Study on the Influence Law of Bolt Preload on the Characteristic Parameters of Bolt Joint Surface

November 07, 2018

The aerostatic bearing (shown in Figure 1) uses air as a lubricant, so the noise is small and the friction is small, which makes it have less heat, less vibration, high rotation precision and less pollution than conventional contact bearings. The system structure is simple and reliable, etc. [1-3], so it has been widely used in various ultra-precision processing equipment. With the rapid development of bearing materials and manufacturing technology, the performance of individual components of aerostatic bearings has been significantly higher, and the weak links of bearing performance mainly come from various joint surfaces [4-5]. Rotary components in aerostatic bearings (rotor assembly - thrust plate - positioning joint - cutter head) are bolted joints between the parts. The characteristics of the bolt joint surface are related to the material properties and manufacturing precision of each component. The most significant factor affecting the stiffness characteristics of the bolt joint surface is the bolt preload force. Therefore, identifying the bolt joint surface
The characteristic parameters and the influence of the bolt warning force on the characteristic parameters of the bolt joint surface are of great significance for improving the overall characteristics of the aerostatic bearing (motion accuracy, anti-vibration performance, etc.). In this paper, the finite element simulation analysis and experimental modal analysis method will be used to identify the characteristic parameters of the bolt joint and the bolt preload force.
Influence the law.
1 Simplified bolt joint
The simplified methods of bolted joints are mainly spring damper element method [6-7] and virtual material method (including fractal theory) [8-9]. The two workpieces are connected by bolts, and the contact surface layer is microscopically point contact, and the contact points can be equivalent (no mass) by the spring damping element, as shown in Fig. 2, that is, the spring damping unit method. The two workpieces are connected by bolts. On the joint surface, it is also assumed that there is a connecting material. The material has elastic modulus, Poisson's ratio and density, as shown in Fig. 3, that is, the virtual material method.
2 Analysis method of stiffness characteristics of bolt joint surface
Since the bolt joint surface has no mass, after the bolt joint surface is equivalent, the vibration equation is
( k + iÏ‰c)x = F ( 1)
Where kâ€”the joint stiffness matrix
câ€”â€”â€”bonding matrix damping matrix
xâ€”â€”â€”relative displacement array
Fâ€”â€”â€”Combination force array
Ï‰â€”â€”â€”the characteristic frequency of the system
It can be known from equation (1) that the main characteristic parameters of the joint surface are stiffness k, damping c and characteristic frequency Ï‰. These characteristic parameters are analyzed by finite element simulation and experimental modal analysis.
2. 1 Finite element simulation analysis method
Using the commercial software Ansys for simulation analysis, the basic process is:
(1) Modeling (using the general 3D modeling software UG8. 0), the model will be simplified and modified appropriately, such as ignoring small grooves, chamfers, etc., in order to balance the accuracy of the calculation. And efficiency; (2) Solve the settings, import the built model into Ansys Workbench, set the corresponding material properties, boundary conditions, etc., and then divide the grid; (3) Solve and post-process. The quality and quantity of the grid are the key to the accuracy and efficiency of numerical simulation. The commonly used grid types and their characteristics are shown in Table 1. Since the structure of the structure itself is simple and has no special structure, in order to improve the simulation efficiency, the finite element simulation of this paper adopts four sides. Body mesh, which is a triangle unit.
2. 2 Experimental modal analysis method
The experimental modal analysis technique is to measure the time history of excitation and response through experiments. The digital signal processing technique is used to obtain the frequency response function or impulse response function, and the nonparametric model of the system is obtained. Then the parameter identification method is used to obtain the system modal parameters. And further determine the dynamic characteristics of the system (such as characteristic frequency, modal stiffness, etc.) [10-11].
Various aspects of a typical experimental modal analysis are shown in Figure 4. A force is generated by a hammer, a force sensor measures the excitation force input into the structure, and a motion sensor (usually an acceleration sensor, also known as an acceleration sensor)
Accelerometer) Measures the vibrational motion of the output. These signals are amplified, filtered, and processed into an analytical processing system. Next, the analysis system will determine the modal characteristics (system pole, mode vector, modal participation factor) of the test piece based on the measured frequency response function. In addition, the animation software will simulate the modal shape of the mechanism on the display.
3 Parameter identification of bolted joint surface and analysis of influence law of bolt preload
In this paper, we will use the rotor-thrust plate assembly in a certain type of aerostatic bearing developed by our company. The rotor-thrust plate is shown in Figure 5. The structural components included are the rotor and the thrust plate, and the bolts are six. Uniform distribution, through finite element simulation and experimental modal analysis method to study the characteristic parameters (stiffness, damping and characteristic frequency) of bolt joint surface and bolt pre-tightening force (because the actual torque test is used to distinguish the pre-tightening Force, so when no special explanation is given, this paper directly uses the value of torque to characterize the value of preload force) on the characteristic frequency of bolt joint surface.
3. 1 Characteristic frequency of structural parts
In order to identify the characteristic parameters of the bolted joint surface and the influence of the bolt preload on the joint surface characteristic parameters, the corresponding characteristic parameters of the structural member should first be identified and excluded. This paper takes the characteristic frequency as the identification feature.
The Ansys Workbench was used to simulate the structural parts [12-13], and the characteristic frequency of the joint surface was identified by excluding the frequency of the structural members.
(1) Numerical simulation analysis of thrust plate
Set the constraints of the thrust plate to be free. Through the simulation analysis, the characteristic frequency and mode shape of the thrust plate and its description are obtained. See Table 2. From the table, the characteristic frequency of the fourth order is 4 437. 7 Hz. This frequency has been
It is beyond the frequency range of interest in this paper, so higher-order modal parameters are no longer analyzed.
(2) Numerical simulation analysis of the rotor
Set the constraint of the rotor to be free. Through the simulation analysis, the first-order characteristic frequency of the rotor is 7154. 9 Hz. This frequency is beyond the frequency range of this paper (â‰¤5 000 Hz), so it is not resolved.
Higher order characteristic frequencies.
3. 2 Identification of characteristic parameters of bolt joint surface
On the basis of obtaining the modal parameters of a single structural member, the experimental modal analysis method will then be adopted (because when the joint surface is included in the part, the accuracy of the modal parameters obtained by numerical simulation is lower than that obtained by the experimental modal analysis method. [10-11]) Perform modal comparison analysis of the rotor-thrust plate assembly. The experimental system is shown in Figure 4, and the experimental site is shown in Figure 6.
Select the appropriate instrument and set the relevant experimental parameters as follows.
(1) Supporting method: Free support, that is, hanging with a sling.
(2) Excitation mode: The whole rotor-thrust plate structure is simple, so single-point point-by-point excitation is adopted; the excitation signal adopts pulse signal, that is, the excitation mode adopts pulse hammer excitation, and the excitation hammer selects PCB086C03 type hammer and
Matching force sensor.
(3) Measurement of output signal (pickup mode): Single-point pickup is used, and output signal (response signal) is measured by a shear accelerometer. Single-axis accelerometer PCB333B30 is selected.
(4) Acquisition and analysis processing system: Select INV3020 series high-performance 24-bit acquisition system and DASP series analysis software from Dongfang to form a complete acquisition and analysis system. The acquisition card is INV3018G acquisition card. Due to the simple structure of the rotor-thrust plate assembly, the detailed modeling, experiment and data processing flow is shown in Figure 7.
Finally, the bolt pre-tightening force is 31 Nm, and the parameters corresponding to the first four-order mode of the rotor-thrust plate assembly are shown in Table 3.
Comparing Tables 2 and 3, you can find:
(1) The first-order mode formed by connecting the rotor and the thrust plate by bolts is the yaw mode of the rotor and the thrust plate. This mode shape does not exist in the modal analysis of the rotor and the thrust plate alone. It is found that, therefore, it is a new mode, that is, it does not appear in any structural member. This mode is called a bolt-bonded surface mode, and its stiffness characteristic is 1.6 Ã— 106 N / Î¼m, and the damping characteristic (damping ratio) is 1. 8%.
(2) The second-order mode of the rotor-thrust plate assembly is consistent with the first-order mode of the thrust plate from the mode shape, so it can be determined that the mode of the step is actually pushing the mode of the plate, but due to the joint surface The introduction makes the characteristic frequency increase, that is to say, the introduction of the bolt joint surface is advantageous for suppressing this mode.
(3) The third-order mode of the rotor-thrust plate assembly is identical to the second-order mode of the thrust plate, but the characteristic frequency is reduced due to the introduction of the joint surface, that is, due to the introduction of the joint surface It is not conducive to suppress this mode.
(4) The fourth-order mode of the rotor-thrust plate assembly and the third-order mode of the thrust plate are identical from the vibration mode, so it can be determined that the mode of the mode is still pushing the mode of the plate, but due to the joint surface The introduction makes the characteristic frequency increase, that is to say, the introduction of the bolt joint surface is advantageous for suppressing this mode.
3. 3 Analysis of the influence of pre-tightening force on the dynamic characteristics of bolt joint surface
The pre-tightening force of the bolt is the most important factor affecting the dynamic characteristics of the bolt joint surface. In this section, the influence of the bolt preload on the characteristic parameters of the bolt joint surface is analyzed by the experimental modal analysis method.
The selection of the entire experimental instrument and the setting of the boundary conditions are unchanged. During the experiment, the pre-tightening force of the bolt is set between 10 Nm and 30 Nm, and the increment of the bolt pre-tightening force is 3 Nm, which is obtained by the pre-tightening force value of each bolt.
The characteristic frequencies of each order are shown in Table 4 (three experiments in total, and the characteristic frequencies of each order are taken as the average of three experiments). The effect of bolt preload on the characteristic frequency of the bolt joint surface is shown in Fig. 8. By observing Table 4 and Figure 8, it can be concluded that as the bolt preload increases, the characteristic frequencies of the various stages increase overall. When analyzing the experiment, when the bolt
When the preload is 14 Nm, the characteristic frequencies of the first and second orders become abnormally large. This is because there is a certain error in the experiment, and since the frequencies of the 1st, 2nd, and 3rd orders are not large, the steps are There is a certain coupling between them, so there is a singularity.
3. 4 Simplification and Equivalent of Bolted Joint Surface in Numerical Simulation
It can be seen from Fig. 8 that when the bolt pre-tightening force is increased to a certain value (more than 26 Nm in this paper), the increase of the characteristic frequency with the increase of the bolt pre-tightening force is slowed down, that is, as long as the bolt pre-tightening force Reach a certain
The numerical value (when the aerostatic bearing studied in this paper is greater than 30 Nm), the increase of the bolt pre-tightening force has little effect on the characteristic frequency of the system. At this time, we can assume that: the bolt joint surface can be directly defined as numerical simulation. Bind contact. When using the Workbench modal module for numerical simulation of components, there are five types of contacts, see Table 5.
In order to verify this hypothesis, the rotor-thrust plate assembly was numerically simulated and compared with the experimental results. During the simulation, the binding between the rotor and the thrust plate is set, and there is no constraint, that is, the free mode is simulated. In the experimental modal analysis, the bolt pre-tightening force is 31 Nm, and other experimental settings are the same as before. The first four modes of the rotor-thrust plate assembly and the corresponding characteristic frequencies are obtained by simulation, and the error of the characteristic frequency obtained by the experiment (absolute value) obtained when the pre-tightening force of the bolt is 31 Nm is calculated. The results are shown in Table 6. .
Comparing with Table 3, it can be found that the vibration modes obtained by the simulation are completely consistent with those obtained through experiments, and the characteristic frequencies are all within 9%. Therefore, when the rotor-thrust plate assembly is simulated and analyzed for its dynamic characteristic parameters, It is credible to define the bolt joint directly as a bound contact.
4 Summary
In this paper, the characteristic parameters of bolt joint surface are identified by finite element simulation and experimental modal analysis method. The influence of bolt preload on the dynamic characteristics of bolt joint surface is analyzed and the following conclusions are drawn:
1) The introduction of the bolted joint surface will result in changes in the overall characteristic parameters of the component (such as changes in the characteristic frequency).
2) Increasing the pre-tightening force of the bolt will generally increase the characteristic frequency of each mode of the whole component, but when the bolt pre-tightening force reaches a certain value (more than 26 Nm in the aerostatic bearing studied in this paper), continue to increase the bolt The pre-tightening force has no significant effect on the characteristic frequency of the system. (When the pre-tightening force of the bolt is up to 30 Nm, the characteristic frequency of each mode is increased by 0.5 Ng when the pre-tightening force of the bolt is 26 Nm.)
3) When the bolt preload force reaches a certain value (more than 30 Nm in the aerostatic bearing studied in this paper), the bolt joint surface can be directly defined as the binding contact when performing numerical simulation.
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