CN114896773A - Method and device for designing bearing clamp moving block of ultrasonic grinder and storage medium - Google Patents
Method and device for designing bearing clamp moving block of ultrasonic grinder and storage medium Download PDFInfo
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Abstract
The embodiment of the specification provides a method and a device for designing a moving block of a bearing clamp of an ultrasonic grinder and a storage medium, wherein the method comprises the following steps: determining a B spline curve of the curved surface of the bearing ring clamp according to the outer surface of the processed workpiece; determining a B spline curved surface of the bearing ring clamp according to the B spline curved surface of the bearing ring clamp; determining a mathematical model adaptive to the outer surface of the processed test piece according to a B spline surface of the curved surface of the bearing ring clamp; and solving a corresponding objective function according to the mathematical model so as to calculate and obtain the optimal solution of the bearing clamp movable block matched with the processed workpiece.
Description
Technical Field
The document relates to the technical field of computers, in particular to a method and a device for designing a moving block of a bearing clamp of an ultrasonic grinding machine and a storage medium.
Background
The conventional ultrasonic strengthening grinding machine can only process bearings which are convenient to clamp and are symmetrical at two sides like cylindrical roller bearings, cannot process tapered roller bearings or other irregular bearings which are inconvenient to clamp, has important research significance in reality like tapered roller bearings or other irregular bearings, and needs to strengthen grinding to research the properties of the bearings so as to improve the surface performance of the bearings.
Disclosure of Invention
The invention aims to provide a method and a device for designing a bearing clamp moving block of an ultrasonic grinder and a storage medium, and aims to solve the problems in the prior art.
The invention provides a design method of a bearing clamp moving block of an ultrasonic grinder, which comprises the following steps:
determining a B spline curve of the curved surface of the bearing ring clamp according to the outer surface of the processed workpiece;
determining a B spline curved surface of the bearing ring clamp according to the B spline curved surface of the bearing ring clamp;
determining a mathematical model adaptive to the outer surface of the processed test piece according to a B spline surface of the curved surface of the bearing ring clamp;
and solving a corresponding objective function according to the mathematical model so as to calculate and obtain the optimal solution of the bearing clamp movable block matched with the processed workpiece.
The invention provides a bearing clamp moving block design device of an ultrasonic grinder, which comprises:
the first determining module is used for determining a B-spline curve of the curved surface of the bearing ring clamp according to the outer surface of the processed workpiece;
the second determining module is used for determining the B spline curved surface of the bearing ring clamp according to the B spline curve of the curved surface of the bearing ring clamp;
the third determining module is used for determining a mathematical model adaptive to the outer surface of the processed test piece according to a B spline surface of the bearing ring clamp surface;
and the solving module is used for solving a corresponding objective function according to the mathematical model so as to calculate and obtain the optimal solution of the bearing clamp moving block matched with the processed workpiece.
The embodiment of the invention also provides a device for designing the moving block of the bearing clamp of the ultrasonic grinder, which comprises: the design method comprises the following steps of a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the computer program realizes the steps of the design method of the bearing clamp movable block of the ultrasonic grinding machine when being executed by the processor.
The embodiment of the invention also provides a computer readable storage medium, wherein an implementation program for information transmission is stored on the computer readable storage medium, and the program is executed by a processor to realize the steps of the design method for the bearing clamp moving block of the ultrasonic grinding machine.
By adopting the embodiment of the invention, the bearing ring clamp matched with the processed test piece can be intelligently designed based on the B-spline surface according to the processed test piece, so that the ultrasonic strengthening grinding machine can process a plurality of important bearings such as tapered roller bearings except cylindrical roller bearings by one hundred percent. By the method, various bearing ring clamps corresponding to the processed workpiece (bearing) can be intelligently processed.
Drawings
In order to more clearly illustrate one or more embodiments or prior art solutions of the present specification, the drawings that are needed in the description of the embodiments or prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present specification, and that other drawings can be obtained by those skilled in the art without inventive exercise.
FIG. 1 is a flow chart of a method of designing a bearing clamp moving block for an ultrasonic grinder in accordance with an embodiment of the present invention;
FIG. 2 is a first schematic view of a bearing ring fixture of an embodiment of the present invention;
FIG. 3 is a second schematic view of a bearing ring fixture of an embodiment of the present invention;
FIG. 4 is a third schematic view of a bearing ring fixture of an embodiment of the present invention;
FIG. 5 is a schematic diagram of a triangulation calculation format according to an embodiment of the invention;
FIG. 6 is a schematic diagram of a device for designing a moving block of a bearing clamp of an ultrasonic grinding machine according to a first embodiment of the present invention;
FIG. 7 is a schematic diagram of a device for designing a moving block of a bearing clamp of an ultrasonic grinder according to a second embodiment of the present invention.
Detailed Description
In order to solve the problems in the prior art, the embodiment of the invention designs a bearing clamp-moving block matched with a processed test piece (bearing) based on response curved surface intelligence, so that the strengthening grinding machine can be enabled to efficiently remove and process tapered roller bearings or other important irregular bearings except cylindrical roller bearings.
In order to make those skilled in the art better understand the technical solutions in one or more embodiments of the present disclosure, the technical solutions in one or more embodiments of the present disclosure will be clearly and completely described below with reference to the drawings in one or more embodiments of the present disclosure, and it is obvious that the described embodiments are only a part of the embodiments of the present disclosure, and not all embodiments. All other embodiments that can be derived by a person skilled in the art from one or more of the embodiments described herein without making any inventive step shall fall within the scope of protection of this document.
Method embodiment
According to an embodiment of the present invention, a method for designing a moving block of a bearing fixture of an ultrasonic grinding machine is provided, fig. 1 is a flowchart of the method for designing a moving block of a bearing fixture of an ultrasonic grinding machine according to an embodiment of the present invention, as shown in fig. 1, the method for designing a moving block of a bearing fixture of an ultrasonic grinding machine according to an embodiment of the present invention specifically includes:
step 101, determining a B-spline curve of the curved surface of the bearing ring clamp according to the outer surface of a processed workpiece; step 101 specifically includes:
given n +1 control points P 0 ，P 1 ，…，P n And one node vector U ═ U 0 ，u 1 ，…，u m The p-th order B-spline curve is defined by the control points and the node vector U, and N is set i And p (u) is the ith p-th B-spline basis function, then the p-th B-spline curve is determined according to equation 1:
wherein a node vector is defined as a set of m +1 non-decreasing numbers, U 0 ≤u 1 ≤u 2 …≤ u m ，u i Is a node;
recursively defining N according to equations 2 and 3 i P (u), where any p-th order spline consists of a linear combination of two adjacent p-1 th order splines:
wherein 0/0 is 0, p represents the power of the spline, and the subscript i represents the serial number of the B-spline;
calculating N according to trigonometric calculation formats i ，p(u)。
102, determining a B-spline curved surface of the bearing ring clamp according to the B-spline curved surface of the bearing ring clamp; step 102 specifically includes:
forming a control grid by (m +1) × (n +1) control points, and determining parameter node vectors in two directions according to a formula 4 and a formula 5;
U＝[u 0 ，u 1 ，…，u m+k+1 ]formula 4;
V＝[v 0 ，v 1 ，…，v m+l+1 ]equation 5;
determining a B-spline surface equation according to formula 6:
wherein u is k ≤u≤u m+l ，v l ≤v≤v n+l ，P i，j Is a control point set P i，j I.e. (i ═ 0, 1, …, m; j ═ 0, 1, …, N), i.e. the set of points in the three-dimensional point cloud, N i，k (u) and N j，l (v) Is a B-spline surface basis function;
and B spline surface fitting is carried out according to the control points, and surface reconstruction based on the B spline curve is carried out.
And calculating the coefficients of the curved B spline surface equation after fitting.
B spline surface fitting is carried out according to the control points, and surface reconstruction based on a B spline curve specifically comprises the following steps:
initializing a B spline surface by using Principal Component Analysis (PCA);
fitting and iterative optimization are carried out on the initialized B spline surface;
initializing the B-spline curve by using a circle;
fitting the initialized B spline curve;
performing a trigonometric calculation format on the B spline curved surface obtained by fitting to obtain a final curved surface model of the B spline curve;
the step of fitting the initialized B-spline curve specifically comprises the following steps:
given (r +1). (s +1) known points { Q k，l 0, 1, …, r; 0, 1, …, r is constructed with a { p, q } sub-surface of (n +1) · (m +1) control points to approximate fit these known points;
parameterization is performed, and a node vector is calculated according to the formula 7-9:
u 0 ＝…＝u p 0, equation 7;
u m-p ＝…＝u m 1, formula 8;
wherein j is 1, …, n-p, I is int (jd), α is jd-I, d is (r +1)/(n-p + 1);
calculating a control point: known points Q for a row in the u direction (s +1) k，0 ，…，Q k，r Performing curve approximation fitting to obtain control vertex R of (s +1) line k，0 ，…，R k，n For the known point R of the (n +1) column in the v direction 0，l ，…，R s，l Performing curve approximation fitting to obtain control vertex P of (n +1) line 0，l ，…，P n，l 。
Calculating the coefficients of the curved B-spline surface equation after fitting specifically comprises:
fix j for P i，j I is 0, 1, …, m; j is 0, 1, …, n, and control vertexes of n +1 parameter curves are respectively obtained along the u direction;
fix i for P i，j i is 0, 1, …, m; when j is 0, 1, …, n, control vertexes of m +1 parameter curves are obtained along the v direction.
103, determining a mathematical model adaptive to the outer surface of the processed test piece according to a B spline surface of the bearing ring clamp surface;
and 104, solving a corresponding objective function according to the mathematical model so as to calculate and obtain an optimal solution of the bearing clamp movable block matched with the machined workpiece.
Finally, in the embodiment of the invention, the processed workpiece can be projected to a three-dimensional space according to the optimal solution, and a bearing clamp moving block matched with the processed workpiece is manufactured by adopting a processing method of electric spark or numerical control milling.
The embodiment of the invention intelligently designs a bearing clamp-moving block matched with a processed test piece (bearing) based on a B spline surface, so that a reinforced grinding machine can efficiently process tapered roller bearings or other important irregular bearings except cylindrical roller bearings.
As shown in fig. 2, 3 and 4, 1 denotes a tapered roller bearing, 2 denotes a bearing ring holder, and 3 denotes an ultrasonic horn. If the processed test piece is a tapered roller bearing, firstly, a proper mathematical model is established according to the outer surface of the tapered roller bearing to be processed, and the specific method is as follows:
given n +1 control points, P 0 ，P 1 ，…，P n And one node vector U ═ U 0 ，u 1 ，…，u m The p-th order B-spline curve is defined by the control points and the node vector U, and N is set i P (u) is the ith p-th B-spline basis function, the formula of the p-th B-spline curve is
Wherein the node vector is defined as if U is a set of m +1 non-decreasing numbers, U 0 ≤u 1 ≤u 2 …≤u m 。u i Called nodes (hits) and the set U is called node vectors (hit vectors). And the order p of the base function, the ith p-th B-spline base function N i P (u) recursion is defined as
Here, 0/0 is defined as 0. Where p represents the power of the spline and the subscript i represents the B-spline index. The recursion formula shows that any p-th order spline can be made up of a linear combination of two adjacent p-1 th order splines. The calculation of Ni, p (u), can be based on the trigonometric calculation format shown in FIG. 5. And then, the B spline surface is formed by constructing a plurality of B spline curves in U and v directions for a plurality of times, a control grid is formed by (m +1) × (n +1) control points, and the parameter node vectors in the two directions are respectively U ═ U [, U ═ 1 [ ] 0 ，u 1 ，…，u m+k+1 ]，V＝[v 0 ，v 1 ，…，v m+l+1 ]. The equation for a B-spline surface is defined as follows
Wherein P is i，j Is a control point set P i，j I.e. (i ═ 0, 1, …, m; (j ═ 0, 1, …, n)), that is, the set of points (local) in the three-dimensional point cloud. N is a radical of i，k (u) and N j，l (v) Is a B-spline surface basis function. The surface reconstruction based on the B-spline curve is essentially to perform B-spline surface fitting according to the control points.
The steps of solving the coefficient of the curved surface equation after fitting are as follows:
fix j for P i，j And (i is 0, 1, …, m, j is 0, 1, …, n) respectively obtaining control vertexes of the n +1 parameter curves along the u direction.
Fix i for P i，j And (i is 0, 1, …, m, j is 0, 1, …, n) respectively finding control vertexes of m +1 parameter curves along the v direction.
The fitting procedure was as follows:
given (r +1). (s +1) known points { Q k，l 0, 1, …, r; l-0, 1, …, r constructs a { p, q } sub-surface with (n +1) · (m +1) control points to approximate fit these known points.
1. Parameterization
2. Solving node vector and solving formulas of internal nodes are different (u direction) u 0 ＝…＝u p ＝0， u m-p ＝…＝u m ＝1
I＝int(jd)α＝jd-i d＝(r+1)/(n-p+1)
3. Control point calculation
It needs to be solved by replacing it with a multiple approximation fit to a curve
First, the known point Q of the u direction (s +1) line k，0 ，…，Q k，r Performing curve approximation fitting to obtain control vertex R of (s +1) line k，0 ，…，R k，n ；
Then for the known point R of the (n +1) column in the v direction 0，l ，…，R s，l Performing curve approximation fitting to obtain control vertex P of (n +1) line 0，l ，…，P n，l ；
The algorithm flow of the curved surface reconstruction based on the B spline curve is as follows:
1. b-spline surfaces are initialized using Principal Component Analysis (PCA).
2. And fitting and iterative optimization are carried out on the initialized B spline surface.
3. The B-spline curve is initialized with a circle.
4. And fitting the initialized B spline curve.
5. And triangularizing the B spline surface obtained by fitting (as shown in FIG. 5) to obtain a final surface model.
Further, the corresponding objective function is solved according to the mathematical model, so that the optimal solution is calculated, and then a bearing clamp-movable block matched with the processed test piece (bearing) is made. The bearing ring clamp can intelligently process a plurality of bearing clamp-movable blocks corresponding to corresponding processed test pieces (bearings), ensures that the processed test pieces are covered by one hundred percent of the sprayed materials of the ultrasonic strengthening grinding machine, and can improve the experimental accuracy of various materials.
In summary, the embodiment of the invention can intelligently design a bearing ring clamp matched with a processed test piece based on a B-spline surface, so that the ultrasonic strengthening grinding machine can process a plurality of important bearings such as tapered roller bearings besides cylindrical roller bearings by a hundred percent coverage. By the method, various bearing ring clamps corresponding to the processed workpiece (bearing) can be intelligently processed.
Apparatus embodiment one
According to an embodiment of the present invention, there is provided an apparatus for designing a moving block of a bearing fixture of an ultrasonic grinding machine, fig. 6 is a schematic diagram of the apparatus for designing a moving block of a bearing fixture of an ultrasonic grinding machine according to an embodiment of the present invention, and as shown in fig. 6, the apparatus for designing a moving block of a bearing fixture of an ultrasonic grinding machine according to an embodiment of the present invention specifically includes:
the first determining module 60 is used for determining a B spline curve of the curved surface of the bearing ring clamp according to the outer surface of the processed workpiece; the first determining module 60 is specifically configured to:
given n +1 control points P 0 ，P 1 ，…，P n And one node vector U ═ U 0 ，u 1 ，…，u m The p-th order B-spline curve is defined by the control points and the node vector U, and N is set i And p (u) is the ith p-th B-spline basis function, then the p-th B-spline curve is determined according to equation 1:
wherein a node vector is defined as a set of m +1 non-decreasing numbers, U 0 ≤u 1 ≤u 2 …≤ u m ，u i Is a node;
recursively defining N according to equations 2 and 3 i P (u), where any p-th order spline consists of a linear combination of two adjacent p-1 th order splines:
wherein 0/0 is 0, p represents the power of the spline, and the subscript i represents the serial number of the B-spline;
calculating N according to trigonometric calculation formats i ，p(u)；
A second determining module 62, configured to determine a B-spline curved surface of the bearing ring fixture curved surface according to the B-spline curve of the bearing ring fixture curved surface; the second determining module 62 is specifically configured to:
forming a control grid by (m +1) × (n +1) control points, and determining parameter node vectors in two directions according to a formula 4 and a formula 5;
U＝[u 0 ，u 1 ，…，u m+k+1 ]formula 4;
V＝[v 0 ，v 1 ，…，v m+l+1 ]equation 5;
determining a B-spline surface equation according to formula 6:
wherein u is k ≤u≤u m+l ，v l ≤v≤v n+l ，P i，j Is a control point set P i，j I.e. (i ═ 0, 1, …, m; j ═ 0, 1, …, N), i.e. the set of points in the three-dimensional point cloud, N i，k (u) and N j，l (v) Is a B-spline surface basis function;
and B spline surface fitting is carried out according to the control points, and surface reconstruction based on the B spline curve is carried out.
And calculating the coefficients of the curved B spline surface equation after fitting.
Wherein, carrying out B-spline surface fitting according to the control points, and carrying out surface reconstruction based on the B-spline curve comprises:
initializing a B spline surface by using Principal Component Analysis (PCA);
fitting and iterative optimization are carried out on the initialized B spline surface;
initializing the B-spline curve by using a circle;
fitting the initialized B spline curve;
performing a trigonometric calculation format on the B spline curved surface obtained by fitting to obtain a final curved surface model of the B spline curve;
the fitting of the initialized B-spline curve specifically comprises the following steps:
given (r +1). (s +1) known points { Q k，l 0, 1, …, r; 1-0, 1, …, r a { p, q } secondary surface constructed with (n +1). (m +1) control points to approximate fit these known points;
parameterization is performed, and a node vector is calculated according to the formula 7-9:
u 0 ＝…＝u p 0, equation 7;
u m-p ＝…＝u m 1, formula 8;
wherein j is 1, …, n-p, I is int (jd), α is jd-I, d is (r +1)/(n-p + 1);
calculating a control point: known points Q for a row in the u direction (s +1) k，0 ，…，Q k，r Performing curve approximation fitting to obtain control vertex R of (s +1) line k，0 ，…，R k，n For the known point R of the (n +1) column in the v direction 0，l ，…，R s，l Performing curve approximation fitting to obtain control vertex P of (n +1) line 0，l ，…，P n，l ；
Wherein calculating the coefficients of the curved B-spline surface equation after fitting specifically comprises:
fix j for P i，j I is 0, 1, …, m; j is 0, 1, …, n, and control vertexes of n +1 parameter curves are respectively obtained along the u direction;
fix i for P i，j i is 0, 1, …, m; when j is 0, 1, …, n, control vertexes of m +1 parameter curves are obtained along the v direction.
A third determining module 64, configured to determine, according to a B-spline surface of the bearing ring fixture curved surface, a mathematical model that is adapted to the outer surface of the processed test piece;
and the solving module 66 is used for solving a corresponding objective function according to the mathematical model so as to calculate an optimal solution of the bearing clamp movable block matched with the machined workpiece.
Preferably, the above apparatus further comprises:
and the manufacturing module is used for projecting the machined workpiece to a three-dimensional space according to the optimal solution, and manufacturing a bearing clamp moving block matched with the machined workpiece by adopting a machining method of electric spark or numerical control milling.
The embodiment of the present invention is an apparatus embodiment corresponding to the above method embodiment, and specific operations of each module may be understood with reference to the description of the method embodiment, which is not described herein again.
Device embodiment II
The embodiment of the invention provides a device for designing a bearing clamp moving block of an ultrasonic grinder, as shown in fig. 7, comprising: a memory 70, a processor 72 and a computer program stored on the memory 70 and executable on the processor 72, which computer program when executed by the processor 72 performs the steps as described in the method embodiments.
Device embodiment III
An embodiment of the present invention provides a computer-readable storage medium, on which an implementation program for information transmission is stored, and the program, when executed by a processor 72, implements the steps as described in the method embodiment.
The computer-readable storage medium of the embodiment includes, but is not limited to: ROM, RAM, magnetic or optical disks, and the like.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. A design method for a bearing clamp moving block of an ultrasonic grinder is characterized by comprising the following steps:
determining a B spline curve of the curved surface of the bearing ring clamp according to the outer surface of the processed workpiece;
determining a B spline curved surface of the bearing ring clamp according to the B spline curved surface of the bearing ring clamp;
determining a mathematical model adaptive to the outer surface of the processed test piece according to a B spline surface of the curved surface of the bearing ring clamp;
and solving a corresponding objective function according to the mathematical model so as to calculate and obtain the optimal solution of the bearing clamp movable block matched with the processed workpiece.
2. The method of claim 1, wherein determining the B-spline curve of the bearing ring fixture surface from the outer surface of the work piece specifically comprises:
given n +1 control points P 0 ，P 1 ，…，P n And one node vector U ═ U 0 ，u 1 ，…，u m The p-th order B-spline curve is defined by the control points and the node vector U, and N is set i And p (u) is the ith p-th B-spline basis function, then the p-th B-spline curve is determined according to equation 1:
wherein a node vector is defined as a set of m +1 non-decreasing numbers, U 0 ≤u 1 ≤u 2 …≤u m ，u i Is a node;
recursively defining N according to equations 2 and 3 i P (u), where any p-th order spline consists of a linear combination of two adjacent p-1 th order splines:
wherein 0/0 is 0, p represents the power of the spline, and the subscript i represents the serial number of the B-spline;
calculating N according to the trigonometric calculation format i ，p(u)。
3. The method of claim 1, wherein determining the B-spline surface of the bearing ring fixture surface from the B-spline curve of the bearing ring fixture surface specifically comprises:
forming a control grid by (m +1) × (n +1) control points, and determining parameter node vectors in two directions according to a formula 4 and a formula 5;
U＝[u 0 ，u 1 ，…，u m+k+1 ]formula 4;
V＝[v 0 ，v 1 ，…，v m+l+1 ]equation 5;
determining a B-spline surface equation according to formula 6:
wherein u is k ≤u≤u m+l ，v l ≤v≤v n+l ，P i，j Is a control point set P i，j A three-dimensional point cloud is a set of points, N, (i) 0, 1 i，k (u) and N j，l (v) Is a B-spline surface basis function;
and B spline surface fitting is carried out according to the control points, and surface reconstruction based on the B spline curve is carried out.
And calculating the coefficients of the curved B spline surface equation after fitting.
4. The method of claim 3, wherein performing B-spline surface fitting based on the control points, and performing B-spline curve-based surface reconstruction specifically comprises:
initializing a B spline surface by using Principal Component Analysis (PCA);
fitting and iterative optimization are carried out on the initialized B spline surface;
initializing the B-spline curve by using a circle;
fitting the initialized B spline curve;
performing a trigonometric calculation format on the B spline curved surface obtained by fitting to obtain a final curved surface model of the B spline curve;
the fitting of the initialized B-spline curve specifically comprises the following steps:
given (r +1). (s +1) known points { Q k，l R, k is 0, 1, · r; i 0, 1.. r is constructed with a { p, q } secondary surface of (n + 1. (m +1) control points to approximate fit these known points;
parameterization is performed, and a node vector is calculated according to the formula 7-9:
u 0 ＝…＝u p 0, equation 7;
u m-p ＝…＝u m 1, formula 8;
wherein j is 1, n-p, I int (jd), α jd-I, d (r +1)/(n-p + 1);
calculating a control point: known points Q for a row in the u direction (s +1) k，0 ，...，Q k，r Performing curve approximation fitting to obtain control vertex R of (s +1) line k，0 ，...，R k，n For the known point R of the (n +1) column in the v direction 0，l ，...，R s，l Performing curve approximation fitting to obtain control vertex P of (n +1) line 0，l ，...，P n，l 。
5. The method of claim 3, wherein computing coefficients of the curved B-spline surface equation after fitting comprises:
fix j for P i，j I is 0, 1,. ·, m; j is 0, 1, n, and control vertexes of n +1 parameter curves are respectively solved along the u direction;
fix i for P i，j i is 0, 1,. said, m; and j is 0, 1, and n, and control vertexes of the m +1 parameter curves are respectively obtained along the v direction.
6. The utility model provides an ultrasonic grinder bearing anchor clamps movable block designing device which characterized in that includes:
the first determining module is used for determining a B-spline curve of the curved surface of the bearing ring clamp according to the outer surface of the processed workpiece;
the second determining module is used for determining the B spline curved surface of the bearing ring clamp according to the B spline curve of the curved surface of the bearing ring clamp;
the third determining module is used for determining a mathematical model adaptive to the outer surface of the processed test piece according to a B spline surface of the bearing ring clamp surface;
and the solving module is used for solving a corresponding objective function according to the mathematical model so as to calculate and obtain the optimal solution of the bearing clamp moving block matched with the processed workpiece.
7. The apparatus of claim 6,
the first determining module is specifically configured to:
given n +1 control points P 0 ，P 1 ，…，P n And one node vector U ═ U 0 ，u 1 ，…，u m The p-th order B-spline curve is defined by the control points and the node vector U, and N is set i And p (u) is the ith p-th B-spline basis function, then the p-th B-spline curve is determined according to equation 1:
wherein a node vector is defined as a set of m +1 non-decreasing numbers, U 0 ≤u 1 ≤u 2 …≤u m ，u i Is a node;
recursively defining N according to equations 2 and 3 i P (u), where any p-th order spline consists of a linear combination of two adjacent p-1 th order splines:
wherein 0/0 is 0, p represents the power of the spline, and the subscript i represents the serial number of the B-spline;
calculating N according to trigonometric calculation formats i ，p(u)；
The second determining module is specifically configured to:
forming a control grid by (m +1) × (n +1) control points, and determining parameter node vectors in two directions according to a formula 4 and a formula 5;
U＝[u 0 ，u 1 ，…，u m+k+1 ]formula 4;
V＝[v 0 ，v 1 ，…，v m+l+1 ]formula 5;
determining a B-spline surface equation according to formula 6:
wherein u is k ≤u≤u m+l ，v l ≤v≤v n+l ，P i，j Is a set of control points P i，j A three-dimensional point cloud is a set of points, N, (i) 0, 1 i，k (u) and N j，l (v) Is a B-spline surface basis function;
and B spline surface fitting is carried out according to the control points, and surface reconstruction based on the B spline curve is carried out.
And calculating the coefficients of the curved B spline surface equation after fitting.
8. The apparatus of claim 7, wherein the second determining module is specifically configured to:
initializing a B spline surface by using Principal Component Analysis (PCA);
fitting and iterative optimization are carried out on the initialized B spline surface;
initializing the B-spline curve by using a circle;
fitting the initialized B spline curve;
performing a trigonometric calculation format on the B spline curved surface obtained by fitting to obtain a final curved surface model of the B spline curve;
the fitting of the initialized B-spline curve specifically comprises the following steps:
given (r +1). (s +1) known points { Q k，l R, k is 0, 1, · r; i 0, 1.. r is constructed with a { p, q } secondary surface of (n + 1. (m +1) control points to approximate fit these known points;
parameterization is performed, and a node vector is calculated according to the formula 7-9:
u 0 ＝…＝u p 0, equation 7;
u m-p ＝…＝u m 1, formula 8;
wherein j is 1, n-p, I int (jd), α jd-I, d (r +1)/(n-p + 1);
calculating a control point: known points Q for a row in the u direction (s +1) k，0 ，...，Q k，r Performing curve approximation fitting to obtain control vertex R of (s +1) line k，0 ，...，R k，n For the known point R of the (n +1) column in the v direction 0，l ，...，R s，l Performing curve approximation fitting to obtain control vertex P of (n +1) line 0，l ，...，P n，l ；
Fix j for P i，j I ═ 0, 1,. ·, m; j is 0, 1, n, and control vertexes of n +1 parameter curves are respectively solved along the u direction;
fix i for P i，j i is 0, 1,. said, m; and j is 0, 1, and n, and control vertexes of the m +1 parameter curves are respectively obtained along the v direction.
9. The utility model provides an ultrasonic grinder bearing anchor clamps movable block designing device which characterized in that includes: a memory, a processor, and a computer program stored on the memory and executable on the processor, the computer program when executed by the processor implementing the steps of the ultrasonic grinder bearing fixture kinetic block design method of any of claims 1 to 5.
10. A computer-readable storage medium, wherein the computer-readable storage medium has stored thereon an information transfer-enabling program, which when executed by a processor, enables the steps of the method of designing a moving block of an ultrasonic grinder bearing fixture as set forth in any one of claims 1 to 5.
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| CN114770229B (en) * | 2022-04-19 | 2024-04-26 | 广州大学 | Bearing ring clamp curved surface design method, device and storage medium |
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