Abstract: This paper analyzes the mechanical model of the composite sealing structure on the piston rod of a servo mechanism. The finite element method is used to simulate the pressing parameters of the piston rod sealing superposition mechanism, the parallel sealing structure, and the shell sealing superposition mechanism during the pressing process. Tooling for guiding, fitting, and leveling is designed to ensure a smooth transition during the pressing feed and to guarantee that the shell axis is coaxial with the pressing force. Experiments using pressing equipment are conducted to verify the relationship between pressing force and displacement, thus quantifying the pressing process. Tests on anti-friction rings of different sizes reveal that the pressure curve can characterize the wear state of the composite seal. This demonstrates the reliability of the pressing process for piston parts of servo mechanisms using pressing equipment, improving pressing accuracy and yield, and showing broad application prospects.
Keywords: press fitting; sealing; piston rod
introduction
The piston rod of the servo actuator is a mechanical part that performs work on the outside of the servo mechanism. Its function is to convert the pressure difference between the two chambers of the actuator into the linear displacement output of the actuator [1]. The piston rod is equipped with a composite seal, which is a dynamic seal. During assembly, its sealing reliability should be ensured. Once the dynamic seal fails, it will affect the dynamic characteristics of the servo mechanism. The piston rod assembly process of the servo actuator has always lacked quantitative parameter control. The traditional operation method is for the operator to use a rubber hammer to knock it into place or push it into place manually. The knocking force depends on the operator's skill and experience. Moreover, the parameters of composite seal parts are not easy to quantify during the installation process. They are easily damaged and there is uncertainty due to human factors. Their quality is an uninspectable item [2]. This paper studies the process method of pressing the piston rod of the servo actuator with CNC press-fitting equipment and proposes a process judgment method for pressing the piston rod of the servo mechanism. The aim is to control the pressing process and improve the assembly quality.
1. Mechanism Analysis of Piston Rod Press-fitting Process
A certain type of electro-hydraulic servo actuator includes a housing, piston rod, support seat, displacement sensor , servo valve, pressure sensor, etc. The process of pressing the piston rod into the housing is studied. Since the sealing ring is a hyperelastic body, it is not easy to simulate its force process. Therefore, necessary assumptions and simplifications are made for the sealing ring in the model [3]. It is assumed that the sealing ring is uniformly compressed when installed in the sealing groove, without any rolling or twisting. The contact force between the piston rod and the sealing ring is calculated by superimposing the pre-tightening force of the sealing ring with the contact force generated by the relative displacement between the piston rod and the sealing ring. An equivalent concentrated force is used to replace the contact force distributed along the surface of the sealing ring. Hertz contact stiffness is used at the gap between the piston rod and the housing and between the piston rod and the end cap, and the influence of damping effect is considered to establish the normal force-displacement relationship at the contact point. The modified Coulomb friction model is used to establish the tangential force-displacement relationship model at the collision contact point [4].
1.1 Contact Force Model
Springs are used to simulate the resistance of an object to deformation, and damping is used to simulate energy dissipation [5-7]. The relationship between the contact force generated during the contact process and the depth and velocity of the mutual penetration at the contact point is given by the following formula:
(1)
Wherein, is the elastic force related to the depth of penetration at the contact point; and is the damping force related to the penetration velocity. The normal elastic contact force is expressed as a power function of the penetration depth, i.e.
(2)
For the contact between the sealing ring and the press-fitting process, the parameters in equation (2) are obtained by calculating and analyzing the contact force of the sealing ring using finite element software, and by fitting the functional relationship between the contact force and the penetration depth.
Regarding the contact between the piston rod and the housing, the parameters in equation (2) can be calculated according to Hertz's elastic contact theory as follows:
(3)
Where: k is the elastic coefficient; penetration depth; Poisson's coefficient; Young's modulus; and , the radius of the shaft and the hole.
The damping in the nonlinear spring-damped model is expressed as:
(4)
The damping coefficient is often taken in the following form:
(5)
In the formula: is the tangential velocity, and is the damping coefficient.
1.2 Friction Model
The friction force calculation model adopts the Coulomb friction model. Coulomb's friction law states that the direction of the friction force is opposite to the relative velocity, and its magnitude satisfies the inequality. Since the friction force power is at its minimum, the relationship between friction force and relative velocity is consistent with Coulomb's friction law. However, due to the difficulty in numerical integration at the moment of velocity inflection caused by the definition of the friction coefficient, the friction force model is modified as follows:
(6)
Where: friction coefficient; normal force; relative tangential velocity; dynamic correction coefficient.
1.3 Press-fit Simulation Analysis
Figure 1 shows a cross-sectional view of the servo actuator housing and piston rod at the initial press-fit position. Based on the contact force and friction force model, the finite element method is used to analyze the force on the composite sealing structure at the three sealing grooves during the piston rod press-fit process, namely the parallel sealing structure, the housing sealing superposition structure, and the piston rod sealing superposition structure.
Figure 1 Schematic diagram of the initial position of the press-fitting process
The housing sealing stack structure is the first sealing structure after press fitting. This stack structure seals on the servo actuator housing and consists of a set of anti-friction rings and sealing rings. Because the sealing ring material is nitrile, with an elastic modulus of 0.00784 GPa and a Poisson's coefficient of 0.47, and the anti-friction ring material is polytetrafluoroethylene, with an elastic modulus of 1.14~1.42 GPa, the elastic modulus of the sealing ring is smaller than that of the retaining ring. The sealing ring undergoes elastic deformation, and the sealing structure generates a force that balances the press fitting force. This force is the sum of the normal force of the contact force and the frictional force. When the press fitting distance is 2.8 mm, the force cloud diagram of the sealing ring is shown in Figure 2(a), where the deformation resistance reaches its maximum, approximately 52 N; after the press fitting distance is 4 mm, the force cloud diagram is shown in Figure 2(b).
a) Pressing distance 2.8mm
b) Pressing distance 4mm
Figure 2 Contact force and displacement cloud diagram of the shell sealing superimposed structure.
The parallel sealing structure is the second sealing structure after press fitting. This parallel structure seals the servo actuator housing and consists of a set of sealing rings and retaining rings. The sealing rings are made of nitrile butadiene, and the retaining rings are made of polytetrafluoroethylene. When the press fitting distance is 2.3 mm, the force cloud diagram of the sealing ring is shown in Figure 3(a), and the total contact force and friction force between the piston rod and the housing reaches approximately 80 N. After a press fitting distance of 4 mm, the force cloud diagram is shown in Figure 3(b).
a) Pressing distance 2.3mm
b) Pressing distance 4mm
Figure 3. Contact force and displacement contour plot of the shell sealing parallel structure
The piston rod sealing stack structure is the third sealing structure passed through during the press-fitting process. This stack structure seals the piston rod and main piston, consisting of a set of sealing rings and anti-friction rings stacked together, with a total press-fitting distance of 3mm. When the press-fitting distance is 2.3mm, the force contour diagram of the sealing ring is shown in Figure 4(a), and the total contact force and friction force between the piston rod and the inner wall of the housing reaches approximately 70N. After the press-fitting distance is 3mm, the force contour diagram is shown in Figure 4(b).
a) Pressing distance 2.3mm
b) Pressing distance 3mm
Figure 4. Contact force and displacement contour plot of the piston rod seal superimposed structure.
2. Piston rod press-fit test study
Precision CNC pressing equipment is used for pressing. The pressing process is positioning and shifting pressing. Based on the displacement measured by the displacement sensor, the material is pressed in at a fixed rate and the normal pressure is monitored in real time to obtain the relationship between displacement and pressing force [8].
The piston rod press-fit design scheme is as follows: ① The pilot fitting fixture is designed to ensure that the composite sealing structure is not damaged and the piston rod remains coaxial with the housing during the press-fit feeding process, as shown in Figure 1. The inner orifice size of the pilot fitting fixture I is Φ38mm to ensure consistency with the cavity, and the outer orifice size is Φ44mm to ensure a smooth transition during the press-fit feeding process. The pilot fitting fixture II protects the piston rod thread and ensures a smooth transition when the piston rod tip is fed; ② The pressure head and base are designed to ensure that the positive pressure of the press-fit equipment is coaxial with the piston rod, while limiting the position of the housing; ③ The pressure plate and base are designed to self-balance during the press-fit feeding process. The base is concave and has an interface for the bottom platform of the press-fit equipment. The spherical diameter of the pressure plate is 160mm, and the surface is graduated for spherical leveling. The housing axis is ensured to be coaxial with the positive pressure, ultimately ensuring "three-axis consistency", as shown in Figure 5. During the test, the product is first installed with the pilot fitting fixture, then the housing is placed in the base groove, and then the press-fit equipment is operated for automatic press-fitting, as shown in Figure 6.
Figure 5. Combination diagram of piston rod press-fitting test scheme
Figure 6. Actual picture of precision CNC press fitting.
3. Press-fitting test verification of piston-type parts
Ten sets of servo actuators and piston rods were tested in a press-fitting experiment, as shown in Figure 7. The local extreme points were measured, and the range of the press-fitting force was obtained.
Figure 7 Piston rod pressing force and displacement curve
The test results show that the pressing process is consistent. As can be seen from the figure, the change in friction force produced 5 peaks. The pressing process is analyzed as follows:
① The first peak value was generated at 3-7mm. This was because the top of the actuator piston rod began to contact the sealing superimposed structure on the housing, resulting in the first peak value with a stress of approximately 45N-55N. After pressing for a distance of 4mm, the deformation resistance disappeared, and the sliding friction force was restored to approximately 35N-40N.
② A second peak occurs at 13-16mm. As the piston rod tip of the actuator begins to contact the parallel sealing structure on the housing, the sealing ring is deformed by the pressure reducing ring, and the pressing force increases. Therefore, an extreme point is generated at the moment when the piston rod tip contacts the pressure reducing ring, with a stress of 100N-135N. After the pressing distance is 4mm, the deformation resistance disappears rapidly, and the sliding friction drops to about 70N. After that, it enters a period of stable sliding friction.
③ A third peak was generated at 23mm to 26mm. Here, due to the influence of the shell and the tooling, the piston rod sealing superposition structure entered the shell. Due to the superposition of elastic deformation and friction, a local extreme point was generated, which was about 124N to 145N. After the pressing distance was 3mm, the deformation resistance disappeared rapidly, and the sliding friction dropped to about 90N. After that, it entered a stable sliding friction period.
④ A fourth peak was generated at 36mm to 37mm. At this point, the piston rod sealing superstructure was squeezed again after the elastic deformation of the sealing ring was released through the inclined hole in the housing. This resulted in a very low point of about 50N to 75N and a very high point of about 120N to 170N. This is a potential safety hazard point. The curve at this point can also clearly show whether the piston rod sealing superstructure has been damaged.
⑤ A fifth peak pressure value was generated at 44mm to 47mm and then stabilized. The friction of the three sealing structures acted on the entire piston rod, which was about 260N to 285N until the final installation was completed.
In summary, the following criteria can be used to determine if the press-fitting is successful:
1. The characteristic intervals corresponding to local extreme points should be clearly corresponding and identifiable;
2. The curve trend should be roughly consistent with the experimental results, and there should be no more peaks that affect the local extreme points;
3. The peak force at the local extreme point corresponding to each characteristic interval should be within the required range.
4. Comparative test verification
To verify the reliability of the criterion obtained by this method and to verify the change in the pressing curve after the wear-reducing ring is damaged, a special specification wear-reducing ring was custom-made. The standard outer diameter of the PTFE wear-reducing ring is mm. The limit, average and out-of-tolerance dimensions were selected for testing, and the entire peak force was measured. The results are shown in Table 1 below.
Table 1 Actual measured dimensions, interference fit, and peak force
After testing, the press-fitting curve within the dimensional range conforms to the trend shown in Figure 7. The output curve for out-of-tolerance results is shown in Figure 8 below.
Figure 8. Corresponding curves for piston rod press-fitting of out-of-tolerance anti-friction ring.
The test results show that the composite seals within the acceptable size range all meet the acceptance criteria. However, the seals with out-of-tolerance dimensions can be barely identified in the first three characteristic intervals. At the fourth moment, the peak value of the local extreme point exceeds 1500N, at which point the seal is damaged. The actual image of the damaged out-of-tolerance seal is shown in Figure 9.
a) Actual image of the wear-resistant ring.
b) Actual image of the damaged piston rod inner seal ring
Figure 9. Actual image of the out-of-tolerance seal after it has been damaged.
5. Conclusion
Through simulation and experimental research, it was found that using precision CNC press-fitting equipment can simulate the changing trends of press-fitting force and displacement during the press-fitting process. The comparison of press-fitting curves of seals of different sizes verifies that this method can monitor the shearing damage of seals. The press-fitting force obtained from the press-fitting curve can be used as a process criterion for press-fitting piston-type parts.
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