In order to predict pressing quality of precision pressfit assembly, pressfit curves and maximum pressmounting force of pressfit 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 pressfit process could thus be simulated on the basis of static structure analysis. To verify the FEA results, experiments were carried out using a pressmounting apparatus. The results show that the pressfit curves obtained by FEA agree closely with the curves obtained using the experimental method. In addition, the maximum pressmounting 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 pressfit curve and max pressmounting force calculated by FEA can be used for predicting the pressing quality during precision pressfit assembly.
The pressing quality of pressfit assembly is extraordinarily important in all its application, especially in aviation and aerospace industry; thus, quality prediction is crucial. The pressing quality of pressfit assembly is related to not only the selection of interference value and diameter but also the pressfit process. However, it has until now been very difficult to predict the pressing quality of a pressfit assembly by a pressfit process analysis method.
In recent years, with the increasing sophistication of computers, FEA is being gradually applied to predict the pressfit quality by analyzing the pressfit process. Benuzzi and Donzella [
Pressfit curves can be divided into two categories, namely, the forcetime curve and the forcedisplacement curve. Many researchers have investigated the influence of different kinds of pressfit curves on the pressing prediction. He and Jia [
The purpose of this paper is to verify the accuracy of the pressfit curves and maximum pressmounting forces obtained from FEA by comparing them with experimental results, in order to determine whether pressfit curves and maximum pressmounting 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 pressfit 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 fourway reversing valve [
Since the microparts are aerospace components assembled by pressfit 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 fourway 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 pressfit curve and maximum pressmounting force are important technical methods for predicting the pressing quality of any pressfit assembly, FEA was implemented in this paper to illustrate how the pressfit curve and maximum pressmounting force were changed in the pressfit process by using ANSYS Workbench. A series of pressfit curves with different interference values were obtained from the analysis. The rational range of pressfit curves can be obtained according to the pressfit curves mentioned above. At the same time, we can obtain the maximum pressmounting forces and their rational range by reading the values of pressfit curves. Finally, by comparing these calculated values with those obtained from an actual pressfit 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
Stressstrain 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 pressfit assembly is based on the parameters above. Pressfit curves and maximum pressmounting force for a hollow shaft pressfit assembly with different interference values were obtained from FEA. These results are given in Figure
Maximum pressmounting force obtained from FEA.
Interference value ( 
12  13  14 


Maximum pressmounting force (N)  715.895  769.506  828.621 
Pressfit curves obtained from FEA.
The fluctuation can be explained as follows. At the beginning of pressfit assembly stage, the two microparts did not contact with each other. So the pressmounting force was 0. However, when these two microparts contacted with each other, the pressmounting force can be increased suddenly to dozens of force.
According to the practical situation of pressfit assembly, the micropart transits noncontact state to contact state, and the pressmounting force changes suddenly from 0 to a certain value. The substeps were increased for obtaining the fluctuation of a pressfit curve. Four kinds of substeps were considered, which included 30 substeps, 50 substeps, 80 substeps, and 100 substeps. The fluctuation of the beginning of pressfit 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 pressfit process is nonlinear and uniform, the nonlinear large deformation option and stepbystep loading option are selected. In the beginning of the pressfit process, the pressmounting force would change suddenly, so more data is required to be collected. There were 130 iterations in the whole simulation of pressfit 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 pressmounting precision requirements, a pressmounting 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 pressmounting process, displacement and the pressmounting force were recorded by grating ruler and a force sensor, respectively. According to the records mentioned above, the pressfit curves were drawn by control software. The device is shown in Figure
The pressmounting apparatus.
In order to validate the accuracy of pressfit curves and maximum pressmounting forces obtained from FEA, a series of experimental tests were implemented on the pressmounting 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 pressmounting process of the microparts, the pressmounting 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 pressmounting force can be fully applied on force sensor. And then the accuracy of measurement can be guaranteed. The type of the force sensor is BK6C which was produced by China Academy of Aerospace Aerodynamics. The scheme of measuring pressmounting force is shown in Figure
The pressmounting 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 pressmounting 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 KA300. The scheme of measuring displacement is shown in Figure
The scheme of measuring displacement.
The pressfit curves and maximum pressmounting forces of microparts with different interference values were obtained from the experiments. These results are given in Figure
Maximum pressmounting forces obtained from experiments.
Number  Maximum pressmounting force (N)  Number  Maximum pressmounting 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 
Pressfit curves obtained from the experiments.
The mean values of maximum pressmounting force with the same interference value were calculated. The results are listed in Table
Mean values of maximum pressmounting forces.
Interference value ( 
12  13  14 


Maximum pressmounting force (N)  740.088  788.189  866.791 
The standard deviations of maximum pressmounting forces with different interference values were calculated for evaluating dispersion degree of the maximum pressmounting forces with different interference values. The calculating method is shown in
According to (
Standard deviations of maximum pressmounting 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 pressmounting forces within the scope of mean value
On the basis of analyses mentioned above, the influence of interference value on the maximum pressmounting force is more significant than other factors (e.g., form error and surface roughness) by comparing maximum pressmounting forces with different interference values.
In the real pressmounting process, the value of the pressmounting force was collected once every 30 ms, and then according to the relationship between pressmounting 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 pressmounting force would change suddenly within a small range. The maximum pressmounting force can be obtained by reading the last value of the pressfit curve. The last value of the pressfit curve is the maximum value of the pressfit curve. The maximum pressmounting forces in Table
As shown in Figure
Comparison of the pressfit curves.
The pressmounting 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 pressmounting force changes suddenly transiting in the initial stage from 0 to a certain value. In the stable stage, the pressmounting force is increased with increasing of the displacement. The increase mentioned above is close to linearity. In the end stage, the increment of the pressmounting 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 pressfit curves follow a reasonable course.
As shown in Table
Comparison among maximum pressmounting 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 pressfit curve and by the maximum pressmounting force. Therefore, as long as the gradient of the pressfit curve does not change significantly and the maximum pressmounting force falls within the range from 715.895 N to 828.621 N, the pressing quality of microparts assembly is qualified.
The simulation of pressfit process was investigated with several interference values, and the pressing quality prediction of pressfit assembly was investigated by pressfit curve and maximum pressmounting force. According to the results, it was found that the FEA method could be applied for predicting the quality of pressfit assemblies. The corresponding conclusions can be drawn as follows:
The pressfit curves obtained from FEA can be used to predict the pressing quality of microparts assembly according to the rational ranges of pressfit curves which are consistent with practical situations basically. In this paper, the rational range of pressfit curves is between a 12
Once pressfit curves are obtained, the maximum pressmounting forces can be obtained by reading the maximum value of pressfit curves. If the maximum value is in the rational scope of maximum pressmounting force, the pressfit assembly is considered successful. The rational scope of maximum pressmounting force is from 715.895 N to 828.621 N. The rational scope was obtained from numerical simulation of pressfit assembly, which was validated by using pressmounting experiments.
The standard to judge the quality of the pressfit curve includes two factors which are the pressmounting force and the gradient of the pressfit curve. The pressmounting force data on the pressfit curve should be in the rational range of maximum pressmounting force. The rational range of the maximum pressmounting force is from 715.895 N to 828.621 N. From the gradient of pressfit curve, there should be a fluctuation in the beginning of the pressfit curve. The pressmounting force should be nearly proportional to the increase of the displacement in the stable stage. In the end stage, the increment of the pressmounting force should be decreased. There are three kinds of unqualified pressfit curves in Figures
The unqualified pressfit curve 1.
The unqualified pressfit curve 2.
The unqualified pressfit curve 3.
There is no contact in the initial pressing stage of the unqualified pressfit curve 1, but once shaft and hole are in contact, the pressmounting force changes suddenly. It can be noted that the gradient of the unqualified pressfit curve 1 is higher than that of the qualified pressfit curves throughout the whole pressing stage. Additionally, the maximum pressmounting 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 pressfit curve 1 is shown in Figure
The gradient of unqualified pressfit curve 2 is equal to qualified pressfit curves in the whole pressing stage, but its pressmounting 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 pressfit curve 2 is shown in Figure
The gradient of unqualified pressfit 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 pressfit surface. The pressmounting 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 pressfit process to get pressfit curves, and then the rational range of pressfit curves is obtained according to the results obtained from FEA. According to the range, it can be confirmed whether pressfit assembly is successful or not. Thereby, all the above work on pressfit assemblies makes further investigations of pressfit curves gradient for analyzing the pressing quality of pressfit assembly possible. Furthermore, it is the final purpose to infer the pressmounting failure causes according to the gradients of pressfit curves and the varieties of maximum pressmounting 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).