Robot grinding contour error compensation method, system and grinding robot

By calculating the actual contour depth error and replanning the contact force, the problem of contour error compensation in robotic grinding was solved using the Preston equation and Hertz contact theory, achieving precise contour error compensation and improved machining quality.

CN116475853BActive Publication Date: 2025-12-23HUAZHONG UNIV OF SCI & TECH +1
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Patent Information

Application Number
CN202310470953.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-04-27
Publication Date
2025-12-23
Estimated Expiration
2043-04-27

AI Technical Summary

Technical Problem

Traditional methods struggle to compensate for contour errors during robotic grinding by correcting the tool position, especially under flexible contact conditions, where existing technologies cannot effectively control contour errors.

Method used

By calculating the actual contour depth error and replanning the contact force, a contact force model is established using the Preston equation and Hertz contact theory. The compensation contact force is calculated to adjust the tool contact force, thereby achieving contour error compensation.

Benefits of technology

Without altering the robot's motion trajectory, it accurately compensates for grinding contour errors, improving machining quality and precision while simplifying the implementation process.

✦ Generated by Eureka AI based on patent content.

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Abstract

This invention discloses a method, system, and grinding robot for compensating contour errors in robotic grinding, belonging to the field of robotic grinding technology. The method includes: controlling the tool to grind according to a plan to obtain the actual contour of the workpiece after grinding; acquiring the discrete point set of the actual contour; and determining the current tool position P. j The desired profile position N achieved by grinding j Find the line P from the set of discrete points. j N j The nearest point D j Calculate line segment N j D j On line P j N j The projected length on the tool position P is used as the tool position point. j The corresponding contour depth error is calculated; based on each contour depth error, the compensation contact force at the corresponding tool position is calculated, and the sum of the current contact force and the compensation contact force is used as the planned contact force for the next workpiece grinding at the corresponding tool position. The robot grinding contour error compensation method provided by this invention focuses on contact force compensation, and can achieve grinding contour error compensation by replanning the contact force without changing the robot's motion trajectory.
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Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of robot grinding processing, and more particularly to a robot grinding profile error compensation method, system and grinding robot. BACKGROUND

[0002] Traditional profile error compensation is generally applied to rigid milling processing of machine tools, and profile error compensation can be achieved by directly correcting the tool position. However, when a robot holding force control grinding and polishing tool is used for grinding, due to the flexible contact between the tool and the workpiece, that is, the desired contact force is applied to the grinding head by the force control mechanism so that it can be tightly attached to the workpiece to be ground and polished, the material removal amount has no direct correspondence with the trajectory, and profile error compensation cannot be achieved by correcting the tool position similar to milling processing of machine tools.

[0003] Currently, when a robot is used for grinding, in order to improve the accuracy of profile grinding, the material removal model accuracy is generally improved, for example, a more accurate material removal model is established by introducing a multiple linear regression method to analyze the material removal depth model parameters; the material removal of the polishing process is optimized by considering the influence of sliding speed on the material removal profile. However, by the above-mentioned way, it is still difficult to consider the factors causing profile error in actual processing, including the change of feed speed caused by the motion characteristics of the robot, the actual fit of the grinding head and the workpiece, the force control accuracy and other factors, so the control ability of profile error is limited. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a robot grinding profile error compensation method, system and grinding robot, which aims to reduce the profile error caused by improper contact force planning.

[0005] To achieve the above-mentioned purpose, according to one aspect of the present application, a robot grinding profile error compensation method is provided, comprising:

[0006] Step S1: controlling the tool to move along the initial profile of the workpiece according to the planned tool position set and to apply the planned contact force for grinding at each tool position, to obtain the actual profile of the workpiece after grinding;

[0007] Step S2: obtaining a discrete point set of the actual profile, and calculating the profile depth error of each tool position after applying the contact force for grinding based on the discrete point set;

[0008] Step S3: calculating the compensation contact force at the corresponding tool position based on each profile depth error, and taking the sum of the current contact force and the compensation contact force as the planned contact force of the next workpiece grinding at the corresponding tool position;

[0009] In step S2, the profile depth error of any tool position P is calculated as follows:j The corresponding contour depth error includes:

[0010] Determine the desired profile position N to be achieved by grinding at the current tool position point Pj. j Find the point set of discrete points of the actual contour that corresponds to the line P. j N j The nearest point D j Calculate line segment N j D j On line P j N j The projected length on the tool position P is used as the tool position point. j The corresponding contour depth error value |Δs j |

[0011] In one embodiment,

[0012] In step S2, the contour depth error is calculated, including the calculation of the contour depth error vector Δs. j ,

[0013]

[0014] Where, |N j D j | represents line segment N j D j Length, F j Indicates the knife point P j The corresponding contact force vector, θ is the vector N j D j With vector F j The included angle;

[0015] In step S3, the compensating contact force is calculated, including the calculation of the vector ΔF of the compensating contact force. j ,

[0016]

[0017] Where f() is the model function of contact force with respect to grinding depth;

[0018] The vector F of the contact force planned at the corresponding tool position point for the next workpiece grinding. j * The calculation formula is:

[0019] F j * =F j +ΔF j .

[0020] In one embodiment, when grinding the first workpiece, in step S1, each tool position point P is planned.j a contact force, comprising: calculating a tool position P j grinding to a desired profile position N j an expected grinding depth of the tool position P j a planned contact force;

[0021] The model function f() of the contact force with respect to the grinding depth is a relational model based on the preston equation and the Hertz contact theory.

[0022] In one embodiment, the model function f() is a relational model of the contact force |F| with respect to the grinding depth s, based on the preston equation and the Hertz contact theory, considering the contact area between the tool grinding head and the workpiece as an ellipse,

[0023]

[0024] where v q is the tangential velocity of the tool, v f is the feed speed of the tool, E' and R' are the equivalent elastic modulus and equivalent curvature radius of grinding respectively, e is the ratio of the major axis to the minor axis of the elliptical contact area, ε(e) is the second kind of elliptic integral, K P is a proportionality constant calibrated by experiments.

[0025] In one embodiment, in step S2, the discrete point set of the actual profile is obtained by:

[0026] scanning the actual profile of the workpiece after grinding using a camera, removing invalid data according to the machining path, and then performing fairing interpolation to obtain the discrete point set of the actual profile.

[0027] In one embodiment, in step S1, the tool position set is a discrete segmentation point determined by dividing the initial profile of the workpiece according to equal arc length.

[0028] According to another aspect of the present application, a robot grinding profile error compensation system is provided, comprising:

[0029] a tool control module for controlling the tool to move along the initial profile of the workpiece according to the planned tool position set and to apply a planned contact force at each tool position for grinding to obtain the actual profile of the workpiece after grinding;

[0030] a profile depth error calculation module for obtaining a discrete point set of the actual profile and calculating a profile depth error caused by a contact force deviation at each tool position based on the discrete point set;

[0031] The contact force update module is used to calculate the compensation contact force at the corresponding tool position point based on each contour depth error, and use the sum of the current contact force and the compensation contact force as the planned contact force for the next workpiece grinding at the corresponding tool position point.

[0032] Among them, the contour depth error calculation module calculates the arbitrary tool position P. j The execution process for the corresponding contour depth error includes:

[0033] Determine the current tool position P j The desired profile position N achieved by grinding j Find the point set of discrete points of the actual contour that corresponds to the line P. j N j The nearest point D j Calculate line segment N j D j On line P j N j The projected length on the tool position P is used as the tool position point. j The corresponding contour depth error value |Δs j |

[0034] In one embodiment,

[0035] The contour depth error calculation module includes a first vector calculation unit, used to calculate the vector Δs of the contour depth error. j The calculation formula is:

[0036]

[0037] Where, |N j D j | represents line segment N j D j Length, F j Indicates the knife point P j The corresponding contact force vector, θ is the vector N j D j With vector F j The included angle;

[0038] The contact force update module includes:

[0039] The second vector calculation unit is used to calculate the vector ΔF of the compensating contact force. j The calculation formula is:

[0040]

[0041] Where f() is the model function of contact force with respect to grinding depth;

[0042] a third vector calculation unit configured to calculate a vector F of the contact force planned for the next workpiece grinding at the corresponding tool position point j * , and the calculation formula is:

[0043] F j * = F j + ΔF j .

[0044] In one of the embodiments, the system further comprises:

[0045] an initial contact force planning module configured to plan the contact force |F| of the first workpiece at each tool position point according to a model function f(), which is a model of the contact force |F| with respect to the grinding depth s,

[0046]

[0047] wherein s is the expected grinding depth of the current tool position point to the desired profile position, v q is the tangential velocity of the tool, v f is the feed speed of the tool, E' and R' are the equivalent elastic modulus and equivalent curvature radius of grinding respectively, e is the ratio of the long axis to the short axis of the elliptical contact area, ε(e) is the second kind of elliptical integral, K P is a proportionality constant calibrated through experiments.

[0048] According to another aspect of the present application, a grinding robot is provided, which comprises a tool and the robot grinding profile error compensation system described above.

[0049] Overall, the above technical solutions conceived by the present application can achieve the following beneficial effects compared with the prior art:

[0050] Since the tool and the workpiece belong to flexible contact when grinding by using the robot, it is difficult to realize the compensation of the profile error by modifying the tool position. The robot grinding profile error compensation method provided by the application focuses on the compensation of the contact force, and the grinding profile error compensation can be realized by re-planning the contact force without changing the robot motion trajectory. Through the compensation of the contact force, the workpiece to be processed has better pertinence, the profile error compensation of the workpiece surface to be processed can be accurately realized, the grinding profile error caused by factors such as material removal modeling, contact force control and robot motion precision is reduced, and the quality of the robot grinding processing is improved. Moreover, the method is simple and easy to implement. Meanwhile, the application calculates the compensation contact force based on the profile depth error, wherein the profile depth error is calculated in a specific way, the calculation accuracy of the profile depth error can be improved, the accuracy of the calculated compensation contact force is higher, the adjustment of the tool contact force is more accurate, and the quality of the robot grinding processing is further improved.

[0051] Preferably, the application adopts vector calculation for the profile depth error, the compensation contact force and the re-planned contact force, the compensation direction of the force can be directly reflected, and the calculation is simple.

[0052] Preferably, the relationship model of the contact force |F| derived by the application about the grinding depth s can more accurately calculate the corresponding contact force to be applied according to the grinding depth, so as to realize accurate compensation. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 It is a step flow chart of the robot grinding profile error compensation method in an embodiment;

[0054] Figure 2 It is a comparison diagram of the initial profile, the expected profile and the actual profile after grinding of the workpiece in an embodiment;

[0055] Figure 3 It is a schematic diagram of calculating the profile depth error in an embodiment;

[0056] Figure 4 It is a comparison result of the current contact force and the updated contact force in an embodiment. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical scheme and advantages of the application clearer, the application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application, and are not used to limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0058] AsFigure 1 The diagram shows the steps of a robot grinding contour error compensation method, which mainly includes the following steps:

[0059] Step S1: Control the tool to move along the initial contour of the workpiece according to the planned tool point set and apply the planned contact force at each tool point to perform grinding, so as to obtain the actual contour of the workpiece after grinding.

[0060] Before grinding, two types of information need to be planned: the set of tool positions for grinding and the contact force applied at each tool position. The grinding head moves along the initial contour of the workpiece according to the planned set of tool positions, pauses briefly at each tool position and applies the corresponding contact force to perform grinding, and then moves from the current tool position to the next tool position to continue grinding in the same way until the entire contour is ground.

[0061] Specifically, when planning the tool point set, the initial curved surface profile of the workpiece can be extracted based on the workpiece's 3D CAD model. This profile is then discretized into a set of points according to equal arc lengths, which serves as the planned tool point set. In other embodiments, the tool point set can also be determined in other ways, as long as the tool points fall on the profile of the curved surface to be machined. It can be understood that the tool point is the contact point between the grinding tool and the profile of the curved surface to be machined. After the initial tool point set is planned, the same tool point set is used for each grinding operation; that is, the tool point set remains unchanged for subsequent grinding operations on the workpiece, and only the contact force applied at each tool point is updated.

[0062] Specifically, when planning the contact force of the first workpiece at each tool point, it can be based on a material removal model. This material removal model actually expresses the relationship between contact force and grinding depth; different grinding depths may correspond to different contact forces. Therefore, it is necessary to first determine the grinding depth of each tool point. After obtaining the initial contour of the workpiece and determining the desired contour that the workpiece needs to be ground, the contact force P at each tool point on the initial contour can be obtained. j Reaching the desired contour position N j The expected grinding depth s to be ground j At the knife point P j After applying a contact force, the contour position can be changed from position P. j Gradually advance inward to the contour position N j The direction in which the contact force is applied is actually from position P. j Proceed to position N j The direction.

[0063] Specifically, in the conventional technology, the material removal model has been relatively mature, which is basically based on the preston equation and the Hertz contact theory for derivation. In the embodiment, the contact area of the grinding head and the workpiece can be regarded as an ellipse, and the derived material removal model is as follows:

[0064]

[0065] where s is the grinding depth, |F| is the contact force required to achieve the grinding depth, v q is the tangential velocity of the tool, v f is the feed speed of the tool, E' and R' are the equivalent elastic modulus and equivalent curvature radius of grinding respectively, e is the ratio of the major axis to the minor axis of the elliptical contact area, ε(e) is the second type of elliptic integral, K P is a proportional constant that needs to be calibrated, which represents the proportional constant determined by other factors in addition to the relative speed and pressure.

[0066] By carrying out a series of grinding and polishing experiments to obtain experimental data of grinding and polishing material removal, the proportional constant K P is calibrated, and thus the material removal depth model of the workpiece material is obtained. When the material removal depth is determined, according to the material removal depth model, the contact force required to be applied when the grinding depth is s can be reversely calculated:

[0067]

[0068] Through the above process, the tool position set {P1, P2, P3,...} and the contact force set {|F1|, |F2|, |F3|,...} required to be applied at each tool position can be planned.

[0069] In an embodiment, the feed direction U of the tool during grinding, the tool axis vector direction V, and the contact force application direction W are set as follows:

[0070]

[0071] where n=(n x , n v , n z ) is the corresponding local surface normal at the contact point, and s is the tangent direction at the contact point.

[0072] After all the parameters are planned, the tool can be controlled to grind the workpiece, and the actual profile of the workpiece after grinding is obtained.

[0073] Step S2: Obtain a discrete point set of the actual profile, and calculate the profile depth error of each tool position after applying the contact force for grinding and polishing based on the discrete point set.

[0074] Among them, the arbitrary tool position P is calculated. j The corresponding contour depth error process includes:

[0075] Determine the current tool position P j The desired profile position N achieved by grinding j Find the point set of discrete points of the actual contour that corresponds to the line P. j N j The nearest point D j Calculate line segment N j D j On line P j N j The projected length on the tool position P is used as the tool position point. j The corresponding contour depth error value |Δs j |

[0076] Figure 2 The image shows a comparison of the initial profile, desired profile, and actual profile after grinding of the workpiece.

[0077] In one embodiment, a blue light camera can be used to scan the actual contour of the ground workpiece. Invalid data is removed based on the machining path, and after obtaining discrete points of the curved contour, smooth interpolation is performed to obtain the actual contour of the machined workpiece. In this case, the actual contour obtained by the digital camera is not a continuous curve but a set of discrete points. Compensation information for each tool position point needs to be calculated based on the actual contour.

[0078] refer to Figure 3 As shown, with an arbitrary tool point P j For example, in the contact force F j Under the influence of the grinding head, it is expected that the self-cutting point P of the grinding head will be desired. j Grind along the direction of the contact force until the desired profile position N is reached. j However, due to the uncontrollable nature of many factors in robotic flexible grinding, the actual grinding completed is at the grinding head's self-cutting point P. j Grind along the direction of the contact force until the actual contour position M is reached. j The tool position point is the contour error, and the magnitude of the error is the desired contour position N. j To the actual contour position M j The distance. However, since the obtained actual contour is a discrete set of points, this set of points may not have a corresponding actual contour position M. j In this invention, the discrete points in the discrete point set of the actual contour are calculated to be perpendicular to the straight line P. j N j Find the distance between them, and locate the line P. j N j The nearest point D j Calculate line segment N j Dj On line P j N j The projected length N on j D j 'As the knife point P j The corresponding contour depth error value |Δs j |,|Δs j |=|N j D j '|≈|N j N j |

[0079] Step S3: Calculate the compensation contact force at the corresponding tool position point based on each contour depth error, and use the sum of the current contact force and the compensation contact force as the planned contact force for the next workpiece grinding at the corresponding tool position point.

[0080] The contour depth error |Δs is obtained at each tool position point. j |After that, the depth error|Δs j By substituting the values ​​into the material removal model, the corresponding compensating contact force can be obtained. The sum of the contact force applied during the current grinding and the corresponding calculated compensating contact force is used as the contact force for the next workpiece at the same tool position. When grinding the next workpiece, according to the initially planned tool position set, the updated contact force is applied at each tool position for grinding. After grinding, the compensating contact force is calculated again to update the contact force for the next workpiece, and so on, until all workpieces are ground.

[0081] Understandably, the contour depth error |Δs| at each tool position point is obtained. j If too much grinding is done, the resulting compensating contact force should be negative, meaning the current contact force should be reduced. If too little grinding is done, the resulting compensating contact force should be positive, meaning the current contact force should be increased.

[0082] In one embodiment, in step S2, the vector of the compensating contact force can be directly calculated, and the direction of the force compensation can also be directly determined. Specifically, the vector Δs of the contour depth error... j The calculation formula is:

[0083]

[0084] Where, |N j D j | represents line segment N j D j Length, F j Indicates the knife point P j The corresponding vector of the contact force, contact force F j The direction is actually to advance from the tool position point to the desired contour position N. j The direction, that is, the vector Pj N j j D j j j D j j N j j D j j D j j D j j N j

[0085] In step S3, the vector ΔF j of the compensation contact force can also be directly calculated, and the calculation formula is as follows:

[0086]

[0087] wherein f() is a model function of the contact force with respect to the grinding depth, that is, the material removal model introduced above.

[0088] At this time, if the grinding is too much, θ is less than 90°, the vector Δs j of the profile depth error is in the same direction as the vector F j of the contact force, the vector ΔF j of the obtained compensation contact force is in the opposite direction of the vector Δs j of the profile depth error, that is, the vector ΔF j of the obtained compensation contact force is in the opposite direction of the vector F j of the contact force, and the updated vector of the contact force is F j j + ΔF j , which actually reduces the contact force. Similarly, if the grinding is too little, θ is greater than 90°, the vector Δs j of the profile depth error is in the opposite direction of the vector F j of the contact force, the vector ΔF j of the obtained compensation contact force is in the opposite direction of the vector Δs j of the profile depth error, that is, the vector ΔF j of the obtained compensation contact force is in the same direction as the vector F j of the contact force, and the updated vector of the contact force is F j * j + ΔF j ​​​​​​​​​​​In essence, this means increasing the contact force. Understandably, the vector calculation can be adjusted flexibly, as long as it satisfies the condition that if too much grinding occurs, the current contact force is reduced, and if too little grinding occurs, the current contact force is increased.

[0089] In one embodiment, for the newly planned contact force, to ensure the smoothness of the contact force, B-splines are used to smooth the discrete contact force. The comparison results between the current contact force and the updated contact force are as follows: Figure 4 As shown.

[0090] Accordingly, the present invention also relates to a robot grinding contour error compensation system, comprising:

[0091] The tool control module is used to control the tool to move along the initial contour of the workpiece according to the planned tool point set and to apply a planned contact force at each tool point to perform grinding, so as to obtain the actual contour of the workpiece after grinding.

[0092] The contour depth error calculation module is used to obtain a discrete point set of the actual contour and calculate the contour depth error caused by the contact force deviation at each tool point based on the discrete point set.

[0093] The contact force update module is used to calculate the compensation contact force at the corresponding tool position point based on each contour depth error, and use the sum of the current contact force and the compensation contact force as the planned contact force for the next workpiece grinding at the corresponding tool position point.

[0094] Among them, the contour depth error calculation module calculates the arbitrary tool position P. j The execution process for the corresponding contour depth error includes:

[0095] Determine the current tool position P j The desired profile position N achieved by grinding j Find the point set of discrete points of the actual contour that corresponds to the line P. j N j The nearest point D j Calculate line segment N j D j On line P j N j The projected length on the surface is used as the numerical value of the contour depth error corresponding to the tool position point |Δs j |

[0096] Specifically, the tool control module executes step S1 as described above, the contour depth error calculation module executes step S2 as described above, and the contact force update module executes step S3 as described above. The specific execution details can be found in the preceding description and will not be repeated here.

[0097] In an embodiment, the profile depth error calculation module comprises a first vector calculation unit configured to calculate a vector Δs of the profile depth error j , the calculation formula is as follows:

[0098]

[0099] wherein |N j D j | represents the length of the line segment N j D j , F j represents the vector of the contact force corresponding to the tool position P j , and θ is the included angle between the vector N j D j and the vector F j ;

[0100] At this time, the contact force updating module comprises:

[0101] a second vector calculation unit configured to calculate a vector ΔF j of the compensation contact force, the calculation formula is as follows:

[0102]

[0103] wherein f() is a model function of the contact force with respect to the grinding depth;

[0104] a third vector calculation unit configured to calculate a vector F j * of the planned contact force of the next workpiece grinding at the corresponding tool position, the calculation formula is as follows:

[0105] F j * =F j +ΔF j .

[0106] In an embodiment, the robot grinding profile error compensation system further comprises an initial contact force planning module configured to plan the contact force |F| of the first workpiece at each tool position according to a model function f() of the contact force |F| with respect to the grinding depth s,

[0107]

[0108] wherein s is the expected grinding depth of the current tool position grinding to the desired profile position, v q is the tangential velocity of the tool, v f is the feed speed of the tool, E' and R' are the equivalent elastic modulus and equivalent curvature radius of grinding respectively, e is the ratio of the long axis to the short axis of the elliptical contact area, ε(e) is the second kind of elliptical integral, K Pfor the experimentally calibrated proportionality constant.

[0109] Correspondingly, the application also relates to a grinding robot, comprising a tool and the robot grinding profile error compensation system, the tool is controlled by the robot grinding profile error compensation system to grind a workpiece and update the contact force when grinding a next workpiece.

[0110] According to the grinding profile error after the initial grinding contact force planning, the application re-plans the contact force, which can reduce the profile error of the robot grinding, and is of great significance to improve the robot grinding profile precision.

[0111] Those skilled in the art will easily understand that the above description is only the preferred embodiment of the application, and is not used to limit the application, any modification, equivalent replacement and improvement within the spirit and principle of the application should be included in the protection scope of the application.

Claims

1. A robot grinding profile error compensation method, characterized by, Comprising: Step S1: controlling the tool to move along the initial profile of the workpiece according to the planned set of tool position points and to grind at each tool position point with the planned contact force to obtain the actual profile of the workpiece after grinding; Step S2: obtaining a discrete point set of the actual profile, and calculating the profile depth error at each tool position point after contact force polishing based on the discrete point set; Step S3: calculating the compensation contact force at the corresponding tool position point based on each profile depth error, and taking the sum of the current contact force and the compensation contact force as the planned contact force at the corresponding tool position point for the next workpiece grinding; wherein in step S2, the arbitrary tool position is calculated The corresponding profile depth error comprises: determine the current tool position desired profile position reached by grinding from the discrete set of points of the actual profile find the point closest in distance calculate the projection length of the line segment on the straight line as tool position the value of the corresponding profile depth error ; In step S2, the profile depth error is calculated, including calculating a vector of the profile depth error , wherein denotes the length of the line segment , denotes the tool position corresponding to the contact force, is the vector and the angle between the vector . In step S3, the compensation contact force is calculated, including calculating a vector of the compensation contact force , wherein is a model function for the contact force with respect to the grinding depth; the vector of the contact force planned for the corresponding tool position point of the next workpiece grinding The calculation formula is: 。 2. The robotic grinding profile error compensation method of claim 1, wherein, When grinding the first workpiece, in step S1, each tool position point is planned. The contact force includes: calculated from the tool position point on the initial contour. Grind to the desired profile position The expected grinding depth is determined based on the model function of contact force with respect to grinding depth. Obtain the knife point Planned contact force; wherein the model function of the contact force with respect to the grinding depth is a relation model based on the preston equation and the hertz contact theory.

3. The robotic grinding profile error compensation method of claim 2, wherein, Model function For the contact force between the grinding head and the workpiece, the contact area is regarded as an ellipse based on the Preston equation and the Hertz contact theory Regarding the relationship model of the grinding depth s, wherein is the tangential velocity of the tool, is the feed velocity of the tool, and are the equivalent elastic modulus and the equivalent radius of curvature of the grinding, respectively, is the ratio of the major axis to the minor axis of the elliptical contact area, is the second kind of elliptic integral, is a proportionality constant calibrated experimentally.

4. The robot grinding profile error compensation method of claim 1, in step S2, obtaining a discrete point set of the actual profile, comprising: Scanning the actual profile of the workpiece after grinding using a camera, removing invalid data according to the machining path, and then performing fairing interpolation on the discrete points of the actual profile to obtain the discrete point set of the actual profile.

5. The robot grinding profile error compensation method of claim 1, in step S1, the set of tool position points are discrete segmentation points determined by dividing the initial profile of the workpiece according to equal arc length.

6. A robot grinding profile error compensation system characterized by, Comprising: a tool control module for controlling the tool to move along the initial profile of the workpiece according to the planned set of tool position points and to grind at each tool position point with the planned contact force to obtain the actual profile of the workpiece after grinding; a profile depth error calculation module for obtaining a discrete point set of the actual profile, and calculating the profile depth error at each tool position point due to contact force deviation based on the discrete point set; a contact force updating module for calculating the compensation contact force at the corresponding tool position point based on each profile depth error, and taking the sum of the current contact force and the compensation contact force as the planned contact force at the corresponding tool position point for the next workpiece grinding; The profile depth error calculation module calculates the profile depth error of any tool position point The corresponding profile depth error execution process includes: determine the current tool position desired profile position reached by grinding from the discrete set of points of the actual profile, find the point closest in distance , calculate the projection length of the line segment on the straight line as tool position corresponding to the numerical value of the profile depth error ; The profile depth error calculation module comprises a first vector calculation unit for calculating a vector of the profile depth error The calculation formula is: wherein denotes the length of the line segment , denotes the vector of the contact force corresponding to the tool position is the vector and the angle between the vector . the contact force updating module comprises: a second vector calculation unit configured to calculate a vector of the compensation contact force , the calculation formula is: wherein is a model function of the contact force with respect to the grinding depth; a third vector calculation unit configured to calculate a vector of the contact force planned for the next workpiece grinding at the corresponding tool position point , the calculation formula is: 。 7. The robotic grinding profile error compensation system of claim 6, wherein, Further comprising: an initial contact force planning module for planning a contact force for the first workpiece at each tool position according to a model function planning a contact force for the first workpiece at each tool position , the model function for the contact force a relationship model with respect to the grinding depth s, where s is the expected grinding depth of the current tool position to the desired profile position, is the tangential velocity of the tool, is the feed velocity of the tool, and are the equivalent elastic modulus and equivalent radius of curvature of grinding, respectively, is the ratio of the major axis to the minor axis of the elliptical contact area, is the second kind of elliptic integral, is the experimentally calibrated proportionality constant.

8. A grinding robot, characterized in that, a robot grinding profile error compensation system comprising a tool and the robot grinding profile error compensation system of claim 6 or 7.

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