CN114888644A - Tool track offline programming method and system for robot constant-force grinding and polishing process - Google Patents
Tool track offline programming method and system for robot constant-force grinding and polishing process Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
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Abstract
The invention provides a tool track off-line programming method and system for a robot constant-force grinding and polishing process, which comprises the following steps: step S1: establishing and calibrating a numerical contact force model and a material removal model of a tool workpiece; step S2: iteratively searching a grinding and polishing subarea higher than a preset priority level according to the redundant material distribution; step S3: planning an optimal initial path direction, optimal tool residence time and optimal adjacent grinding and polishing path intervals in the extracted sub-regions through a material removal model; step S4: and outputting an executable file corresponding to the robot system. The method is efficient and practical, is suitable for grinding and polishing tools with general shapes and workpiece curved surfaces, and can improve the surface precision. The invention is used for carrying out force-controlled grinding and polishing, so that the industrial robot can efficiently generate an optimal grinding and polishing path on a complex workpiece curved surface, thereby improving the processing precision.
Description
Technical Field
The invention relates to the field of polishing, in particular to a tool track offline programming method and system for a robot constant force grinding and polishing process.
Background
Grinding and polishing are an important process in the surface treatment process of workpieces, mainly depend on manpower at present, have severe production environment, low efficiency and no guarantee of quality consistency, and are urgently required to be changed into an automatic and intelligent production mode. The robot constant-force grinding and polishing is widely applied in industry at present, but the robot constant-force grinding and polishing still has technical bottlenecks in aspects of technological parameter optimization, track off-line programming and the like, and ideal material removal on complex parts cannot be realized.
Based on the contact force and material removal model, the tool path and process parameters such as feed speed, feed direction, normal contact force, tool rotation speed of the polishing tool can be optimized. The tool tilt angle can also be optimized as an additional process parameter in the disc burnishing process. But for the task of achieving a desired material removal depth at a given point of the workpiece, this can be achieved simply by planning the tool dwell time on the path. Tool dwell time can be obtained by solving a linear least squares equation with feed rate constraints. With the overlap between adjacent polish path material removal profiles, the path spacing can be optimized to further reduce residual height. Xi et al propose a polishing path planning algorithm that can achieve uniform removal of material on a free-form surface workpiece. Liao et al propose a sanding force planning algorithm that can achieve a desired material removal profile.
For workpieces with complex structures, uniform and consistent polishing of the surface is difficult to achieve if the tool path is planned in a single area. In recent years, researchers have proposed different methods for planning a machining path based on region division, such as dividing a free-form surface into a plurality of flat surfaces based on surface topology and normal direction. Then, the tool movement pattern and sweep direction for each flat patch are determined. Atkar et al propose a hierarchical path planning method that automatically segments the surface according to surface geometry to obtain simple sub-regions. Olivieri et al propose a continuous surface segmentation method based on surface curvature, normal direction and surface topology to generate a swept path. In addition to surface segmentation methods based on geometric information, there are task-specific constraints such as processing error distribution, robot stiffness and local interference avoidance, which are direction dependent.
Therefore, the current grinding and polishing path and process parameter planning research based on the contact force model has several unsolved key problems: aiming at 'side-surface' contact in an end grinding process, how to semi-analytically and numerically establish a nonlinear relation between a normal contact force and a normal displacement of a grinding and polishing tool, and how to calculate pressure distribution in a contact area, so that an explicit relation between a material removal rate and each process parameter can be obtained; secondly, for a curved surface workpiece with high complexity, such as an automobile hub, the existing surface segmentation method is difficult to realize on a workpiece point cloud with a plurality of spokes, grooves and various complex substructures.
Patent document CN105269565B (application number: CN201510718150.0) discloses an offline programming and correcting method for a six-axis grinding and polishing industrial robot, which specifically includes modeling, extracting workpiece processing path information, processing point data, generating a robot processing motion joint angle, generating a robot processing motion track, simulating a robot grinding and polishing motion, generating a robot motion key parameter conversion module and code, correcting a position of an abrasive belt, correcting a pose and a singular pose, and correcting a grinding and polishing working environment. The invention cannot efficiently generate an optimal grinding and polishing path on a complex workpiece curved surface.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a tool track offline programming method and system for a robot constant-force grinding and polishing process.
The invention provides a tool track offline programming method for a robot constant-force grinding and polishing process, which comprises the following steps:
step S1: establishing and calibrating a numerical contact force model and a material removal model of a tool workpiece;
step S2: iteratively searching a grinding and polishing subarea with high priority according to the distribution of redundant materials;
step S3: planning an optimal initial path direction, optimal tool residence time and optimal adjacent grinding and polishing path intervals in the extracted sub-regions through a material removal model;
and repeatedly executing the steps S1 to S3 until the surface material of the workpiece is removed to a preset depth, and outputting an executable motion command corresponding to the robot system.
Preferably, in the step S1:
the numerical contact force model expresses the curved surface of the workpiece as discrete point cloud, and the contact pressure distribution on the point cloud of the workpiece under constant grinding and polishing force is calculated based on the nonlinear stress-strain relation and the point-surface numerical distance formula;
the material removal model predicts the material removal depth generated when the grinding and polishing tool feeds on the workpiece point cloud according to the numerical contact force model;
the workpiece point cloud is obtained by scanning through a three-dimensional CAD model or a three-dimensional scanner
Expressed in the world coordinate system as:
where N is the number of workpiece sampling points, W k Is the kth workpiece sampling point, x k Is the x-coordinate, y, of the workpiece sampling point k Is the y coordinate, z, of the workpiece sampling point k Is the z coordinate of the workpiece sampling point;
the grinding and polishing tool is arranged at the tail end of the robot, the robot applies positive pressure along the normal direction of the workpiece to the workpiece through the grinding and polishing tool, the positive pressure along the normal direction of the workpiece is normal contact force, the grinding and polishing tool is driven by a main shaft to rotate at high speed and is used for removing redundant materials on the surface of the workpiece, the grinding and polishing tool consists of I virtual springs vertical to the bottom surface of a grinding and polishing disc, and the normal contact force is calculated as the weighted sum of the pressures of all discrete disc points:
wherein, F N The normal contact force is shown as I, the number of discrete virtual springs is shown as I, and the thickness of the grinding and polishing disk is shown as H;
the contact pressure distribution is based on a non-linear stress-strain relationship:
calculating to obtain;
wherein h is i Is the ith one on the discContact depth of discrete points, p i Is the contact pressure at the ith discrete point, E is defined as the modulus of the nonlinear material, beta is defined as the stress-strain power exponent, determined by tool loading experiments, and deltaS i Is the area of a discrete cell on the disc tool;
the normal contact force is maintained at F d Maximum contact depth h 0 The contact pressure distribution is calculated according to the stress-strain relation and the iteration solution on the tool frame { O ] is obtained through the estimation of a numerical contact force model T Maximum contact depth h at 0 。
Preferably, in the step S2:
the sub-region is a workpiece point cloud neighborhood which meets space distance and normal change limitation;
the priority index is the depth weighted sum of redundant materials in the sub-region with a Gaussian kernel function as weight;
the subregion searching method selects the workpiece point with the maximum priority index as the central point of the high-priority grinding and polishing subregion;
the grinding and polishing sub-area is defined as a workpiece point W i All to the center point W i Is less than R I Set of workpiece points of (a):
Subregion i ＝{W k |Dist(W i ,W k )≤R I }
wherein, Subreglion i Denotes the ith sub-region, R I Defining the radius of interest as a parameter selected manually; dist represents a direction weighted distance function defined as follows:
wherein the content of the first and second substances,
represents a workpiece point W k In the normal direction of (c), n Wi Represents a workpiece point W i In the normal direction of (a), w o Is the normal phase of change of the workpiece pointFor the weight coefficient of the position change of the workpiece point, the weight coefficient is set as Dist (W) i ,W k ) Given as the gaussian kernel function of the argument:
wherein, Re i Is a workpiece point W i P is the sampling density of the workpiece point cloud, sigma is the standard deviation of the gaussian kernel function, and sigma is alpha R I The value of alpha is in a preset interval; as the machining efficiency needs to be considered when positioning the grinding and polishing subareas, the tool frame is assumed to be O T W is the workpiece point i Tool movement cost Dist ({ O) T },W i ) Is defined as:
wherein n is T Representing the axial direction of the polishing disc, the priority index being defined at each sampled workpiece point; the priority index includes two parts: the first part is the mean redundant material depth and the second part reflects the tool movement cost;
wherein, the color i Indicating the priority index of the ith sub-region, w m A weight coefficient that is a tool movement cost relative to an average redundant material depth; selecting the workpiece point with the highest priority as the central point of the high-priority grinding and polishing sub-area:
wherein, the CenterIndex * A center point index representing a high priority polish sub-region;
the high priority sub-region is thus defined as follows:
wherein, Subreglion * Representing the generated high-priority grinding and polishing subarea;
in each generated high-priority grinding and polishing subarea, a grinding and polishing mode of parallel paths is selected, the path direction is parallel to the y axis, and the variables to be optimized have the direction angle theta and the position x of the path n And the time T of tool residence on each path n 。
Preferably, in the step S3:
the optimal initial path direction is the direction selected to cover the most redundant material in the sub-region;
the optimal tool residence time is obtained by solving a linear least square problem which takes the depth minimization of redundant materials near a grinding and polishing path as a target and takes the feeding speed and the speed change of the robot as constraints by using a material removal model;
the optimal adjacent grinding and polishing path interval is obtained by solving a unimodal function extreme value problem which takes the minimization of the mean square error of the depth of the redundant materials between the adjacent paths as a target.
Preferably, the optimal path direction angle θ is defined as the direction containing the most redundant materials, and the formula is as follows:
wherein, theta * Indicating the optimum path direction angle, Re k Representing the redundant material depth of the kth workpiece point;
measure the nearby workpiece point W of each grinding and polishing path pair k The degree of influence, the metric function of the degree of influence is given by:
wherein Φ (x) represents the removal profile function defined by the above equation, and w represents the width of the polishing path;
the grinding and polishing path x is x n Is represented as
And
sampling the grinding and polishing path from top to bottom, wherein the projection distance interval of sampling points is delta, and the projection of the path sampling points on a local x-y plane is given by the following formula:
the tool axis lies in the same plane as the plane defined by the tool feed direction and the approximate workpiece normal, for each sample path point
Attitude of tool
Given by:
wherein theta is the included angle between the disc and the tangent plane of the workpiece,
is the normal direction of the jth path point, f is the tool feed direction, and R is the tool radius;
by MR n Denotes a path x ═ x n Corresponding material removal matrix, matrix elements
Equal to the material removal rate of the ith workpiece point at the jth tool sampling location; residence time T at all the sampling path points n Is recorded as:
t i (i＝1,2,…,|Q n |) is the tool's dwell time at the ith path point, | Q n L is the sampling number of the path point; the material removal depth is equal to the MR n ·T n ；
Tool dwell time T, since the purpose of planning the tool dwell time is to remove all redundant material n* Obtained by solving the following constrained linear least squares problem:
s.t.t min ≤T n ≤t max
wherein, t min And t max Representing the shortest and longest dwell times of the tool at a certain workpiece point; in the robot motion command, the feed speed can be obtained by calculating the inverse of the tool residence time, i.e.: v. of f,k n ＝1/t k n ；
Adding the feed rate variation limit as an additional constraint to the above equation yields:
s.t.t min ≤T n ≤t max
wherein
Representing a tool residence time difference matrix;
the nth stripThe grinding and polishing path is x ═ x n After planning, the redundant material distribution before and after polishing along the path is recorded as Re (n-1) And Re (n) The tool moves from the left side to the right side of the grinding and polishing sub-area, and the next optimal path position x needs to be found n+1 From x n To x n+1 The square and mean of the workpiece point redundant material depths in between are minimized:
wherein x is n+1 * For the next optimal grinding and polishing path position, L is the variance of the redundant material distribution;
when searching the next optimal path x ═ x n+1 When calculating the path x ═ x n+1 Still used at the time of dwell time on is along path x ═ x n Depth distribution Re of redundant material before polishing (n-1) Regarding the cost function as a minimum point position at x n To x n+1 A single-peak function between, finding the next path position x by golden section method n+1 ；
And the high-priority grinding and polishing subarea searching algorithm generates a new high-priority grinding and polishing subarea according to the updated redundant material distribution on the surface of the workpiece until the material on the workpiece is removed to reach the ideal depth.
The invention provides a tool track offline programming system for a robot constant-force grinding and polishing process, which comprises the following steps:
module M1: establishing and calibrating a numerical contact force model and a material removal model of a tool workpiece;
module M2: iteratively searching a grinding and polishing subarea with high priority according to the distribution of redundant materials;
module M3: planning an optimal initial path direction, optimal tool residence time and optimal adjacent grinding and polishing path intervals in the extracted sub-regions through a material removal model;
and repeatedly triggering the module M1 to the module M3 until the surface material of the workpiece is removed to a preset depth, and outputting an executable motion command corresponding to the robot system.
Preferably, in said module M1:
the numerical contact force model expresses the curved surface of the workpiece as discrete point cloud, and the contact pressure distribution on the point cloud of the workpiece under constant grinding and polishing force is calculated based on the nonlinear stress-strain relation and the point-surface numerical distance formula;
the material removal model predicts the material removal depth generated when the grinding and polishing tool feeds on the workpiece point cloud according to the numerical contact force model;
the workpiece point cloud is obtained by scanning through a three-dimensional CAD model or a three-dimensional scanner
Expressed in the world coordinate system as:
where N is the number of workpiece sampling points, W k Is the kth workpiece sampling point, x k Is the x-coordinate, y, of the workpiece sampling point k Is the y coordinate, z, of the workpiece sampling point k Is the z coordinate of the workpiece sampling point;
the grinding and polishing tool is arranged at the tail end of the robot, the robot applies positive pressure along the normal direction of the workpiece to the workpiece through the grinding and polishing tool, the positive pressure along the normal direction of the workpiece is normal contact force, the grinding and polishing tool is driven by a main shaft to rotate at high speed and is used for removing redundant materials on the surface of the workpiece, the grinding and polishing tool consists of I virtual springs vertical to the bottom surface of a grinding and polishing disc, and the normal contact force is calculated as the weighted sum of the pressures of all discrete disc points:
wherein, F N The normal contact force is shown as I, the number of discrete virtual springs is shown as I, and the thickness of the grinding and polishing disk is shown as H;
the contact pressure distribution is based on a non-linear stress-strain relationship:
calculating to obtain;
wherein h is i Is the contact depth of the ith discrete point on the disk, p i Is the contact pressure at the ith discrete point, E is defined as the modulus of the nonlinear material, beta is defined as the stress-strain power exponent, determined by tool loading experiments, and deltaS i Is the area of a discrete cell on the disc tool;
the normal contact force is maintained at F d Maximum contact depth h 0 The contact pressure distribution is calculated according to the stress-strain relation and the iteration solution on the tool frame { O ] is obtained through the estimation of a numerical contact force model T Maximum contact depth h at 0 。
Preferably, in said module M2:
the sub-region is a workpiece point cloud neighborhood which meets space distance and normal change limitation;
the priority index is the depth weighted sum of redundant materials in the sub-region with a Gaussian kernel function as weight;
the subregion searching method selects the workpiece point with the maximum priority index as the central point of the high-priority grinding and polishing subregion;
the grinding and polishing sub-area is defined as a workpiece point W i All to the center point W i Is less than R I Set of workpiece points of (a):
Subregion i ＝{W k |Dist(W i ,W k )≤R I }
wherein, Subreglion i Denotes the ith sub-region, R I Defining the radius of interest as a parameter selected manually; dist represents a direction weighted distance function defined as follows:
wherein the content of the first and second substances,
represents a workpiece point W k In the normal direction of (c), n Wi Represents a workpiece point W i In the normal direction of (a), w o Is the weight coefficient of the normal change of the workpiece point relative to the change of the position of the workpiece point, and the weight coefficient is given by Dist (W) i ,W k ) Given as the gaussian kernel function of the argument:
wherein, Re i Is a workpiece point W i P is the sampling density of the workpiece point cloud, sigma is the standard deviation of the gaussian kernel function, and sigma is alpha R I The value of alpha is in a preset interval; as the machining efficiency needs to be considered when positioning the grinding and polishing subareas, the tool frame is assumed to be O T W is the workpiece point i Tool movement cost Dist ({ O) T },W i ) Is defined as:
wherein n is T Representing the axial direction of the polishing disc, the priority index being defined at each sampled workpiece point; the priority index includes two parts: the first part is the mean redundant material depth and the second part reflects the tool movement cost;
wherein, the color i Priority index, w, representing the ith sub-region m A weight coefficient that is a tool movement cost relative to an average redundant material depth; selecting the workpiece point with the highest priority as the central point of the high-priority grinding and polishing sub-area:
wherein, the CenterIndex * A center point index representing a high priority polish sub-region;
the high priority sub-region is thus defined as follows:
wherein, Subreglion * Representing the generated high-priority grinding and polishing subarea;
in each generated high-priority grinding and polishing subarea, a grinding and polishing mode of parallel paths is selected, the path direction is parallel to the y axis, and the variables to be optimized have the direction angle theta and the position x of the path n And the time T of tool residence on each path n 。
Preferably, in said module M3:
the optimal initial path direction is the direction selected to cover the most redundant material in the sub-region;
the optimal tool residence time is obtained by solving a linear least square problem which takes the depth minimization of redundant materials near a grinding and polishing path as a target and takes the feeding speed and the speed change of the robot as constraints by using a material removal model;
the optimal adjacent grinding and polishing path interval is obtained by solving a unimodal function extreme value problem which takes the minimization of the mean square error of the depth of the redundant materials between the adjacent paths as a target.
Preferably, the optimal path direction angle θ is defined as the direction containing the most redundant material, and the formula is as follows:
wherein, theta * Represents the optimal path direction angle, Re k Representing the redundant material depth of the kth workpiece point;
measure the nearby workpiece point W of each grinding and polishing path pair k The degree of influence, the metric function of the degree of influence is given by:
wherein Φ (x) represents the removal profile function defined by the above equation, and w represents the width of the polishing path;
the grinding and polishing path x is x n Is represented as
And
sampling the grinding and polishing path from top to bottom, wherein the projection distance interval of sampling points is delta, and the projection of the path sampling points on a local x-y plane is given by the following formula:
the tool axis lies in the same plane as the plane defined by the tool feed direction and the approximate workpiece normal, for each sample path point
Attitude of tool
Given by:
wherein theta is an included angle between the disc and a tangent plane of the workpiece,
is the normal direction of the jth path point, f is the tool feed direction, and R is the tool radius;
by MR n Denotes a path x ═ x n Corresponding material removal matrix, matrix elements
Equal to the material removal rate of the ith workpiece point at the jth tool sampling location; residence time T at all the sampling path points n Is recorded as:
t i (i＝1,2,…,|Q n |) is the tool's dwell time at the ith path point, | Q n L is the sampling number of the path point; the material removal depth is equal to the MR n ·T n ；
Tool dwell time T, since the purpose of planning the tool dwell time is to remove all redundant material n* Obtained by solving the following constrained linear least squares problem:
s.t.t min ≤T n ≤t max
wherein, t min And t max Representing the shortest and longest dwell times of the tool at a certain workpiece point; in the robot motion command, the feed speed can be obtained by calculating the inverse of the tool residence time, i.e.: v. of f,k n ＝1/t k n ；
Adding the feed rate variation limit as an additional constraint to the above equation yields:
s.t.t min ≤T n ≤t max
wherein
Representing a tool residence time difference matrix;
the n-th grinding and polishing path is x ═ x n After planning, the redundant material distribution before and after polishing along the path is recorded as Re (n-1) And Re (n) The tool moves from the left side to the right side of the grinding and polishing sub-area, and the next optimal path position x needs to be found n+1 From x n To x n+1 The square and mean of the workpiece point redundant material depths in between are minimized:
wherein x is n+1 * For the next optimal grinding and polishing path position, L is the variance of the redundant material distribution;
when searching the next optimal path x ═ x n+1 When calculating the path x ═ x n+1 Still used at the time of dwell time on is along path x ═ x n Depth distribution Re of redundant material before polishing (n-1) Regarding the cost function as a minimum point position at x n To x n+1 A single-peak function between, finding the next path position x by golden section method n+1 ；
And the high-priority grinding and polishing subarea searching algorithm generates a new high-priority grinding and polishing subarea according to the updated redundant material distribution on the surface of the workpiece until the material on the workpiece is removed to reach the ideal depth.
Compared with the prior art, the invention has the following beneficial effects:
1. by using the invention to carry out force-controlled grinding and polishing, the industrial robot can efficiently generate an optimal grinding and polishing path on a complex workpiece curved surface, thereby improving the processing precision;
2. the method is efficient and practical, and is suitable for grinding and polishing tools and workpiece curved surfaces with general shapes.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a flow chart of the algorithm proposed by the present invention;
FIG. 2 is a schematic view of a contact force model of the polishing tool and the workpiece;
FIG. 3 is a schematic view of a polishing sub-region;
FIG. 4 is a schematic view of the polishing path within a sub-region;
FIG. 5 is a redundant material distribution update diagram on the hub component;
FIG. 6 is a graph of simulation results;
FIG. 7 is a schematic view of the planned grinding and polishing path in the first 10 sub-regions of the hub part.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Example 1:
the invention provides a tool track offline programming method for a robot constant-force grinding and polishing process. The method aims to achieve ideal material removal amount on the curved surface of the complex workpiece. Firstly, in order to predict the material removal depth on the curved surface of the workpiece, the method establishes a contact pressure distribution model on the point cloud of the workpiece based on the nonlinear stress-strain relationship. By using a gaussian kernel function to find a high priority polishing region, the polishing tool can achieve preferential polishing of a portion of the workpiece having a greater amount of redundant material. By using a zig-zag path and optimizing the initial path direction, the polishing tool is able to polish in the direction of the greatest amount of redundant material in the high priority regions. A tool feeding speed and adjacent path distance optimization model which aims at minimizing the depth mean square error of redundant materials and is constrained by the feeding speed and speed change of a robot is established in a high-priority polishing area, and the model is solved by using a constrained linear least square algorithm to obtain a tool track in the high-priority polishing area. Finally, a high priority region is generated through iteration and the tool trajectory is planned within until the material removal depth over the entire workpiece surface reaches the desired value. The generated tool trajectory may generate an executable file according to the particular robotic system.
According to the tool trajectory offline programming method for the robot constant-force grinding and polishing process, as shown in fig. 1 to 7, the tool trajectory offline programming method comprises the following steps:
step S1: establishing and calibrating a numerical contact force model and a material removal model of a tool workpiece;
specifically, in the step S1:
the numerical contact force model expresses the curved surface of the workpiece as discrete point cloud, and the contact pressure distribution on the point cloud of the workpiece under constant grinding and polishing force is calculated based on the nonlinear stress-strain relation and the point-surface numerical distance formula;
the material removal model predicts the material removal depth generated when the grinding and polishing tool feeds on the workpiece point cloud according to the numerical contact force model;
the workpiece point cloud is obtained by scanning through a three-dimensional CAD model or a three-dimensional scanner
Expressed in the world coordinate system as:
where N is the number of workpiece sampling points, W k Is the kth workpiece sampling point, x k Is the x-coordinate, y, of the workpiece sampling point k Is the y coordinate, z, of the workpiece sampling point k A z coordinate of a workpiece sampling point;
the grinding and polishing tool is arranged at the tail end of the robot, the robot applies positive pressure along the normal direction of the workpiece to the workpiece through the grinding and polishing tool, the positive pressure along the normal direction of the workpiece is normal contact force, the grinding and polishing tool is driven by a main shaft to rotate at high speed and is used for removing redundant materials on the surface of the workpiece, the grinding and polishing tool consists of I virtual springs vertical to the bottom surface of a grinding and polishing disc, and the normal contact force is calculated as the weighted sum of the pressures of all discrete disc points:
wherein, F N The normal contact force is shown as I, the number of discrete virtual springs is shown as I, and the thickness of the grinding and polishing disk is shown as H;
the contact pressure distribution is based on a non-linear stress-strain relationship:
calculating to obtain;
wherein h is i Is the contact depth of the ith discrete point on the disk, p i Is the contact pressure at the ith discrete point, E is defined as the modulus of the nonlinear material, beta is defined as the stress-strain power exponent, determined by tool loading experiments, and deltaS i Is the area of a discrete cell on the disc tool;
the normal contact force is maintained at F d Maximum contact depth h 0 Estimated according to a numerical contact force model, according to a stress-strain relationshipThe contact pressure distribution is calculated, and the in-tool frame { O ] is iteratively solved by a Newton secant method T Maximum contact depth h at 0 。
Step S2: iteratively searching a grinding and polishing subarea with high priority according to the distribution of redundant materials;
specifically, in the step S2:
the sub-region is a workpiece point cloud neighborhood which meets space distance and normal change limitation;
the priority index is the depth weighted sum of redundant materials in the sub-region with a Gaussian kernel function as weight;
the subregion searching method selects the workpiece point with the maximum priority index as the central point of the high-priority grinding and polishing subregion;
the grinding and polishing sub-area is defined as a workpiece point W i All to the center point W i Is less than R I Set of workpiece points of (a):
Subregion i ＝{W k |Dist(W i ,W k )≤R I }
wherein, Subreglion i Denotes the ith sub-region, R I Defining the radius of interest as a parameter selected manually; dist represents a direction weighted distance function defined as follows:
wherein, the first and the second end of the pipe are connected with each other,
represents a workpiece point W k In the normal direction of (c), n Wi Represents a workpiece point W i In the normal direction of (a), w o Is the weight coefficient of the normal change of the workpiece point relative to the change of the position of the workpiece point, and the weight coefficient is given by Dist (W) i ,W k ) Given as the gaussian kernel function of the argument:
wherein, Re i Is a workpiece point W i P is the sampling density of the workpiece point cloud, sigma is the standard deviation of the Gaussian kernel function, and sigma is alpha R I The value of alpha is in a preset interval; as the machining efficiency needs to be considered when positioning the grinding and polishing subareas, the tool frame is assumed to be O T W is the workpiece point i Tool movement cost Dist ({ O) T },W i ) Is defined as:
wherein n is T Representing the axial direction of the grinding and polishing disk, and the priority index is defined at each sampled workpiece point; the priority index includes two parts: the first part is the mean redundant material depth and the second part reflects the tool movement cost;
wherein, the color i Indicating the priority index of the ith sub-region, w m A weight coefficient that is a tool movement cost relative to an average redundant material depth; selecting the workpiece point with the highest priority as the central point of the high-priority grinding and polishing sub-area:
wherein, the CenterIndex * A center point index representing a high priority polish sub-region;
the high priority sub-region is thus defined as follows:
wherein, Subreglion * High excellence in expression generationFirstly, grinding and polishing a subarea;
in each generated high-priority grinding and polishing subarea, a grinding and polishing mode of parallel paths is selected, the path direction is parallel to the y axis, and the variables to be optimized have the direction angle theta and the position x of the path n And the time T of tool residence on each path n 。
Step S3: planning an optimal initial path direction, optimal tool residence time and optimal adjacent grinding and polishing path intervals in the extracted sub-regions through a material removal model;
specifically, in the step S3:
the optimal initial path direction is the direction selected to cover the most redundant material in the sub-region;
the optimal tool residence time is obtained by solving a linear least square problem which takes the depth minimization of redundant materials near a grinding and polishing path as a target and takes the feeding speed and the speed change of the robot as constraints by using a material removal model;
the optimal adjacent grinding and polishing path interval is obtained by solving a unimodal function extreme value problem which aims at minimizing the depth mean square error of redundant materials between adjacent paths.
Specifically, the optimal path direction angle θ is defined as the direction containing the most redundant materials, and the formula is as follows:
wherein, theta * Indicating the optimum path direction angle, Re k Representing the redundant material depth of the kth workpiece point;
measure the nearby workpiece point W of each grinding and polishing path pair k The degree of influence, the metric function of the degree of influence is given by:
wherein Φ (x) represents the removal profile function defined by the above equation, and w represents the width of the polishing path;
the grinding and polishing path x is x n Is represented as
And
sampling the grinding and polishing path from top to bottom, wherein the projection distance interval of sampling points is delta, and the projection of the path sampling points on a local x-y plane is given by the following formula:
the tool axis lies in the same plane as the plane defined by the tool feed direction and the approximate workpiece normal, for each sample path point
Attitude of tool
Given by:
wherein theta is the included angle between the disc and the tangent plane of the workpiece,
is the normal direction of the jth path point, f is the tool feed direction, and R is the tool radius;
by MR n Denotes a path x ═ x n Corresponding material removal matrix, matrix elements
Equal to the material of the ith workpiece point at the jth tool sampling locationMaterial removal rate; residence time T at all the sampling path points n Is recorded as:
t i (i＝1,2,…,|Q n |) is the tool's dwell time at the ith path point, | Q n L is the sampling number of the path point; the material removal depth is equal to the MR n ·T n ；
Tool dwell time T, since the purpose of planning the tool dwell time is to remove all redundant material n* Obtained by solving the following constrained linear least squares problem:
s.t.t min ≤T n ≤t max
wherein, t min And t max Representing the shortest and longest dwell times of the tool at a certain workpiece point; in the robot motion command, the feed speed can be obtained by calculating the inverse of the tool residence time, i.e.: v. of f,k n ＝1/t k n ；
Adding the feed rate variation limit as an additional constraint to the above equation yields:
s.t.t min ≤T n ≤t max
wherein
Representing a tool residence time difference matrix;
the n-th grinding and polishing path is x ═ x n After planning, the redundant material distribution before and after polishing along the path is recorded asRe (n-1) And Re (n) The tool moves from the left side to the right side of the grinding and polishing sub-area, and the next optimal path position x needs to be found n+1 From x n To x n+1 The square and mean of the workpiece point redundant material depths in between are minimized:
wherein x is n+1 * For the next optimal grinding and polishing path position, L is the variance of the redundant material distribution;
when searching the next optimal path x ═ x n+1 When calculating the path x ═ x n+1 Still used at the time of dwell time on is along path x ═ x n Depth distribution Re of redundant material before polishing (n-1) Regarding the cost function as a minimum point position at x n To x n+1 A single-peak function between, finding the next path position x by golden section method n+1 ；
And the high-priority grinding and polishing subarea searching algorithm generates a new high-priority grinding and polishing subarea according to the updated redundant material distribution on the surface of the workpiece until the material on the workpiece is removed to reach the ideal depth.
And repeatedly executing the steps S1 to S3 until the surface material of the workpiece is removed to a preset depth, and outputting an executable motion command corresponding to the robot system.
Example 2:
example 2 is a preferred example of example 1, and the present invention will be described in more detail.
The tool trajectory offline programming method for the robot constant-force grinding and polishing process provided by the invention can be understood as a specific implementation manner of a tool trajectory offline programming system for the robot constant-force grinding and polishing process by those skilled in the art, that is, the tool trajectory offline programming system for the robot constant-force grinding and polishing process can be implemented by executing the step flow of the tool trajectory offline programming method for the robot constant-force grinding and polishing process.
The invention provides a tool track offline programming system for a robot constant-force grinding and polishing process, which comprises the following steps:
module M1: establishing and calibrating a numerical contact force model and a material removal model of a tool workpiece;
specifically, in the module M1:
the numerical contact force model expresses the curved surface of the workpiece as discrete point cloud, and the contact pressure distribution on the point cloud of the workpiece under constant grinding and polishing force is calculated based on the nonlinear stress-strain relation and the point-surface numerical distance formula;
the material removal model predicts the material removal depth generated when the grinding and polishing tool feeds on the workpiece point cloud according to the numerical contact force model;
the workpiece point cloud is obtained by scanning through a three-dimensional CAD model or a three-dimensional scanner
Expressed in the world coordinate system as:
where N is the number of workpiece sampling points, W k Is the kth workpiece sampling point, x k Is the x-coordinate, y, of the workpiece sampling point k Is the y coordinate, z, of the workpiece sampling point k Is the z coordinate of the workpiece sampling point;
the grinding and polishing tool is arranged at the tail end of the robot, the robot applies positive pressure along the normal direction of the workpiece to the workpiece through the grinding and polishing tool, the positive pressure along the normal direction of the workpiece is normal contact force, the grinding and polishing tool is driven by a main shaft to rotate at high speed and is used for removing redundant materials on the surface of the workpiece, the grinding and polishing tool consists of I virtual springs vertical to the bottom surface of a grinding and polishing disc, and the normal contact force is calculated as the weighted sum of the pressures of all discrete disc points:
wherein, F N The normal contact force is I, the number of discrete virtual springs is I, and the thickness of the grinding and polishing disk is H;
the contact pressure distribution is based on a non-linear stress-strain relationship:
calculating to obtain;
wherein h is i Is the contact depth of the ith discrete point on the disk, p i Is the contact pressure at the ith discrete point, E is defined as the modulus of the nonlinear material, beta is defined as the stress-strain power exponent, determined by tool loading experiments, and deltaS i Is the area of a discrete cell on the disc tool;
the normal contact force is maintained at F d Maximum contact depth h 0 The contact pressure distribution is calculated according to the stress-strain relation and the iteration solution on the tool frame { O ] is obtained through the estimation of a numerical contact force model T Maximum contact depth h at 0 。
Module M2: iteratively searching a grinding and polishing subarea with high priority according to the distribution of redundant materials;
specifically, in the module M2:
the sub-region is a workpiece point cloud neighborhood which meets space distance and normal change limitation;
the priority index is the depth weighted sum of redundant materials in the sub-region with a Gaussian kernel function as weight;
the subregion searching method selects the workpiece point with the maximum priority index as the central point of the high-priority grinding and polishing subregion;
the grinding and polishing subarea is defined as a workpiecePoint W i All to the center point W i Is less than R I Set of workpiece points of (a):
Subregion i ＝{W k |Dist(W i ,W k )≤R I }
wherein, Subreglion i Denotes the ith sub-region, R I Defining the radius of interest as a parameter selected manually; dist represents a direction weighted distance function defined as follows:
wherein the content of the first and second substances,
represents a workpiece point W k In the normal direction of (c), n Wi Represents a workpiece point W i In the normal direction of (a), w o Is the weight coefficient of the normal change of the workpiece point relative to the change of the position of the workpiece point, and the weight coefficient is represented by Dist (W) i ,W k ) Given as the gaussian kernel function of the argument:
wherein, Re i Is a workpiece point W i P is the sampling density of the workpiece point cloud, sigma is the standard deviation of the gaussian kernel function, and sigma is alpha R I The value of alpha is in a preset interval; as the machining efficiency needs to be considered when positioning the grinding and polishing subareas, the tool frame is assumed to be O T W is the workpiece point i Tool movement cost Dist ({ O) T },W i ) Is defined as:
wherein n is T Indicating the axial direction of the grinding and polishing disk, the priority index being at each sampled workpieceDefining points; the priority index includes two parts: the first part is the mean redundant material depth and the second part reflects the tool movement cost;
wherein, the color i Indicating the priority index of the ith sub-region, w m A weight coefficient that is a tool movement cost relative to an average redundant material depth; selecting the workpiece point with the highest priority as the central point of the high-priority grinding and polishing sub-area:
wherein, the CenterIndex * A center point index representing a high priority polish sub-region;
the high priority sub-region is thus defined as follows:
wherein, Subreglion * Representing the generated high-priority grinding and polishing subarea;
in each generated high-priority grinding and polishing subarea, a grinding and polishing mode of parallel paths is selected, the path direction is parallel to the y axis, and the variables to be optimized have the direction angle theta and the position x of the path n And the time T of tool residence on each path n 。
Module M3: planning an optimal initial path direction, optimal tool residence time and optimal adjacent grinding and polishing path intervals in the extracted sub-regions through a material removal model;
specifically, in the module M3:
the optimal initial path direction is the direction selected to cover the most redundant material in the sub-region;
the optimal tool residence time is obtained by solving a linear least square problem which takes the depth minimization of redundant materials near a grinding and polishing path as a target and takes the feeding speed and the speed change of the robot as constraints by using a material removal model;
the optimal adjacent grinding and polishing path interval is obtained by solving a unimodal function extreme value problem which takes the minimization of the mean square error of the depth of the redundant materials between the adjacent paths as a target.
Specifically, the optimal path direction angle θ is defined as the direction containing the most redundant materials, and the formula is as follows:
wherein, theta * Represents the optimal path direction angle, Re k Representing a redundant material depth for a kth workpiece point;
measure the nearby workpiece point W of each grinding and polishing path pair k The degree of influence, the metric function of the degree of influence is given by:
wherein Φ (x) represents the removal profile function defined by the above equation, and w represents the width of the polishing path;
the grinding and polishing path x is x n Is represented as
And
sampling the grinding and polishing path from top to bottom, wherein the projection distance interval of sampling points is delta, and the projection of the path sampling points on a local x-y plane is given by the following formula:
the tool axis lies in the same plane as the plane defined by the tool feed direction and the approximate workpiece normal, for each sample path point
Tool attitude
Given by:
wherein theta is the included angle between the disc and the tangent plane of the workpiece,
is the normal direction of the jth path point, f is the tool feed direction, and R is the tool radius;
by MR n Denotes a path x ═ x n Corresponding material removal matrix, matrix elements
Equal to the material removal rate of the ith workpiece point at the jth tool sampling location; residence time T at all the sampling path points n Is recorded as:
t i (i＝1,2,…,|Q n | Q) is the tool's dwell time at the ith path point n L is the sampling number of the path points; the material removal depth is equal to the MR n ·T n ；
Tool dwell time T, since the purpose of planning the tool dwell time is to remove all redundant material n* Obtained by solving the following constrained linear least squares problem:
s.t.t min ≤T n ≤t max
wherein, t min And t max Representing the shortest and longest dwell time of the tool at a certain workpiece point; in the robot motion command, the feed speed can be obtained by calculating the inverse of the tool residence time, i.e.: v. of f,k n ＝1/t k n ；
Adding the feed rate variation limit as an additional constraint to the above equation yields:
s.t.t min ≤T n ≤t max
wherein
Representing a tool residence time difference matrix;
the n-th grinding and polishing path is x ═ x n After planning, the redundant material distribution before and after polishing along the path is recorded as Re (n-1) And Re (n) The tool moves from the left side to the right side of the grinding and polishing sub-area, and the next optimal path position x needs to be found n+1 From x n To x n+1 The square and mean of the workpiece point redundant material depths in between are minimized:
wherein x is n+1 * For the next optimal polishing path position, L is the variance of the redundant material distribution；
When searching the next optimal path x ═ x n+1 When calculating the path x ═ x n+1 Still used when the dwell time is on is along path x ═ x n Depth distribution Re of redundant material before polishing (n-1) Regarding the cost function as a minimum point position at x n To x n+1 A single-peak function between, finding the next path position x by golden section method n+1 ；
And the high-priority grinding and polishing subarea searching algorithm generates a new high-priority grinding and polishing subarea according to the updated redundant material distribution on the surface of the workpiece until the material on the workpiece is removed to reach the ideal depth.
And repeatedly triggering the module M1 to the module M3 until the surface material of the workpiece is removed to a preset depth, and outputting an executable motion command corresponding to the robot system.
Example 3:
example 3 is a preferred example of example 1, and the present invention will be described in more detail.
A tool track offline programming method for a robot force-controlled grinding and polishing process comprises the following steps: establishing and calibrating a numerical contact force and material removal model of a tool workpiece; iteratively searching a high-priority grinding and polishing sub-area according to the distribution of redundant materials; planning an optimal initial path direction, tool residence time (feeding speed) and adjacent grinding and polishing path intervals in the extracted sub-regions; an executable motion instruction (e.g., G-code) corresponding to the robotic system is output.
The numerical contact force and material removal model is characterized in that the numerical contact force model expresses a workpiece curved surface as discrete point cloud, and based on a nonlinear stress-strain relation and a point-surface numerical distance formula, the contact pressure distribution on the workpiece point cloud under constant grinding and polishing force is calculated; the material removal model is characterized in that the material removal depth generated when the grinding and polishing tool feeds on the workpiece point cloud is rapidly predicted according to the numerical contact force model.
The searching method of the high-priority grinding and polishing subarea is characterized in that the subarea is a workpiece point cloud neighborhood which meets the space distance and normal variation limitation; the priority index is defined as the depth weighted sum of redundant materials with a Gaussian kernel function as weight in a subregion; the sub-area searching method selects the workpiece point with the maximum priority index as the central point of the high-priority grinding and polishing sub-area.
The initial path direction, tool residence time and adjacent polishing path interval planning method in the sub-area is characterized in that the optimal initial path direction is selected as the direction which covers the most redundant materials in the sub-area; the optimal tool residence time is obtained by solving a linear least square problem which takes the depth minimization of redundant materials near a grinding and polishing path as a target and takes the feeding speed and the speed change of the robot as constraints by using the material removal model; the optimal adjacent grinding and polishing path interval is obtained by solving a unimodal function extreme value problem which takes the minimization of the mean square error of the depth of the redundant materials between the adjacent paths as a target.
Aiming at the defects of the prior art, the invention provides a tool track offline programming method for a robot force control grinding and polishing process, which comprises the following steps: establishing and calibrating a numerical contact force and material removal model of a tool workpiece; iteratively searching a high-priority grinding and polishing sub-area according to the distribution of redundant materials; and planning the optimal initial path direction, tool residence time (feed speed) and adjacent grinding and polishing path intervals in the extracted sub-area.
The workpiece point cloud can be obtained by scanning through a three-dimensional CAD model or a three-dimensional scanner. Workpiece point cloud
Can be expressed as:
where N is the number of workpiece sampling points. W is a group of k Is the kth workpiece sampling point, x k Is the x-coordinate, y, of the workpiece sampling point k Is the y coordinate, z, of the workpiece sampling point k Is the z coordinate of the workpiece sampling point;
the numerical contact force model calculates the contact pressure distribution on the workpiece based on the nonlinear stress-strain assumption and the numerical distance formula, and the model schematic diagram is shown in fig. 2.
The disc-shaped grinding and polishing tool is arranged at the tail end of the robot, the robot applies positive pressure (hereinafter referred to as normal contact force) along the normal direction of the workpiece to the workpiece through the grinding and polishing tool, and the grinding and polishing tool is driven by the main shaft to rotate at high speed and is used for removing redundant materials on the surface of the workpiece. The polishing tool can be assumed to consist approximately of I virtual springs perpendicular to the bottom surface of the polishing disk.
The normal contact force may be calculated as a weighted sum of the pressures of all discrete puck points.
Wherein, F N The normal contact force is shown as I, the number of discrete virtual springs is shown as I, and the thickness of the grinding and polishing disk is shown as H;
the contact pressure distribution is based on a non-linear stress-strain relationship:
and (4) calculating. h is i Is the contact depth of the ith discrete point on the disk, p i Is the contact pressure at the ith discrete point. E is defined as the nonlinear material modulus and β is defined as the stress-strain power exponent and can be determined by tool loading experiments. Delta S i Is the area of a discrete cell on the puck tool.
The specific calculation process of the normal contact force is given by algorithm 1:
because the maximum contact in the constant force grinding and polishing processThe depth is unknown and the contact force is known. Assuming that the normal contact force remains F d Maximum contact depth h 0 The contact pressure distribution can be estimated according to a numerical contact force model and then calculated according to the stress-strain relation. Since the contact force is the maximum contact depth h 0 So that the tool frame { O ] can be solved iteratively by Newton's secant method T Maximum contact depth h at 0 。
Calculating the contact depth h 0 The pseudo code of (2) is shown as algorithm 2.
The invention provides a grinding and polishing subarea searching algorithm based on priority indexes, which iteratively generates a grinding and polishing subarea according to the distribution of redundant materials on a workpiece.
As shown in FIG. 3, the polishing sub-area is defined as a work point W i All to the center point W i Is less than R I Set of workpiece points of (a):
Subregion i ＝{W k |Dist(W i ,W k )≤R I }
wherein Subreglion i Denotes the ith sub-region, R I Defined as the radius of interest, is a parameter that is manually selected. Dist represents a direction weighted distance function defined as follows:
wherein Re i Is a workpiece point W i P is the sampling density of the workpiece point cloud, and sigma is the standard deviation of the Gaussian kernel function, which is set as alpha R in the invention I . Suggested values of alpha in the interval 0.2,1]And (4) the following steps. As the machining efficiency needs to be considered when positioning the grinding and polishing subareas, the tool frame is assumed to be O T W is the workpiece point i The tool movement cost is defined as:
wherein n is T Showing the axial direction of the abrasive polishing disc. The priority index is defined at each sampled workpiece point. The priority index includes two parts: the first part is the average redundant material depth and the second part reflects the tool movement cost.
Wherein, the color i Indicating the priority index of the ith sub-region, w m Is a weight coefficient of tool movement cost versus average redundant material depth. Selecting the workpiece point with the highest priority as the central point of the high-priority grinding and polishing sub-area:
CenterIndex * a center point index representing a high priority polish sub-region;
the high priority sub-region is thus defined as follows:
Subregion * indicating the resulting high priority polish sub-region.
In each generated high-priority grinding and polishing subarea, a grinding and polishing mode of a parallel path is selected (the direction of the path is parallel to the y axis), and the variables to be optimized have the direction angle theta of the path and the position (or the distance) x n And the time T of tool residence on each path n 。
The optimal path direction angle θ is defined as the direction containing the most redundant material, and is given as follows:
wherein, theta * Indicating the optimum path direction angle, Re k Representing the redundant material depth for the k-th workpiece point.
In the above formula, the first and second carbon atoms are,
measure the nearby workpiece point W of each grinding and polishing path pair k The degree of influence, the metric function of the degree of influence is given by:
wherein Φ (x) represents the removal profile function defined by the above equation, and w represents the width of the polishing path;
as shown in fig. 4, the polishing path x is x n Is represented as
And
the grinding and polishing path is sampled from top to bottom, and the sampling point is thrownThe shadow distance interval is δ, and the projection of the path sample point on the local x-y plane is given by:
the tool axis is assumed to lie in the same plane as the plane defined by the tool feed direction and the approximate normal to the workpiece. For each sampling path point
The tool pose may be given by:
wherein theta is the included angle between the disc and the tangent plane of the workpiece,
is the normal direction of the jth path point, f is the tool feed direction, and R is the tool radius;
by MR n Denotes a path x ═ x n Corresponding material removal matrix, matrix elements
Equal to the material removal rate of the ith workpiece point at the jth tool sampling location. The residence time at all the sampling path points is recorded as:
t i (i＝1,2,…,|Q n |) is the tool's dwell time at the ith path point, | Q n L is the sampling number of the path point;
the material removal depth is equal to the MR n ·T n . Since the purpose of planning the tool residence time is to remove all redundant material, the tool residence time can be determined by solving for the following bandsThe constrained linear least squares problem yields:
s.t.t min ≤T n ≤t max
wherein t is min And t max Indicating the shortest and longest dwell times of the tool at a certain workpiece point. In the robot motion command, the feed speed can be obtained by calculating the inverse of the tool residence time, i.e.: v. of f,k n ＝1/t k n 。
The feed rate variation limit may be added as an additional constraint to the above equation, resulting in:
s.t.t min ≤T n ≤t max
wherein
Representing a tool residence time difference matrix.
Assuming that the nth grinding and polishing path is x ═ x n It has been planned that the distribution of the redundant material before and after polishing along this path is denoted Re (n-1) And Re (n) . The tool moves from the left side to the right side of the grinding and polishing sub-area, and the next optimal path position x needs to be found n+1 From x n To x n+1 The square and mean of the workpiece point redundant material depths in between are minimized:
x n+1 * for the next optimal grinding and polishing path position, L is the variance of the redundant material distribution;
when searching the next optimal path x ═ x n+1 When calculating the path x ═ x n+1 Still used at the time of dwell time on is along path x ═ x n Depth distribution Re of redundant material before polishing (n-1) . The cost function can be viewed as one minutiae location at x n To x n+1 A single-peak function between, finding the next path position x by golden section method n+1 . The pseudo code is given by algorithm 3.
The local workpiece trajectory planning algorithm is respectively carried out on the left side and the right side of the initial path until the new path reaches the left and right boundaries of the sub-region. The high-priority grinding and polishing sub-region searching algorithm generates a new high-priority grinding and polishing sub-region according to the updated redundant material distribution on the surface of the workpiece until the material on the workpiece is removed to reach an ideal depth, and the overall flow chart of the algorithm provided by the invention is shown in fig. 1.
Example 4:
example 4 is a preferred example of example 1, and the present invention will be described in more detail.
As shown in fig. 1, the specific process of this embodiment includes: first, workpiece point cloud information is read from a workpiece CAD file or three-dimensional scanning data. And generating redundant material distribution according to the shape error of the workpiece, and searching for an optimal grinding and polishing subarea according to a high-priority grinding and polishing subarea searching method. And planning the optimal initial path direction, tool residence time (feed speed) and adjacent grinding and polishing path intervals in the extracted sub-area. And respectively carrying out the local workpiece track planning algorithm on the left side and the right side of the initial path until the new path position reaches the left and right boundaries of the sub-region. And then, generating a new high-priority grinding and polishing subarea by the grinding and polishing subarea searching algorithm according to the updated workpiece redundant material distribution, repeating the process until the surface material of the workpiece is removed to reach an ideal depth, and finally outputting an executable file corresponding to the robot system.
Aiming at a workpiece with a complex shape, namely an automobile hub (figure 5), the method provided by the invention is used for planning the track of the grinding and polishing workpiece, and verification is carried out on an actual robot-controlled grinding and polishing system. The method comprises the following specific steps:
step 1: and inputting point cloud information of the workpiece, and searching a high-priority grinding and polishing subarea.
The workpiece point cloud can be obtained by scanning through a three-dimensional CAD model or a three-dimensional scanner. The workpiece point cloud may be represented in the world coordinate system as:
calculating the reward of each subarea on the workpiece:
wherein Re i Is a workpiece point W i P is the sampling density of the workpiece point cloud, and sigma is the standard deviation of the Gaussian kernel function, which is set to 0.5R in the invention I . Assume the tool frame is O T W is the workpiece point i The tool movement cost is defined as:
for each workpiece point its priority index is calculated. The priority indicator comprises a sub-region reward
And tool movement cost Dist ({ O) T },W i ) Calculated from the following formula:
wherein, w m Is a weight coefficient of tool movement cost versus average redundant material depth. Selecting the workpiece point with the highest priority as the central point of the high-priority grinding and polishing sub-area:
the high priority sub-region is given by:
step 2: optimizing initial path direction
The optimal path direction angle θ is defined as the direction containing the most redundant material, and is given as follows:
in the above formula, the first and second carbon atoms are,
measure the nearby workpiece point W of each grinding and polishing path pair k The degree of influence, the metric function of the degree of influence is given by:
and step 3: optimizing the dwell time (feed speed) of the work on the path
Grinding and polishing path x is x n Is represented as
And
sampling the grinding and polishing path from top to bottom, wherein the projection distance interval of sampling points is delta, and the projection of the path sampling points on a local x-y plane is as follows:
the tool pose on the path may be given by:
wherein theta is the included angle between the disc and the tangent plane of the workpiece.
Using MR n Denotes a path x ═ x n Corresponding material removal matrix, matrix elements
Equal to the material removal rate of the ith workpiece point at the jth tool sampling location. Residence time at all sampling path points is noted as
Tool residence time can be found by solving the following constrained linear least squares problem:
s.t.t min ≤T n ≤t max
wherein
Representing a tool residence time difference matrix, t min And t max Indicating workerWith the shortest and longest dwell times at a certain workpiece point.
In a robotic execution file, the feed rate may be obtained by calculating the inverse of the tool residence time, i.e.: v. of f,k n ＝1/t k n 。
And 4, step 4: optimized Path position (Adjacent Path Interval)
Assuming that the nth grinding and polishing path is x ═ x n It has been planned that the distribution of the redundant material before and after polishing along this path is denoted Re (n-1) And Re (n) . The tool moves from the left side to the right side of the grinding and polishing sub-area, and the next optimal path position x needs to be found n+1 From x n To x n+1 The square and mean of the workpiece point redundant material depths in between are minimized:
when searching the next optimal path x ═ x n+1 When calculating the path x ═ x n+1 Still used at the time of dwell time on is along path x ═ x n Depth distribution Re of redundant material before polishing (n-1) . The cost function can be viewed as one minutiae location at x n To x n+1 A single-peak function between, finding the next path position x by golden section method n+1 . The pseudo code is given by algorithm 3.
5) And (5) circulating the step 1 to the step 4, and reducing the error between the removal depth of the surface material of the workpiece and the expected removal depth value after each circulation. The cycle is ended until the surface material of the workpiece is removed to reach the ideal depth, and finally an executable file corresponding to the robot system is output.
6) Results of the experiment
For the hub workpiece and the initial redundant material depth profile set thereon as shown in FIG. 5, a total of 25 polish sub-regions were generated. From the simulation results (fig. 6), it can be seen that the material removal depth at the specified location of the hub reached the desired value of 60 microns. The paths generated by the algorithm in the first 10 polish sub-regions are shown in figure 7. Therefore, the force control grinding and polishing is carried out by using the grinding and polishing tool track planning algorithm, so that the industrial robot can efficiently generate an optimal grinding and polishing path on the curved surface of the complex workpiece, and the processing precision is improved.
Those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and various modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps such that the systems, apparatus, and various modules thereof are provided in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.
The foregoing description has described specific embodiments of the present invention. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (10)
1. A tool track offline programming method for a robot constant-force grinding and polishing process is characterized by comprising the following steps:
step S1: establishing and calibrating a numerical contact force model and a material removal model of a tool workpiece;
step S2: iteratively searching a grinding and polishing subarea with high priority according to the distribution of redundant materials;
step S3: planning an optimal initial path direction, optimal tool residence time and optimal adjacent grinding and polishing path intervals in the extracted sub-regions through a material removal model;
and repeatedly executing the steps S1 to S3 until the surface material of the workpiece is removed to a preset depth, and outputting an executable motion command corresponding to the robot system.
2. The off-line tool trajectory programming method for the robot constant-force grinding and polishing process as claimed in claim 1, wherein in the step S1:
the numerical contact force model expresses the curved surface of the workpiece as discrete point cloud, and the contact pressure distribution on the point cloud of the workpiece under constant grinding and polishing force is calculated based on the nonlinear stress-strain relation and the point-surface numerical distance formula;
the material removal model predicts the material removal depth generated when the grinding and polishing tool feeds on the workpiece point cloud according to the numerical contact force model;
the workpiece point cloud is obtained by scanning through a three-dimensional CAD model or a three-dimensional scanner
Expressed in the world coordinate system as:
where N is the number of workpiece sampling points, W k Is the kth workpiece sampling point, x k Is the x-coordinate, y, of the workpiece sampling point k Is the y coordinate, z, of the workpiece sampling point k Is the z coordinate of the workpiece sampling point;
the grinding and polishing tool is arranged at the tail end of the robot, the robot applies positive pressure along the normal direction of the workpiece to the workpiece through the grinding and polishing tool, the positive pressure along the normal direction of the workpiece is normal contact force, the grinding and polishing tool is driven by a main shaft to rotate at high speed and is used for removing redundant materials on the surface of the workpiece, the grinding and polishing tool consists of I virtual springs vertical to the bottom surface of a grinding and polishing disc, and the normal contact force is calculated as the weighted sum of the pressures of all discrete disc points:
wherein, F N The normal contact force is shown as I, the number of discrete virtual springs is shown as I, and the thickness of the grinding and polishing disk is shown as H;
the contact pressure distribution is based on a non-linear stress-strain relationship:
calculating to obtain;
wherein h is i Is the contact depth of the ith discrete point on the disk, p i Is the contact pressure at the ith discrete point, E is defined as the modulus of the nonlinear material, beta is defined as the stress-strain power exponent, determined by tool loading experiments, and deltaS i Is the area of a discrete cell on the disc tool;
normal contact force maintained at F d Maximum contact depth h 0 The contact pressure distribution is calculated according to the stress-strain relation and the iteration solution on the tool frame { O ] is obtained through the estimation of a numerical contact force model T Maximum contact depth h at 0 。
3. The off-line tool trajectory programming method for the robot constant-force grinding and polishing process as claimed in claim 1, wherein in the step S2:
the sub-region is a workpiece point cloud neighborhood which meets space distance and normal change limitation;
the priority index is the depth weighted sum of redundant materials in the sub-region with a Gaussian kernel function as weight;
the subregion searching method selects the workpiece point with the maximum priority index as the central point of the high-priority grinding and polishing subregion;
the grinding and polishing sub-area is defined as a workpiece point W i All to the center point W i Is less than R I Set of workpiece points of (a):
Subregion i ＝{W k |Dist(W i ,W k )≤R I }
wherein, Subreglion i Denotes the ith sub-region, R I Defining the radius of interest as a parameter selected manually; dist represents a direction weighted distance function defined as follows:
wherein the content of the first and second substances,
represents a workpiece point W k In the direction of the normal of the (c),
represents a workpiece point W i In the normal direction of (a), w o Is the weight coefficient of the normal change of the workpiece point relative to the change of the position of the workpiece point, and the weight coefficient is given by Dist (W) i ,W k ) Given as the gaussian kernel function of the argument:
wherein Re i Is a workpiece point W i P is the sampling density of the workpiece point cloud, sigma is the standard deviation of the Gaussian kernel function, and sigma is alpha R I The value of alpha is in a preset interval; as the machining efficiency needs to be considered when positioning the grinding and polishing subareas, the tool frame is assumed to be O T W is the workpiece point i Tool movement cost Dist ({ O) T },W i ) Is defined as:
wherein n is T Indicating grinding or polishing discsAn axial direction, the priority index being defined at each sampled workpiece point; the priority index includes two parts: the first part is the mean redundant material depth and the second part reflects the tool movement cost;
wherein, the color i Indicating the priority index of the ith sub-region, w m A weight coefficient that is a tool movement cost relative to an average redundant material depth; selecting the workpiece point with the highest priority as the central point of the high-priority grinding and polishing sub-area:
wherein, the CenterIndex * A center point index representing a high priority polish sub-region;
the high priority sub-region is thus defined as follows:
wherein, Subreglion * Representing the generated high-priority grinding and polishing subarea;
in each generated high-priority grinding and polishing subarea, a grinding and polishing mode of parallel paths is selected, the path direction is parallel to the y axis, and the variables to be optimized have the direction angle theta and the position x of the path n And the time T of tool residence on each path n 。
4. The off-line tool trajectory programming method for the robot constant-force grinding and polishing process as claimed in claim 1, wherein in the step S3:
the optimal initial path direction is the direction selected to cover the most redundant material in the sub-region;
the optimal tool residence time is obtained by solving a linear least square problem which takes the depth minimization of redundant materials near a grinding and polishing path as a target and takes the feeding speed and the speed change of the robot as constraints by using a material removal model;
the optimal adjacent grinding and polishing path interval is obtained by solving a unimodal function extreme value problem which takes the minimization of the mean square error of the depth of the redundant materials between the adjacent paths as a target.
5. The tool trajectory offline programming method for the robot constant-force grinding and polishing process as recited in claim 4, wherein:
the optimal path direction angle θ is defined as the direction containing the most redundant material, and the formula is as follows:
wherein, theta * Indicating the optimum path direction angle, Re k Representing a redundant material depth for a kth workpiece point;
measure the nearby workpiece point W of each grinding and polishing path pair k The degree of influence, the metric function of the degree of influence is given by:
wherein Φ (x) represents the removal profile function defined by the above equation, and w represents the width of the polishing path;
the grinding and polishing path x is x n Is represented as
And
sampling the grinding and polishing path from top to bottom, wherein the projection distance interval of sampling points is delta, and the projection of the path sampling points on a local x-y plane is given by the following formula:
the tool axis lies in the same plane as the plane defined by the tool feed direction and the approximate workpiece normal, for each sample path point
Attitude of tool
Given by:
wherein theta is the included angle between the disc and the tangent plane of the workpiece,
is the normal direction of the jth path point, f is the tool feed direction, and R is the tool radius;
by MR n Denotes a path x ═ x n Corresponding material removal matrix, matrix elements
Equal to the material removal rate of the ith workpiece point at the jth tool sampling location; residence time T at all the sampling path points n Is recorded as:
t i (i＝1,2,…,|Q n i) is the tool on the ith pathDwell time of a point, | Q n L is the sampling number of the path point; the material removal depth is equal to the MR n ·T n ；
Tool dwell time since the purpose of planning tool dwell time is to remove all redundant material
Obtained by solving the following constrained linear least squares problem:
s.t.t min ≤T n ≤t max
wherein, t min And t max Representing the shortest and longest dwell times of the tool at a certain workpiece point; in the robot motion command, the feed speed can be obtained by calculating the inverse of the tool residence time, i.e.: v. of f,k n ＝1/t k n ；
Adding the feed rate variation limit as an additional constraint to the above equation yields:
s.t.t min ≤T n ≤t max
wherein
Representing a tool residence time difference matrix;
the n-th grinding and polishing path is x ═ x n After planning, the redundant material distribution before and after polishing along the path is recorded as Re (n-1) And Re (n) The tool moves from the left side to the right side of the grinding and polishing sub-area, and the next optimal path position x needs to be found n+1 From x n To x n+1 Workpiece point in betweenThe square and mean of the redundant material depth is minimized:
wherein x is n+1 * For the next optimal grinding and polishing path position, L is the variance of the redundant material distribution;
when searching the next optimal path x ═ x n+1 When calculating the path x ═ x n+1 Still used at the time of dwell time on is along path x ═ x n Depth distribution Re of redundant material before polishing (n-1) Regarding the cost function as a minimum point position at x n To x n+1 A single-peak function between, finding the next path position x by golden section method n+1 ；
And the high-priority grinding and polishing subarea searching algorithm generates a new high-priority grinding and polishing subarea according to the updated redundant material distribution on the surface of the workpiece until the material on the workpiece is removed to reach the ideal depth.
6. A tool track offline programming system for a robot constant-force grinding and polishing process is characterized by comprising:
module M1: establishing and calibrating a numerical contact force model and a material removal model of a tool workpiece;
module M2: iteratively searching a grinding and polishing subarea with high priority according to the distribution of redundant materials;
module M3: planning an optimal initial path direction, optimal tool residence time and optimal adjacent grinding and polishing path intervals in the extracted sub-regions through a material removal model;
and repeatedly triggering the module M1 to the module M3 until the surface material of the workpiece is removed to a preset depth, and outputting an executable motion command corresponding to the robot system.
7. The off-line tool trajectory programming system for a robotic constant-force polish process of claim 6, wherein in said module M1:
the numerical contact force model expresses the curved surface of the workpiece as discrete point cloud, and the contact pressure distribution on the point cloud of the workpiece under constant grinding and polishing force is calculated based on the nonlinear stress-strain relation and the point-surface numerical distance formula;
the material removal model predicts the material removal depth generated when the grinding and polishing tool feeds on the workpiece point cloud according to the numerical contact force model;
the workpiece point cloud is obtained by scanning through a three-dimensional CAD model or a three-dimensional scanner
Expressed in the world coordinate system as:
where N is the number of workpiece sampling points, W k Is the kth workpiece sampling point, x k Is the x-coordinate, y, of the workpiece sampling point k Is the y coordinate, z, of the workpiece sampling point k A z coordinate of a workpiece sampling point;
the grinding and polishing tool is arranged at the tail end of the robot, the robot applies positive pressure along the normal direction of the workpiece to the workpiece through the grinding and polishing tool, the positive pressure along the normal direction of the workpiece is normal contact force, the grinding and polishing tool is driven by a main shaft to rotate at high speed and is used for removing redundant materials on the surface of the workpiece, the grinding and polishing tool consists of I virtual springs vertical to the bottom surface of a grinding and polishing disc, and the normal contact force is calculated as the weighted sum of the pressures of all discrete disc points:
wherein, F N The normal contact force is shown as I, the number of discrete virtual springs is shown as I, and the thickness of the grinding and polishing disk is shown as H;
the contact pressure distribution is based on a non-linear stress-strain relationship:
calculating to obtain;
wherein h is i Is the contact depth of the ith discrete point on the disk, p i Is the contact pressure at the ith discrete point, E is defined as the modulus of the nonlinear material, beta is defined as the stress-strain power exponent, determined by tool loading experiments, and deltaS i Is the area of a discrete cell on the disc tool;
the normal contact force is maintained at F d Maximum contact depth h 0 The contact force is obtained according to the estimation of a numerical contact force model, the contact pressure distribution is calculated according to the stress-strain relation, and the tool frame { O } is iteratively solved through a Newton secant method T Maximum contact depth h at 0 。
8. The off-line tool trajectory programming system for a robotic constant-force polish process of claim 6, wherein in said module M2:
the sub-region is a workpiece point cloud neighborhood which meets space distance and normal change limitation;
the priority index is the depth weighted sum of redundant materials in the sub-region with a Gaussian kernel function as weight;
selecting a workpiece point with the maximum priority index as a central point of a high-priority grinding and polishing subarea by the subarea searching method;
the grinding and polishing sub-area is defined as a workpiece point W i All to the center point W i Is less than R I Set of workpiece points of (a):
Subregion i ＝{W k |Dist(W i ,W k )≤R I }
wherein, Subreglion i Denotes the ith sub-region, R I Defining the radius of interest as a parameter selected manually; dist represents a direction weighted distance function defined as follows:
wherein the content of the first and second substances,
represents a workpiece point W k In the direction of the normal of the (c),
represents a workpiece point W i In the normal direction of (a), w o Is the weight coefficient of the normal change of the workpiece point relative to the change of the position of the workpiece point, and the weight coefficient is given by Dist (W) i ,W k ) Given as the gaussian kernel function of the argument:
wherein, Re i Is a workpiece point W i P is the sampling density of the workpiece point cloud, sigma is the standard deviation of the Gaussian kernel function, and sigma is alpha R I The value of alpha is in a preset interval; as the machining efficiency needs to be considered when positioning the grinding and polishing subareas, the tool frame is assumed to be O T W is the workpiece point i Tool movement cost Dist ({ O) T },W i ) Is defined as:
wherein n is T Representing the axial direction of the polishing disc, the priority index being defined at each sampled workpiece point; the priority index includes two parts: the first part being an averageRedundant material depth, the second part reflects tool movement cost;
wherein, the color i Indicating the priority index of the ith sub-region, w m A weight coefficient that is a tool movement cost relative to an average redundant material depth; selecting the workpiece point with the highest priority as the central point of the high-priority grinding and polishing sub-area:
wherein, the CenterIndex * A center point index representing a high priority polish sub-region;
the high priority sub-region is thus defined as follows:
wherein, Subreglion * Representing the generated high-priority grinding and polishing subarea;
in each generated high-priority grinding and polishing subarea, a grinding and polishing mode of parallel paths is selected, the path direction is parallel to the y axis, and the variables to be optimized have the direction angle theta and the position x of the path n And the time T of tool residence on each path n 。
9. The off-line tool trajectory programming system for a robotic constant-force polish process of claim 6, wherein in said module M3:
the optimal initial path direction is the direction selected to cover the most redundant material in the sub-region;
the optimal tool residence time is obtained by solving a linear least square problem which takes the depth minimization of redundant materials near a grinding and polishing path as a target and takes the feeding speed and the speed change of the robot as constraints by using a material removal model;
the optimal adjacent grinding and polishing path interval is obtained by solving a unimodal function extreme value problem which takes the minimization of the mean square error of the depth of the redundant materials between the adjacent paths as a target.
10. The robot-constant-force grinding and polishing process-oriented tool trajectory offline programming system of claim 9, wherein:
the optimal path direction angle θ is defined as the direction containing the most redundant material, and the formula is as follows:
wherein, theta * Represents the optimal path direction angle, Re k Representing a redundant material depth for a kth workpiece point;
measure the nearby workpiece point W of each grinding and polishing path pair k The degree of influence, the metric function of the degree of influence is given by:
wherein Φ (x) represents the removal profile function defined by the above equation, and w represents the width of the polishing path;
the grinding and polishing path x is x n Is represented as
And
sampling the grinding and polishing path from top to bottom, wherein the projection distance interval of sampling points is delta, and the projection distance of path sampling points on a local x-y planeThe shadow is given by:
the tool axis lies in the same plane as the plane defined by the tool feed direction and the approximate workpiece normal, for each sample path point
Attitude of tool
Given by:
wherein theta is the included angle between the disc and the tangent plane of the workpiece,
is the normal direction of the jth path point, f is the tool feed direction, and R is the tool radius;
by MR n Denotes a path x ═ x n Corresponding material removal matrix, matrix elements
Equal to the material removal rate of the ith workpiece point at the jth tool sampling location; residence time T at all the sampling path points n Is recorded as:
t i (i＝1,2,…,|Q n |) is the tool's dwell time at the ith path point, | Q n L is the sampling number of the path point; the material removal depth is equal to the MR n ·T n ；
Tool dwell time since the purpose of planning tool dwell time is to remove all redundant material
Obtained by solving the following constrained linear least squares problem:
s.t.t min ≤T n ≤t max
wherein, t min And t max Representing the shortest and longest dwell times of the tool at a certain workpiece point; in the robot motion command, the feed speed can be obtained by calculating the inverse of the tool residence time, i.e.: v. of f,k n ＝1/t k n ；
Adding the feed rate variation limit as an additional constraint to the above equation yields:
s.t.t min ≤T n ≤t max
wherein
Representing a tool residence time difference matrix;
the n-th grinding and polishing path is x ═ x n After planning, the redundant material distribution before and after polishing along the path is recorded as Re (n-1) And Re (n) The tool moves from the left side to the right side of the grinding and polishing sub-area, and the next optimal path position x needs to be found n+1 From x n To x n+1 The square sum mean of the workpiece point redundant material depths in between is minimized:
wherein x is n+1 * For the next optimal grinding and polishing path position, L is the variance of the redundant material distribution;
when searching the next optimal path x ═ x n+1 When calculating the path x ═ x n+1 Still used at the time of dwell time on is along path x ═ x n Depth distribution Re of redundant material before polishing (n-1) Regarding the cost function as a minimum point position at x n To x n+1 A single-peak function between, finding the next path position x by golden section method n+1 ；
And the high-priority grinding and polishing subarea searching algorithm generates a new high-priority grinding and polishing subarea according to the updated redundant material distribution on the surface of the workpiece until the material on the workpiece is removed to reach the ideal depth.
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