A method for calculating the internal pressure of an air extrusion film for a piezoelectric tactile feedback device

Abstract

A method for calculating the internal pressure of an air extrusion film for a piezoelectric tactile feedback device, the method comprising the following steps: obtaining a fluid element within the extrusion film, performing a force analysis on the fluid element in two directions, namely the x-axis and the y-axis, to obtain a force balance equation in the x-axis direction and a force balance equation in the y-axis direction, and obtaining the velocities of the fluid in the x-axis and y-axis directions according to the properties of Newtonian fluid; finding the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the spatial variable X, performing a difference processing on the pressure with respect to time T and space X, and replacing the partial derivatives with difference quotients to obtain a difference equation for the pressure; according to the boundary conditions of the internal pressure of the extrusion film, setting an initial iteration pressure value P<supgt;0< / supgt; and an iteration error within the extrusion film and then performing iteration, and terminating the iteration after the absolute value of the pressure difference obtained from two consecutive iterations is less than the iteration error, to obtain the internal pressure of the extrusion film. This method has guiding significance for the design of piezoelectric tactile feedback devices.

Description

Technical Field

[0001] The present invention belongs to the field of piezoelectric tactile feedback devices, and relates to a method for calculating the internal pressure of an air extrusion film for a piezoelectric tactile feedback device. Background Art

[0002] Touch is becoming an important object for sensory simulation. In order to experience rich natural touch sensations, tactile feedback devices have emerged. With the appearance of tactile feedback devices, people's interest in human-computer interaction and natural tactile feedback has been increased. Tactile feedback devices excited by piezoelectric elements are widely used due to their advantages such as fast response speed, wide driving frequency band, large vibration intensity, delicate and realistic vibration experience, low acoustic noise, and low power consumption, and can achieve tactile diversity without changing the actual shape of the object surface. A main principle for achieving tactile diversity by exciting the touch surface with piezoelectric elements is the air extrusion film effect. Since there are many gaps in the contact area between the finger and the touch surface, when the piezoelectric element excites the touch surface to vibrate, an air extrusion film will be formed between the finger skin and the touch surface at a specific frequency and amplitude. The average value of the pressure inside the film is greater than the atmospheric pressure, which reduces the friction force between the two surfaces, thereby achieving different touch sensations. Due to the complexity of the finger skin structure and properties, the current solution for the pressure inside the air extrusion film is to equivalently treat the contact between the finger skin and the touch surface as two smooth surfaces with an initial gap (as shown in Figure 1 ), and the analytical solution of the pressure inside the film is obtained by assuming that the extrusion number is infinite, that is, the vibration frequency is infinite. This equivalent model has the following deficiencies: First, it does not consider the inconsistency of the amplitudes at each point on the touch surface. Second, the obtained pressure inside the film is only applicable to the case where the vibration frequency of the touch surface is very large and is not applicable to low-frequency vibrations. Third, it cannot reflect the change in pressure when the finger is at different positions on the touch surface. These deficiencies result in the piezoelectric tactile feedback device fabricated based on this theory not achieving the best tactile effect. Summary of the Invention

[0003] In order to solve the above problems, the technical solution adopted by the present invention is: A method for calculating the internal pressure of an air extrusion film for a piezoelectric tactile feedback device, the method comprising the following steps:

[0004] Obtain a fluid microelement inside the extrusion film, perform a force analysis on the fluid microelement in two directions of the x-axis and the y-axis to obtain a force balance equation in the x-axis direction and a force balance equation in the y-axis direction, and according to the properties of Newtonian fluid, obtain the velocities of the fluid in the x-axis and y-axis directions;

[0005] According to the fluid continuity equation, the change amounts of the fluid mass in the x, y, and z directions are obtained respectively. Combining with the velocities of the fluid in the x-axis and y-axis directions, and considering the no-slip condition of the fluid at the boundary, the dynamic equation of the pressure in the squeeze film with respect to time and space is obtained by using the Leibniz formula rule.

[0006] A contact model between the finger skin surface and the touch surface is established. Based on the steady-state response of the touch surface under the excitation of the piezoelectric element and the simplified finger skin profile function, the gap between the finger skin surface and the touch surface is obtained.

[0007] The partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the space variable X are obtained. The pressure is differentiated with respect to time T and space X, and the difference quotient is used to replace the partial derivative to obtain the difference equation of the pressure.

[0008] According to the boundary conditions of the pressure in the squeeze film, the initial iterative pressure value P in the squeeze film is set. 0 And after setting the iterative error, iteration is carried out. When the absolute value of the pressure difference obtained from the two consecutive iterations is less than the iterative error, the iteration is terminated, and the pressure in the squeeze film is obtained.

[0009] Furthermore, the force balance equations in the x-axis direction and the y-axis direction are respectively:

[0010]

[0011]

[0012] Wherein: Equation (1) is the force balance equation of the fluid microelement in the squeeze film in the x direction; Equation (2) is the force balance equation of the fluid microelement in the squeeze film in the y direction, p is the pressure in the squeeze film, and τ is the shear stress received by the fluid microelement.

[0013] Furthermore, the velocities of the fluid in the x and y directions are:

[0014]

[0015]

[0016] Wherein: u is the velocity of the fluid in the film in the x direction, v is the velocity of the fluid in the film in the y direction, u 0 , v 0 are respectively the velocities of the touch surface in the x and y directions, u 1 , v 1 are respectively the velocities of the finger skin in the x and y directions, h is the thickness of the squeeze film, and η is the air viscosity.

[0017] Further, the process of obtaining the change amounts of the fluid mass in the x, y, and z directions respectively according to the fluid continuity equation, combining the velocities of the fluid in the x-axis and y-axis directions, and then obtaining the dynamic equation of the pressure in the squeeze film with respect to time and space by using the Leibniz formula rule based on the no-slip condition of the fluid at the boundary is as follows:

[0018] According to the fluid continuity equation, the change amounts of the fluid mass in the x, y, and z directions are obtained respectively. Then, according to the fact that the change amount of the total fluid mass is equal to the change amount of the density multiplied by the volume, we have:

[0019]

[0020] m x is the change amount of the fluid mass in the x direction, and m y is the change amount of the fluid mass in the y direction; m z is the change amount of the fluid mass in the z direction, t is the time variable, and ρ is the fluid density;

[0021] Using the Leibniz formula rule where differentiation and integration can be interchanged, and based on the no-slip condition of the fluid at the boundary, we get EQ1:

[0022]

[0023] Due to the movement of the finger skin and the one-dimensional touch surface under vibration, and since the influence of the finger movement speed on the pressure in the film can be ignored, the above equation can obtain the dynamic equation EQ2 of the pressure in the squeeze film with respect to time and space. The expression of EQ2 is as follows.

[0024]

[0025] Further: The process of obtaining the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the space variable X, performing a difference processing on the pressure with respect to time T and space X, and replacing the partial derivatives with difference quotients to obtain the difference equation of the pressure is as follows:

[0026] A contact model between the finger skin surface and the touch surface is established. To enhance the tactile sensation, the excitation frequency of the piezoelectric element is the resonance frequency of the touch surface. The coordinate systems of the steady-state response of the touch surface and the finger skin contour are established respectively. According to the relationship between the two coordinate systems, the thickness of the squeeze film in the contact area between the two surfaces is simplified to EQ3:

[0027]

[0028] The dimensionless forms of EQ2 and EQ3 are EQ4 and EQ5 respectively:

[0029]

[0030] H = 1 + òsin(T)sin(k 1 X 1 ) + δcos(k 2 X 2 ) (20)

[0031] Where: T = wt, P is the dimensionless form of the pressure, p a is the atmospheric pressure, p is the pressure inside the squeeze film, ω is the frequency of vibration of the touch surface, h is the gap between the touch surface and the finger skin, h 0 is the initial average gap between the finger skin and the touch surface, h v is the amplitude of the touch surface, l 0 is the contact length between the touch surface and the finger skin, λ is the wavelength, L is the finger skin epidermal ridge pitch, l c is the position of the finger on the touch surface;

[0032] The partial derivatives of EQ5 with respect to the time variable T and the spatial variable X are:

[0033]

[0034] After transforming EQ4 and expanding it, we get EQ6:

[0035]

[0036] S = P 2 (23)

[0037] Where: S represents the square of the dimensionless pressure;

[0038] Performing a difference operation on the pressure with respect to time T and space X, and replacing the partial derivatives with difference quotients, we get:

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] Substituting the difference quotient into EQ6 gives the difference equation EQ7 for the pressure. The expression of EQ7 is as follows:

[0046]

[0047] Where: P i,j is the pressure value at the (i,j) node, and S i,j is the square of the pressure value at the (i,j) node, and H i,j is the squeeze film thickness at the (i,j) node.

[0048] Furthermore, the boundary condition of the pressure inside the squeeze film is:

[0049]

[0050] Where: when time T = 0, the pressure inside the squeeze film is the atmospheric pressure, i.e., P i,j (T = 0) = 1, and S i,j (T = 0) = 1. At the boundaries of the squeeze film, i.e., at X = 0 and X = 1, the pressure is the atmospheric pressure, i.e., P i,j (X = 0, X = 1) = 1, and S i,j (X = 0, X = 1) = 1.

[0051] A device for calculating the pressure inside the air squeeze film of a piezoelectric tactile feedback device, comprising:

[0052] An acquisition module: used to acquire fluid micro-elements inside the squeeze film, perform force analysis on the fluid micro-elements in the x-axis and y-axis directions, obtain the force balance equations in the x-axis direction and the force balance equations in the y-axis direction, and obtain the velocities of the fluid in the x-axis and y-axis directions according to the properties of Newtonian fluid;

[0053] A calculation module I: used to obtain the change amounts of the fluid mass in the x-axis, y-axis, and z-axis directions respectively according to the fluid continuity equation, combine the velocities of the fluid in the x-axis and y-axis directions, and then, based on the non-slip condition of the fluid at the boundary and using the Leibniz formula rule, obtain the dynamic equation of the pressure inside the squeeze film with respect to time and space;

[0054] A modeling module: used to establish a contact model between the finger skin surface and the touch surface, and obtain the gap between the finger skin surface and the touch surface according to the steady-state response of the touch surface under the excitation of the piezoelectric element and the simplified finger skin profile function;

[0055] A calculation module II: used to find the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the space variable X, perform a difference processing on the pressure with respect to time T and space X, and replace the partial derivatives with difference quotients to obtain the difference equation of the pressure;

[0056] An iteration module: used to set the initial iteration pressure value P inside the squeeze film according to the boundary condition of the pressure inside the squeeze film 0Iterate after considering the iterative error. Terminate the iteration when the absolute value of the pressure difference obtained from the two consecutive iterations is less than the iterative error, and the pressure inside the squeeze film can be obtained.

[0057] A method for calculating the pressure inside the air squeeze film of a piezoelectric tactile feedback device provided by the present invention establishes a new contact model between the finger skin and the touch surface, obtains the gap between the two surfaces at any moment, and calculates the numerical solution of the pressure inside the film by taking the difference of the time and space variables. The pressure inside the film obtained by this method is applicable to any vibration frequency and is more accurate. It can not only deepen the understanding of the air squeeze film effect, but also has guiding significance for the design of piezoelectric tactile feedback devices. Brief Description of the Drawings

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0059] Figure 1 It is a diagram of the first contact model between the finger and the touch surface;

[0060] Figure 2 It is a diagram of the second contact model between the finger and the touch surface;

[0061] Figure 3 It is a force analysis diagram of the fluid element inside the squeeze film along the x direction;

[0062] Figure 4 It is a force analysis diagram of the fluid element inside the squeeze film along the y direction;

[0063] Figure 5 It is a flowchart of the pressure iteration. Detailed Embodiments

[0064] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail the present invention.

[0065] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part rather than all of the embodiments of the present invention. The following description of at least one exemplary embodiment is actually only illustrative and in no way restricts the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0066] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments of the present invention. As used herein, unless otherwise clearly specified in the context, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0067] Unless otherwise specifically stated, the relative arrangements, numerical expressions and values of the components and steps set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be clear that, for the sake of convenience of description, the dimensions of the various parts shown in the drawings are not drawn in actual proportional relationships. Technologies, methods and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the said technologies, methods and devices should be regarded as part of the authorization specification. In all the examples shown and discussed here, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that like reference numerals and letters denote like items in the following drawings, and thus, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0068] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by orientation words such as "front, rear, upper, lower, left, right", "lateral, vertical, perpendicular, horizontal" and "top, bottom" are generally based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description. Without contrary description, these orientation words do not indicate and imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and thus cannot be construed as limiting the scope of protection of the present invention. The orientation words "inside, outside" refer to the inside and outside relative to the contour of each component itself.

[0069] For ease of description, spatial relative terms, such as "above", "over", "on the upper surface", "upper", etc., may be used herein to describe the spatial positional relationship of one device or feature to other devices or features as shown in the figures. It should be understood that the spatial relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is inverted, a device described as "above" or "over" other devices or structures will then be positioned "below" or "beneath" the other devices or structures. Thus, the exemplary term "above" can include both orientations of "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and corresponding interpretations of the spatial relative descriptions used herein will be made.

[0070] In addition, it should be noted that the use of terms such as "first", "second", etc. to limit components is merely for the convenience of differentiating the corresponding components. Without additional statements, the above terms have no special meanings, and thus should not be construed as limiting the protection scope of the present invention.

[0071] A method for calculating the internal pressure of an air extrusion film for a piezoelectric tactile feedback device, the method comprising the following steps:

[0072] Obtain a fluid element in the extrusion film, perform a force analysis on the fluid element in two directions of the x-axis and the y-axis to obtain equilibrium equations in the two directions, and according to the properties of Newtonian fluid, obtain the velocities of the fluid in the x-axis and y-axis directions;

[0073] According to the fluid continuity equation, obtain the change amounts of the fluid mass in the x, y, and z directions respectively, combine the velocities of the fluid in the x-axis and y-axis directions, and then according to the no-slip condition of the fluid at the boundary, use the Leibniz formula rule to obtain the dynamic equation of the internal pressure of the extrusion film with respect to time and space;

[0074] Establish a contact model between the finger skin surface and the touch surface, as Figure 2 shown, obtain the gap between the two surfaces at any moment, and obtain the gap between the finger skin surface and the touch surface according to the steady-state response of the touch surface under the excitation of the piezoelectric element and the simplified finger skin profile function; the internal pressure of the film obtained by this model is applicable to any vibration frequency and is more accurate, which can not only deepen the understanding of the air extrusion film effect, but also has guiding significance for the design of the piezoelectric tactile feedback device.

[0075] Obtain the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the space variable X, perform a difference processing on the pressure with respect to time T and space X, and use the difference quotient to replace the partial derivative to obtain the difference equation of the pressure;

[0076] According to the boundary conditions of the pressure in the squeeze film, set the initial iterative pressure value P in the squeeze film 0 and the iterative error ERR, and then perform iteration. After the absolute value of the pressure difference obtained from two consecutive iterations is less than the iterative error, terminate the iteration to obtain the pressure in the squeeze film.

[0077] Furthermore, the force balance equation of the microelement in the x-axis direction is as follows Figure 3 shown;

[0078]

[0079] The force balance equation of the microelement in the y-axis direction is respectively as follows Figure 4 shown;

[0080]

[0081] Simplify formula (1) to get

[0082]

[0083] where p is the pressure in the squeeze film and τ is the shear stress received by the fluid microelement.

[0084] Since air belongs to Newtonian fluid, there is

[0085]

[0086] Substitute formula (3) into formula (2) and then perform double integral with respect to z on both sides to get

[0087]

[0088] According to the velocity boundary conditions, there is

[0089] z = 0, u = u 0 ; z = h, u = u 1 (6)

[0090] Substitute formula (6) into formula (5) to get

[0091]

[0092] According to the force balance of the microelement in the y direction, similarly, we can get

[0093]

[0094] where u is the velocity of the fluid in the film in the x direction, v is the velocity of the fluid in the film in the y direction, u 0 , v 0 are the velocities of the touch surface in the x and y directions respectively, u 1 , v1 are the velocities of the finger skin in the x and y directions respectively, h is the thickness of the squeeze film, η is the air viscosity, τ is the shear stress in the x direction acting on the fluid element,

[0095] According to the fluid continuity equation:

[0096] Change in the mass of the fluid in the x direction:

[0097]

[0098] Change in the mass of the fluid in the y direction:

[0099]

[0100] Change in the mass of the fluid in the z direction:

[0101]

[0102]

[0103] m x is the change in the mass of the fluid in the x direction, m y is the change in the mass of the fluid in the y direction; m z is the change in the mass of the fluid in the z direction, t is the time variable, and ρ is the fluid density;

[0104] Substituting Eqs. (8) - (10) into Eq. (11) gives

[0105]

[0106] Integrating both sides of Eq. (12) from 0 to h and using the Leibnitz rule which allows interchange of differentiation and integration gives EQ1:

[0107]

[0108] Then according to no - slip at the boundary of the fluid:

[0109]

[0110] Substituting u and v and simplifying gives EQ2:

[0111]

[0112] where: u, v, and w are the velocities of the fluid element in the x, y, and z directions respectively, u 1 , u 0 are the velocity of the finger skin in the x direction and the velocity of the touch surface in the x direction respectively, v 1 , v 0are the velocities of the finger skin and the touch surface along the y - direction respectively, and w 1 , w 0 are the velocities of the finger skin and the touch surface along the z - direction respectively, and h is the thickness of the squeeze film.

[0113] Since the research is on the motion of the finger skin and a one - dimensional touch surface under vibration, and the influence of the finger moving speed on the pressure in the film can be ignored, the above formula can be simplified as:

[0114]

[0115] To establish the contact model between the finger skin and the touch surface, in order to enhance the tactile sensation, the excitation frequency of the piezoelectric element is the resonance frequency of the touch surface. The coordinate systems of the steady - state response of the touch surface and the finger - skin contour are established respectively. According to the relationship between the two coordinate systems, the thickness of the squeeze film in the contact area between the two surfaces can be simplified to EQ3:

[0116]

[0117] The dimensionless forms of EQ2 and EQ3 are EQ4 and EQ5 as follows:

[0118]

[0119] H = 1+òsin(T)sin(k 1 X 1 )+δcos(k 2 X 2 ) (20)

[0120] Where: T = wt, P is the dimensionless form of the pressure, p a is the atmospheric pressure, p is the pressure in the squeeze film, ω is the vibration frequency of the touch surface, h is the gap between the touch surface and the finger skin, h 0 is the initial average gap between the finger skin and the touch surface, h v is the amplitude of the touch surface, l 0 is the contact length between the touch surface and the finger skin, λ is the wavelength, L is the finger - skin epidermal ridge pitch, l c is the position of the finger on the touch surface.

[0121] The partial derivatives of EQ5 with respect to the time variable T and the space variable X are:

[0122]

[0123]

[0124] After transforming EQ4 and expanding it, we get EQ6:

[0125]

[0126] S = P 2 (24)

[0127] Where: S represents the square of the dimensionless pressure;

[0128] Performing a difference operation on the pressure with respect to time T and space X, and replacing the partial derivative with a difference quotient, we get:

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] Substituting equations (22) - (29) into equation (19), we get

[0136]

[0137] Equation (30) is simplified to obtain the difference equation of the pressure:

[0138]

[0139] The boundary conditions of the pressure in the squeeze film are:

[0140]

[0141] Furthermore, in this application, the finite difference method is used to solve the pressure in the squeeze film. When using the finite difference method to solve the pressure distribution in the air squeeze film, within the squeeze film region, grids are divided according to the difference step sizes Δx and Δt. X is divided into m equal parts, and T is divided into n equal parts. In this way, there are (m + 1)(n + 1) grid points in the squeeze film region. The pressure values at each node are used to form various order difference quotients, and the difference quotient is used to replace the partial derivative in the equation, discretizing the partial differential equation into a set of linear algebraic equations. The solution P of the linear algebraic equation i,j is the pressure value of the squeeze film. The successive over-relaxation iteration method is used to find the numerical solution of the non-homogeneous linear equations. First, the pressure values of the boundary nodes are determined (S 0,j = 1, S m,j = 1, S i,0= 1), and then assign the initial value S to other internal nodes i,j (i = 1 to m - 1, j = 1 to n). According to Equation (32), calculate S successively i,j (i = 1 to m - 1, j = 1 to n). Each time the S value of an internal node is calculated, it will replace the original S value of that node. After all internal nodes have been calculated once, the second approximate distribution S 1 i,j is obtained, which is more accurate than the first approximate value S i,j . Then recalculate according to Equation (32) to obtain an S 1 i,j that is more accurate than 2 i,j . And so on. After k iterations, a sufficiently accurate solution S k i,j is obtained. Finally, calculate the pressure value of each node according to Equation (33). To determine whether the pressure distribution calculated in each iteration meets the accuracy requirements and thus decide whether to terminate the iteration process, usually judge according to the relative convergence criterion of Equation (34):

[0142]

[0143] Set the initial pressure value P 0 in the squeeze film and the iteration error ERR, and then perform iteration. After the absolute value of the pressure difference obtained from the current and previous two iterations is less than the iteration error, terminate the iteration, thereby obtaining the pressure in the squeeze film. The iteration flow chart is as Figure 5 shown.

[0144] A device for calculating the pressure in the air squeeze film of a piezoelectric tactile feedback device, comprising:

[0145] Acquisition module: used to acquire fluid micro-elements in the squeeze film, perform force analysis on the fluid micro-elements in the x-axis and y-axis directions, obtain the force balance equations in the x-axis direction and the force balance equations in the y-axis direction, and obtain the velocities of the fluid in the x-axis and y-axis directions according to the properties of Newtonian fluid;

[0146] Calculation module I: used to obtain the change amounts of the fluid mass in the x-axis, y-axis, and z-axis directions respectively according to the fluid continuity equation, combine the velocities of the fluid in the x-axis and y-axis directions, and then use the Leibniz formula rule according to the non-slip condition of the fluid at the boundary to obtain the dynamic equation of the pressure in the squeeze film with respect to time and space;

[0147] Establishment module: used to establish the contact model between the finger skin surface and the touch surface, and obtain the gap between the finger skin surface and the touch surface according to the steady-state response of the touch surface under the excitation of the piezoelectric element and the simplified finger skin contour function;

[0148] Calculation Module II: It is used to find the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the spatial variable X, perform a difference processing on the pressure in terms of time T and space X, replace the partial derivatives with difference quotients, and obtain the difference equation of the pressure;

[0149] Iteration Module: It is used to set the initial iteration pressure value P in the squeeze film according to the boundary conditions of the pressure in the squeeze film 0 and perform iteration after setting the iteration error. After the absolute value of the pressure difference obtained from the previous and current iterations is less than the iteration error, the iteration is terminated to obtain the pressure in the squeeze film.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the internal pressure of an air extrusion film for a piezoelectric tactile feedback device, characterized in that: This method includes the following steps: Obtain a fluid microelement in the extrusion film, perform a force analysis on the fluid microelement in the x-axis and y-axis directions, obtain the force balance equations in the x-axis direction and the force balance equations in the y-axis direction, and according to the properties of Newtonian fluids, obtain the velocities of the fluid in the x-axis and y-axis directions; According to the fluid continuity equation, respectively obtain the change amounts of the fluid mass in the x, y, and z directions, combine the velocities of the fluid in the x-axis and y-axis directions, and then according to the no-slip condition of the fluid at the boundary, use the Leibniz formula rule to obtain the dynamic equation of the pressure in the extrusion film with respect to time and space; Establish a contact model between the finger skin surface and the touch surface, and obtain the gap between the finger skin surface and the touch surface according to the steady-state response of the touch surface under the excitation of the piezoelectric element and the simplified finger skin contour function; Find the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the space variable X, perform a difference processing on the pressure with respect to time T and space X, and use the difference quotient to replace the partial derivative to obtain the difference equation of the pressure; According to the boundary conditions of the pressure in the squeeze film, set the initial iterative pressure value P in the squeeze film 0 and perform iteration after setting the iterative error. After the absolute value of the pressure difference obtained from the two consecutive iterations is less than the iterative error, terminate the iteration to obtain the pressure in the squeeze film; The process of finding the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the space variable X, performing a difference processing on the pressure with respect to time T and space X, and using the difference quotient to replace the partial derivative to obtain the difference equation of the pressure is as follows: Establish a contact model between the finger skin surface and the touch surface. To enhance the tactile sensation, the excitation frequency of the piezoelectric element is the resonance frequency of the touch surface. Respectively establish the coordinate system of the steady-state response of the touch surface and the finger skin contour coordinate system. According to the relationship between the two coordinate systems, the thickness of the extrusion film in the contact area between the two surfaces is simplified to EQ3: （18） The dimensionless forms of EQ2 and EQ3 are EQ4 and EQ5 respectively: （19） （20） Wherein: , , , , , , , , , , P is the dimensionless form of the pressure, p a is the atmospheric pressure, p is the pressure inside the squeeze film, ω is the frequency of vibration of the touch surface, h is the gap between the touch surface and the finger skin, h 0 is the initial average gap between the finger skin and the touch surface, h v is the amplitude of the touch surface, l 0 is the contact length between the touch surface and the finger skin, λ is the wavelength, L is the epidermal ridge pitch of the finger skin, is the position of the finger on the touch surface; The partial derivative of EQ5 with respect to the time variable T and the space variable X is: （21） After transforming EQ4 and expanding it, it becomes EQ6: （22） (23) Wherein: S represents the square of the dimensionless pressure; Perform a difference processing on the pressure with respect to time T and space X, and use the difference quotient to replace the partial derivative to obtain: （24） （25） （26） （27） （28） （29） Substitute the difference quotient into EQ6 to obtain the difference equation EQ7 of the pressure. The expression of EQ7 is as follows, （30） Wherein: P i,j is the pressure value at the (i,j) node, S i,j is the square of the pressure value at the (i,j) node, H i,j is the squeeze film thickness at the (i,j) node.

2. The method according to claim 1, characterized in that, The force balance equations in the x-axis direction and the force balance equations in the y-axis direction are respectively: （1） （2） Wherein: Equation (1) is the equilibrium equation of the force on the fluid element in the x direction within the squeeze film; Equation (2) is the equilibrium equation of the force on the fluid element in the y direction within the squeeze film. p is the pressure within the squeeze film. τ is the shear stress received by the fluid element.

3. The method according to claim 1, characterized in that, The velocities of the fluid in the x and y directions are: （7） （8） Wherein: is the velocity of the fluid in the film along the x direction, is the velocity of the fluid in the film along the y direction, , are the velocities of the touch surface along the x and y directions respectively, , are the velocities of the finger skin along the x and y directions respectively, is the thickness of the extrusion film, is the air viscosity.

4. The method according to claim 1, characterized in that, The process of obtaining the dynamic equation of the pressure in the extrusion film with respect to time and space according to the fluid continuity equation, respectively obtaining the change amounts of the fluid mass in the x, y, and z directions, combining the velocities of the fluid in the x-axis and y-axis directions, and then according to the no-slip condition of the fluid at the boundary, using the Leibniz formula rule is as follows: According to the fluid continuity equation, respectively obtain the change amounts of the fluid mass in the x, y, and z directions, and then according to the total change amount of the fluid mass being equal to the change amount of the density multiplied by the volume, obtain: （9）～（12） is the change in the fluid mass in the x - direction, is the change in the fluid mass in the y - direction; is the change in the fluid mass in the z - direction, t is the time variable, ρ is the fluid density; Using the Leibniz formula rule where differentiation and integration can be exchanged, according to the no-slip condition of the fluid at the boundary, obtain EQ1: （14） Due to the movement of the finger skin and the one-dimensional touch surface under vibration, and since the influence of the finger movement speed on the pressure inside the film can be ignored, the dynamic equation EQ2 of the pressure inside the squeeze film with respect to time and space can be obtained from the above equation, and the expression of EQ2 is as follows. （17） 5. The method according to claim 1, wherein, the boundary conditions of the pressure inside the squeeze film are: （32） where: when time T = 0, the pressure inside the squeeze film is the atmospheric pressure, i.e., , , the pressures at the boundaries of the squeeze film, i.e., X = 0 and X = 1, are the atmospheric pressure, i.e., , .

6. An apparatus for calculating the pressure inside an air squeeze film for a piezoelectric tactile feedback device, characterized in that: comprising: an acquisition module: configured to acquire a fluid microelement inside the squeeze film, perform a force analysis on the fluid microelement in two directions of the x-axis and the y-axis, obtain the force balance equation in the x-axis direction and the force balance equation in the y-axis direction, and obtain the velocities of the fluid in the x-axis and y-axis directions according to the properties of Newtonian fluid; a calculation module I: configured to obtain the change amounts of the fluid mass in the x-axis, y-axis, and z-axis directions respectively according to the fluid continuity equation, combine the velocities of the fluid in the x-axis and y-axis directions, and then use the Leibniz formula rule based on the non-slip condition of the fluid at the boundary to obtain the dynamic equation of the pressure inside the squeeze film with respect to time and space; a modeling module: configured to establish a contact model between the finger skin surface and the touch surface, and obtain the gap between the finger skin surface and the touch surface according to the steady-state response of the touch surface under the excitation of the piezoelectric element and the simplified finger skin profile function; a calculation module II: configured to obtain the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the space variable X, perform a difference processing on the pressure with respect to time T and space X, and replace the partial derivatives with difference quotients to obtain the difference equation of the pressure; Iterative module: used to set the initial iterative pressure value P in the squeeze film according to the boundary conditions of the pressure in the squeeze film 0 and perform iteration after setting the iterative error. When the absolute value of the pressure difference obtained from the previous and current iterations is less than the iterative error, the iteration is terminated to obtain the pressure in the squeeze film; the process of obtaining the partial derivatives of the gap between the finger skin surface and the touch surface with respect to the time variable T and the space variable X, performing a difference processing on the pressure with respect to time T and space X, and replacing the partial derivatives with difference quotients to obtain the difference equation of the pressure is as follows: Establish a contact model between the finger skin surface and the touch surface. To enhance the tactile sensation, the excitation frequency of the piezoelectric element is the resonance frequency of the touch surface. Respectively establish the coordinate system of the steady-state response of the touch surface and the coordinate system of the finger skin profile. According to the relationship between the two coordinate systems, the thickness of the squeeze film in the contact area between the two surfaces is simplified to EQ3: （18） The dimensionless forms of EQ2 and EQ3 are EQ4 and EQ5 respectively: （19） （20） Wherein: , , , , , , , , , , P is the dimensionless form of the pressure, p a is the atmospheric pressure, p is the pressure inside the squeeze film, ω is the frequency of vibration of the touch surface, h is the gap between the touch surface and the finger skin, h 0 is the initial average gap between the finger skin and the touch surface, h v is the amplitude of the touch surface, l 0 is the contact length between the touch surface and the finger skin, λ is the wavelength, L is the pitch of the epidermal ridges of the finger skin, is the position of the finger on the touch surface; The partial derivatives of EQ5 with respect to the time variable T and the space variable X are: （21） After transforming EQ4 and expanding it, it becomes EQ6: （22） (23) Wherein: S represents the square of the dimensionless pressure; Perform a difference processing on the pressure with respect to time T and space X, and replace the partial derivatives with difference quotients to obtain: （24） （25） （26） （27） （28） （29） Substitute the difference quotient into EQ6 to obtain the difference equation EQ7 of the pressure. The expression of EQ7 is as follows, （30） Wherein: P i,j is the pressure value at the (i, j) node, S i,j is the square of the pressure value at the (i, j) node, H i,j is the squeeze film thickness at the (i, j) node.

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