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

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

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

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Bolt Thread nomenclature Figure 1

Relationship between the applied tightening torque and bolt preload F_f

Equation 1
T_f = T_s + T_w = K · F_f · d

Where:

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

Equation 2
K = 1 / ( 2 · d ) ( P / π + µ_s · d₂ · sec α^' + µ_w · D_w )

Where:

P = screw thread pitch
µ_s = coefficient of friction between threads
d₂ = pitch diameter of the thread
µ_w = coefficient of friction between bearing surfaces
D_w = 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),
β = thread helix, or lead, angle.

Equation 4
β = l / ( 2πr )

Where:

r = thread radius (i.e., one-half the nominal diameter d)
l = thread lead = P

When the bearing surface contact area is circular,

Equation 5
D_w = 2/3 · ( D_o³ - D_i³ ) / ( D_o² - D_i² )

Where:

D_o = outside diameter bearing surface contact area
D_i = inside diameter bearing surface contact area

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

Equation 6
T_s = F_f / 2 ( P / π + µ_s · d₂ · sec α^' )

Equation 7
T_w = ( F_f / 2 ) · µ_s · D_w

Where:

F_f, P, µ, d2, α′, µ_s, and D_w are as previously defined.

Equation 8
T_fy = K · F_fy · d

where the yield clamping force F_fy is given by:

Equation 9
F_fy = σ_y · A_s / { 1 + 3 [ 2 / d_A ( P / π + µ_s · d₂ ·sec(α') ) ]² }

Where:

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

Equation 10
d_A = ( 4 A_s / 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, µ_s	Between Bearing Surfaces, µ_w
Between Threads, µ_s	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
Bolt and Nut Fine-Screw Threads
JIS B 0207 thread standard (ISO 724)

Coefficient of Friction K
Between Threads, µ_s	Between Bearing Surfaces, µ_w
Between Threads, µ_s	0.08	0.10	0.12	0.15	0.20	0.25	0.30	0.35	0.40	0.45
0.08	0.106	0.118	0.130	0.148	0.177	0.207	0.237	0.267	0.296	0.326
0.10	0.117	0.129	0.141	0.158	0.188	0.218	0.248	0.278	0.307	0.337
0.12	0.128	0.140	0.151	0.169	0.199	0.229	0.259	0.288	0.318	0.348
0.15	0.144	0.156	0.168	0.186	0.215	0.245	0.275	0.305	0.334	0.364
0.20	0.171	0.183	0.195	0.213	0.242	0.272	0.302	0.332	0.361	0.391
0.25	0.198	0.210	0.222	0.240	0.270	0.299	0.329	0.359	0.389	0.418
0.30	0.225	0.237	0.249	0.267	0.297	0.326	0.356	0.386	0.416	0.445
0.35	0.252	0.264	0.276	0.294	0.324	0.353	0.383	0.413	0.443	0.472
0.40	0.279	0.291	0.303	0.321	0.351	0.381	0.410	0.440	0.470	0.500
0.45	0.306	0.318	0.330	0.348	0.378	0.408	0.437	0.467	0.497	0.527

Relationship between Bolt Elongation and Axial Tightening Tension