Study on Self-relaxation Mechanism of Bolted Connections under Vibration Conditions
In order to study the self-relaxation mechanism of bolt connection under vibration conditions, the three-dimensional bolt connection finite element model considering thread is established by ANSYS parametric language, the preload force is loaded by cooling method, and the transverse vibration transient analysis of bolt connection is carried out. The lateral excitation amplitude is studied. The initial preload, the threaded engagement surface, the bolt head and the bearing surface of the nut, and the friction factor of the joint surface between the joints affect the self-relaxation of the bolt connection.
The results show that the complete slip in the transverse vibration occurs first at the threaded engagement surface; the smaller the lateral excitation amplitude, the larger the initial preload, the larger the friction coefficient of the threaded engagement surface and the bolt head and nut bearing surface, the bolt connection The relaxation is less likely to occur; when the excitation amplitude is constant, the friction coefficient of the joint surface between the joints has no effect on the self-relaxation, but the larger the friction factor, the larger the shear load required for lateral vibration.
The research results are of great significance for understanding the self-relaxation of bolt connections and guiding the anti-loose design.
When the vibration is connected, the self-relaxation caused by the external cyclic shear load is second only to the fatigue failure, resulting in leakage, uneven force caused by fatigue fracture, reducing the dynamic performance of the whole machine and other adverse consequences, and even causing safety accidents. Therefore, it is important to study the self-relaxation of the bolted connection of vibration.
Self-relaxation and anti-looseness of bolted joints have been studied. Junker designed the Jonker test machine and studied the self-relaxation behavior of the bolted joint under lateral cyclic loading, and found that the bolted joint is more prone to self-relaxation.
Hess et al. studied the self-relaxation of bolted joints under transverse shear load through experiments and finite element simulations. It is proposed that the self-relaxation has four stages, that is, the sliding phase of the threaded meshing surface and the bearing surface, the complete sliding of the threaded mating surface and the bearing surface. The partial slip phase, the partial sliding of the threaded mating surface and the complete sliding phase of the bearing surface, the threaded mating surface and the bearing surface are completely slipped.
Nassar et al. used a linear model to study the thread inclination, pre-tightening force, the fit of the pores and the thread, the friction coefficient between the thread surface and the bearing surface, and the influence of the lateral vibration on the bolt. Nassar et al. proposed a more accurate analytical model to explain the bolt connection. Relaxation, and experimental research, check the analytical model.
The theoretical and experimental models of the above studies are based on the Jonker test machine, ignoring the joint friction between the joints, which is inconsistent with the actual.
Jiang et al. designed a new self-relaxation experimental device, combined with finite element simulation to study the self-relaxation of bolted joints. It is considered that self-relaxation can be divided into two stages, that is, the first stage of relaxation and nut rotation due to the temporary hysteresis of plastic material hysteresis The second stage relaxation of the clamping force loss is caused, and the friction coefficient of the joint surface is considered, but the thread spiral effect is not considered in the finite element simulation, and the self-relaxation of the bolt connection caused by the nut rotation is ignored.
Wang Dansheng et al. Experimental study on bolting relaxation detection of steel frame structures based on piezoelectric admittance. The results show that the method can better identify the looseness of the bolt connection, but does not analyze the cause of the loosening of the bolt connection of the steel frame structure.
Yang Guangxue et al. studied the anti-loose mechanism of the new anti-loose nut and used the three-dimensional finite element method to study the additional bending moment, the initial pre-tightening force and the influence of the locknut on the loosening of the bolt connection under the transverse cyclic load.
Based on the above research, a three-dimensional finite element model of bolted joints is established. The lateral vibration transient simulation is applied to the bolts by the cooling method. The excitation amplitude, the initial preload, the frictional relationship between the threaded meshing surface and the bearing surface are studied. The friction coefficient of the joint surface affects the self-relaxation of the bolt connection.
1. Research on self-relaxing simulation method of bolt connection
1.1 Parametric finite element modeling of bolted joints
The finite element method is used to study the self-relaxation caused by the nut rotation under the lateral vibration condition of the bolt connection. The finite element model must take into account the spiral effect of the thread, ie the establishment of a threaded three-dimensional bolted finite element model. The bolted finite element model is established by ANSYS parametric language programming, see Figure 1(a).
Among them, the bolt is composed of screw and thread, and is obtained by the body bonding command VGLUE as one body and then meshed; the nut modeling is similar to the bolt, and the bolt and nut finite element model is shown in Fig. 1(b).
Figure 1 Three-dimensional finite element model of bolted connection
The model geometry is: bolt nominal diameter D=12mm, bolt head diameter D1=16.6mm, bolt head height KW=7.5mm, nut height H=13mm, pitch p=1.75mm, bolt length L=64mm, connecting plate 80 mm × 80 mm × 20 mm (the two plates are the same size), the pores are δ/2 = 0.5 mm, and the thread profile angle is 60°.
High-strength steel for bolt material, elastic modulus E1=210GPa, Poisson's ratio Ï…1=0.3, density Ï1=7.9×103kg/m3, yield limit 640 MPa; connecting plate material selected Q235 steel, elastic modulus E2=210GPa, mooring Pine ratio Ï… 2 = 0.3, density Ï 2 = 7.9 × 103 kg / m 3 , yield limit 235 MPa.
1.2 Contact establishment and constraint application
1.2.1 Contact pair establishment
In this paper, the slip between the contact surfaces is considered. Therefore, the TTAGE170 is used as the target unit, and the CONTA173 which can simulate the slip is used as the contact unit to establish the contact pair on the thread meshing surface, the bolt head bearing surface, the nut bearing surface and the joint joint surface. And define the contact unit keyword KEYOPT(2)=0 to select the augmented Lagrangian algorithm as the contact algorithm, and define the keyword KEYOPT(5)=1 to realize the automatic closing gap.
The friction factor of the thread engagement surface, the bolt head pressure bearing surface, the nut pressure bearing surface and the joint joint surface is defined as μ1, μ2, μ3, respectively, by establishing the contact pair and defining the material friction factor method.
The friction coefficient of each joint surface is found in the literature, specifically paraffin lubrication (0.05), MoS2 grease lubrication (0.1), mechanical lubricant lubrication (0.17) and dry friction (0.2).
1.2.2 Constraint application
For the actual project where the bolt connection of a fixed motor such as a machine tool is caused by a cyclic load to cause a joint to move in a single direction, the upper plate of the model is fixed so that the lower plate has a certain degree of freedom.
Therefore, all the nodes on the upper surface of the upper plate are fully constrained, and all the nodes on the upper surface of the upper plate and the coordinate plane XOZ are constrained by Y-direction displacement, and all the nodes on the upper surface of the upper plate and the coordinate plane YOZ are subjected to X-direction displacement constraint; All nodes on both surfaces parallel to the coordinate plane XOZ perform Y-direction displacement constraints.
1.3 bolted pre-tightening
Considering that the pre-tightening unit cannot withstand the shear load and cannot be applied in the lateral vibration transient analysis, the bolting method is used to apply the bolt to the pre-tightening force.
The cooling method reduces the temperature of the bolt pre-tightening part by setting the thermal expansion coefficient of the bolt material, so that the bolt shrinks, but the joint has restrained the bolt deformation to generate the pulling force inside the bolt, and the simulated bolt pre-tightening force is achieved, which can effectively simulate the force of the bolt connection. .
The temperature difference required to apply the preload is
In the formula:
F is the preload force;
α is the thermal expansion coefficient of the bolt material;
l is the length of the bolt pretensioning part;
Cb is the bolt stiffness;
Cm is the stiffness of the joint.
Using the static solver, set the reference temperature with the TREF command and apply a preload force to the bolt by applying a temperature load to the bolt using the BFV command. After solving, enter the post-processor, select the nut thread unit model, and see the equivalent stress cloud diagram, as shown in Figure 2.
Figure 2 Stress waveform of nut thread after pre-tightening
It can be seen from Fig. 2 that the stress of the first ring of the meshing thread is the largest, and the stress of each ring is successively decreased, which is consistent with the bolt connection stress distribution.
1.4 Lateral vibration transient analysis of bolted joints
The self-relaxing finite element analysis of the bolt connection is carried out, and the transverse excitation δx is applied for the transient analysis after the bolt connection is pre-tensioned.
The δx formula is
Δx=δ0sin(ωt) (2)
In the formula:
Δ0 ≤ δ/2 is the excitation amplitude;
ω is the angular frequency.
Using the bolt-connected finite element model of Fig. 1, the friction factor of each joint surface is set to μ1=μ2=μ3=0.1, and the pre-tightening force F=10730N is applied for static analysis.
After the solution, the transient analysis solver is applied, and the X-direction displacement load δx=0.2sin (3600t) is applied to all the nodes on the parallel side surface of the lower plate and the coordinate surface YOZ, and the time step is t=0.0125s, and the complete transient analysis is performed. The simulation ends when =0.325s.
2. Analysis of self-relaxation mechanism of bolt connection
2.1 Analysis of self-relaxation process of bolt connection
After the end of the simulation, the X-direction force of all the nodes for applying the displacement load is extracted as the shear force, and the shear load load curve with the lateral displacement of the plate is also called the shear load hysteresis curve, as shown in Fig. 3.
Figure 3 Relationship between shear load and lateral displacement of the lower plate
In the figure, the ordinate span size can be used to measure the bolt joint shear stiffness. The larger the span, the greater the shear stiffness.
Fig. 4 is a contact state of the thread engagement surface of the A, B, C, and D points and the bearing surface of the nut.
Figure 4 Threaded mating surface and nut bearing surface contact state
It can be seen from Fig. 4 that the threaded engagement faces of points A and C are completely slipped, and the bearing surface of the nut is partially slipped, and the slip position is exactly corresponding, so that the bearing surface of the nut can be slipped in one cycle; B, D Partial slippage also occurs at the point; the slip is most severe at the excitation amplitude, and the threaded engagement surface is completely slipped before the nut bearing surface, ie the slack of the bolt connection first occurs on the threaded engagement surface.
The sliding position of the bearing surface of the A and C points is symmetrical, which can realize the nut slip in one cycle.
The Z-direction force of all the nodes on the lower surface of the upper plate is extracted as the residual pre-tightening force, and its time-dependent curve is shown in Fig. 5.
Figure 5 Residual preload force versus time curve
It can be seen from Fig. 5 that the amount of preload reduction in one cycle is small. As can be seen in conjunction with Figure 4, local slip can cause loose bolting.
2.2 Influence of vibration amplitude on self-relaxation
In order to investigate the effect of the lateral vibration amplitude on the self-relaxation of the bolt connection, only the modified parameters δ0 are 0.02, 0.1, 0.2, 0.3, 0.4 in the simulation, and different amplitude comparison experiments are carried out. The change in bolting preload force when the transverse vibration amplitude is different is shown in Fig. 6.
Figure 6 Residual preload force curve with different amplitudes
It can be seen from Fig. 6 that the preload force change curve is almost parallel to the coordinate axis when the amplitude is 0.02 and 0.1. At this time, the preload force loss is small and negligible; when the amplitude is 0.2, 0.3, 0.4, the preload force loss is obvious. It indicates that the bolt connection is not only self-relaxing due to the lateral vibration, but self-relaxation occurs after the lateral vibration amplitude reaches a certain value.
The residual preload force changes when the amplitudes are 0.2, 0.3, and 0.4. The larger the transverse vibration amplitude, the faster the preload force loss. The shear load hysteresis curve is different when the transverse vibration amplitude is different.
Figure 7 Shear load hysteresis curve with different amplitudes
It can be seen from Fig. 7 that the larger the amplitude, the larger the shear load required.
2.3 The effect of initial preload force on self-relaxation
In order to investigate the influence of the initial preload force on the self-relaxation of the bolt connection, the pre-tightening of different sizes is only carried out in the static analysis, and the initial pre-tightening force is 3kN, 10.73kN, 21.32kN, 29.93kN for different initial preload Contrast the simulation. The percentage change curve of the preload force at the initial preload force is shown in Figure 8.
Figure 8 Loss percentage change curve for different initial preload
It can be seen from Fig. 8 that the larger the initial preload force, the smaller the percentage of bolt connection preload loss during lateral vibration, and the less self-relaxing occurs. The shear load hysteresis curve at different initial preload forces is shown in Figure 9.
Fig. 9 Shear load hysteresis curve with different initial preload
It can be seen from Fig. 9 that the larger the initial preload force is, the larger the ordinate coordinate of the shear load hysteresis curve is. The larger the shear load is required to reach a certain amplitude, the larger the pre-tightening force of the bolt connection is, the larger the lateral stiffness is, the more difficult it is to occur. Self-relaxing.
2.4 Friction factor on self-relaxation
2.4.1 Friction factor μ1 affects the self-relaxation of bolt connections
In order to investigate the influence of the friction coefficient of the threaded mating surface on the self-relaxation of the bolt connection, only the modified parameters μ1 of 0.05, 0.1, 0.17, and 0.2 were used to compare the friction factors of different thread mating surfaces. The residual preload force versus time curve for the friction factor of different threaded mating surfaces is shown in Fig. 10.
Fig. 10 Curve of residual preload force at different μ1
It can be seen from Fig. 10 that the preloading speed is not obvious when μ1 is 0.17 and 0.2, but the preloading speed is very obvious when μ1 is 0.05 and 0.1. The larger the friction coefficient of the thread meshing surface is, the larger the friction force is. It is difficult to self-relax. The shear load hysteresis curve for different thread engagement surfaces is shown in Figure 11.
Figure 11 Shear load hysteresis curve at different μ1
It can be seen from Fig. 11 that the larger the μ1, the larger the shear load, but the difference is not obvious, indicating that the thread friction factor has little effect on the lateral stiffness of the bolt connection.
2.4.2 Friction factor μ2 affects the self-relaxation of bolt connection
In order to investigate the influence of the friction factor μ2 of the bearing surface of the screw head and the bearing surface of the nut on the self-relaxation of the bolt connection, only the modified μ2 is modified to be 0.05, 0.1, 0.17, and 0.2 for the comparison of different friction factors μ2. The residual preload force change curve with different friction factors μ2 is shown in Fig. 12.
Fig. 12 Curve of residual preload force at different μ2
It can be seen from Fig. 12 that the smaller the μ2 is, the larger the preload force loss is when μ2 is 0.1, 0.17, 0.2; the preload force change is not in accordance with the law when μ2 is 0.05. Contrary to other simulation results, but it does not explain the model or solution error, because the degree of freedom of the bolt head and nut in the finite element simulation is not limited, which is different from other simulations.
The bolt head or nut freedom is not limited, and the friction coefficient of the bearing surface is very small. The relative slip caused by the lateral movement of the lower plate is very small, so the self-relaxation speed of the bolt connection is very small. The shear load hysteresis curves for different friction factors μ2 are shown in Fig. 13.
Figure 13 Shear load hysteresis curve at different μ2
It can be seen from Fig. 13 that the friction factors μ2 and μ1 have little influence on the lateral stiffness of the bolt connection.
2.4.3 Friction factor μ3 affects the self-relaxation of bolt connection
The comparison parameter μ2 was modified to 0.05, 0.1, 0.17, and 0.2 for comparative simulation of different friction factors μ3. The residual preload force variation curves for different friction factors μ3 are shown in Fig. 14.
Figure 14 Residual preload force curve at different μ3
It can be seen from Fig. 14 that the different μ3 corresponding pre-tightening force changes are substantially the same, that is, μ3 has less influence on the self-relaxation of the bolt connection when the lateral amplitude is constant. The transverse shear load hysteresis curve with different friction factors μ3 is shown in Fig. 15.
Figure 15 Shear load hysteresis curve at different μ3
It can be seen from Fig. 15 that the larger the μ3, the larger the span of the ordinate of the shear load hysteresis curve. It shows that the larger the friction coefficient of the joint surface is, the larger the lateral stiffness of the bolt connection is, and the less the bolt connection is, the more self-relaxing occurs.
3, conclusion
In this paper, the finite element method is used to simulate the self-relaxation of the bolt connection subjected to lateral vibration. The lateral amplitude, the initial preload, the friction coefficient of the thread meshing surface, the friction coefficient of the bolt head and the nut bearing surface, and the friction coefficient of the joint surface of the joint are mainly studied. The bolt connection is self-relaxing and the results are as follows:
(1) Partial slippage of the threaded engagement surface or the bearing surface may result in loss of preload force, and the thread engagement surface completely slips before the bearing surface.
(2) The larger the amplitude, the more easily the self-relaxation occurs in the bolt connection; the smaller the initial pre-tightening force is, the smaller the loss percentage is, the less the bolt connection is less self-relaxing; the larger the friction coefficient of the thread meshing surface and the bearing surface is, the more difficult the bolt connection is. Self-relaxation; the friction coefficient of the joint surface of the joint has little effect on the self-relaxation of the same amplitude, and has a great influence on the lateral stiffness of the bolt connection.
When the bolted connection is loosened, priority should be given to changing the friction state of the threaded mating surface and the friction state of the bearing surface; the maximum initial preload should be applied as much as possible without affecting the bolting strength; without affecting the bolt connection pressure distribution and connection sealing, etc. Under the premise of performance, the friction of the joint surface should be increased as much as possible.
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