# Nut Factor

## Description

Bolted joints are one of the most common elements in construction and machine design. They consist of fasteners that capture and join other parts, and are secured with the mating of screw threads.The nut factor K accounts for the thread geometry, friction, pitch. When ISO and Unified National Standard threads are used the nut factor is as shown.A study of the effect of torquing two samples, one lubricated and the other unlubricated, 1/2 in.- 20 UNF bolts to 800 lb-in, produced the same mean preload of 7700 lbf. The preloads for the unlubricated bolt sample had a standard deviation from the mean value of 1100 lbf, whereas the lubricated sample had a standard deviation of 680 lbf. If the preload value and torques are used in the above relation to solve for the nut factor it is found to be K = 0.208, which is very close to the recommended value of 0.20

Related formulas## Variables

K | nut factor (dimensionless) |

d_{m} | mean thread diameter, close to pitch diameter (m) |

d | nominal bolt diameter (m) |

P | thread pitch (m) |

π | pi |

μ | friction coefficient in the threads (dimensionless) |

a | half the thread angle (typically 60°) = 30° (deg) |

μ_{c} | friction coefficient under torqued head or nut (dimensionless) |