Curved surface flexible grinding and polishing tool and workpiece curved surface shape machining control method

Abstract

The invention discloses a control method for machining a curved surface shape of a workpiece by a curved surface flexible grinding and polishing tool. According to the flexible grinding and polishing tool, a grinding and polishing head structure is divided into an elastic layer and an abrasive layer, and the abrasive layer is a contact layer used for making contact with the workpiece. After the whole grinding and polishing head is bonded to the connecting plate, regular textures are cut off on the surface of the grinding material layer through laser, and patterns of the regular textures are divided into an enveloping type and an array type. According to the Hertz theory, it can be obtained that the contact contour of the grinding and polishing head is approximate to a circle, and an exponential function contact stress distribution model is provided. After the stress distribution model and the linear velocity distribution model of each point in the contact area of the grinding and polishing tool and the workpiece are solved respectively, the material removal rate of each point in the contact area can be obtained according to the Preston equation, and the material removal contour is obtained through analysis, so that the problems existing in the machining process of a traditional tool can be effectively solved; and the ultra-precision machining level can be remarkably improved, and the requirements of modern industrial manufacturing for high-precision and high-efficiency machining are met.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of precision machining, in particular to a curved surface flexible grinding and polishing tool and a workpiece curved surface surface shape machining control method. BACKGROUND

[0002] Under the development trend of miniaturization of optoelectronic devices, lightweight of aerospace optical systems, and precision of semiconductor equipment, the processing demand of curved surface optical elements is increasing at a rate of 18% per year. The core challenge faced by the global precision manufacturing field focuses on the coordinated control of nanoscale surface accuracy and sub-micron surface quality. The contradiction between the physical properties of traditional rigid grinding and polishing tools and the processing requirements is increasingly prominent when dealing with hard and brittle materials such as K9 optical glass and silicon carbide ceramics with complex curvature characteristics. There are many limitations in the traditional grinding and polishing process. It is difficult to effectively control the material removal rate during the machining process, especially when machining complex shapes or large-area workpieces, local removal is too much or insufficient, which not only reduces the processing efficiency, but also increases the difficulty of subsequent correction. Another problem is the heat generated during the machining process. In ultra-precision machining, the accumulation of heat may cause thermal deformation of the workpiece surface, thereby affecting the machining accuracy. Due to the structural characteristics of traditional rigid grinding and polishing tools, it is often difficult to effectively dissipate the heat generated during the machining process, thereby limiting the improvement of processing efficiency and quality. In addition, the service life of traditional tools is also affected by wear and heat accumulation during the machining process, increasing the processing cost. In order to overcome the defects of traditional grinding and polishing tools, and to process more and more curved surface optical elements, it is particularly important to develop a flexible grinding and polishing tool. SUMMARY

[0003] In view of the problems existing in the prior art, the present application provides a curved surface flexible grinding and polishing tool and a workpiece curved surface surface shape machining control method, which not only effectively solves the problems existing in the machining process of traditional tools, but also significantly improves the level of ultra-precision machining, and meets the demand of modern industrial manufacturing for high-precision and high-efficiency machining.

[0004] The present application is realized by the following technical solutions:

[0005] A curved surface flexible grinding and polishing tool for workpiece curved surface surface shape machining control method, comprising the following steps:

[0006] Based on Hertz theory, a contact stress distribution model of the contact area between the grinding and polishing tool and the workpiece is established;

[0007] Based on the attitude of the grinding and polishing head, the grinding and polishing inclination angle and the grinding and polishing deflection angle of the grinding and polishing head are defined, and then a linear velocity distribution model of the contact area between the grinding and polishing head and the workpiece during the machining process is established;

[0008] Based on the Preston equation, the material removal rate of each point in the contact area is obtained through the contact stress distribution model and the linear velocity distribution model, and then the removal profile in the machining process can be obtained; based on the removal profile control, the surface shape of the workpiece is machined.

[0009] Preferably, based on the Hertz theory, the contact stress distribution model of the contact area between the polishing tool and the workpiece is established, specifically:

[0010] According to the Hertz theory, the contact area between the polishing head of the polishing tool and the workpiece is approximated as a circle, and a coordinate system is established with the center of the circular contact area (x, y) as the origin, wherein the z-axis is perpendicular to the contact area, the y-axis is the movement direction, and the radius r of the contact area between the polishing head and the workpiece is obtained;

[0011] During the machining process, a uniform load is applied to the center of the contact area of the curved surface polishing tool, and the uniform load area is πr 2 , so that the center of the uniform load coincides with the center of the contact area of the curved surface polishing tool, and the normal force I is obtained;

[0012] Based on the radius r of the contact area and the normal force I, the contact stress distribution model of the circular contact area is established.

[0013] Preferably, the radius r of the contact area between the polishing head and the workpiece is specifically:

[0014]

[0015] In the formula, I is the normal polishing force of the polishing contact point, R e is the equivalent contact radius, E * is the relative elastic modulus.

[0016] Preferably, the contact stress distribution model is specifically:

[0017]

[0018] In the formula, r is the radius of the contact area between the polishing head and the workpiece, I is the normal polishing force of the polishing contact point, and k is the width-height ratio coefficient of the contact area.

[0019] Preferably, the linear velocity distribution model in the contact area between the polishing head and the workpiece during the machining process is specifically:

[0020] Based on the posture of the polishing head, the polishing inclination angle and the polishing deflection angle of the polishing head are defined, that is, the pitch angle β and the yaw angle λ, and the axial unit vector and the angular velocity vector of the polishing head are obtained;

[0021] Based on the axial unit vector and the angular velocity vector of the polishing head, assume that a point P on the contact area between the polishing tool and the workpiece is in the coordinate system o-xyz, and the coordinates of the point P are (x Py P ,0), the vector from the center of the polishing head to point P is have where R is the radius of the polishing head, the tangential velocity v t is obtained by the tangential velocity v t The linear velocity of the polishing head is obtained by the tangential velocity v tx , and the linear velocity distribution model of the contact area between the polishing head and the workpiece in the machining process is obtained.

[0022] Preferably, the expression of the linear velocity distribution model is:

[0023]

[0024] In the formula, λ is the yaw angle, β is the pitch angle, ω is the angular velocity, v tx and v ty are the tangential velocities of the polishing head on the X-axis and the Y-axis, respectively.

[0025] Preferably, based on the Preston equation, the material removal rate of each point in the contact area is obtained by the contact stress distribution model and the linear velocity distribution model, specifically:

[0026] Based on the Preston formula, the contact stress distribution model and the linear velocity distribution model are combined to describe the material removal function of the polishing head fixed-point polishing, and the material removal height model under different parameters is obtained, wherein the material removal function profile radius is the radius length of the polishing tool in the contact area of the workpiece surface, and the peak removal rate is the maximum removal depth per unit time,

[0027] wherein the material removal rate, and the specific expression is:

[0028] Δh(x,y)=K p p(x,y)v(x,y)T

[0029] In the formula, Δh(x,y) is the material removal amount of the polishing tool at any point (x,y) on the contact surface of the workpiece; Kp is the Preston constant; p(x,y) and v(x,y) are the contact stress and relative linear velocity of the polishing contact surface, respectively; and T is the dwell time of the polishing tool at the polishing point of the workpiece surface.

[0030] Preferably, the removal profile in the machining process is specifically:

[0031] When the pitch angle is 0°, that is, the polishing head has no yaw angle, the removal profile is W-shaped;

[0032] When the pitch angle is greater than 0°, that is, the polishing head has a yaw angle, the removal profile is inverted V-shaped.

[0033] Preferably, in the processing process, the energy absorption capacity of the elastic layer of the polishing tool is evaluated by analyzing the stress-strain curve of the elastic layer under uniaxial compression load, so as to improve the processing stability, and specifically:

[0034] The elastic layer of the polishing tool absorbs energy through the plastic deformation platform area under uniaxial compression, and the absorbed energy W satisfies:

[0035]

[0036] Wherein, W is the absorbed energy, ε is the deformation amount of the workpiece in the processing process, and σ is the stress corresponding to ε.

[0037] A curved surface flexible polishing tool, comprising, an abrasive layer and an elastic layer;

[0038] The abrasive layer is rolled on the elastic layer to form a polishing head, and the polishing head is bonded to a circular arc connecting rod.

[0039] The surface of the abrasive layer is processed by laser to have heat dissipation texture, and the heat dissipation texture includes envelope type and array type.

[0040] Wherein, the envelope type heat dissipation texture is designed by adopting the continuous trajectory of spiral line, concentric circle or involute, and is matched with the curvature change of the hemispherical surface.

[0041] The array type heat dissipation texture is designed by adopting the combination array of high-density triangular grid, quadrilateral gradual change, polar region hexagonal honeycomb structure or circular gradual change.

[0042] The polishing head is a hemispherical structure.

[0043] Preferably, the flexible polishing tool is used in the grinding stage after optical element grinding and before polishing, and based on the Preston formula as the curved surface fixed abrasive removal function, the surface profile control and surface roughness control of hard and brittle materials are realized.

[0044] Compared with the prior art, the present application has the following beneficial technical effects:

[0045] The flexible polishing tool of the present application can better adapt to the shape changes of the workpiece surface during processing by introducing the composite structure of the elastic layer and the abrasive layer. At the same time, by optimizing the structural design and material selection of the tool, the material removal rate can be better controlled, and the uniformity and precision of the processed surface can be improved. In addition, the flexible polishing tool can also effectively dissipate the heat generated during processing by special structural design, such as processing regular texture on the surface of the abrasive layer, and the pattern is divided into envelope type and array type to meet the needs of different processing environments, thereby further improving the processing efficiency and quality. Not only can it effectively solve the problems existing in the processing of traditional tools, but also can significantly improve the level of ultra-precision machining, meet the needs of modern industrial manufacturing for high-precision and high-efficiency processing. The research and application of such tools have important practical significance and broad application prospects for promoting the technological progress and industrial upgrading of related industries.

[0046] The present application also proposes a method for processing the curved surface of a workpiece. According to Hertz theory, the contact profile of the polishing head is approximately circular, and an exponential function contact stress distribution model is proposed. After obtaining the stress distribution model and linear velocity distribution model of each point in the contact area between the polishing tool and the workpiece, the material removal rate of each point in the contact area can be obtained according to the Preston equation. Through the combination of different bias angles, different sizes, and different elastic modulus polishing heads, high-efficiency and high-precision processing can be realized.

[0047] Further, by utilizing the energy absorption performance of the elastic layer and controlling the density and yield stress of the elastic body, the impact resistance of the tool is improved, the vibration during processing is reduced, the processing quality is improved, and the service life of the flexible polishing tool is prolonged to a certain extent.

[0048] Further, the flexible polishing tool of the present application is used in the grinding stage after optical element grinding and before polishing, and based on the Preston formula as the curved surface fixed abrasive removal function, the surface shape control and surface roughness control of the workpiece of hard and brittle material are realized, which can improve the surface quality after grinding and accelerate the convergence speed of subsequent polishing. The rigid layer of the polishing tool can effectively remove the surface of the optical element, and the flexible layer can make the optical surface removal uniform and controllable through elastic strain, so the flexible polishing tool can greatly improve the efficiency and quality of optical element processing. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor.

[0050] Figure 1 is a structural diagram of a flexible polishing tool of the present application;

[0051] Figure 2 is a schematic diagram of surface cutting texture of the abrasive layer of the present application;

[0052] Figure 3 is a schematic diagram of a contact posture model of the flexible polishing tool;

[0053] Figure 4 is a schematic diagram of curved surface machining and removal profile of the flexible polishing tool;

[0054] In the drawings, 1 is an abrasive layer; 2 is an elastic layer; 3 is a connecting plate; 4 is a flexible polishing tool; and 5 is a curved workpiece. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the following will combine the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of the present application.

[0056] A specific curved surface flexible polishing tool workpiece curved surface surface shape machining control method includes the following steps:

[0057] Step 1), a curved surface flexible polishing tool polishing head structure as shown in Figure 1 , Figure 1 1 is an abrasive layer, and 2 is an elastic layer made of a material with a small elastic modulus such as rubber or polyurethane to serve as an intermediate layer. After the entire 1 and 2 polishing head is bonded to the connecting plate, a pattern as shown in Figure 2 is processed on the surface of the abrasive layer by laser to dissipate heat generated during the machining process and form effective and uniform removal. The height of the elastic layer of the flexible polishing tool is h1, and the height of the abrasive layer is h2.

[0058] According to the surface of the abrasive layer, a pattern is cut out by laser as shown in Figure 2 to dissipate the heat generated in the ultra-precision machining process, and the pattern is divided into envelope type and array type. Since the curved flexible polishing head is hemispherical, the pattern design needs to prevent the influence caused by the contact between the polishing head and the workpiece during high-speed machining.

[0059] The envelope type pattern closely fits the curvature change of the hemispherical curved surface through continuous trajectories such as spiral lines, concentric circles or involutes (Fig. a and Fig. c). This design ensures that the heat dissipation channel always extends along the main load direction of the polishing head, which conforms to the centrifugal force distribution law during high-speed rotation. The variable pitch spiral line (such as dense in the equatorial region and sparse in the polar region) is used to adapt to the load distribution, avoiding the alternating stress concentration phenomenon when the pattern gap contacts the workpiece at high speed.

[0060] The array type pattern adopts a combination array of high-density triangular grid, quadrilateral gradual change, polar hexagonal honeycomb structure, and circular gradual change (Fig. b and Fig. d), realizes spatial regulation of thermal and mechanical properties, effectively suppresses high-frequency vibration, and strengthens directional heat dissipation and dynamic balance control.

[0061] Step 2) According to the Hertz theory, the contact area between the polishing head of the polishing tool and the workpiece is approximated as a circle, and a coordinate system is established with the center of the circular contact area (x, y) as the origin, wherein the z-axis is perpendicular to the contact area, and the y-axis is the motion direction, to obtain the contact area radius r between the polishing head and the workpiece;

[0062] A uniform load is applied to the center of the contact area of the curved polishing tool during machining, and the uniform load area is πr 2 , so that the center of the uniform load coincides with the center of the contact area of the curved polishing tool, and the normal force I is obtained, which is specifically:

[0063] During machining, the workpiece applies a distributed load to the abrasive layer. Due to the elastic layer of the spherical polishing tool, an elastic contact area will be formed between the polishing head and the workpiece. The curvature radius of the contact area is much larger than the radius of the polishing head, and the contact area of the two spheres is an elliptical shape, which can be approximated as a circle as shown in Figure 3 . And the nonlinearity of the thin plate contact stress distribution is inevitable. An exponential function contact stress distribution model is used to describe the non-linear distribution shape of the saddle type, parabolic type and bell-shaped surface, etc. Combined with the Hertz theory, the contact stress distribution model in the contact area between the polishing head and the workpiece during machining can be obtained.

[0064] Specifically, a coordinate system is established with any point P in the contact area as the origin, wherein the z-axis is perpendicular to the contact area, and the y-axis is the motion direction, and the expression formula of the contact area is:

[0065] x 2 +y2 = r 2 (1)

[0066] where r is the radius of the contact area between the polishing head and the workpiece, which is:

[0067]

[0068] where I is the normal polishing force at the polishing contact point, R e is the equivalent radius of curvature of the contact, E * is the relative modulus of elasticity.

[0069] Let the elastic modulus of the elastic layer of the flexible polishing tool be E1, the elastic modulus of the abrasive layer be E2, and the equivalent elastic modulus of the polishing head as a whole be E t which can be calculated by the Reuss model, then the equivalent elastic modulus E t and the equivalent Poisson's ratio υ t of the polishing head can be calculated by the following formula:

[0070]

[0071] Let E w be the Young's modulus of elasticity of the workpiece, υ w be the Poisson's ratio of the workpiece, and k1 and k2 be the relative principal curvatures of the polishing contact point, which are related to the curvatures of the contact point of the polishing head and the workpiece, then:

[0072]

[0073] In the process of polishing a plane, a uniform load q(x, y) (in units of (N / m 2 )) is applied to the center of the contact area of the curved polishing tool, the area of the uniform load is πr 2 , and the center of the uniform load coincides with the center of the contact area of the curved polishing tool.

[0074] Now the normal polishing force I at the polishing contact point is calculated. Let the deformation of the polishing head under the workpiece during the polishing process be ε, and E1 be the elastic modulus of the polishing head. Since the elastic modulus of the abrasive layer is much larger than that of the elastic layer, E1 is approximately equal to the elastic modulus of the elastic layer. The contact area is circular with a radius of r, and the total contact stress δ is:

[0075]

[0076] Then the normal polishing force I at the polishing contact point can be obtained as:

[0077] I = πr 2 εE1 (8)

[0078] In combination with the definition of step 1), an exponential function contact stress distribution model is as follows:

[0079]

[0080] where p(x, y) is the contact stress distribution model function under distributed load, A, B, C are undetermined coefficients determined by the load form, the geometric properties and material properties of the abrasive layer, which can describe the nonlinear distribution shapes such as saddle, parabolic and bell-shaped curved surface at the same time.

[0081] According to the definition of step 1), the width-height ratio of the abrasive layer in the contact area is λ = 2r / h2, and the contact stress at the center (0, 0) of the circular contact area is the average contact stress multiplied by the width-height ratio coefficient k = k(λ), that is, formula (10):

[0082]

[0083] where Ω is the distributed load area, and since the circular contact area is rotationally symmetric, the contact stress distribution of the substrate is also rotationally symmetric, that is:

[0084] p(x, y) = p(-x, y) = p(x, -y) = p(-x, -y) (11)

[0085] Let the normal polishing force I of the polishing contact point be:

[0086]

[0087] Substituting formula (10) gives:

[0088]

[0089] Since the abrasive layer area coincides with the distributed load area, we have:

[0090]

[0091] Solving the equation group from formula (9) to formula (14) can obtain the corresponding undetermined coefficients A, B, C.

[0092] Under the condition of free four-side boundary and considering the symmetry condition which does not affect the contact stress, A can satisfy the following formula:

[0093] A = 0 (15)

[0094] Substituting the center coordinates (0, 0) into formula (9) gives:

[0095] p(0, 0) = A + B (16)

[0096] From formula (13), we have:

[0097]

[0098] Substituting equations (12) and (17) into the contact stress distribution model and integrating along the region, we get:

[0099]

[0100] Solve this equation using the integral method of polar coordinate transformation, let:

[0101]

[0102] Equation:

[0103]

[0104] Further simplification yields:

[0105]

[0106] The undetermined coefficients C satisfy equation (15), which can be expanded using Taylor series:

[0107]

[0108] R n (C) represents the remainder term of the Taylor expansion. This invention uses a two-level Taylor series to obtain:

[0109]

[0110] Finally, the contact stress distribution model of the abrasive layer in the circular contact area under uniform load, including the aspect ratio coefficient, is obtained as follows:

[0111]

[0112] This allows us to obtain the contact stress at each contact point of the flexible polishing tool.

[0113] Step 3) For the attitude of the polishing head, the polishing tilt angle and polishing yaw angle need to be defined, which are the pitch angle β and the yaw angle λ. The pitch angle is the unit vector z. t The angle between the x-axis and the z-axis is the yaw angle z. t Projecting z onto the xoy plane t The angle between the z-axis and the x-axis. The local coordinate system is first rotated by an angle λ around the z-axis, then by an angle β around the y-axis. The resulting coordinate system is parallel to the grinding head coordinate system, i.e.:

[0114]

[0115] Then the axial unit vector z of the grinding and polishing head t =xsinβcosλ+ysinβsinλ+zcosβ, and simultaneously the angular velocity vector It can be represented as

[0116] Based on the axial unit vector of the polishing head and the angular velocity vector, a point P on the contact area between the polishing tool and the workpiece is set, the coordinates of which in the coordinate system o-xyz are (x P ,y P ,0), and the vector from the center of the polishing head to the point P is has wherein R is the radius of the polishing head, and the tangential velocity v t generated by the rotation of the polishing head is obtained. t The linear velocity of the polishing head is obtained through the tangential velocity v t , and the linear velocity distribution model of the contact area between the polishing head and the workpiece in the machining process is obtained, which is used for analyzing and calculating the material removal rate of a point in the polishing machining process.

[0117] Suppose a point P on the contact surface, the coordinates of which in the coordinate system o-xyz are (x P ,y P ,0), and the vector from the center of the polishing head to the point P is has wherein R is the radius of the polishing head. The tangential velocity v t generated by the rotation of the polishing head is:

[0118]

[0119] Since the rotational speed of the polishing head is much greater than the feed speed, the relative motion speed between the polishing head and the workpiece is simplified as the rotational speed of the polishing head, that is:

[0120]

[0121] The center position v1 of the flexible polishing head is 0, and the corresponding linear velocity increases continuously with the increase of the deflection attitude angle, and the edge linear velocity reaches the maximum. The removal profile is calculated as shown in Figure 4 , the edge removal amount of the polishing head is the largest, and the middle is the smallest. Different pitch angles β will change the linear velocity of each point in the contact area, and the longer the distance from the Z t axis, the greater the speed. The yaw angle λ will change the orientation of the speed distribution area under the same pitch angle β.

[0122] Step 4) In the process of the flexible polishing tool performing the machining task, the energy absorption performance as a key performance of the elastic material plays an extremely important potential effect.

[0123] When the elastic layer is under the action of uniaxial compression load, the stress-strain curve of the polishing head of the flexible polishing tool exhibits a relatively wide platform region, which means that the stress can be maintained in a stable state within a large strain range, thereby efficiently absorbing a large amount of energy by virtue of the shaping deformation,

[0124] With the increase of the relative density of the elastic body, the energy absorbed by the elastic layer in the compression process also increases in the same volume. The energy absorption capacity of the elastic body is related to the yield stress and the length of the yield section, and can extend the service life of the flexible polishing tool to a certain extent, maintain the stability in the polishing process, greatly stabilize the polishing force actually acting on the workpiece surface, and significantly reduce the noise generated in the polishing process and the vibration transmitted to the tool handle / spindle. When the elastic layer is compressed to a certain strain, the size of the absorbed energy is equivalent to the integral of the stress-strain function within the strain range:

[0125]

[0126] Wherein, W is the absorbed energy, ε is the strain, and σ is the stress corresponding to the strain ε.

[0127] With the increase of the relative density of the elastic body, the energy absorbed by the elastic layer in the compression process also increases in the same volume. The energy absorption capacity of the elastic body is related to the yield stress and the length of the yield section, and can extend the service life of the flexible polishing tool to a certain extent.

[0128] Step 5) According to the Preston equation, the stress distribution model and the linear velocity distribution model in the contact area can be used to obtain the material removal rate of each point in the contact area, and then the removal profile in the machining process can be obtained.

[0129] According to the Preston formula, the material removal function of the fixed-point polishing of the polishing head can be described as a linear equation as shown in the formula, and the material removal height model under different parameters can be obtained. The removal function profile radius is the length of the contact circle radius, and the peak removal rate is the maximum removal depth per unit time, and the expression is:

[0130] Δh(x,y)=K p p(x,y)v(x,y)T

[0131] In the formula, Δh(x,y) is the material removal amount of any point (x,y) on the contact surface; K p is the Preston constant, which is determined by factors other than the velocity and the pressure; p(x,y) and v(x,y) are the normal pressure and the relative linear velocity of the point on the polishing contact surface; and T is the dwell time of the polishing head at the polishing point.

[0132] The material removal profile thereof can be obtained from formula (17) and formula (20), and the material removal profile isFigure 4 It can be obtained that the removal height is a "W" type when the pitch angle is 0°, that is, the polishing head is not biased, and the polishing head is perpendicular to the contact area; and the removal height is an inverted "V" type when the pitch angle is greater than 0°, that is, the polishing head is processed with a bias angle. Through the combination of polishing heads with different bias angles, different sizes and different elastic moduli, high-efficiency and high-precision processing can be realized.

[0133] In the description of the present application, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential" and the like is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0134] It should be noted that the terms "first", "second", and the like in the description and claims of the present application and the above drawings are used to distinguish similar objects, and do not necessarily indicate or imply a specific order or sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0135] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connection", "fixing" and the like should be understood broadly, for example, it can be fixed connection, or detachable connection, or integrated; it can be mechanical connection, or electrical connection, or communication; it can be directly connected, or indirectly connected through intermediate medium, or the communication between two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances. When a component is referred to as "fixed to" another component, it can be directly on the other component or there can be a middle component. When a component is considered to be "connected" to another component, it can be directly connected to another component or there can be a middle component. When a component is considered to be "set on" another component, it can be directly set on another component or there can be a middle component.

[0136] In the present application, unless specifically stated and limited otherwise, the first feature is "on" or "under" the second feature can include that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, the first feature is "on", "above" and "over" the second feature includes that the first feature is directly above and obliquely above the second feature, or only means that the first feature is higher in horizontal height than the second feature. The first feature is "under", "below" and "underneath" the second feature includes that the first feature is directly above and obliquely above the second feature, or only means that the first feature is lower in horizontal height than the second feature.

[0137] It should be understood that the terms "comprise" and "contain" as used in the specification and the appended claims, indicate the presence of the described features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0138] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description of the application herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items.

[0139] The above description is only the preferred embodiment of the present application, and is not intended to limit the present application in any form; any person skilled in the art can easily implement the present application according to the drawings and the above description; however, any person skilled in the art can make some changes, modifications and equivalent changes to the above-mentioned technical content without departing from the scope of the technical solutions of the present application; at the same time, any equivalent changes, modifications and evolution of the above-mentioned embodiments according to the essential technology of the present application are still within the protection scope of the technical solutions of the present application.

Claims

1. A method for controlling the processing of a workpiece curved surface by a curved surface flexible polishing tool, characterized in that, The method comprises the following steps: A contact stress distribution model of a contact area between a polishing tool and a workpiece is established based on Hertz theory; Based on the posture of the polishing head, the polishing inclination angle and the polishing deflection angle of the polishing head are defined, and a linear velocity distribution model in the contact area between the polishing head and the workpiece in the machining process is established; Based on the Preston equation, the material removal rate of each point in the contact area is obtained through the contact stress distribution model and the linear velocity distribution model, and then the removal profile in the machining process can be obtained; The curved surface profile of the workpiece is machined based on the removal profile.

2. The method according to claim 1, wherein the method is characterized in that, The contact stress distribution model of the contact area between the polishing head and the workpiece is established based on Hertz theory, specifically: According to Hertz theory, the contact area between the polishing head of the polishing tool and the workpiece is approximated as a circle, and a coordinate system is established with the center of the circular contact area (x, y) as the origin, wherein the z-axis is perpendicular to the contact area, and the y-axis is the motion direction, to obtain the contact area radius r between the polishing head and the workpiece; A uniform load is applied to the center of the contact area of the curved surface grinding and polishing tool during the processing process, and the area of the uniform load is πr 2 The center of the uniform load is coincided with the center of the contact area of the curved surface grinding and polishing tool, and a normal force I is obtained. Based on the contact area radius r and the normal force I, the contact stress distribution model of the circular contact area is established.

3. The method according to claim 2, wherein the method is characterized in that, The contact area radius r between the polishing head and the workpiece is specifically: where I is the normal polishing force at the polishing contact point, R e is the contact equivalent radius of curvature, E * is the relative modulus of elasticity.

4. The method according to claim 2, wherein, The contact stress distribution model is specifically: In the formula, r is the contact area radius between the polishing head and the workpiece, I is the normal polishing force of the polishing contact point, and k is the width-height ratio coefficient of the contact area.

5. The method according to claim 1, wherein the method is characterized in that, The linear velocity distribution model in the contact area between the polishing head and the workpiece in the machining process is specifically: Based on the posture of the polishing head, the polishing inclination angle and the polishing deflection angle of the polishing head are defined, that is, the pitch angle β and the yaw angle λ, to obtain the axial unit vector and the angular velocity vector of the polishing head; Based on the axial unit vector of the polishing head and the angular velocity vector, a point P on the contact area between the polishing tool and the workpiece is set, the coordinates of which in the coordinate system o-xyz are (x P ,y P ,0), and the vector from the center of the polishing head to the point P is n, which has wherein R is the radius of the polishing head, and the tangential velocity v t generated by the rotation of the polishing head is obtained, and the linear velocity of the polishing head is obtained through the tangential velocity v t , that is, the linear velocity distribution model of the contact area between the polishing head and the workpiece in the machining process is obtained. The expression of the linear velocity distribution model is: In the formula, λ is the yaw angle, β is the pitch angle, ω is the angular velocity, v tx and v ty are the tangential velocities of the polishing head on the X-axis and Y-axis, respectively.

6. The method according to claim 1, wherein the method is characterized in that, Based on the Preston equation, the material removal rate of each point in the contact area is obtained through the contact stress distribution model and the linear velocity distribution model, specifically: Based on the Preston formula, the contact stress distribution model and the linear velocity distribution model are combined to describe the material removal function of the polishing head in the fixed-point polishing, and the material removal height model under different parameters is obtained, wherein the material removal function profile radius is the radius length of the contact area of the polishing tool on the workpiece surface, and the peak removal rate is the maximum removal depth per unit time, The specific expression of the material removal rate is: Δh(x,y) = K p p(x,y)v(x,y)T In the formula, Δh(x, y) is the material removal amount of the polishing tool at any point (x, y) on the contact surface of the workpiece; Kp is the Preston constant; p(x, y) and v(x, y) are the contact stress and the relative linear velocity of the polishing contact surface, respectively; T is the dwell time of the polishing tool at the polishing point on the workpiece surface.

7. The method according to claim 1, wherein the method is characterized in that, The removal profile in the machining process is specifically: When the pitch angle is 0°, that is, the polishing head has no deflection angle, the removal profile is W-shaped; When the pitch angle is greater than 0°, that is, the polishing head has a deflection angle, the removal profile is inverted V-shaped.

8. The method of claim 1, wherein: In the machining process, the energy absorption capacity of the elastic layer of the polishing tool under uniaxial compression load is evaluated by analyzing the stress-strain curve of the elastic layer under uniaxial compression, so as to improve the machining stability, specifically: The elastic layer of the polishing tool absorbs energy through the plastic deformation platform area under uniaxial compression, and the absorbed energy W satisfies: Wherein, W is the absorbed energy, epsilon is the deformation of the workpiece in the process of pressing, sigma is the stress corresponding to epsilon.

9. A curved surface flexible polishing tool, characterized in that, It comprises an abrasive layer and an elastic layer. The abrasive layer is rolled on the elastic layer to form a polishing head, and the polishing head is bonded to the arc-shaped connecting rod. The surface of the abrasive layer is processed by laser to have heat dissipation textures, which include envelope type and array type. The envelope type heat dissipation texture is designed by adopting continuous trajectories of helix, concentric circle or involute to match the curvature change of the hemispherical surface. The array type heat dissipation texture is designed by adopting the combination array of high-density triangular mesh, quadrilateral gradual change, polar hexagonal honeycomb structure or circular gradual change. The polishing head is a hemispherical structure.

10. The curved flexible polishing tool of claim 9, wherein, The flexible polishing tool is used in the grinding stage before polishing of the optical element, and based on the Preston formula as the curved surface fixed abrasive removal function, the surface profile control and surface roughness control of the hard and brittle material workpiece are realized.

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