A method for constructing a simulation analysis model for micro-hemispherical shell forming

Abstract

The present invention provides a method for constructing a micro-hemispherical shell forming simulation analysis model, which is characterized in that: a two-dimensional model is established in the simulation software according to the half-section of a disc and boundary conditions are set; the model includes a rectangular structure and a concave structure, the rectangular structure corresponds to a glass layer, and the concave structure corresponds to a substrate layer; the boundary conditions include geometric parameter boundary conditions of the two-dimensional model, material parameter boundary conditions of the rectangular structure and the concave structure, and air pressure parameter boundary conditions inside and outside the two-dimensional model. Based on the process mechanism, the present invention establishes an analysis model for the complex free-forming micro-hemispherical shell forming process, which can accurately simulate the actual process and facilitate the prediction of the micro-hemispherical shell morphology and the initial parameter design.

Description

Technical Field

[0001] The invention belongs to the field of micro-electromechanical technology, and in particular relates to a method for constructing a micro-hemispherical shell forming simulation analysis model. Background Art

[0002] Inertial technology has special advantages such as autonomy, concealment, and anti-interference when applied to navigation and guidance. With its unique comprehensive advantages in cost, volume, weight, and power consumption (CSWaP), high-precision micro-electromechanical system (MEMS) gyroscopes are constantly expanding their application needs in the military and defense fields. With the development of micro-electromechanical technology, the application trend of inertial technology is moving towards lightweight, miniaturization, and low power consumption. The micro-hemispherical resonant gyroscope has the potential to combine the high precision of traditional hemispherical gyroscopes with the small size of MEMS devices, and is currently recognized as one of the important development directions of high-performance miniaturized gyroscopes.

[0003] As the core component of the micro-hemispherical resonant gyroscope, the micro-hemispherical shell resonator is crucial to the high performance of the micro-hemispherical resonant gyroscope. The free forming preparation method has been proven to have the advantages of achieving high-performance micro-hemispherical shell resonators and mass production, but the micro-hemispherical shell resonator is formed in one step under this process method. In addition, the morphology of the micro-hemispherical shell resonator is difficult to adjust later. There is an urgent need for forming analysis models and methods to simulate the actual process and reveal the influence of pre-forming parameter design on the micro-hemispherical shell morphology, so as to guide the pre-forming parameter design around the desired morphology parameters. Compared with the processing test method, it has flexible, fast and huge cost advantages. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a method for constructing a micro-hemispherical shell molding simulation analysis model to solve the problem of micro-hemispherical shell molding process simulation verification.

[0005] The present invention achieves the above technical objectives through the following technical means.

[0006] A method for constructing a micro-hemispherical shell molding simulation analysis model is characterized in that: a two-dimensional model is established in simulation software according to a half-section of a disc and boundary conditions are set up; the model includes a rectangular structure and a concave structure, the rectangular structure corresponds to a glass layer, and the concave structure corresponds to a substrate layer; the boundary conditions include geometric parameter boundary conditions of the two-dimensional model, material parameter boundary conditions of the rectangular structure and the concave structure, and air pressure parameter boundary conditions inside and outside the two-dimensional model.

[0007] Furthermore, the simulation software is CIMSOL Multiphysics.

[0008] Furthermore, the geometric parameter boundary conditions include the geometric dimensions of the central axis and the cross section.

[0009] Furthermore, the geometric dimensions of the cross section include the inner diameter r of the annular groove. c , annular groove width, annular groove depth h c , the width of the outer frame of the annular groove, the thickness of the glass layer h g and basal layer thickness.

[0010] Furthermore, the material parameter boundary conditions include the density of the rectangular structure, the dynamic viscosity of the rectangular structure, the density of the concave structure, and the dynamic viscosity of the concave structure.

[0011] Furthermore, in the air pressure parameter boundary condition, the external pressure is P 0 , the internal pressure is P i *V c / (V c +V s ), where P i is the initial internal pressure, V c is the volume of the annular groove, V s is the inner volume of the hemispherical shell.

[0012] Furthermore, the inner volume V of the hemispherical shell is s Obtained through real-time integral calculation.

[0013] Furthermore, the integral operator intop in the simulation software is used to perform integral calculation: V s =intop(z*cosin), where z is the vertical left side corresponding to each micro-segment on the inner curve of the hemispherical shell, and cosin is the ratio of the projection of each micro-segment on the horizontal axis to this micro-segment.

[0014] Furthermore, the rectangular structure and the concave-shaped structure are respectively divided into grids, wherein the concave-shaped structure is set as a fixed grid, and the rectangular structure is set as a dynamic grid.

[0015] The beneficial effects of the present invention are:

[0016] (1) The present invention provides a method for constructing a micro-hemispherical shell forming simulation analysis model. Based on the process mechanism, the method establishes an analysis model for the complex free-forming micro-hemispherical shell forming process, which can accurately simulate the actual process and facilitate the micro-hemispherical shell morphology prediction and initial parameter design.

[0017] (2) Based on the characteristics of the micro-hemispherical shell as an axisymmetric shape, an equivalence based on two-dimensional axisymmetry is performed. Compared with directly constructing a three-dimensional simulation analysis model, the present invention can greatly reduce the hardware equipment requirements for simulation analysis and greatly improve the time efficiency of analysis.

[0018] (3) The micro-hemispherical shells prepared by the free forming method are non-standard hemispherical shells (non-equal radius and non-equal thickness). There is a huge error in directly modeling the micro-hemispherical shells. The morphological parameters of the micro-hemispherical shells obtained based on this model are more consistent with the micro-hemispherical shells processed by the actual process, which provides great convenience and high accuracy for further frequency analysis and energy loss analysis of the micro-hemispherical shells. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the micro-hemispherical shell forming process;

[0020] Figure 2 It is a schematic diagram of a two-dimensional simulation model of a micro-hemispherical shell of the present invention;

[0021] Figure 3 is the ratio of different internal and external pressures P in the model of the present invention i / P 0 Comparison of the molding appearance of the lower micro-hemispherical shell;

[0022] Figure 4 is the depth h of different annular grooves in the model of the present invention c Comparison of the molding appearance of the lower micro-hemispherical shell;

[0023] Figure 5 is the thickness of different shell materials (glass) in the model of the present invention h g Comparison of the molding appearance of the lower micro-hemispherical shell;

[0024] Figure 6 r is the inner diameter of the annular groove in the model of the present invention. c Comparison of the molding appearance of the lower micro-hemispherical shell. DETAILED DESCRIPTION

[0025] Embodiments of the present invention are described in detail below, examples of the illustrated embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0026] 1. Technical solution

[0027] like Figure 1 The figure shows a schematic diagram of the current micro-hemispherical shell forming process. First, an annular groove is engraved on the silicon wafer as a substrate, and the glass is bonded to the substrate to form a disc. Then, the glass is melted by heating and driven by the internal and external pressure difference, so that the glass expands and bulges to form a micro-hemispherical shell.

[0028] like Figure 2What is shown is a half-section cut along the center axis of the disc. Taking CIMSOL Multiphysics simulation software as an example, in a computer equipped with the above simulation software (the computer contains basic hardware units such as processors and memories), a two-dimensional geometric model is established according to the above half-section of the disc. The model includes a rectangular structure located at the upper part and a concave structure located at the lower part. The upper rectangular structure corresponds to the glass layer of the disc, and the lower concave structure corresponds to the base layer of the disc. The corresponding boundary conditions of the above model include geometric parameter boundary conditions, material parameter boundary conditions and air pressure parameter boundary conditions.

[0029] The geometric parameter boundary conditions are:

[0030] Boundary condition 1: the central axis, which is attached to one side of the rectangular structure and the concave structure. The central axis corresponds to the central axis of the disc. The central axis is fixed, that is, the movable displacement is set to 0 in the simulation software;

[0031] Boundary condition 2: The geometric dimensions of the cross section, including edge line ab, edge line bc, edge line cd, edge line de, edge line be, edge line cg, edge line fg, edge line gh; edge line ab corresponds to the inner diameter r of the annular groove c , the side line bc and the side line de correspond to the width of the annular groove, that is, the side line ab + the side line bc (or the side line de) is equal to the outer diameter R of the annular groove c , the edge lines be and cd correspond to the annular groove depth h c , the edge cg corresponds to the width of the outer frame of the annular groove, and the edge fg corresponds to the thickness of the glass layer h g , the edge line gh corresponds to the thickness of the basal layer.

[0032] The material parameter boundary conditions are:

[0033] Boundary condition 3: Density and dynamic viscosity of rectangular structure;

[0034] Boundary condition 4: Density and dynamic viscosity of the concave structure.

[0035] The air pressure parameter boundary condition is:

[0036] Boundary condition 5: External pressure P 0 ;

[0037] Boundary Condition 6: Internal Pressure P i *V c / (V c +V s );where P i is the initial internal pressure, V c is the volume of the annular groove, V sis the volume of the inner cavity of the hemispherical shell. The hemispherical shell is formed by the softened glass bulging outward under the drive of the internal and external pressure difference. The inner edge bc of the hemispherical shell becomes a continuously changing curve until the internal and external pressures reach a state of equilibrium. Therefore, the inner cavity volume of the micro-hemispherical shell V s is the quantity that changes with the simulation process; the V s It can be obtained by real-time integral calculation through the built-in integral operator intop of the simulation software, and the relevant settings are V s =intop(z*cosin), where z is the z coordinate (i.e., the vertical coordinate, along the up and down direction as shown in the figure, parallel to the central axis) corresponding to each micro-segment on the curve bc in the hemispherical shell, and cosin refers to the ratio of the projection of each micro-segment on the horizontal axis (along the left and right direction as shown in the figure, perpendicular to the central axis) relative to this micro-segment.

[0038] The rectangular structure and the concave structure in the above model are meshed according to the requirements of the finite element analysis method, where the concave structure is set as a fixed mesh and the rectangular structure is set as a dynamic mesh.

[0039] After creating a two-dimensional simulation model in the simulation software as described above, the software simulation test of the micro-hemispherical shell forming process can be carried out.

[0040] The above model is a two-dimensional plane model. If a corresponding three-dimensional micro-hemispherical shell model needs to be generated, the above two-dimensional model only needs to be rotated 360° around its axis to generate a rotational body.

[0041] 2. Theoretical Argumentation

[0042] (1) Since the wafer is placed in a sealed high-temperature box for heating, and the volume of the gas inside the high-temperature box remains unchanged, according to Charles' law, during the heating process, the gas pressure outside the wafer (i.e. inside the high-temperature box) can be expressed as:

[0043] P 0 (T) = (1 + βT)P 0 (0)

[0044] Where P 0 Refers to the external pressure of the disc, P 0 (T) is the external pressure at temperature T, P 0 (0) is the external pressure at 0°C, β is the thermal expansion coefficient of the gas, and for the ideal case β = 1 / 273.

[0045] Similarly, the internal pressure of the disc can be expressed as:

[0046] P i (T) = (1 + βT)P i (0)

[0047] Where P iGenerally refers to the internal pressure of the disc, P i (T) is the internal pressure at temperature T, P i (0) is the internal pressure at 0°C.

[0048] From the above two formulas, we can get:

[0049]

[0050] Therefore, it is proved that the ratio between the internal and external pressures of the disc is not affected by the temperature increase.

[0051] (2) When the temperature reaches the softening point of the glass, it remains constant. Therefore, the glass undergoes morphological changes in this constant temperature state. According to Boyle's law, we can obtain:

[0052] P i *V c =P′ i *(V c +V s )

[0053] Where P′ i It is the internal pressure after the glass changes its shape (the inner cavity of the micro-hemispherical shell expands).

[0054] The above formula can be transformed into:

[0055]

[0056] When the glass cavity expands to the point where the internal and external pressures are balanced, P' i =P 0 , so the above formula is transformed into:

[0057]

[0058] The volume of the annular groove Where R c is the outer diameter of the annular groove, r c h is the inner diameter of the annular groove, c is the depth of the annular groove, the above formula is further transformed into:

[0059]

[0060] This proves that the expansion shape of the micro-hemispherical shell is related to the ratio of the internal and external pressures. Annular groove inner diameter r c , annular groove outer diameter R c and the annular groove depth h c Therefore, this theoretical analysis proves that several boundary conditions defined in the simulation model of the present invention have a decisive influence on the simulation test results.

[0061] 3. Effect Test

[0062] Based on the simulation model created above, the forming morphology of the micro-hemispherical shell is tested by controlling different variables (boundary conditions).

[0063] like Figure 3 Shown are different internal and external pressure ratios P i / P 0 Below, the micro-hemispherical shell molding shape is intuitively compared;

[0064] like Figure 4 Shown are different annular groove depths h c Below, the micro-hemispherical shell molding shape is intuitively compared;

[0065] like Figure 5 Shown are different shell material (glass) thickness h g Below, the micro-hemispherical shell molding shape is intuitively compared;

[0066] like Figure 6 The following figure shows the inner diameter of the annular groove under different r c Below, the micro-hemispherical shell molding appearance is intuitively compared.

[0067] Through the above actual tests, the micro-hemispherical shell forming process simulation test model created by the present invention can intuitively and accurately simulate the actual forming effect, and measure the morphology of the micro-hemispherical shell under different parameters, so as to assist enterprises or scientific researchers in determining the process structure parameters of the micro-hemispherical shell to be prepared.

[0068] In the description of the present invention, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside" and "outside" etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0069] The present invention is not limited to the above-mentioned embodiments. Any obvious improvement, substitution or deformation that can be made by those skilled in the art without departing from the essential content of the present invention belongs to the protection scope of the present invention.

Claims

1. A method for constructing a micro-hemispherical shell forming simulation analysis model, characterized in that: A two-dimensional model is established in the simulation software according to the half-section of the wafer and boundary conditions are set; the model includes a rectangular structure and a concave structure, the rectangular structure corresponds to the glass layer, and the concave structure corresponds to the substrate layer; the boundary conditions include geometric parameter boundary conditions of the two-dimensional model, material parameter boundary conditions of the rectangular structure and the concave structure, and air pressure parameter boundary conditions inside and outside the two-dimensional model; The geometric parameter boundary conditions include the geometric dimensions of the center axis and the cross section; The material parameter boundary conditions include the density of the rectangular structure, the dynamic viscosity of the rectangular structure, the density of the concave structure, and the dynamic viscosity of the concave structure; The pressure parameter boundary conditions include the external pressure P0 and the internal pressure P i *V c / (V c +V s ), where P i is the initial internal pressure, V c is the volume of the annular groove, V s is the inner volume of the hemispherical shell.

2. The method for constructing a micro-hemispherical shell forming simulation analysis model according to claim 1, characterized in that: The simulation software is CIMSOL Multiphysics.

3. The method for constructing a micro-hemispherical shell forming simulation analysis model according to claim 1, characterized in that: The geometric dimensions of the cross section include the inner diameter r of the annular groove c , annular groove width, annular groove depth h c , the width of the outer frame of the annular groove, the thickness of the glass layer h g and basal layer thickness.

4. The method for constructing a micro-hemispherical shell forming simulation analysis model according to claim 2, characterized in that: The inner volume V of the hemispherical shell s Obtained through real-time integral calculation.

5. The method for constructing a micro-hemispherical shell forming simulation analysis model according to claim 4, characterized in that: Use the integral operator intop in the simulation software to perform integral calculation: V s =intop(z*cosin), where z is the vertical left side corresponding to each micro-segment on the inner curve of the hemispherical shell, and cosin is the ratio of the projection of each micro-segment on the horizontal axis to this micro-segment.

6. The method for constructing a micro-hemispherical shell forming simulation analysis model according to claim 1, characterized in that: The rectangular structure and the concave-shaped structure are respectively divided into grids, wherein the concave-shaped structure is set as a fixed grid and the rectangular structure is set as a dynamic grid.

Images