# Blog

## Discussion on How to Calculate the Bolt Preload (Tightening Torque)

Bolted connection is the most common detachable connection method in mechanical equipment installation. In order to ensure the rigidity and anti-loosening ability of the bolt threaded connection in use, it is necessary to pre-tighten during assembly, and how determining the pre-tightening torque becomes a problem that needs to be studied. If the preload torque is too large, the connection will fail, and if it is too small, it will not meet the proper use requirements. Therefore, determining the tightening torque of the bolts has become an essential issue in assembly work.

## Analysis of Stress Condition of Bolted Connection Pair

Bolted connections are generally applied in groups, and the force transmission method, number and arrangement need to be designed according to the structure of the connected parts and the load of the connecting parts. In general, the stress conditions of the bolt joint are as follows:

(1) Pure axial force, the bolt is only subjected to axial force;

(2) Lateral force, the radial force of bolt;

(3) Rotational moment, such as wheel flange connection;

(4) Overturning moment, also called overturning moment.

Among them, (1) and (4) the bolt connection pair is under tension, and (2) and (3) the bolt connection pair can be under tension or shear force.

## Analysis of Tightening Torque in Anti-loosening Measures of Bolted Connection Pairs

There are three commonly used anti-loosening methods for bolted connections in engineering applications: frictional anti-loosening, mechanical anti-loosening and permanent anti-loosening. Among them, mechanical anti-loosening and frictional anti-loosening are called detachable anti-loosening. In installation applications, tightening torque needs to be applied. Permanent anti-loosening is called non-removable anti-loosening, which cannot be reused, so it is less used in mechanical equipment assembly work.

(1) Common friction and anti-loosening methods include the use of spring washers, self-locking nuts and double nuts. In the spring washer anti-loosening method, the tightening torque increases the compression torque of the spring washer, but because the value of the compression torque is not large, it is often ignored in the calculation. In the self-locking nut anti-loosening method, the tightening torque is the same as that of ordinary bolts. In the anti-loosening method of double nuts (top nuts), the tightening torque of the front and rear nuts should be considered.

(2) Common mechanical anti-loosening methods: use split pins, stop gaskets and string wire ropes, etc. Mechanical methods mostly use mechanical structures such as split pins to prevent the bolts from returning. The tightening torque of this method is the same as that of the ordinary method.

(3) Permanent anti-loosening methods include edge punching anti-loosening, bonding anti-loosening, etc. This method is generally used for permanent connection and cannot be disassembled, but its tightening torque is not the same as that of ordinary methods.

For the tightening torque of the bolted connection pair, the mechanical anti-loosening method and the permanent anti-loosening method are both single-nut tightening, and the tightening torque is the same as that of the general tension bolt connection. In the anti-loosening method of friction, the spring washer anti-loosening increases the pressing torque of the spring washer on the basis of the single nut tightening during tightening. When tightening the double nut method, it is necessary to pay attention to the difference in the tightening torque of the front and rear nuts, which needs to be treated separately.

## Analysis and Calculation of Relationship between Axial Force and Tightening Torque

The tightening torque is exerted by the torsional motion of the hydraulic wrench. The torsional torque T of the torsional motion mainly overcomes the thread resistance torque T1 of the thread pair and the end face friction torque T2 between the nut and the supporting surface of the connected piece. That is, the following formula can be obtained:

1

In the formula: T―tightening torque; F0—pre-tightening force, N;ω—thread rising angle;—thread equivalent friction angle; d2—thread pitch diameter, mm;

μ—the friction factor between the nut and the bearing surface of the connector;

Dw – the diameter of the nut or washer connected to the support plane;

d0—the outer diameter of the thread;

d—nominal diameter of the thread, mm;

K – Tightening torque coefficient,

Therefore, when the bolts are of the same size, the axial preload of the bolts is proportional to the tightening torque, and the proportionality factor is the tightening torque coefficient K.

The calculation of the value of the coefficient K is a relatively complicated process. Generally speaking, for ordinary coarse thread M12~M64 threads, the tightening torque coefficient generally varies within a certain range.

It can be considered that when the model of bolts, nuts, washers, connected parts and other parts is selected, the tightening torque coefficient is fixed under the determined working environment and working state. That is to say, in this case, the magnitude of the required preload directly determines the magnitude of the tightening torque that should be applied.

According to formula (1), the tightening torque and the bolt pre-tightening force have a linear relationship. Therefore, after the tightening torque is determined and controlled in the early operation, the pre-tightening force value can be calculated by experimental or theoretical methods. Due to the influence of the coefficient K value, the uncertainty of friction coefficient and geometric parameters, under a certain tightening torque, the variation range of the preload force value is relatively large. Therefore, the accuracy of controlling the bolt pre-tightening force by the tightening torque is not very high, and the error is about 25%, and the maximum can even reach about 40%.

This creates a contradiction: on the one hand, the specific value of the required preload force can be designed according to the application conditions and requirements, but on the other hand, the required preload force cannot be accurately applied in reality to achieve its The design value can only be determined by applying a certain tightening torque. Therefore, the following discussion only considers the purely linear relationship between tightening torque and preload and ignores this error.

## How to determine bolt preload (tightening torque)

Under normal circumstances, a flange connection body connected by N bolts and nuts pairs, while giving a certain tightening force F, generates an internal pressure Fx in the connection body. For this type of coupling for fluids with a certain internal pressure, the following four points must be considered when designing the tightening torque of the bolts:

(1) Ensure the strength of the bolt, that is, it is not allowed to lose the function of the connecting body due to the yield failure of the bolt due to excessive tightening torque.

(2) Ensure the strength of the thread, and prevent the thread from tripping due to excessive tightening torque.

(3) Ensure the strength of the flange, and the flange cannot be damaged due to excessive tightening torque.

(4) Ensure the performance of gaskets and washers, and ensure that the connection is not in place due to too small tightening torque, and the bolts are not damaged due to excessive tightening torque.

### Consider the strength of the bolt

It is generally stipulated that the preload stress of the tightened threaded connection shall not be greater than 80% of its material yield point σs. For steel bolts for general connections, the recommended preload limits are as follows:

Carbon steel bolts F0=(～)σSAS

Alloy steel bolt F0=(～)σSAS

In the formula: σs—the yield point of the bolt material, Mpa; As—the nominal stress cross-sectional area of the bolt, mm2;

For important bolted connections, there must be a method to control and measure the preload. The commonly used methods are:

(1) Torque method: When the torque wrench is used to measure the tightening torque, the preload coefficient Q=[1] is generally taken, and the indicated value of the torque wrench should be: M=0.2PD

(2) Nut angle method: After the nut is screwed to the point of contact with the connected part, it is rotated by a certain angle to obtain the required pre-tightening force.

(3) Bolt pre-stretching method: pre-stretch the bolt to the required deformation by heating, and then tighten the nut. After cooling, the bolt is shortened and the connection is pre-tightened. In this method, the bolt is not affected by the tightening torque, and the strength of the bolt is improved to a certain extent, but a pre-deformation device is required.

This calculation method of tightening torque, which simply considers bolt strength, has certain limitations. However, when there is no sealing requirement and the strength of the connected parts is high enough, it can be used as the actual tightening torque, especially in the tightening of anchor bolts, which is more common and suitable.

### Consider the strength of the thread

The proper tightening torque is required to ensure that the threads can be tightened without damage to the threads or nuts. This requires that the tightening torque must be between the screw-in torque and the limit torque. There are many factors that will affect the rotational torque and limit torque. The more important factors are the type, size, nut composition, hardness, thickness, etc. of the thread.

However, the thread teeth and other dimensions of standard bolts and nuts are specified according to the principle of equal strength and experience. When using standard parts, these parts do not require strength calculations. However, after the non-standard parts are used together, or after the material is changed, the strength of the thread needs to be further calculated to determine the limit tightening torque. The calculation method of this thread strength can be found in the relevant manuals.

Consider the strength of the connected pieces. When bolting flanges or other connectors, the strength of the connected parts is also an important factor to consider.

Of course, this pre-tightening force is the minimum pre-tightening force required by the bolt, and the calculated tightening torque is also the minimum tightening torque. Within a suitable size range, the tightening torque should take a larger value. Therefore, according to the most basic sealing requirements, the minimum tightening torque of the bolt is obtained.

### Determination of tightening torque

Proper tightening torque is very important for bolted joints. The first step in determining the tightening torque is to calculate a suitable preload force F. After the above analysis, it can be determined that the appropriate range of F is F1~Min (F2, F3, F4, F5). Among them, F1-the minimum compression force of the gasket to ensure the seal; F2-the compression force to destroy the gasket or washer; F3-the compression force to destroy the thread; F4-the maximum pre-tightening force available for the bolt; F5-to make the The tensile force of the compression surface failure.

Considering the use of standard fasteners and ignoring the extreme case of failure of the connected parts, it can be considered that in the bolted connection, the magnitude of the preload should be within the range of F1 to Min (F2, F4). Generally speaking, the tightening torque should take a large value within a suitable range, because the greater the axial force of the bolt, the better its anti-loosening performance and fatigue resistance, and the higher the efficiency of the bolt. So the most suitable preload force should be Min (F2, F4). That is to say, in the calculation process of the preload force, the maximum compression force that the gasket can bear is mainly considered, and the maximum allowable compression force of the bolt is calculated at the same time, and the smaller value of the two is taken.

## Summarize

In many cases, in the calculation of the tightening torque, only one or two cases are often considered, and the bolt tightening torque is analyzed and summarized without comprehensively considering a variety of different working conditions from the calculation of the minimum and maximum tightening torque. calculation method. In this paper, a more comprehensive theoretical calculation method of bolt tightening torque is obtained through discussion.