A method for analyzing key structural parameters of lateral airbag polishing

Abstract

This invention discloses a method for analyzing key structural parameters in lateral airbag polishing. First, a finite element analysis (FEM) simulation is performed on the entire robotic arm and polishing head, comprehensively considering the effects of gravity, horizontal polishing reaction force, and gas pressure within the cylinder on the robotic arm's deformation. This yields the strain distribution of the robotic arm, determining the structural parameters of the adapter plate that best meet the deformation requirements. Then, a FEM analysis is performed on the polishing process of the workpiece surface. The strain distribution results are imported into path planning software and compared with the required removal function shape to select the airbag layer structural parameters that best meet the surface shape accuracy requirements for the corresponding removal surface. This method for analyzing key structural parameters in lateral airbag polishing aims to more closely approximate real-world processing conditions, providing a valuable reference for the structural design of the robotic arm and polishing head. It makes the model closer to actual processing conditions, giving the simulation results stronger practical guidance.

Description

Technical Field

[0001] This invention relates to the field of optical component processing technology, and in particular to a method for analyzing key structural parameters of lateral airbag polishing. Background Technology

[0002] Airbag polishing is a novel optical component processing method, particularly suitable for aspherical surface processing. It offers advantages such as high removal efficiency, good adhesion, easy surface shape control, uniform material removal, and high precision. Currently, airbag polishing primarily employs end-face polishing, where the polishing head contacts the mirror surface vertically downwards. However, in integrally machined optical systems with multiple reflective mirrors, where each reflective surface is typically distributed within the cavity's inner wall, direct end-face polishing can easily lead to interference problems. Therefore, a lateral airbag polishing method has emerged, where the polishing head is angled 90° and mounted on a robotic arm for horizontal polishing.

[0003] The study of removal function distribution and pressure distribution in the polishing head contact area directly determines polishing uniformity and surface accuracy, and is crucial for airbag polishing path planning and polishing mechanism research. Currently, the Preston equation serves as the fundamental theory describing the material removal mechanism; however, existing methods for studying removal functions, such as nonlinear least squares numerical fitting and orthogonal experimental methods, have certain limitations: they rely on a large amount of experimental data and have low computational efficiency; when solving complex polishing contact areas, accuracy and cost are difficult to balance; they cannot recreate the entire dynamic process of airbag polishing, making it difficult to study the continuous changes in stress and strain; and the multivariate coupling effects during polishing (such as airbag precession angle, rotational speed, and gas pressure) exhibit strong nonlinear characteristics, making traditional methods less applicable. These factors lead to excessively long process optimization cycles and insufficient economic efficiency in existing research methods, making finite element analysis an important research method for removing function distribution and contact area pressure distribution.

[0004] Finite element analysis (FEA), through discretized modeling and mathematical approximation, can efficiently simulate the dynamic mechanical behavior of the contact area during airbag polishing. Compared to traditional methods, finite element simulation can accurately analyze the pressure distribution and material removal characteristics under complex geometries, avoiding experimental trial-and-error costs. It can also intuitively reproduce the transient response of the polishing process (such as flexible airbag deformation and abrasive particle trajectory), providing a visual basis for process parameter configuration. Furthermore, combined with multiphysics coupling analysis, finite element technology can overcome the limitations of traditional simplified models, significantly improving the accuracy of removal function prediction under complex working conditions. However, existing finite element analysis methods are only applicable to end-face polishing analysis, where the gravity direction is the same as the polishing indentation direction, neglecting the influence of overall robotic arm structural changes on the polishing process. In actual lateral polishing processes, factors affecting the polishing effect, such as gravity, horizontal polishing force, and lateral deformation of the robotic arm, cannot be ignored. Summary of the Invention

[0005] In view of the above-mentioned defects or deficiencies in the existing technology, it is desirable to provide a method for analyzing key structural parameters of lateral airbag polishing. This method comprehensively considers the influence of gravity and horizontal polishing force, studies the overall structural change trend of the robotic arm, and analyzes the contact pressure distribution and removal function distribution of the polishing head on the machined surface. The aim is to more closely approximate the real processing conditions, provide an effective reference for the structural design of the robotic arm and polishing head, and overcome the defects of the existing airbag polishing simulation process.

[0006] This invention provides a method for analyzing key structural parameters of lateral airbag polishing. By sequentially performing finite element analysis on the overall robotic arm and polishing head, and the dynamic process of the polishing head contacting the workpiece surface, the accuracy of airbag polishing simulation is improved. The method specifically includes the following steps:

[0007] 1) Import the geometric models of the robotic arm and polishing head into the finite element analysis software, and set the material parameters and the contact type between the geometric structures;

[0008] 2) Perform fine mesh generation on the adapter plate, cylinder and polishing head of the robotic arm, and automatically generate mesh for the rest of the parts, and set constraints and loads;

[0009] 3) The solution scheme is set as total deformation, equivalent strain of all geometric structures, and equivalent stress;

[0010] 4) After the total deformation, equivalent strain and equivalent stress of all geometric structures are solved, stress and strain analysis is performed on the shell of the lateral polishing device and the adapter plate between the device and the robotic arm to evaluate whether the size and material are suitable for the polishing system.

[0011] 5) When there are requirements for the deformation of the robotic arm, repeatedly modify the material and thickness of the adapter plate, and repeat steps 1) to 3) until the structural parameters of the adapter plate that best meet the deformation requirements are determined.

[0012] 6) Import the geometric models of the airbag polishing head and the workpiece into the finite element analysis software, ensuring that the airbag part of the polishing head is exactly tangent to the surface being machined and adjust the precession angle; set the material parameters and the contact type between the geometric structures.

[0013] 7) Set the side of the polishing head base as a revolute joint and apply a rotational load to the revolute joint; simulate the inflation pressure inside the airbag in the form of nodal pressure; apply a displacement load to the workpiece and apply standard Earth gravity to all geometric objects; perform fine meshing on the workpiece surface and the airbag part of the polishing head, and automatically mesh the rest.

[0014] 8) The solution scheme is set as the total deformation and the stress and strain distribution on the machined surface;

[0015] 9) Screen and evaluate the best combination of polishing parameters, import the strain distribution results on the polished surface obtained in steps 8) to 9) into the path planning software, and compare them with the required removal function shape;

[0016] 10) When there are requirements for the surface shape accuracy of the removed surface, repeatedly modify the structural parameters of the airbag layer and repeat steps 6) to 9) until the airbag layer structural parameters that best meet the surface shape accuracy requirements of the corresponding removed surface are selected.

[0017] Furthermore, the material parameters set in step 1) all include the material's Poisson's ratio, Young's modulus, density, and yield strength.

[0018] Furthermore, the material parameters set in step 6) all include the material's Poisson's ratio, Young's modulus, density, yield strength, and tensile strength.

[0019] Furthermore, in step 1), the contact type between the geometric structures is specifically set as follows: the contact pair between the cylinder inner wall and the piston is a frictionless contact, and the contact type of the remaining contact pairs is set as a bonded contact.

[0020] Furthermore, the constraint conditions and load settings in step 2) include standard Earth gravity, cylinder pressure, and horizontal polishing reaction force. Specifically, the constraint condition is set to "fixed support" and applied to the upper surface of the robotic arm adapter plate. Four loads are added: standard Earth gravity G, cylinder pressures F1 and F2, and polishing reaction force F3. The standard Earth gravity G is applied to all geometric structures. Cylinder pressures F1 and F2 are applied to the inner end face of the cylinder and the piston face, respectively. The polishing reaction force F3 is applied to the polishing head. According to the force relationship, F1 and F2 are a pair of reaction forces with equal magnitude and both directions are along the normal direction of the force surface and outward from the cylinder. F3 is horizontal and faces the polishing head surface.

[0021] Furthermore, the actual pressure inside the cylinder can be measured or simulated using a coupled fluid dynamics module to obtain the specific values ​​of F1 and F2.

[0022] Furthermore, in step 6), the contact type between the geometric structures is specifically set as follows: the contact type between the outermost layer of the polishing head airbag and the surface being processed is frictional contact, and the friction coefficient is determined according to the material of the surface being processed and the outermost layer of the airbag. All other contact pairs are set as bonded contact.

[0023] Further, the specific operation of step 7) is as follows: simulate the inflation pressure F inside the airbag in the form of nodal pressure. First, perform fine meshing on the inner wall of the airbag. Then, create a named selection set using the meshed cells and set it as the object to which the nodal pressure is applied. The magnitude of the nodal pressure is set to the inflation pressure. Set the side of the polishing head base as a revolute joint, with the central axis of the polishing head as the axis of rotation. Release the rotational degree of freedom and apply a rotational load to the revolute joint. The rotational speed is set to the polishing head speed v. Select the five faces of the workpiece other than the surface to be processed as objects and apply a displacement load. The direction is along the normal direction of the surface to be processed and towards the polishing head. The displacement magnitude is set to the downward pressure d of the polishing head. Apply standard Earth gravity to all geometric objects. The direction of standard Earth gravity is perpendicular to the normal direction of the surface to be processed.

[0024] Compared with the prior art, the beneficial effects of the present invention are:

[0025] The method for analyzing key structural parameters of lateral airbag polishing in this invention first performs finite element simulation on the entire robotic arm and polishing head, comprehensively considering the influence of gravity, horizontal polishing reaction force, and gas pressure inside the cylinder on the lateral deformation of the overall robotic arm structure, to obtain the strain distribution of the robotic arm and determine the structural parameters of the adapter plate that best meet the deformation requirements. On this basis, the process of the polishing head contacting the workpiece surface is further simulated locally, and the strain distribution results are imported into the path planning software. Compared with the required removal function shape, the airbag layer structural parameters that best meet the surface shape accuracy requirements of the corresponding removal surface are selected. The effect of gravity on the workpiece and polishing head is considered, which makes the model closer to the real processing conditions and makes the simulation results more instructive for practice.

[0026] It should be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of the present invention, nor is it intended to restrict the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0027] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0028] Figure 1 A simulation model diagram of the overall force distribution of the robotic arm and polishing head;

[0029] Figure 2 A simulation model of the forces acting on the surface being polished by the airbag polishing head;

[0030] Figure 3 A flowchart of a finite element analysis method for a lateral airbag polishing process provided in an embodiment of the present invention;

[0031] Figure 4 This is a strain distribution diagram on the machined surface;

[0032] Figure 5 This is a stress distribution diagram on the machined surface;

[0033] Figure 6 The actual removal function shape diagram obtained after importing the strain distribution results on the polished surface into the path planning software;

[0034] Figure 7 The shape diagram for the required removal function. Detailed Implementation

[0035] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0036] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] Traditional finite element simulations of airbag polishing often focus on the analysis of end-face polishing while neglecting side-face polishing. Two main problems with this method are: ignoring the impact of overall structural changes on simulation accuracy, such as… Figure 1 Due to the unique nature of side polishing, the horizontal polishing reaction force combined with the robot arm's own weight can cause a certain lateral deformation tendency in the robot arm. This can lead to the polishing head potentially failing to contact the workpiece surface at the set precession angle and pressure, resulting in errors. Ignoring the influence of gravity on the polishing process, such as... Figure 2 Due to the special nature of lateral polishing, the polishing head needs to be rotated 90° to make lateral contact with the surface being processed. The direction of gravity changes significantly relative to the direction of the polishing force, making the traditional simulation method of the polishing head directly contacting the surface being processed vertically no longer applicable.

[0038] This method aims to more closely approximate real-world processing conditions by avoiding the two aforementioned scenarios. Specifically, firstly, a finite element simulation is performed on the robotic arm and polishing head as a whole. The effects of gravity, horizontal polishing reaction force, and gas pressure within the cylinder on the deformation of the robotic arm are comprehensively considered to obtain the strain distribution of the robotic arm and determine the structural parameters of the adapter plate that best meet the deformation requirements. Then, a finite element analysis is performed on the polishing process of the polishing head on the surface being processed. The strain distribution results are imported into the path planning software and compared with the required removal function shape to select the airbag layer structural parameters that best meet the surface shape accuracy requirements for the corresponding removal surface.

[0039] Please refer to Figures 1-7The present invention provides a method for analyzing key structural parameters of lateral airbag polishing. By performing finite element analysis on the overall robotic arm and polishing head, and the dynamic process of the polishing head contacting the workpiece surface, the accuracy of airbag polishing simulation is improved. The method includes the following steps:

[0040] Steps 1) to 5) below are for finite element analysis of the robotic arm and polishing head as a whole;

[0041] 1) Import the geometric models of the robotic arm and polishing head into the finite element analysis software, and set the material parameters and the contact type between the geometric structures;

[0042] The material parameters set include Poisson's ratio, Young's modulus, density, and yield strength.

[0043] The contact type between the geometric structures is specifically set as follows: the contact pair between the cylinder inner wall and the piston is frictionless contact, and the contact type of the other contact pairs is set as bonded contact.

[0044] 2) Perform fine mesh generation on the adapter plate, cylinder and polishing head of the robotic arm, and automatically generate mesh for the rest of the parts, and set constraints and loads;

[0045] The constraint conditions and load settings include standard Earth gravity, cylinder pressure, and horizontal polishing reaction force. Specifically, the constraint condition is set as "fixed support" and applied to the upper surface of the robotic arm adapter plate. Four loads are added: standard Earth gravity G, cylinder pressures F1 and F2, and polishing reaction force F3. The standard Earth gravity G is applied to all geometric structures. Cylinder pressures F1 and F2 are applied to the inner end face of the cylinder and the piston face, respectively. The polishing reaction force F3 is applied to the polishing head. According to the force relationship, F1 and F2 are a pair of reaction forces, which should be equal in magnitude and both in the direction of the normal to the force surface, towards the outside of the cylinder. F3 is horizontal and faces the polishing head surface.

[0046] Preferably, the actual pressure inside the cylinder can be measured or a fluid dynamics module can be coupled for simulation to obtain the specific values ​​of F1 and F2.

[0047] 3) The solution scheme is set as total deformation, equivalent strain of all geometric structures, and equivalent stress;

[0048] 4) After the total deformation, equivalent strain and equivalent stress of all geometric structures are solved, stress and strain analysis is performed on the shell of the lateral polishing device and the adapter plate between the device and the robotic arm to evaluate whether the size and material are suitable for the polishing system.

[0049] 5) When there are requirements for the deformation of the robotic arm, repeatedly modify the material and thickness of the adapter plate and repeat steps 1) to 3) until the structural parameters of the adapter plate that best meet the deformation requirements are determined. That is, the adapter plate parameters that best meet the deformation requirements are a plate thickness of 6mm and a material of aluminum alloy.

[0050] Steps 6) to 10) below are finite element analysis of the dynamic process of the airbag polishing head contacting the surface being processed;

[0051] 6) Import the geometric models of the airbag polishing head and the workpiece into the finite element analysis software, ensuring that the airbag part of the polishing head is exactly tangent to the surface being machined, and adjust the precession angle θ, which is the angle between the central axis of the polishing head and the normal to the surface being machined; set the material parameters and the contact type between the geometric structures.

[0052] The material parameters set include Poisson's ratio, Young's modulus, density, yield strength, and tensile strength.

[0053] The contact type between the geometric structures is specifically set as follows: the contact type between the outermost layer of the polishing head airbag and the surface being processed is frictional contact, and the coefficient of friction is determined according to the material of the surface being processed and the outermost layer of the airbag. All other contact pairs are set as bonded contact.

[0054] 7) Set the side of the polishing head base as a revolute joint and apply a rotational load to the revolute joint; simulate the inflation pressure inside the airbag in the form of nodal pressure; apply a displacement load to the workpiece and apply standard Earth gravity to all geometric objects; perform fine meshing on the workpiece surface and the airbag part of the polishing head, and automatically mesh the rest.

[0055] The specific operation involves simulating the inflation pressure F inside the airbag using nodal pressure. First, the inner wall of the airbag is finely meshed. Then, a named selection set is created using the meshed cells and set as the object to which the nodal pressure is applied. The magnitude of the nodal pressure is set to the inflation pressure. The side of the polishing head base is set as a revolute joint, with the central axis of the polishing head as the axis of rotation. The rotational degree of freedom is released, and a rotational load is applied to this revolute joint. The rotational speed is set to the polishing head speed v. The five faces of the workpiece other than the surface to be processed are selected as objects, and a displacement load is applied. The direction is along the normal direction of the surface to be processed and towards the polishing head. The displacement magnitude is set to the downward pressure d of the polishing head. Standard Earth gravity is applied to all geometric objects. The direction of standard Earth gravity is perpendicular to the normal direction of the surface to be processed.

[0056] Preferably, since each layer of the airbag structure is relatively thin, the size of the mesh should be selected to avoid the occurrence of a single-layer mesh structure. At the same time, in order to improve the computing speed, the mesh division accuracy of the outer layer of the airbag structure can be slightly lower than that of the inner layer.

[0057] 8) The solution scheme is set as the total deformation and the stress and strain distribution on the machined surface;

[0058] For specific reference, please see the image below. Figure 4 This is a strain distribution diagram on the machined surface;

[0059] Figure 5 This is a stress distribution diagram on the machined surface;

[0060] 9) Screen and evaluate the best combination of polishing parameters, import the strain distribution results on the polished surface obtained in steps 8) to 9) into the path planning software, and compare them with the required removal function shape;

[0061] For specific reference, please see the image below. Figure 6 The actual removal function shape diagram obtained after importing the strain distribution results on the polished surface into the path planning software;

[0062] Figure 7 The required shape diagram for the removal function;

[0063] 10) When there are requirements for the surface shape accuracy of the removal surface, repeatedly modify the structural parameters of the airbag layer and repeat steps 6) to 9) until the airbag layer structural parameters that best meet the surface shape accuracy requirements for the corresponding removal surface are selected as follows: inner rubber layer thickness 0.5mm, 304 steel layer thickness 0.2mm, outer rubber thickness 1mm, and polyurethane layer thickness 0.5mm.

[0064] The purpose of this invention is to overcome the shortcomings of existing airbag polishing simulation processes and provide a finite element analysis method more suitable for lateral airbag polishing. It comprehensively considers the influence of gravity and horizontal polishing force, studies the overall structural change trend of the robotic arm, and analyzes the contact pressure distribution and removal function distribution of the polishing head on the machined surface. The aim is to more closely approximate the real processing conditions and provide an effective reference for the structural design of the robotic arm and polishing head.

[0065] In the description of this specification, the terms "connection," "installation," and "fixing," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0066] In the description of this specification, the terms "one embodiment," "some embodiments," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0067] The above are merely preferred embodiments of this application and are not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for analyzing key structural parameters of lateral airbag polishing, characterized in that, The accuracy of airbag polishing simulation is improved by sequentially performing finite element analysis on the overall robotic arm and polishing head, as well as the dynamic process of the polishing head contacting the workpiece surface. The specific steps include the following: 1) Import the geometric models of the robotic arm and polishing head into the finite element analysis software, and set the material parameters and the contact type between the geometric structures; 2) Perform fine mesh generation on the adapter plate, cylinder and polishing head of the robotic arm, and automatically generate mesh for the rest of the parts, and set constraints and loads; 3) The solution scheme is set as total deformation, equivalent strain of all geometric structures, and equivalent stress; 4) After the total deformation, equivalent strain and equivalent stress of all geometric structures are solved, stress and strain analysis is performed on the shell of the lateral polishing device and the adapter plate between the device and the robotic arm to evaluate whether the size and material are suitable for the polishing system. 5) When there are requirements for the deformation of the robotic arm, repeatedly modify the material and thickness of the adapter plate, and repeat steps 1) to 3) until the structural parameters of the adapter plate that best meet the deformation requirements are determined. 6) Import the geometric models of the airbag polishing head and the workpiece into the finite element analysis software, ensuring that the airbag part of the polishing head is exactly tangent to the surface being machined and adjust the precession angle; set the material parameters and the contact type between the geometric structures. 7) Set the side of the polishing head base as a revolute joint and apply a rotational load to the revolute joint; simulate the inflation pressure inside the airbag in the form of nodal pressure; apply a displacement load to the workpiece and apply standard Earth gravity to all geometric objects; perform fine meshing on the workpiece surface and the airbag part of the polishing head, and automatically mesh the rest. 8) The solution scheme is set as the total deformation and the stress and strain distribution on the machined surface; 9) Screen and evaluate the best combination of polishing parameters, import the strain distribution results on the polished surface obtained in steps 8) to 9) into the path planning software, and compare them with the required removal function shape; 10) When there are requirements for the surface shape accuracy of the removed surface, repeatedly modify the structural parameters of the airbag layer and repeat steps 6) to 9) until the airbag layer structural parameters that best meet the surface shape accuracy requirements of the corresponding removed surface are selected.

2. The method for analyzing key structural parameters of lateral airbag polishing according to claim 1, characterized in that, The material parameters set in step 1) include Poisson's ratio, Young's modulus, density, and yield strength.

3. The method for analyzing key structural parameters of lateral airbag polishing according to claim 1, characterized in that, The material parameters set in step 6) include Poisson's ratio, Young's modulus, density, yield strength, and tensile strength.

4. The method for analyzing key structural parameters of lateral airbag polishing according to claim 1, characterized in that, In step 1), the contact type between the geometric structures is specifically set as follows: the contact pair between the cylinder inner wall and the piston is frictionless contact, and the contact type of the other contact pairs is set as bonded contact.

5. The method for analyzing key structural parameters of lateral airbag polishing according to claim 1, characterized in that, The constraint conditions and load settings in step 2) include standard Earth gravity, cylinder pressure, and horizontal polishing reaction force. Specifically, the constraint condition is set to "fixed support" and applied to the upper surface of the robotic arm adapter plate. Four loads are added: standard Earth gravity G, cylinder pressures F1 and F2, and polishing reaction force F3. The standard Earth gravity G is applied to all geometric structures. Cylinder pressures F1 and F2 are applied to the inner end face of the cylinder and the piston face, respectively. The polishing reaction force F3 is applied to the polishing head. According to the force relationship, F1 and F2 are a pair of reaction forces with equal magnitude and both directions are along the normal direction of the force surface and outward from the cylinder. F3 is horizontal and faces the polishing head surface.

6. The method for analyzing key structural parameters of lateral airbag polishing according to claim 5, characterized in that, The actual pressure inside the cylinder can be measured or simulated using a coupled fluid dynamics module to obtain the specific values ​​of F1 and F2.

7. The method for analyzing key structural parameters of lateral airbag polishing according to claim 1, characterized in that, In step 6), the contact type between the geometric structures is specifically set as follows: the contact type between the outermost layer of the polishing head airbag and the surface to be processed is frictional contact, and the friction coefficient is determined according to the material of the surface to be processed and the outermost layer of the airbag. All other contact pairs are set as bonded contact.

8. The method for analyzing key structural parameters of lateral airbag polishing according to claim 1, characterized in that, The specific operation of step 7) is as follows: simulate the inflation pressure F inside the airbag in the form of nodal pressure. First, perform fine meshing on the inner wall of the airbag. Then, create a named selection set using the meshed cells and set it as the object to which the nodal pressure is applied. The magnitude of the nodal pressure is set to the inflation pressure. Set the side of the polishing head base as a revolute joint, with the central axis of the polishing head as the axis of rotation. Release the rotational degree of freedom and apply a rotational load to the revolute joint. The magnitude of the rotational speed is set to the polishing head speed v. Select the five faces of the workpiece other than the surface to be processed as objects and apply a displacement load. The direction is along the normal direction of the surface to be processed and towards the polishing head. The magnitude of the displacement is set to the downward pressure d of the polishing head. Apply standard Earth gravity to all geometric objects. The direction of standard Earth gravity is perpendicular to the normal direction of the surface to be processed.

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