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**Summary:**

Bolted connections firmly hold two or more connected parts by clamping force between them.

The coefficient of friction of the bearing surface and the thread are two critical factors that affect the clamping force.

In this article, the focus is on the process of assembling high-strength bolts for the slewing ring of a large crane.

The article begins by analyzing the theoretical relationship between installation torque, coefficient of friction, torque coefficient and clamping force.

Next, through a comparative tightening test under fully lubricated conditions for the thread and bearing thread and surface, it is demonstrated that the lubrication condition has a significant impact on the reliability of fastener installation and the dispersion of the torque coefficient and of the friction coefficient.

Under full lubrication, the dispersion of friction coefficient and torque coefficient is smaller, resulting in greater stability and reliability of bolted connections.

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**Preface**

Bolted connections are a mechanical connection mode commonly used in lifting machines. Its reliability is crucial to the overall performance of lifting machines, especially for the high-strength bolted connections of important components such as the slewing ring.

A reliable bolted connection is essential for the normal operation of the product, and a failure in the connection may result in serious safety accidents.

The purpose of a bolted connection is to ensure that two or more connected parts are tightly fitted together. To withstand the movement load, sufficient clamping force must be maintained between the connected parts to ensure their reliable connection and normal operation.

Insufficient clamping force can result in lateral slippage between the two parts, which places the screw under unnecessary shear stress and can lead to screw fracture.

Therefore, improving the reliability and stability of high-strength bolted connections has become increasingly important. Inadequate tightening parameters or process control can negatively impact the reliability of the threaded connection and cause failures.

From the perspective of reducing the dispersion of clamping force and optimizing the tightening process, this paper determines the installation torque and tightening process of high-strength bolts for the slewing ring of large lifting equipment through theoretical analysis and comparison of test data.

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**1. Theoretical analysis**

1.1 The torque coefficient can be determined using the following formula, which is based on the relationship between the tightening torque and the clamping force.

Where:

- K – torque coefficient;
- T — Tightening torque;
- F — Clamping force;
- D – Nominal thread diameter

1.2 According to GBT16823.3, the screw torque must meet

Where,

- Q: Screw pitch
- μth: Thread friction coefficient
- μb: Coefficient of friction of the supporting surface of the nut or bolt
- d2: Pitch diameter of the thread
- dh: Inner diameter of the bearing surface in contact
- d0: External diameter of the bearing surface.

**When installing screws, the tightening torque T can be divided into three parts:**

The bearing surface friction torque (Tb) is the torque consumed by friction between the nut and the washer plane.

The thread torque (Tth) and clamping force (F) are consumed by the friction between the screw thread and the nut thread (body).

During fastener connection installation, most of the installation torque is lost due to these two sources of friction.

Therefore, the final friction coefficient (μb) and thread friction coefficient (μth) are the main factors that affect the clamping force (F).

Clamping force can vary greatly depending on friction coefficients.

The dispersion of the end face friction coefficient (μb) and the thread friction coefficient (μth) directly determines the stability of the clamping force (F). See Figure 1.

1.3 The thread friction coefficient can be calculated and determined approximately through the relationship between the thread torque and the clamping force, using the following formula.

1.4 The bearing surface friction coefficient can be calculated and determined approximately based on the relationship between the bearing surface friction torque and the clamping force using the following formula.

The torque coefficient, thread friction coefficient and bearing surface friction coefficient can be determined by measuring the tightening torque, thread torque, bearing surface friction torque and clamping force.

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**2. Test analysis**

The influence of torque coefficient, thread friction coefficient and bearing surface friction coefficient on clamping force in bolted connections under different conditions was analyzed and studied by testing the tightening process of different series of mounting bolts of the rotating ring. The testing equipment used is a vertical friction coefficient tester manufactured by Schatz, Germany, and the testing method follows GB/T 16823.3 standards.

Total torque, thread torque, bearing surface friction torque and clamping force are measured using a torque/angle sensor and a clamping force sensor. The torque coefficient, thread friction coefficient and end face friction coefficient can be automatically calculated using formulas (1), (3) and (4) on the test equipment.

Bolts selected for installing the slewing ring of a large crane are tested to simulate real assembly conditions. The test nuts are replaced with real nuts, and their materials, processing equipment and assembly process are consistent with the final products.

The screw specifications are:

- Standard: DIN931
- Size: M48-10.9
- Material: 40CrNiMo
- Surface Finish: Dacromet

The corresponding washer is:

- Standard: DIN6919
- Inner diameter: 49mm
- Outer diameter: 82mm

The replacement test nuts are made of domestic 960 material.

A silver-based high-temperature anti-seize agent is used as a lubricant.

Two groups of comparative tests were carried out to compare the influence of the lubrication state on the friction coefficient, torque coefficient and connection dispersion.

In one group, the grease was applied evenly to the threaded part of the screw, but not to the bearing surface of the washer. In the other group, the grease was applied to both the threaded part of the screw and the upper surface of the washer bearing surface. See Table 1 for test data.

table 1

Lubrication method | Number | F（KN） | T（Nm） | K | 1st | 1b | 1tot |

Complete lubrication | 1# | 1000.3 | 5389.39 | 0.11 | 0.08 | 0.09 | 0.08 |

two# | 1000.1 | 5185.81 | 0.11 | 0.07 | 0.09 | 0.08 | |

3# | 1000.24 | 5515.26 | 0.11 | 0.08 | 0.09 | 0.09 | |

4# | 1000.1 | 5683.1 | 0.12 | 0.09 | 0.09 | 0.09 | |

5# | 1000.1 | 5238.65 | 0.11 | 0.08 | 0.08 | 0.08 | |

6# | 1000.24 | 5394.05 | 0.11 | 0.08 | 0.09 | 0.08 | |

7# | 1000.37 | 5578.98 | 0.12 | 0.09 | 0.08 | 0.09 | |

8# | 1000.1 | 5768.57 | 0.12 | 0.08 | 0.1 | 0.09 | |

Thread lubrication only | 1# | 1000.1 | 6568.71 | 0.15 | 0.09 | 0.13 | 0.1 |

3# | 1000.4 | 5998.86 | 0.13 | 0.07 | 0.13 | 0.09 | |

4# | 1000.1 | 6716.1 | 0.15 | 0.09 | 0.14 | 0.11 | |

5# | 1000.3 | 5733.3 | 0.12 | 0.07 | 0.1 | 0.08 | |

6m | 1000.1 | 5982.98 | 0.13 | 0.08 | 0.12 | 0.09 | |

7# | 1000.2 | 5356.29 | 0.11 | 0.07 | 0.1 | 0.08 | |

8# | 1000.1 | 5990.22 | 0.13 | 0.09 | 0.13 | 0.09 |

Figures 3 and 4 present the curves of the support surface friction coefficient (μ_b) and the thread friction coefficient (μ_th) under two different lubrication conditions: lubrication of the thread only and complete lubrication, respectively.

The results indicate that the thread friction coefficient (μ_th) under lubricated conditions ranges from 0.07 to 0.09 and remains relatively stable.

In comparison, the rolling surface friction coefficient (μ_b) under lubricated conditions is relatively stable, with values ranging from 0.08 to 0.1 for all eight groups of samples. On the other hand, without lubrication, the friction coefficient of the support surface varies from 0.1 to 0.14, presenting low stability and great dispersion among the eight groups of samples.

Figure 5 shows the torque coefficient curve (K) under two lubrication conditions: thread lubrication only and complete lubrication.

The results reveal that the torque coefficient (K) of the eight groups of samples under full lubrication conditions ranges from 0.11 to 0.12, with stable values and minimal dispersion.

In contrast, the torque coefficient (K) of the screw-lubricated sample has a wider range, from 0.11 to 0.15, with low stability and greater dispersion.

Figures 6 and 7 show the torque tightening force curves during the screw tightening process under two lubrication conditions: thread-only lubrication and full lubrication, respectively.

The results indicate that, when the same tightening torque is applied, the clamping force under full lubrication is greater than under thread lubrication alone, and the dispersion of the curves within the same group of samples is smaller.

Data from the two groups of comparative tests show that applying lubricant to the bearing surface significantly reduces the coefficient of friction and the coefficient of torque by approximately 15% and improves stability. This demonstrates that applying lubricant to the bearing surface is an effective method for reducing the torque coefficient and increasing stability.

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**3. Industry Status**

In construction machinery, fasteners are typically installed using the torque method, which is straightforward, simple and easy to operate. Installation torque is determined by the coefficient of friction and an accurate numerical value is crucial. However, ignoring the dispersion of the coefficient of friction, known as standard deviation, can significantly impact the reliability of the bolted connection.

Currently, the national standard GB/T 1231-2000 defines the standards for pairs of high-strength bolt connections in steel structures. The torque coefficient (K) is specified as 0.11-0.15, with standard deviation ≤ 0.01.

Many users only focus on the torque coefficient and believe that once it is determined, the installation torque can be established immediately, leading to a clamping connection. However, standard deviation is often overlooked. If the standard deviation exceeds 0.01, the pre-tightening force of individual bolts will vary during installation. If the standard deviation is too large or too small, some pairs of fastener connections may be over- or under-tightened, which may pose a risk to installation reliability.

On the other hand, if the torque coefficient is large and the standard deviation is less than 0.01, the dispersion of the connection pair is minimal and the force on each pair of fasteners is relatively uniform. An increased torque coefficient during installation may lead to a higher torque value, but will not cause excessive tightening or looseness, leading to greater installation reliability and safety.

In conclusion, from a certain perspective, standard deviation is more important than torque coefficient.

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**4. Conclusion**

Thread friction coefficient, bearing surface friction coefficient, and torque coefficient are critical technical parameters that must be understood and mastered when installing pairs of fastener connections. Currently, these parameters are widely recognized and considered by most users during installation.

A lower coefficient of friction leads to a lower coefficient of torque. When determining installation torque, a lower torque coefficient results in a higher clamping force.

On the other hand, a higher torque coefficient leads to a lower clamping force. If the torque coefficient is small to a certain extent, the clamping force generated by a certain torque may exceed the strength limit of the screw, causing the high-strength screw to stretch or even break due to fatigue.

On the other hand, if the torque coefficient is too large, the clamping force generated will be too small and the fastener connecting pair will not work properly, causing play.

The state of lubrication has a significant impact on the thread friction coefficient, bearing surface friction coefficient and torque coefficient values. In general, fastener connection pairs with rough product surfaces and noticeable machining marks will have higher torque coefficient and friction coefficient values.

However, after lubrication, these values can decrease significantly. In addition, lubrication also affects the dispersion of thread friction coefficient, bearing surface friction coefficient and torque coefficient. The dispersion of these values is smaller under lubrication, ensuring greater stability and reliability of the bolted connection.