Design method and system for variable cross-section ultrahigh pressure plunger structure

Abstract

The invention discloses a method and a system for designing a variable cross-section ultrahigh pressure plunger structure, comprising the following steps: firstly setting load and boundary conditions of a plunger, then determining an inner cavity structure of the variable cross-section plunger by constructing a shape function of the variable cross-section plunger, and then obtaining deformation distribution of the surface of the current plunger based on finite element simulation calculation, and finally, iteratively optimizing parameters of the shape function of the inner cavity of the plunger by adopting a gradient descent method until a termination condition is met, and obtaining an optimal variable cross-section ultrahigh-pressure plunger structure. According to the variable-cross-section ultrahigh-pressure plunger structure and the design method thereof, the inner and outer pressure difference of the plunger is matched with the cross section rigidity by changing the cross section structure of the inner cavity of the plunger, so that the surface deformation of the plunger is remarkably reduced, the deformation resistance and the lightweight requirement are both considered, machining is convenient, and large-scale engineering application prospects are achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydraulic pumps, and particularly relates to a design method and system for a super-high pressure plunger structure with a variable cross-section. Background Technique

[0002] Axial piston pumps are widely used in fields such as aerospace and construction machinery due to their high working pressure, high power density, and compact structure. With the continuous improvement of the power density requirements of hydraulic systems, piston pumps are continuously developing towards higher pressure and lighter weight. Increasing the pressure level is beneficial to reducing the size and weight of equipment. Research shows that when the pressure level is increased from 21 MPa to 56 MPa, the weight of the hydraulic system can be reduced by 30%, and the volume can be reduced by 40%. However, the pressure levels of existing commercial piston pumps are generally 21 MPa - 35 MPa, making it difficult to meet the application requirements of super-high pressure conditions of 56 MPa and higher pressures.

[0003] Excessive deformation of parts is the key technical bottleneck restricting the application of piston pumps under super-high pressure conditions. During operation, a lubrication gap in the micron range needs to be maintained between the plunger and the cylinder bore to balance the sealing and load-bearing functions under high-pressure conditions. However, the uneven pressure difference distribution generated by the super-high pressure oil acting on the inner and outer surfaces of the plunger will cause significant irregular deformation. This not only easily leads to poor sealing of the mating surface and increased leakage, but also results in excessive local contact pressure, causing sticking and wear of the plunger pair, directly affecting the working performance and service life.

[0004] Traditional plungers generally adopt a cylindrical inner cavity design with a constant cross-section. Although simply increasing the wall thickness can reduce local deformation, it will inevitably lead to an increase in weight. This will not only directly affect the power density of the piston pump, but also, when the plunger rotates at high speed, the inertial force will exacerbate the overturning moment, further deteriorating the load-bearing and lubrication states of other friction pairs. Therefore, there is an urgent need for a plunger structure design method that can balance the requirements of high pressure and light weight. Summary of the Invention

[0005] The purpose of the present invention is to provide a design method and system for a super-high pressure plunger structure with a variable cross-section, which can significantly reduce the surface deformation of the plunger while ensuring the light-weight requirement of the plunger, and promote the development of piston pumps towards higher pressure.

[0006] The object of the present invention is to provide a design method for a super-high pressure plunger structure with a variable cross-section. By changing the inner cavity cross-section design of the plunger, the pressure difference between the inside and outside of the plunger is matched with the cross-section stiffness to reduce the surface deformation of the plunger under super-high pressure conditions, including the following steps: (1) setting the loads and boundary conditions on the plunger;

[0007] (2) Construct a plunger with a variable inner cavity cross-section, design the variable shape of the plunger inner cavity cross-section to match the pressure difference between the inside and outside of the plunger and the cross-section stiffness; define the change of the inner wall radius of the plunger along the axial direction as the shape function S(a1, a2, … a i ), and determine the inner cavity structure of the variable cross-section plunger;

[0008] (3) Based on the boundary conditions and the plunger geometric structure, through finite element simulation calculation, obtain the deformation distribution D(a1, a2, … a i ) on the current plunger surface;

[0009] (4) Based on the gradient descent method, iteratively optimize the parameters a of the plunger inner cavity shape function i ;

[0010] (5) Judge whether the termination condition is satisfied. If not, repeat steps (2) to (4) until the termination condition is satisfied, that is, obtain the optimal variable cross-section ultra-high pressure plunger structure.

[0011] Further, in step (1), determine the loads on the inner and outer wall surfaces of the plunger based on the axial displacement on the plunger surface, the axial length of the plunger, the high load pressure of the plunger pump, and the low pressure of the plunger pump housing.

[0012] Further, in step (2), the variable cross-section inner cavity structure includes a conical inner cavity, an arc-shaped inner cavity, and a stepped inner cavity, and their corresponding shape functions are respectively:

[0013]

[0014]

[0015]

[0016] Where a i is the regulation parameter of the shape function; specifically, a t1 , a t2 are the regulation parameters of the conical inner cavity shape function, a c1 , a c2 are the regulation parameters of the arc-shaped inner cavity shape function, a s1 , a s2 … a sk are the regulation parameters of the stepped inner cavity shape function, k is the number of steps set, and the geometric structure of the plunger inner cavity can be flexibly changed by adjusting the parameters.

[0017] Further, in step (4), the gradient descent optimization algorithm first calculates the partial derivative of the objective function with respect to each parameter to obtain the gradient vector, and then updates the shape parameters along the gradient descent direction;

[0018] Further, the shape parameter ai The search domain of

[0019]

[0020] In the formula, ρ is the material density and m is the designed mass of the plunger. S N (a i ) is the upper boundary of the shape function, i.e., the outer cylindrical surface of the plunger; S S (a i ) is the lower boundary of the shape function, i.e., the variable cross-section profile; S E (a i ) is the left boundary of the shape function, i.e., the end face of the plunger; S W (a i ) is the right boundary of the shape function, i.e., the end face of the plunger near the ball head.

[0021] Furthermore, in step (5), the termination condition is whether the change degree of the surface deformation range of the current step relative to that of the previous step meets the requirements.

[0022] On the other hand, the present invention provides a design system for a design method of a variable cross-section ultra-high pressure plunger structure, and the system includes:

[0023] A plunger cross-section design module, configured to construct a plunger with a variable inner cavity cross-section, design the variable shape of the inner cavity cross-section of the plunger, and match the pressure difference inside and outside the plunger with the cross-section stiffness; define the change of the inner wall radius of the plunger along the axial direction as a shape function S(a1, a2,... a i ), and determine the inner cavity structure of the variable cross-section plunger;

[0024] A simulation calculation module, configured to obtain the deformation distribution D(a1, a2,... a i ) of the current plunger surface through finite element simulation calculation based on the boundary conditions and the plunger geometric structure;

[0025] An iterative optimization module, configured to iteratively optimize the parameters a i of the shape function of the inner cavity of the plunger based on the gradient descent method; until the termination condition is met, that is, the optimal variable cross-section ultra-high pressure plunger structure is obtained.

[0026] The beneficial effects of the design method of the variable cross-section ultra-high pressure plunger structure proposed by the present invention are as follows:

[0027] 1. It breaks through the design paradigm of the traditional homogeneous plunger structure. On the premise of meeting the requirements of plunger light weight, through variable cross-section design, the pressure difference inside and outside the plunger is matched with the cross-section stiffness, which can significantly reduce the surface deformation of the plunger and is applicable to ultra-high pressure working conditions;

[0028] 2. Users can flexibly select various variable cross-section structures such as conical, arc-shaped, and stepped to balance the anti-deformation performance and lightweight requirements according to the actual operating conditions of the plunger pump.

[0029] 3. The structural design of the variable cross-section does not require improving the material or surface quality, does not increase additional costs, and is easy to process, showing the prospect of large-scale engineering applications. Brief Description of the Drawings

[0030] Figure 1 It is a flowchart of a design method for a super-high pressure plunger structure of the present invention.

[0031] Figure 2 It is the load distribution on the plunger.

[0032] Figure 3 They are the plunger structures before and after optimization.

[0033] Figure 4 They are the comparisons of the deformation amounts of different plunger structures. Detailed Embodiments

[0034] To more clearly illustrate the embodiments of the present invention, the present invention will be further described below in conjunction with the drawings and specific embodiments.

[0035] As Figure 1 shown, the present invention provides a design method for a variable cross-section super-high pressure plunger structure, including the following steps:

[0036] Step 1: Set the load and boundary conditions on the plunger. The plunger ball head is a fixed constraint, and the oil load p inner received on the inner wall surface of the plunger is the load pressure of the plunger pump, while the load p outter on the outer wall surface of the plunger is determined by the oil film pressure formed by it and the cylinder bore, and the pressure distribution is obtained by solving the pressure control equation of the annular gap flow:

[0037] (1)

[0038] (2)

[0039] In the formula, x is the axial displacement on the plunger surface, L p is the axial length of the plunger, p H is the load high pressure of the plunger pump, p c is the shell low pressure of the plunger pump. The load distribution is as Figure 2 shown.

[0040] Step 2: Construct the shape function and determine the inner cavity structure of the variable cross-section plunger. Define the change in the radius of the inner wall surface of the plunger along the axial direction as the shape function S. For the inner cavity of a traditional cylindrical plunger with a constant cross-section, its inner cavity radius remains constant along the axial direction and can be expressed as the following shape function:

[0041] (3)

[0042] where r p is the constant inner cavity radius.

[0043] As can be seen from the above analysis, the pressure difference between the inside and outside of the plunger wall is not uniform along the axial direction, but gradually increases from the bottom surface of the plunger to the ball head direction. However, the wall thickness of the traditional plunger is uniformly distributed along the axial direction. Therefore, the stiffness of the plunger wall does not match the pressure difference distribution, resulting in significant surface deformation. Inspired by this, the present invention proposes a variable cross-section ultra-high pressure plunger structure. In the area near the ball head where the pressure difference is large, the inner cavity cross-section is reduced to increase the interface stiffness and suppress deformation; in the area near the bottom of the plunger where the pressure difference is small, the inner cavity cross-section is appropriately increased to meet the lightweight requirements of the plunger; in the middle area, a gradually changing cross-section is preferably used to avoid wall stress concentration. The variable cross-section inner cavity can have various forms, including a conical inner cavity, an arc-shaped inner cavity, a stepped inner cavity, etc.

[0044] The radius of the conical inner cavity decreases linearly along the axial direction, and its shape function is:

[0045] (4)

[0046] where a t1 , a t2 are the adjustment parameters of the shape function of the conical inner cavity.

[0047] The arc-shaped inner cavity structure optimizes the stress distribution through continuous changes in curvature:

[0048] (5)

[0049] where a c1 , a c2 are the adjustment parameters of the shape function of the arc-shaped inner cavity.

[0050] The stepped inner cavity structure is the most convenient for processing, and realizes segmented stiffness strengthening by discrete wall thickness jumps:

[0051] (6)

[0052] where a s1 , a s2 … a ska is the control parameter of the stepped inner cavity shape function, and k is the number of steps set.

[0053] By adjusting the parameter a of the shape function i the geometric structure of the plunger inner cavity can be flexibly controlled to balance the anti-deformation performance and the lightweight requirement.

[0054] Step 3: According to the aforementioned plunger structure and boundary condition settings, through finite element simulation calculation, obtain the deformation distribution D on the current plunger surface.

[0055] (7)

[0056] Step 4: Based on the gradient descent method, iteratively optimize the parameter a of the plunger inner cavity shape function i so that the deformation of the plunger surface is minimized, that is:

[0057] (8)

[0058] Calculate the partial derivative of the objective function with respect to each parameter to obtain the gradient vector:

[0059] (9)

[0060] Update the shape parameter along the gradient descent direction:

[0061] (10)

[0062] At the same time, in order to ensure the lightweight requirement of the plunger, the mass of the ultra-high pressure plunger should not exceed the design value. Therefore, the search domain of the parameter a i should satisfy the following constraints:

[0063] (11)

[0064] where ρ is the material density and m is the designed mass of the plunger. S N (a i ) is the upper boundary of the shape function, that is, the outer cylindrical surface of the plunger; S S (a i ) is the lower boundary of the shape function, that is, the variable cross-section contour; S E (a i ) is the left boundary of the shape function, that is, the end face of the plunger; S W (a i ) is the right boundary of the shape function, that is, the end face of the plunger near the ball head.

[0065] Step 5: Repeat Steps 2 to 4 until the termination condition is reached, that is, obtain the optimal ultra-high pressure plunger structure. The termination condition is:

[0066] (12)

[0067] Where ∆D j is the surface deformation range of the current step, and ε is the convergence residual.

[0068] Taking the plunger structure of a certain 7 mL / r plunger pump product as an example, the present invention optimizes the design in the forms of a conical inner cavity, an arc-shaped inner cavity, and a stepped inner cavity respectively. The mass of the plunger remains unchanged before and after the optimization design. The corresponding ultra-high pressure plunger structure after optimization is as Figure 3 shown.

[0069] Based on the finite element model, the surface deformation of different plunger structures under the high-pressure condition of 42 MPa was simulated, and the deformation amount of each plunger along the axial direction was extracted. The results are as Figure 4 shown. It can be seen that the traditional plunger shows an obvious uneven deformation distribution under the action of high-pressure oil. In the bottom area of the plunger, the radial dimension is reduced by 2.34 μm, while in the direction close to the ball head, the plunger expands radially by 2.51 μm, resulting in a surface deformation range of 4.85 μm. Considering that the design tolerance of the general plunger pair clearance is about 8 - 12 μm to ensure the lubrication state, this deformation range will significantly increase the risk of the plunger getting stuck and worn during operation.

[0070] The design of the ultra-high pressure plunger with variable internal cross-section provided by the present invention can significantly reduce the surface deformation of the plunger. The forms of the conical inner cavity, the arc-shaped inner cavity, and the stepped inner cavity all have good deformation suppression effects. The stepped inner cross-section plunger is the most convenient to process, with a surface deformation range of 2.4 μm, and the deformation amount is reduced by 50.51% compared with the traditional plunger. However, the stepped structure may bring certain stress concentration. The arc-shaped inner cross-section has the best deformation suppression effect, with a maximum deformation amount of 1.89 μm, which is reduced by 61% compared with the traditional plunger. However, the processing requirements are higher. The performance of the conical inner cross-section plunger is more comprehensive, with a maximum deformation amount of 1.94 μm, which is reduced by 60% compared with the traditional plunger. It not only has a good deformation suppression effect but also has a relatively low processing cost. In actual engineering applications, users can freely choose the variable cross-section ultra-high pressure plunger structure according to their own needs, weighing the anti-deformation ability and processing cost.

[0071] On the other hand, the present invention also provides a design system for a design method of an ultra-high pressure plunger structure with variable cross-section. The system includes:

[0072] A plunger cross-section design module, used to construct a plunger with a variable inner cavity cross-section, design the changing shape of the plunger inner cavity cross-section, and make the internal and external pressure difference of the plunger match the cross-section stiffness; define the change of the inner wall radius of the plunger along the axial direction as a shape function S(a1, a2,... a i )), and determine the inner cavity structure of the variable cross-section plunger;

[0073] The simulation calculation module is used to obtain the deformation distribution D(a1, a2, … a i ) on the current plunger surface through finite element simulation calculation based on the boundary conditions and the plunger geometric structure;

[0074] The iterative optimization module is used to iteratively optimize the parameters a of the plunger inner cavity shape function based on the gradient descent method i ; until the termination condition is met, that is, the optimal variable cross-section ultra-high pressure plunger structure is obtained.

[0075] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A design method for a super-high pressure plunger structure with variable cross-section, characterized in that, Including the following steps: (1) Set the load and boundary conditions on the plunger; (2) Construct a plunger with a variable inner cavity cross-section, design the varying shape of the inner cavity cross-section of the plunger to match the pressure difference inside and outside the plunger with the cross-section stiffness; define the change of the inner wall radius of the plunger along the axial direction as the shape function S(a1, a2, … a i ), and determine the inner cavity structure of the variable cross-section plunger; (3) Based on the boundary conditions and the plunger geometry, through finite element simulation calculation, the deformation distribution D(a1, a2, … a i ) of the current plunger surface is obtained; (4) Based on the gradient descent method, iteratively optimize the parameter a of the plunger inner cavity shape function i ; (5) Determine whether the termination condition is satisfied. If not, repeat steps (2) to (4) until the termination condition is met, that is, the optimal variable cross-section ultra-high pressure plunger structure is obtained.

2. The design method of a variable cross-section ultra-high pressure plunger structure according to claim 1, characterized in that: In step (1), the loads on the inner and outer wall surfaces of the plunger are determined based on the axial displacement on the plunger surface, the axial length of the plunger, the high pressure of the load of the plunger pump, and the low pressure of the housing of the plunger pump.

3. The design method of a variable cross-section ultra-high pressure plunger structure according to claim 1, characterized in that: In step (2), the variable cross-section inner cavity structure includes a conical inner cavity, an arc-shaped inner cavity, and a stepped inner cavity, and their corresponding shape functions are respectively: ； ； ； where a i is the regulation parameter of the shape function; specifically, a t1 , a t2 is the regulation parameter of the conical inner cavity shape function, a c1 , a c2 is the regulation parameter of the arc-shaped inner cavity shape function, a s1 , a s2 … a sk is the regulation parameter of the stepped inner cavity shape function, k is the number of steps set, and the geometric structure of the plunger inner cavity can be flexibly changed by adjusting the parameters.

4. The design method of a variable cross-section ultra-high pressure plunger structure according to claim 1, characterized in that: In step (4), the gradient descent optimization algorithm first calculates the partial derivatives of the deformation distribution with respect to each parameter to obtain the gradient vector, and then updates the shape parameters along the gradient descent direction.

5. The design method of a variable cross-section ultra-high pressure plunger structure according to claim 4, characterized in that: Shape parameter a i The search domain is restricted by the requirement of plunger weight reduction, and the search range of the parameter space should satisfy: ； where ρ is the material density and m is the designed mass of the plunger; S N (a i ) is the upper boundary of the shape function, i.e., the outer cylindrical surface of the plunger; S S (a i ) is the lower boundary of the shape function, i.e., the variable cross-section profile; S E (a i ) is the left boundary of the shape function, i.e., the end face of the plunger; S W (a i ) is the right boundary of the shape function, i.e., the end face of the plunger near the ball head.

6. The design method of a variable cross-section ultra-high pressure plunger structure according to claim 1, characterized in that: In step (5), the termination condition is whether the change degree of the surface deformation difference in the current step relative to the surface deformation difference in the previous step meets the requirements.

7. A design system for a design method of a super-high pressure plunger structure with a variable cross-section according to any one of claims 1-6, characterized in that, The system includes: The plunger cross-section design module is used to construct a plunger with a variable inner cavity cross-section, design the changing shape of the inner cavity cross-section of the plunger, and match the pressure difference inside and outside the plunger with the cross-section stiffness; define the change of the inner wall radius of the plunger along the axial direction as a shape function S(a1, a2, … a i ), and determine the inner cavity structure of the variable cross-section plunger; The simulation calculation module is used to obtain the deformation distribution D(a1, a2, … a i ) on the current plunger surface through finite element simulation calculation based on the boundary conditions and the plunger geometric structure; An iterative optimization module, which is used to iteratively optimize the parameter a of the plunger inner cavity shape function based on the gradient descent method i ; until the termination condition is met, that is, the optimal variable cross-section ultra-high pressure plunger structure is obtained.

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