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Xiamen Zhisen Electromechanical Equipment Co.,Ltd

ADD: Room 501, No.213 Long Shan South Road, Siming District, Xiamen, China

Contact: Melissa zheng

TEL: 86-592-5791296

Mobile: 86-185 5923 6160

E-mail: zsmachinery@163.com

Lead screw Torque

The torque required to lift or lower a load can be calculated by "unwrapping" one revolution of a thread. This is most easily described for a square or buttress thread as the thread angle is 0 and has no bearing on the calculations. The unwrapped thread forms a right angle triangle where the base is *horizontally* in the direction opposite the direction of the frictional force. Using this free-body diagram the torque required to lift or lower a load can be calculated:^{[8]}^{[9]}

Screw material | Nut material | |||
---|---|---|---|---|

Steel | Bronze | Brass | Cast iron | |

Steel, dry | 0.15–0.25 | 0.15–0.23 | 0.15–0.19 | 0.15–0.25 |

Steel, machine oil | 0.11–0.17 | 0.10–0.16 | 0.10–0.15 | 0.11–0.17 |

Bronze | 0.08–0.12 | 0.04–0.06 | - | 0.06–0.09 |

where

*T*= torque*F*= load on the screw*d*= mean diameter_{m}= coefficient of friction (common values are found in the table to the right)

*l*= lead- =
= lead angle

Based on the T_{lower} equation it can be found that the screw is self-locking when the coefficient of friction is greater than the tangent of the lead angle. An equivalent comparison is when the friction angle is greater than the lead angle ( ).^{[11]} When this is not true the screw will *back-drive*, or lower under the weight of the load.^{[8]}

The efficiency, calculated using the torque equations above, is:^{[12]}^{[13]}

For screws that have a thread angle other than zero, such as a trapezoidal thread, this must be compensated as it increases the frictional forces. The equations below takes this into account:^{[12]}^{[14]}

where

is one half the thread angle.If the leadscrew has a collar in which the load rides on then the frictional forces between the interface must be accounted for in the torque calculations as well. For the following equation the load is assumed to be concentrated at the mean collar diameter (d_{c}):^{[12]}

where *d _{c}* is the mean collar diameter. For collars that use thrust bearings the frictional loss is negligible and the above equation can be ignored.

Material combination | Starting | Running |
---|---|---|

Soft steel / cast iron | 0.17 | 0.12 |

Hardened steel / cast iron | 0.15 | 0.09 |

Soft steel / bronze | 0.10 | 0.08 |

Hardened steel / bronze | 0.08 | 0.06 |

Nut material | Safe loads [psi] | Speed |
---|---|---|

Bronze | 2500–3500 | Low speed |

Bronze | 1600–2500 | 10 fpm |

Cast iron | 1800–2500 | 8 fpm |

Bronze | 800–1400 | 20–40 fpm |

Cast iron | 600–1000 | 20–40 fpm |

Bronze | 150–240 | 50 fpm |

The running speed for a leadscrew (or ball screw) is typically limited to, at most, 80% of the calculated critical speed. The critical speed is the speed that excites the natural frequency of the screw. For a steel leadscrew or steel ballscrew, the critical speed is approximately^{[17]}

where

*N*= critical speed in RPMd

_{r}= smallest (root) diameter of the leadscrew in inches*L*= length between bearing supports in inches*C*= .36 for one end fixed, one end free*C*= 1.00 for both ends simple*C*= 1.47 for one end fixed, one end simple*C*= 2.23 for both ends fixed

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