 As / π )1/2

Torque Coefficients K for Metric Hexagon Head
Bolt and Nut Coarse Screw Threads
JIS B 0205 (ISO 724) thread standard

 Coefficient of Friction K Between Threads, µs Between Bearing Surfaces, µw 0.08 0.10 0.12 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.08 0.117 0.130 0.143 0.163 0.195 0.228 0.261 0.293 0.326 0.359 0.10 0.127 0.140 0.153 0.173 0.206 0.239 0.271 0.304 0.337 0.369 0.12 0.138 0.151 0.164 0.184 0.216 0.249 0.282 0.314 0.347 0.380 0.15 0.153 0.167 0.180 0.199 0.232 0.265 0.297 0.330 0.363 0.396 0.20 0.180 0.193 0.206 0.226 0.258 0.291 0.324 0.356 0.389 0.422 0.25 0.206 0.219 0.232 0.252 0.284 0.317 0.350 0.383 0.415 0.448 0.30 0.232 0.245 0.258 0.278 0.311 0.343 0.376 0.409 0.442 0.474 0.35 0.258 0.271 0.284 0.304 0.337 0.370 0.402 0.435 0.468 0.500 0.40 0.285 0.298 0.311 0.330 0.363 0.396 0.428 0.461 0.494 0.527 0.45 0.311 0.324 0.337 0.357 0.389 0.422 0.455 0.487 0.520 0.553

Torque Coefficients K for Metric Hexagon Head