Calculations
Torque Calculator is based on the equations given in the book "Construction Elements in Mechanical Engineering" (ISBN 978-3-642-24300-4). To calculate the admissible load \(F_{Vzul}\), the admissible tensile strength \(\sigma_{VM}\) is calculated as per following equation:
$$\sigma_{VM} = \frac{\nu_{Vv}R_{p0.2}}{\sqrt{1+3\left(2\frac{d_{2}}{d_{0}}\cdot\left(\frac{P}{\pi\cdot d_{2}}+\frac{\mu_{G}}{\cos\left(\frac{\alpha}{2}\right)}\right)\right)^{2}}}$$
Where:
- \(\nu_{Vv}\): utilization factor of the yield point stress
- \(R_{p0.2}\): 0,2 % proof stress of the bolt according to DIN EN ISO 898-1
- \(d_2\): pitch diameter of the bolt thread
- \(d_0\): diameter at the relevant smallest cross section
of the bolt
- \(P\): pitch of the thread
- \(\mu_G\): coefficient of friction in the thread
With \(\sigma_{VM}\) the admissible load \(F_{Vzul}\) is calculated as per following equation:
$$F_{Vzul} = \sigma_{VM} \cdot A_{0}$$
Where:
- \(A_{0}=\frac{\pi\cdot d_s^2}{4}\)
- \(d_s=\frac{d_2+d_3}{2}\): diameter at stress cross section
- \(d_3\): minor diameter of the bolt thread
The torque \(M_{SAM}\) which needs to be applied, is calculated as:
$$M_{SAM} = F_{Vzul}(\frac{P}{2\pi}+\frac{d_2}{2}\cdot \frac{\mu_G}{\cos (\frac{\alpha}{2})}+\mu_K\cdot\frac{D_K+D_C}{4} )$$
Where:
- \(\alpha\): flank angle of the thread
- \(\mu_K\): coefficient of friction in the head bearing
area
- \(D_K\): outer diameter of supporting surface of nut
- \(D_C\): inner diameter of supporting surface of nut
Frequently Asked Questions
Friction
The determination of the friction coefficient is quiet complicated, but yet very important. Check if there are any values available from the bolt manufacturer. The friction coefficient can considerably differ depending on the type / extent of the lubrication! A good source is the standard VDI 2230, which gives some ranges for \(\mu_G\) and \(\mu_K\) at room temperatures. Also you can check out following file:
Link.
More information about calculations
Check out VDI 2230 "Systematic calculation of high duty bolted joints, Joints with one cylindrical bolt", it explains very detailed all the calculation steps with a lot of background data.
