In order to predict pressing quality of precision press-fit assembly, press-fit curves and maximum press-mounting force of press-fit assemblies were investigated by finite element analysis (FEA). The analysis was based on a 3D Solidworks model using the real dimensions of the microparts and the subsequent FEA model that was built using ANSYS Workbench. The press-fit process could thus be simulated on the basis of static structure analysis. To verify the FEA results, experiments were carried out using a press-mounting apparatus. The results show that the press-fit curves obtained by FEA agree closely with the curves obtained using the experimental method. In addition, the maximum press-mounting force calculated by FEA agrees with that obtained by the experimental method, with the maximum deviation being 4.6%, a value that can be tolerated. The comparison shows that the press-fit curve and max press-mounting force calculated by FEA can be used for predicting the pressing quality during precision press-fit assembly.
The pressing quality of press-fit assembly is extraordinarily important in all its application, especially in aviation and aerospace industry; thus, quality prediction is crucial. The pressing quality of press-fit assembly is related to not only the selection of interference value and diameter but also the press-fit process. However, it has until now been very difficult to predict the pressing quality of a press-fit assembly by a press-fit process analysis method.
In recent years, with the increasing sophistication of computers, FEA is being gradually applied to predict the press-fit quality by analyzing the press-fit process. Benuzzi and Donzella [
Press-fit curves can be divided into two categories, namely, the force-time curve and the force-displacement curve. Many researchers have investigated the influence of different kinds of press-fit curves on the pressing prediction. He and Jia [
The purpose of this paper is to verify the accuracy of the press-fit curves and maximum press-mounting forces obtained from FEA by comparing them with experimental results, in order to determine whether press-fit curves and maximum press-mounting force that are established on the basis of the results obtained from FEA can be considered reasonably accurate and ultimately whether the pressing quality of a press-fit assembly can be judged according to these two indicators.
Electrohydraulic servo valve is a core component of electrohydraulic servo control system used regularly in aeronautic and aerospace field. It is composed of torque motor and four-way reversing valve [
Since the microparts are aerospace components assembled by press-fit assembly, the thin wall of the shaft will be deflected when both wings of hole are produced with deflection. Because the thin wall of the shaft is deflected, the spool of the four-way reversing valve will be moved. Thereby the oil pressure on the two sides of the spool will become different, and then the position, speed, or force can be controlled. Finally, the flight attitude of the flying vehicle can be corrected.
Since press-fit curve and maximum press-mounting force are important technical methods for predicting the pressing quality of any press-fit assembly, FEA was implemented in this paper to illustrate how the press-fit curve and maximum press-mounting force were changed in the press-fit process by using ANSYS Workbench. A series of press-fit curves with different interference values were obtained from the analysis. The rational range of press-fit curves can be obtained according to the press-fit curves mentioned above. At the same time, we can obtain the maximum press-mounting forces and their rational range by reading the values of press-fit curves. Finally, by comparing these calculated values with those obtained from an actual press-fit process, it could be determined whether the calculated values fell within a range of rational accuracy enough to allow for their practical application.
The geometric model is shown in Figure
Geometric model (units: mm).
Their mechanical properties are listed in Table
Mechanical properties of 3J1 and 1J50.
Material | Young’s modulus (MPa) | Poisson’s ratio | Yield strength (MPa) | Tangential modulus (MPa) |
---|---|---|---|---|
3J1 | 157000 | 0.34 | 686 | 942 |
1J50 | 186000 | 0.3 | 882 | 1116 |
Table
Stress-strain laws of materials in plastic zone.
Stress (3J1) (MPa) | Strain (3J1) | Stress (1J50) (MPa) | Strain (1J50) |
---|---|---|---|
690 | 0.00495 | 887 | 0.00615 |
793 | 0.00989 | 946 | 0.01194 |
844 | 0.01505 | 1004 | 0.01600 |
895 | 0.02002 | 1061 | 0.02000 |
942 | 0.02229 | 1116 | 0.02243 |
Load and boundary conditions are shown in Figure
Contact definition.
Contact model | Surface to surface |
---|---|
Type | Frictional |
Coefficient of friction | 0.09 |
Offset | Set manually |
Behavior | Asymmetric |
Formulation | Penalty function |
Penetration tolerance (FTOLN) | 0.5 |
Element | CONTA 174 and TARGE 170 |
Load and boundary conditions.
The value of 0.09 assumed for friction coefficient is a calculating value. The calculating method is shown as follows [
According to
According to (
1/2 finite element model meshed by hexahedral element is shown in Figure
Finite element method model of 1/2 microparts.
According to practical situations, when the interference value is less than 12
The equivalent stress of microparts.
The simulation of press-fit assembly is based on the parameters above. Press-fit curves and maximum press-mounting force for a hollow shaft press-fit assembly with different interference values were obtained from FEA. These results are given in Figure
Maximum press-mounting force obtained from FEA.
Interference value ( |
12 | 13 | 14 |
|
|||
Maximum press-mounting force (N) | 715.895 | 769.506 | 828.621 |
Press-fit curves obtained from FEA.
The fluctuation can be explained as follows. At the beginning of press-fit assembly stage, the two microparts did not contact with each other. So the press-mounting force was 0. However, when these two microparts contacted with each other, the press-mounting force can be increased suddenly to dozens of force.
According to the practical situation of press-fit assembly, the micropart transits noncontact state to contact state, and the press-mounting force changes suddenly from 0 to a certain value. The substeps were increased for obtaining the fluctuation of a press-fit curve. Four kinds of substeps were considered, which included 30 substeps, 50 substeps, 80 substeps, and 100 substeps. The fluctuation of the beginning of press-fit curve agrees well with the practical situation when the number of substeps is 100. In addition, the slope of the fluctuation is nearly uniform when the number of substeps is more than 100.
Since the analysis of the press-fit process is nonlinear and uniform, the nonlinear large deformation option and step-by-step loading option are selected. In the beginning of the press-fit process, the press-mounting force would change suddenly, so more data is required to be collected. There were 130 iterations in the whole simulation of press-fit process. That meant dividing the 4.8 mm displacement into 13 steps, each of which had to be subdivided into 10 steps. The calculated results are shown in Figure
According to FEA results and press-mounting precision requirements, a press-mounting apparatus was developed for assembling microparts. The apparatus consists of two functional modules: pressing module and parts alignment module. The pressing module is applied for assembling armature components, which includes grating ruler, guide shaft, straight push road, force sensor, moving beam,
The machine vision device was responsible for images acquisition of two parts to be pressed. In the press-mounting process, displacement and the press-mounting force were recorded by grating ruler and a force sensor, respectively. According to the records mentioned above, the press-fit curves were drawn by control software. The device is shown in Figure
The press-mounting apparatus.
In order to validate the accuracy of press-fit curves and maximum press-mounting forces obtained from FEA, a series of experimental tests were implemented on the press-mounting device. 18 samples were prepared for the series of experiments. Their shape errors and surface roughness were approximately identical. Table
Interference values of samples.
Number | Interference value ( |
Number | Interference value ( |
---|---|---|---|
Sample 1 | 12 | Sample 10 | 14 |
Sample 2 | 12 | Sample 11 | 14 |
Sample 3 | 14 | Sample 12 | 14 |
Sample 4 | 13 | Sample 13 | 12 |
Sample 5 | 12 | Sample 14 | 13 |
Sample 6 | 13 | Sample 15 | 13 |
Sample 7 | 13 | Sample 16 | 12 |
Sample 8 | 13 | Sample 17 | 14 |
Sample 9 | 12 | Sample 18 | 14 |
In the press-mounting process of the microparts, the press-mounting force is measured by force sensor which is installed on optics platform and connected with the bottom lower beam. The lower beam is located in floating status through coordinating with guide shaft and linear bearings. Thereby the press-mounting force can be fully applied on force sensor. And then the accuracy of measurement can be guaranteed. The type of the force sensor is BK-6C which was produced by China Academy of Aerospace Aerodynamics. The scheme of measuring press-mounting force is shown in Figure
The press-mounting apparatus.
The displacement is measured by the grating ruler. The grating reading head is fixed on the moving beam. Crust of the grating ruler is installed on aluminum alloy section. The bottom of aluminum alloy section is fixed on the lower beam. Since the upper beam can be deformed by the press-mounting force, the top of aluminum alloy section is jointed with the upper beam by guide frame which is composed of aluminum alloy section; thereby, the top of aluminum alloy section is located in floating status, and then the accuracy of measurement can be guaranteed. The type of the grating ruler is KA-300. The scheme of measuring displacement is shown in Figure
The scheme of measuring displacement.
The press-fit curves and maximum press-mounting forces of microparts with different interference values were obtained from the experiments. These results are given in Figure
Maximum press-mounting forces obtained from experiments.
Number | Maximum press-mounting force (N) | Number | Maximum press-mounting force (N) |
---|---|---|---|
Sample 1 | 726.381 | Sample 10 | 840.496 |
Sample 2 | 721.369 | Sample 11 | 863.086 |
Sample 3 | 890.297 | Sample 12 | 882.399 |
Sample 4 | 771.017 | Sample 13 | 746.021 |
Sample 5 | 744.942 | Sample 14 | 784.168 |
Sample 6 | 795.316 | Sample 15 | 805.081 |
Sample 7 | 783.760 | Sample 16 | 741.121 |
Sample 8 | 789.793 | Sample 17 | 875.797 |
Sample 9 | 760.696 | Sample 18 | 875.669 |
Press-fit curves obtained from the experiments.
The mean values of maximum press-mounting force with the same interference value were calculated. The results are listed in Table
Mean values of maximum press-mounting forces.
Interference value ( |
12 | 13 | 14 |
|
|||
Maximum press-mounting force (N) | 740.088 | 788.189 | 866.791 |
The standard deviations of maximum press-mounting forces with different interference values were calculated for evaluating dispersion degree of the maximum press-mounting forces with different interference values. The calculating method is shown in
According to (
Standard deviations of maximum press-mounting forces.
Interference value ( |
12 | 13 | 14 |
|
|||
Standard deviation (N) | 14.302 | 11.570 | 15.290 |
It is not difficult to see that the ratio of maximum press-mounting forces within the scope of mean value
On the basis of analyses mentioned above, the influence of interference value on the maximum press-mounting force is more significant than other factors (e.g., form error and surface roughness) by comparing maximum press-mounting forces with different interference values.
In the real press-mounting process, the value of the press-mounting force was collected once every 30 ms, and then according to the relationship between press-mounting force and displacement, these curves can be drawn. It is found that these curves are not smooth due to the existence of surface roughness on the contact surface. In addition, due to the existence of cylindrical errors on the whole contact surfaces, the press-mounting force would change suddenly within a small range. The maximum press-mounting force can be obtained by reading the last value of the press-fit curve. The last value of the press-fit curve is the maximum value of the press-fit curve. The maximum press-mounting forces in Table
As shown in Figure
Comparison of the press-fit curves.
The press-mounting process is divided into three stages, namely, initial stage, stable stage, and final stage. Since the micropart transits from noncontact state to contact state, the press-mounting force changes suddenly transiting in the initial stage from 0 to a certain value. In the stable stage, the press-mounting force is increased with increasing of the displacement. The increase mentioned above is close to linearity. In the end stage, the increment of the press-mounting force will be decreased, since elastic deformation is generated on the end of the contact surface. According to the analysis mentioned above, the numerical and experimental press-fit curves follow a reasonable course.
As shown in Table
Comparison among maximum press-mounting forces.
Interference value ( |
Experimental results (N) | Simulating results (N) | Deviation |
---|---|---|---|
12 | 740.088 | 715.895 | 3.3% |
13 | 788.189 | 769.506 | 2.5% |
14 | 866.791 | 828.621 | 4.6% |
According to our analysis, the pressing quality of microparts is determined by the shape of the press-fit curve and by the maximum press-mounting force. Therefore, as long as the gradient of the press-fit curve does not change significantly and the maximum press-mounting force falls within the range from 715.895 N to 828.621 N, the pressing quality of microparts assembly is qualified.
The simulation of press-fit process was investigated with several interference values, and the pressing quality prediction of press-fit assembly was investigated by press-fit curve and maximum press-mounting force. According to the results, it was found that the FEA method could be applied for predicting the quality of press-fit assemblies. The corresponding conclusions can be drawn as follows: The press-fit curves obtained from FEA can be used to predict the pressing quality of microparts assembly according to the rational ranges of press-fit curves which are consistent with practical situations basically. In this paper, the rational range of press-fit curves is between a 12 Once press-fit curves are obtained, the maximum press-mounting forces can be obtained by reading the maximum value of press-fit curves. If the maximum value is in the rational scope of maximum press-mounting force, the press-fit assembly is considered successful. The rational scope of maximum press-mounting force is from 715.895 N to 828.621 N. The rational scope was obtained from numerical simulation of press-fit assembly, which was validated by using press-mounting experiments. The standard to judge the quality of the press-fit curve includes two factors which are the press-mounting force and the gradient of the press-fit curve. The press-mounting force data on the press-fit curve should be in the rational range of maximum press-mounting force. The rational range of the maximum press-mounting force is from 715.895 N to 828.621 N. From the gradient of press-fit curve, there should be a fluctuation in the beginning of the press-fit curve. The press-mounting force should be nearly proportional to the increase of the displacement in the stable stage. In the end stage, the increment of the press-mounting force should be decreased. There are three kinds of unqualified press-fit curves in Figures
The unqualified press-fit curve 1.
The unqualified press-fit curve 2.
The unqualified press-fit curve 3.
There is no contact in the initial pressing stage of the unqualified press-fit curve 1, but once shaft and hole are in contact, the press-mounting force changes suddenly. It can be noted that the gradient of the unqualified press-fit curve 1 is higher than that of the qualified press-fit curves throughout the whole pressing stage. Additionally, the maximum press-mounting force shown in curve 1 is higher than the upper limit (828.621 N). The above discussions indicate that the hole is tilted by the operator, which results in a certain angle between the top surface of the hole and the pressing surface. The unqualified press-fit curve 1 is shown in Figure
The gradient of unqualified press-fit curve 2 is equal to qualified press-fit curves in the whole pressing stage, but its press-mounting forces exceed the upper limit at each point. At the same time, the equivalent stress is nearly equal to the yield limit, since a bilinear isotropic hardening model is applied. However, the area of plastic deformation exceeds the acceptable range. This means that the interference is too great. The unqualified press-fit curve 2 is shown in Figure
The gradient of unqualified press-fit curve 3 is too high in the first half section. The above sign indicates that there is a conical shape error in the first half section of shafts press-fit surface. The press-mounting force of the first half pressing section is more than the upper limit, since the value of the conical shape error exceeds 2
As mentioned above, FEA can be applied in simulation of the press-fit process to get press-fit curves, and then the rational range of press-fit curves is obtained according to the results obtained from FEA. According to the range, it can be confirmed whether press-fit assembly is successful or not. Thereby, all the above work on press-fit assemblies makes further investigations of press-fit curves gradient for analyzing the pressing quality of press-fit assembly possible. Furthermore, it is the final purpose to infer the press-mounting failure causes according to the gradients of press-fit curves and the varieties of maximum press-mounting forces.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This project is supported by the National Nature Science Foundation of China (no. 51075058) and the Fundamental Research Funds for the Central Universities (DUT10ZDG04).