CN108896230B - A finite element-based method for ultrasonic testing of bolt tightening force and determination of key testing parameters - Google Patents

Abstract

The invention proposes a method for ultrasonic testing of bolt tightening force and determination of key testing parameters based on finite element, and the method is suitable for nondestructive measurement of bolt tightening force by ultrasonic sound time method. Combining the finite element theory with the principle of acoustic elasticity, the principle model of ultrasonic testing of bolt tightening force is established. By establishing the finite element model of the bolt and the statics simulation, the axial stress distribution law of the bolt on the ultrasonic propagation path is obtained, so as to determine the shape factor of the bolt. Combined with the acousto-elastic coefficient of the bolt material measured by the critical refraction longitudinal wave, the ultrasonic detection coefficient of the bolt tightening force was calculated. The method has low cost and good adaptability, and can realize accurate and rapid determination of detection coefficients.

Description

A finite element-based ultrasonic testing of bolt tightening force and determination of key testing parameters method

1. Technical field

The invention relates to the technical field of bolt fastener testing, and provides a finite element-based ultrasonic testing method for bolt tightening force and a method for determining key testing parameters.

2. Background technology

Bolted connections are widely used in armored vehicles, aerospace, special machinery and other industrial fields due to their advantages of simple assembly, convenient disassembly, high efficiency, low cost, and good adaptability. For different types of bolts, in order to ensure the working quality and reliability of the mechanical equipment, a certain pre-tightening force must be given to the bolts. The bolts with excessive pre-tightening force are prone to fracture under the action of axial load, and the pre-tightening force is too small. The required clamping effect cannot be achieved, so accurately controlling the size of the pre-tightening force and monitoring the size of the axial force in the service state of the bolt is very important to ensure the quality of the bolted connection and the safety of the structure.

In practical engineering, the commonly used bolt pre-tightening force measurement techniques and methods include torque wrench method, resistance strain gauge method, optical measurement mechanics method, ultrasonic measurement method, etc. Among them, the resistance strain gauge method and the optical measuring mechanics method are less used in engineering due to the limitation of detection principle and measurement conditions; the torque wrench method is the most commonly used bolt preload control and measurement method in engineering. The discreteness of the friction coefficient between the threaded surface of the nut and the contact surface of the nut and the connected part leads to the discreteness of the torque coefficient. In practical applications, a large error will also occur, up to about 30%. The key and premise of the ultrasonic measurement method is to obtain the accurate mathematical relationship between the ultrasonic propagation time and the tightening force, that is, the measurement coefficient. The general method is to obtain the measurement coefficients under different specifications of bolts and connection states through a large number of experiments, which is costly. , poor adaptability, which is not conducive to the engineering application of the ultrasonic testing method of bolt tightening force.

The invention proposes a method for ultrasonic testing of bolt tightening force and determination of key testing parameters based on finite element. The method has low cost and good adaptability, can realize accurate and rapid determination of testing parameters, and is conducive to promoting bolt tightening force. Engineering application of ultrasonic testing technology and fast on-site measurement of bolt tightening force.

3. Content of the Invention

The purpose of the present invention is to provide a method for ultrasonic detection of bolt tightening force and determination of key detection parameters, which is used to accurately and quickly detect bolt tightening force. The purpose of accurate, non-destructive and rapid detection is achieved, and the practicability of ultrasonic testing technology for bolt tightening force is improved.

The concrete technical scheme of the present invention is as follows:

(1) Based on finite element theory and sonoelasticity theory, establish the mathematical relationship between bolt tightening force and ultrasonic propagation time difference, and establish the principle model of bolt tightening force ultrasonic detection;

(2) According to the specification and clamping distance of the bolt, establish a finite element model of the bolt connection structure (including bolts, nuts, and connected parts), and perform statics simulation to obtain the axial stress data on the bolt axis, and calculate the bolt shape factor .

(3) According to the "GB/T32073-2015 Nondestructive Testing Method for Ultrasonic Critical Refraction Longitudinal Wave Testing of Residual Stresses", the loading experiment was carried out on the standard tensile specimen of the same material as the bolt. In order to improve the detection time resolution, one-dimensional fast Fourier transform The interpolation algorithm and cross-correlation algorithm process the sampled data, and perform linear fitting on the loading stress and the measured time difference, and finally obtain the acoustic elastic coefficient of the bolt material.

(4) The bolt shape factor, acoustic elastic coefficient and other bolt material property parameters are brought into the detection principle model, so as to determine the ultrasonic detection coefficient of bolt tightening force.

4. Description of the attached drawings

Figure 1 Bolt-nut mesh model;

Fig. 2 The finite element simulation model of bolted connection structure;

Figure 3. Original data and interpolation waveforms before and after bolt loading;

Figure 4. Ultrasonic longitudinal wave excitation and propagation path in the tested bolt;

Five, the specific implementation

Specific embodiments of the present invention are described in detail below:

1. The principle of ultrasonic longitudinal wave detection of bolt tightening force based on finite element

According to the theory of sonoelasticity, when an isotropic solid material is subjected to a stress in one direction, the sound velocity of ultrasonic longitudinal waves propagating along the stress direction can be deduced as:

V _L (σ)=V _L0 (1-K _L σ) (1)

In formula (1):

_VL — longitudinal wave speed of sound;

V _{L0 ——the} longitudinal wave sound speed in zero stress state;

K _L — longitudinal wave acoustic elasticity coefficient;

σ——stress, it is specified that the tensile stress is positive and the compressive stress is negative.

Since the stress distribution inside the bolt is not uniform, and the propagation path of the ultrasonic wave is along the axis of the bolt, under the action of the tightening force F, the axial stress on the axis of the bolt can be expressed as:

σ=σ(F,z) (2)

z represents the axial position of the bolt.

Divide the ultrasonic propagation path into several small units with a length of Δz. When the unit size is small enough, it can be considered that the stress on this section of the path is the same, and the resulting acoustic time changes:

where E is the Young's modulus of the bolt material.

In general, K _L is of the order of 10 ^-11 , σ is of the order of 10 ⁸ , and K _L σ<<1, so formula (3) can be further simplified to obtain:

Suppose the number of units on the bolt axis is N, when the ultrasonic excitation and reception methods of spontaneous and self-receiving are adopted, the ultrasonic propagation process includes forward and return travel, then the total propagation time change of ultrasonic longitudinal waves in the bolt caused by the tightening force F :

Let the original length of the bolt be L ₀ , when the element size is small enough, the above formula can be written in integral form:

Assuming that for bolts of the same specification, under the condition of the same clamping distance, the stress on the axis is proportional to the tightening force, then formula (2) can be expressed as:

σ=σ(F,z)=F·m(z) (7)

m(z) reflects the axial stress distribution on the axis of the bolt under the action of unit tightening force.

Substituting equation (7) into equation (6), we get:

make

The formula (8) is finally simplified to:

λ is defined as the bolt shape factor, which is related to the specification, shape and clamping distance of the bolt; k is called the ultrasonic testing coefficient of bolt tightening force. Since V _L0 , K _L , and E are all inherent properties of the bolt material, therefore, For bolts of the same material, when the ultrasonic method is used to measure the tightening force of the bolt, the detection coefficient is only related to the bolt shape factor.

2. Determine the bolt shape factor

The invention uses the finite element simulation software to establish the finite element model of the bolt connection, obtains the axial stress distribution state of the bolt through statics simulation calculation, and provides a new method for determining the force range of the bolt and the bolt shape factor λ.

In order to accurately express the rise angle and profile angle of the thread, so as to obtain the accurate force state of the thread part, the Hypermesh tool is used, and the overall hexahedral thread meshing strategy is used to establish a finite element mesh model of M10×1.5 bolt connection, and use ABAQUS The software calculates and post-processes the model. In order to improve the calculation efficiency and ensure the calculation accuracy at the same time, the mesh densification is carried out on the thread part.

The material properties, contacts, boundary conditions, and applied loads of the model are defined in ABAQUS software, and calculated and post-processed. The external thread surface of the bolt is selected as the main surface, the internal thread surface of the nut is the slave surface, the normal behavior of the contact surface is defined as hard contact, and the tangential behavior is defined as penalty function Coulomb friction. Since the force and deformation of the connected parts are not concerned and the relative slippage between the connected parts and the bolts and nuts is very small, the analytical rigid body torus is used to simulate the contact surfaces with the bolts or nuts. The contact state is set to bind, and at the same time, all the degrees of freedom of the contact surface with the bolt head are restricted by the boundary conditions, and only the degree of freedom of the surface of the connected part in contact with the nut is retained in the axial direction, and is applied at the reference point at the center of the ring Axial load.

Extract the axial position coordinate z _n and the axial stress σ _n at the nodes on the ultrasonic propagation path. Since the size of the model element is small enough, the bolt shape factor can be calculated by formula (12):

According to formula (7), σ∝F, then λ has nothing to do with F.

3. Acoustic elasticity coefficient of bolt material

The present invention adopts the critical refraction longitudinal wave, and carries out the loading experiment on the standard tensile sample of the same material as the bolt according to the "GB/T32073-2015 Nondestructive Testing Method for Residual Stress Ultrasonic Critical Refraction Longitudinal Wave Detection" to determine the acoustic elastic coefficient of the bolt material.

The propagation time difference of the critically refracted longitudinal wave in a fixed sound path l:

Within the yield limit of the bolt material, the tensile specimen is stably loaded by the electronic tensile testing machine, and the time difference t _i before and after loading and the loading stress σ _i displayed by the testing machine are detected at every certain stress value. Linear fitting is performed by the least square method, and then the acoustic elastic coefficient K _L of the bolt material is calculated.

4. Sampling signal interpolation and cross-correlation processing

The operating frequency of the ultrasonic transducer for detection is 0.5-10MHz. According to the sampling theorem, when the sampling frequency is greater than 2 times the highest frequency in the signal, the digital signal after sampling completely retains the information in the original waveform signal. In practical applications Ensure that the sampling frequency is 2.56 to 4 times the highest frequency of the signal. The present invention selects an ultrasonic signal data acquisition card with a sampling frequency of 100 MHz, which can not only acquire ultrasonic fundamental frequency signals, but also obtain high-order harmonic signals caused by ultrasonic nonlinearity.

Since the effect of acoustic time variation caused by the tightening force is weak, usually at the nanometer level, and the sampling period is 10ns, it is necessary to interpolate the sampling data before and after loading. This method uses the Matlab tool to perform one-dimensional fast Fourier on the original sampling data Leaf interpolation processing realizes up-sampling, thereby improving the time resolution, and the interpolation multiple can be adjusted according to the actual detection needs.

Because the waveforms before and after loading are similar, there is only a certain delay, and other feature information is exactly the same, so by correlating the waveform data under the action of the interpolated tightening force with the natural state, that is, the interpolated waveform data before loading, more accurate results can be obtained. sound time difference.

5. Determination of bolt tightening force ultrasonic measurement coefficient and tightening force measurement

The results of equations (12) and (14), and the longitudinal wave sound velocity V _L0 and Young's modulus E of the bolt material are brought into equation (10) to obtain the ultrasonic measurement coefficient of bolt tightening force:

F=k·t.

Claims (3)

1. a bolt fastening force ultrasonic detection method based on finite elements is characterized by comprising the following steps:

(1) establishing a bolt fastening force ultrasonic detection principle model: combining a finite element theory with a bolt fastening force ultrasonic detection technology based on an acoustic elasticity theory, introducing a bolt shape factor concept, and establishing a bolt fastening force ultrasonic detection principle model:

wherein F represents a bolt fastening force, V_L0Representing the longitudinal wave velocity, K, in a zero stress state_LThe method comprises the steps of representing a longitudinal wave acoustic elastic coefficient, wherein E is the Young modulus of a bolt material, lambda is a bolt shape factor, k is a bolt fastening force ultrasonic detection coefficient, and t is the total propagation time variation of ultrasonic longitudinal waves in a bolt caused by a bolt fastening force F;

(2) determining a bolt form factor: the method comprises the following steps of establishing a finite element mesh model of a bolt connection structure by adopting an integral hexahedral thread meshing strategy and finite element simulation software, and obtaining the axial stress distribution state of the bolt through static simulation calculation, so as to determine the stress range of the bolt and the shape factor lambda of the bolt: defining material property, contact, boundary condition and fastening force load of the model according to actual conditions, simplifying the connected piece into a plane analysis rigid body, setting the contact state of the connected piece with a bolt and a nut as binding, and setting the axial position coordinate z of a junction on an ultrasonic propagation path_nAnd axial stress σ_nExtraction is performed, and since the model cell size is sufficiently small, the form factor of the bolt can be calculated using equation (3):

wherein L is₀M (z) reflects the axial stress distribution of the bolt on the axis under the action of unit fastening force for the original length of the bolt, and the stress distribution inside the bolt is not uniform and is ultrasonicThe propagation path is along the axis of the bolt, so under the effect of the fastening force F, the axial stress σ on the bolt axis can be expressed as:

σ＝σ(F,z) (4)

z represents the axial position of the bolt, and assuming that the magnitude of stress on the axis is proportional to the fastening force for the same specification of the bolt at the same clamping distance, equation (4) can be expressed as:

σ＝σ(F,z)＝F·m(z) (5)

when σ ∈ F is expressed by the formula (5), λ is independent of F;

(3) determining the acoustic elastic coefficient of the bolt material: making a standard tensile sample which is the same as the bolt material, carrying out a loading experiment, calibrating the acoustic elastic coefficient by using the critical refraction longitudinal wave, and measuring the propagation time difference of the critical refraction longitudinal wave in a fixed acoustic path l:

within the yield limit of the bolt material, the tensile sample is stably loaded through an electronic tensile testing machine, and the time difference t before and after loading is detected at certain stress values_iAnd the loading stress sigma displayed by the testing machine_iLinear fitting is carried out by a least square method, and then the acoustic elastic coefficient K of the bolt material is calculated_L：

(4) Substituting the bolt shape factor, the acoustic elastic coefficient and other bolt material attribute parameters into a detection principle model to obtain the mathematical relationship between the bolt fastening force and the ultrasonic propagation time: the results of the expressions (3) and (7) and the longitudinal wave sound velocity V of the bolt material_L0And substituting the elastic modulus E into the formula (2) to obtain the ultrasonic measurement coefficient of the bolt fastening force:

F＝k·t。

2. the method according to claim 1, wherein the ultrasonic transducer for detection operates in a self-generating and self-receiving mode, the operating frequency is 0.5-10 MHz, and the appropriate operating frequency is selected according to the bolt material and the length to reduce the attenuation of the ultrasonic wave in the propagation process and obtain an effective echo signal.

3. The method according to claim 1 or 2, wherein one-dimensional fast fourier interpolation processing and cross-correlation operation are performed on the ultrasonic head wave signal sampling data before and after loading to improve time resolution and detection accuracy.

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