CN114021269A - Structural improvement and grinding track innovation design method and system of ultrasonic straight-edged knife - Google Patents
Structural improvement and grinding track innovation design method and system of ultrasonic straight-edged knife Download PDFInfo
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Abstract
The invention discloses a method and a system for structure improvement and grinding track innovation design of an ultrasonic straight-edged knife, wherein the method comprises the following steps: firstly, providing a model with a smooth transition blade on the basis of analyzing the structure of a cutter body of an ultrasonic straight-blade cutter and improving the design; establishing a workpiece coordinate system XYZ at the center of the root part of the straight-edged knife tool, and establishing a model of smooth transition of the knife edge under the coordinate system, wherein the model comprises mathematical models of a parallel knife edge curve, an arc knife edge curve and an end straight-edged curve; step three, verifying whether the blade curve is in smooth transition or not, and checking the correctness of the blade curve model; step four, establishing a local coordinate system X based on the grinding point P according to the processing technology of the ultrasonic straight-edged knifeLYLZL(ii) a Calculating the position of the center of the grinding wheel under a local coordinate system according to the grinding attitude of the grinding wheel, wherein the position comprises the center position of the grinding wheel and a grinding wheel shaft vector; step six, obtaining the workpiece with the grinding wheel center through coordinate conversionAnd obtaining the grinding track of the grinding wheel in smooth transition relative to the cutting edge of the ultrasonic knife by an expression in a coordinate system.
Description
Technical Field
The invention belongs to the technical field of cutter processing, relates to the structure improvement and precise grinding processing technology of an ultrasonic cutter, and particularly relates to a structure improvement and grinding track innovative design method of an ultrasonic straight-edged cutter.
Background
The ultrasonic cutter is a nonstandard cutter, has special application, is mainly used for processing and cutting composite materials in the aerospace field such as aramid fiber honeycombs and the like, has extremely high requirements on the symmetry degree and the surface precision of the cutter, and is also required to have higher surface quality because the cutter is subjected to cutting processing under the assistance of ultrasonic and the abrasion of the ultrasonic vibration to the cutter is also intensified. The cutter is a multi-linear combined plane cutter which consists of four edge lines, the four edge lines are symmetrically distributed on two sides of the center line of the cutter, the included angle between the two edge lines on one side is 170 degrees, and the connected edge surfaces are not in smooth transition. The existing processing method is to grind a single blade surface under a fixed angle, and finally, 8 blade surfaces which are symmetrically distributed up and down, left and right are processed.
The working part of the improved arc ultrasonic knife mainly comprises a straight blade and an arc blade. Starting from a mathematical model for establishing a cutting edge curve, grinding process setting is carried out on a cutter face, at present, grinding technologies of vertical milling cutters are researched more, but the grinding transition problem of the cutter face is rarely researched. Based on the method, the mathematical modeling of the ultrasonic straight-edge cutter arc transition, the cutter position track algorithm when the grinding wheel grinds each cutting surface and the like are mainly researched.
Disclosure of Invention
Aiming at the problems of arc transition of the edge of the ultrasonic straight-edged knife and the grinding track of the edge surface in the prior art, the invention provides a method and a system for improving the structure of the ultrasonic straight-edged knife and innovatively designing the grinding track.
The purpose of the invention is realized by the following technical scheme:
a structure improvement and grinding track innovation design method of an ultrasonic straight-edged knife comprises the following steps:
firstly, providing a model with a smooth transition blade on the basis of analyzing the structure of a cutter body of an ultrasonic straight-blade cutter;
establishing a workpiece coordinate system XYZ at the center of the root part of the straight-edged knife tool, and establishing a model of smooth transition of the knife edge under the coordinate system, wherein the model comprises a parallel knife edge curve, a circular arc knife edge curve and a mathematical model of an end straight-edged curve;
step three, verifying whether the blade curve is in smooth transition or not, and checking the correctness of the blade curve model;
step four, establishing a local coordinate system X based on the grinding point P according to the processing technology of the ultrasonic straight-edged knifeLYLZL；
Fifthly, calculating the position of the center of the grinding wheel under a local coordinate system according to the grinding attitude of the grinding wheel, wherein the position comprises the center position of the grinding wheel and a grinding wheel shaft vector;
and step six, obtaining an expression of the center of the grinding wheel under a workpiece coordinate system through coordinate conversion, and thus obtaining a grinding track of the grinding wheel in smooth transition relative to the cutting edge of the ultrasonic knife.
Preferably, in the step one, the structural shape of the ultrasonic straight-blade knife body is as follows: the upper part, the lower part and the left part are respectively symmetrical, the included angle of two edge lines on one side is 170 degrees, and smooth transition does not exist between corresponding edge surfaces.
Preferably, the step is a modified design, and the blade can be smoothly transited after the modified design.
The ultrasonic cutter is a nonstandard cutter for processing special materials, and firstly, the structural parameters of the cutter are defined. The total length of the cutter is L which is 55.7 mm; the width b of the tail part of the cutter is 13 mm; when the blade is not in arc transition, the length of the tail straight blade is H1-23.09 mm; the included angle of the two straight edges at the end part is 20 degrees; the included angle between the upper and lower blade surfaces is beta which is 26 degrees; the thickness d of the cutter is 1.6 mm. The edge angle is formed between adjacent edge lines on two sides of the ultrasonic cutter, the edge does not form smooth transition, the durability and the smoothness of the cutter are influenced, and the phenomenon that cutting is difficult to flow out during machining is caused. Therefore, two adjacent straight line blades are designed into blades with three arc transitions of a parallel blade, an arc blade and an end straight line blade, wherein the arc blades are in arc transition connection with the other two blades. The design can correspondingly improve the surface quality of the ultrasonic cutter during machining and reduce the abrasion of ultrasonic vibration to the cutter.
Preferably, in the second step, a workpiece coordinate system XYZ is established and fixed on the workpiece, the origin of coordinates is located at the starting central point of the tail of the tool, the coordinate axis X coincides with the axis of the workpiece, and the direction of the coordinate axis Y, Z is determined by using a right-hand rule, and the coordinate system is used for describing the geometric parameters of the tool and the geometric shape of the tool. The smooth transition edge curve established based on the workpiece coordinate system is as follows:
(1) parallel edge curve:
(2) arc blade curve:
(3) end straight edge curve:
defining the geometrical parameters of the cutter after the arc transition, wherein L1 is the length of the parallel cutting edge, L1＝H1-c；RtThe radius is the self-defined radius of the arc blade; c is RtSine value of (c ═ R)tTan (. alpha./2); theta is a central angle corresponding to the arc section of the cutter, namely an included angle between a tangent line of the arc blade and the X-axis direction, and theta is more than or equal to 0 and less than or equal to 10 degrees; l2 is the linear distance from the origin of the workpiece coordinate system to the end point of the circular arc blade, L2＝H1+ c · cos (α); alpha is an included angle between the curve of the end straight blade and the X axis, namely, half of the included angle of the two straight blades at the end, and alpha is 10 degrees; a is half of the width of the knife edge, and a is b/2- (L-H)1)·tan(α)。
Preferably, in the third step, in order to verify the correctness of the established blade curve model, the blade curve model in circular arc transition is subjected to three-dimensional simulation in Matlab, and the simulation result shows that the blade curve model in circular arc transition is correct.
Preferably, in the fourth step, the grinding point P is defined as a point of the edge of the grinding surface of the grinding wheel, and a local coordinate system X is established based on the grinding point PLYLZLThe local coordinate system is obtained by the rotation transformation and the translation transformation of a workpiece coordinate system; the origin O of the local coordinate system is positioned on the edge line, the cutting plane of the edge is taken through the point, the plane must pass through the center of the grinding wheel, and the radius of the diameter of the grinding wheel on the cutting plane is the real radius R of the cutterg(ii) a Defining the tangential direction of the edge curve as coordinate system XLCoordinate axis YLIs in the direction of the normal to the edge curve, the coordinate axis ZLIs on the edge face; the local coordinate system is used for determining the relative positions of different parts of the grinding wheel machining tool and solving the grinding track of the grinding wheel when the cutting edge is ground, and the coordinate system moves along with the grinding point on the cutting edge curve.
Preferably, in the fourth step, the grinding point P is defined as a point of the edge of the grinding surface of the grinding wheel, and a local coordinate system X based on the grinding point P is established according to the processing technology of the ultrasonic straight-edged toolLYLZLThe local coordinate system is obtained by the rotation transformation and the translation transformation of the workpiece coordinate system. First, the workpiece coordinate system XYZ is translated to the edge curve, (x, y, z) is any point on the edge. The coordinate system after translation is XYZ1mIts translation matrix T1：
Preferably, in the fifth step, the grinding wheel used for grinding the ultrasonic cutter is a CBN bowl-shaped grinding wheel, the grinding method is to grind and process the edge surface by using the large end surface of the bowl-shaped grinding wheel, and the upper edge surface and the lower edge surface naturally form a blade; the center of the grinding wheel is defined as the geometric center of the grinding surface of the grinding wheel, the attitude of the grinding edge surface of the grinding wheel is defined through a specific grinding process method, and the position of the center of the grinding wheel under a normal section coordinate system is solved based on the grinding attitude.
Preferably, in the fifth step, the position of the grinding wheel center under the local coordinate system is calculated according to the grinding attitude of the grinding wheel, wherein the position includes the grinding wheel center position and the grinding wheel axis vector. In actual grinding, since the end edge face of the tool is first ground by clamping the tool tail portion side with the jig, the tool is used as the slave tool in calculationThe grinding path of the end facet begins. Obtaining a translation matrix in the fourth step, and then carrying out XYZ on the coordinate system1mAround Z1mRotating the shaft anticlockwise by an angle alpha to obtain a coordinate system XYZ2mWith a rotation matrix of T2Then coordinate system XYZ is set2mAround X2mThe shaft rotates clockwise
Obtaining a local coordinate system XLYLZLWith a rotation matrix of T3。
Position of the grinding point P in the local coordinate system:
the position of the grinding wheel center under a local coordinate system:
expression of the grinding wheel axis vector in the local coordinate system:
(1) through coordinate conversion, the expression of the center of the grinding wheel in a workpiece coordinate system when the edge face of the end part of the cutter is ground is as follows:
similarly, the expression of the grinding wheel axis vector in the workpiece coordinate system when the end edge face of the cutter is ground is as follows:
(2) the grinding track of the edge face of the circular arc part of the cutter is expressed as follows:
obtaining a translation matrix in the fourth step, and then carrying out XYZ on the coordinate system1mAround Z1mRotating the shaft anticlockwise by an angle theta to obtain a coordinate system XYZ2mWith a rotation matrix of T2', then the coordinate system XYZ2mAround X2mThe shaft rotates clockwise
Obtaining a coordinate system XLYLZLWith a rotation matrix of T3The same as above.
Through coordinate conversion, the expression of the center of the grinding wheel in a workpiece coordinate system when the cutting face of the circular arc part of the cutter is ground is as follows:
similarly, the expression of the grinding wheel axis vector in the workpiece coordinate system when the cutting edge surface of the circular arc part of the cutter is ground is as follows:
(3) the grinding track of the parallel edge face of the tail part of the cutter is expressed as follows:
obtaining a translation matrix in the fourth step, and then carrying out XYZ on the coordinate system1mAround X1mThe shaft rotates clockwise
Obtaining a coordinate system XLYLZLWith a rotation matrix of T3。
Through coordinate conversion, when the tail part of the tool is ground to be parallel to the edge face of the cutting edge, the expression of the center of the grinding wheel in a workpiece coordinate system is as follows:
and similarly, the expression of the grinding wheel axis vector in the workpiece coordinate system when the tail part of the grinding tool is parallel to the edge face of the cutting edge is as follows:
preferably, in the sixth step, an expression of the center of the grinding wheel in the workpiece coordinate system is obtained through coordinate conversion calculation between the local coordinate system and the workpiece coordinate system, and the grinding track expression of the grinding wheel in smooth transition with respect to the cutting edge of the ultrasonic knife is obtained as follows:
(1) grinding track of parallel blade face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t is3Is a rotation transformation matrix; [ x ] ofLSyLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the parallel blade edge surface is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TThe expression of the grinding wheel axis vector under a local coordinate system is shown;
(2) grinding track of arc edge face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t'2、T3Is a rotation transformation matrix; [ x ] ofLS yLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the circular-arc blade edge surface is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TThe expression of the grinding wheel axis vector under a local coordinate system is shown;
(3) grinding track of end edge face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t is2、T3Is a rotation transformation matrix; [ x ] ofLS yLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the edge face of the end cutting edge is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TIs the expression of the grinding wheel axis vector in a local coordinate system.
The invention also discloses a structural improvement and grinding track innovation design system of the ultrasonic straight-edged knife, which comprises the following modules:
the model extraction module of smooth transition of the cutting edge extracts a model of smooth transition of the cutting edge on the basis of analyzing the structure of the cutter body of the ultrasonic straight-edge cutter;
the model establishing module of smooth transition of the cutting edge establishes a workpiece coordinate system XYZ at the center of the root of the straight-edged knife, and establishes a model of smooth transition of the cutting edge under the coordinate system, wherein the model comprises mathematical models of a parallel cutting edge curve, an arc cutting edge curve and an end straight-edged curve;
the verification module is used for verifying whether the blade curve is in smooth transition or not and verifying the correctness of the blade curve model;
a coordinate system establishing module for establishing a local coordinate system X based on the grinding point P according to the processing technique of the ultrasonic straight-edged knifeLYLZL；
The position calculating module calculates the position of the center of the grinding wheel under a local coordinate system according to the grinding attitude of the grinding wheel, wherein the position comprises the center position of the grinding wheel and a grinding wheel shaft vector;
and outputting a grinding track module for the smooth transition of the ultrasonic knife edge, and obtaining an expression of the center of the grinding wheel in a workpiece coordinate system through coordinate conversion to obtain the grinding track of the grinding wheel in the smooth transition of the ultrasonic knife edge.
The invention has the beneficial effects that:
based on the geometrical structural characteristics of the multi-linear combined plane of the ultrasonic cutter, the invention designs a mathematical model of the circular arc transition of the edge line of the cutter, constructs a local coordinate system taking a grinding point P as a coordinate origin, establishes a novel grinding model for the edge surface of the ultrasonic cutter through a coordinate conversion principle on the basis, calculates the motion track of a grinding wheel during grinding the edge surface, and realizes the smooth transition between the edge and the edge surface. Therefore, the theoretical defect that the cutter can only be ground at a fixed angle in the grinding process is overcome, and reference is provided for the cutter in the process of solving a grinding track algorithm. The invention improves the surface quality of the ultrasonic cutter during grinding, reduces the abrasion of ultrasonic vibration to the cutter and prolongs the service life of the ultrasonic cutter.
Drawings
FIG. 1 is a flow chart of a structural improvement and grinding track innovative design method of an ultrasonic cutter.
Fig. 2 is a schematic structural diagram of the body of the ultrasonic straight-edge cutter, including structural parameters of the cutter.
Fig. 3 is a schematic structural view of an ultrasonic cutter after structural modification, including specific structural parameters.
Figures 4a-4c are schematic diagrams of grinding attitudes of the grinding wheels for grinding the edge faces of the end part of the tool, the arc part of the edge faces and the parallel edge face, and the grinding wheels are reduced by 0.5 times for coordination. Including in particular the position of the object coordinate system and the local coordinate system.
FIG. 5 is a schematic representation of the edge line simulation after the tool edge line has undergone an arc transition.
Fig. 6 is a schematic view of the CBN grinding wheel profile and the location of the grinding point P.
Fig. 7 is a block diagram of a structural improvement and grinding track innovation design system of the ultrasonic straight-edge knife.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1 to 6, the method for improving the structure and innovatively designing the grinding track of the ultrasonic straight-edged blade of the present embodiment includes the following steps:
the method comprises the following steps: providing a model with smooth transition of the blade and improving the design on the basis of analyzing the structure of the ultrasonic straight-blade knife body;
step two: establishing a workpiece coordinate system XYZ at the center of the root part of the straight-edged knife tool, and establishing a model of smooth transition of the knife edge under the coordinate system, wherein the model comprises a parallel knife edge curve, a circular arc knife edge curve and a mathematical model of an end straight-edged curve;
step three: verifying whether the blade curve is in smooth transition in Matlab, and checking the correctness of the blade curve model;
step four: establishing a local coordinate system X based on a grinding point P according to the processing technology of the ultrasonic straight-edged knifeLYLZL；
Step five: calculating the position of the center of the grinding wheel under a local coordinate system according to the grinding attitude of the grinding wheel, wherein the position comprises the center position of the grinding wheel and a wheel axis vector;
and sixthly, obtaining an expression of the center of the grinding wheel under a workpiece coordinate system through coordinate conversion, thus obtaining a grinding track of the grinding wheel in smooth transition relative to the cutting edge of the ultrasonic knife.
In the first step, edges and corners are formed between adjacent edge lines on two sides of the ultrasonic cutter, the cutting edges do not form smooth transition, two adjacent linear cutting edges are designed into cutting edges with three circular arc transition of parallel cutting edges, circular arc cutting edges and end linear cutting edges, and circular arc transition connection is formed between the circular arc cutting edges and the other two cutting edges. After the first step of improved design, the knife edge can be smoothly transited.
Specifically, an included angle between two adjacent straight line blades is taken as an angular bisector, and a point A is taken from the angular bisector, so that the distance from the point A to the two straight line blades is RtWith point A as the center of circle RtThe radius draws an arc line, the arc line intersects with the two straight line edges at two points B, C, the arc BC is an arc edge curve, the straight line part from the edge end to the point B is an end straight line edge, and the straight line part from the edge tail to the point C is a parallel edge. Reference may be made in particular to fig. 3.
Establishing a workpiece coordinate system fixed on the workpiece, wherein a coordinate axis X is coincident with the axis of the workpiece, the direction of the coordinate axis Y, Z is determined by adopting a right-hand rule, and the coordinate system is used for describing the geometric parameters and the geometric shape of the tool; the smooth transition edge curve established based on the workpiece coordinate system is as follows:
(1) parallel edge curve:
(2) arc blade curve:
(3) end straight edge curve:
defining the geometrical parameters of the cutter after the arc transition, wherein L1 is the length of the parallel cutting edge, L1＝H1-c；RtThe radius is the self-defined radius of the arc blade; c is RtSine value of (c ═ R)tTan (. alpha./2); theta is a central angle corresponding to the arc section of the cutter, namely an included angle between a tangent line of the arc blade and the X-axis direction, and theta is more than or equal to 0 and less than or equal to 10 degrees; l2 is a tool from the origin of the workpiece coordinate system to the circular arcLinear distance of edge points, L2＝H1+ c · cos (α); alpha is an included angle between the curve of the end straight blade and the X axis, namely, half of the included angle of the two straight blades at the end, and alpha is 10 degrees; a is half of the width of the knife edge, and a is b/2- (L-H)1)·tan(α)。
And in the third step, verifying whether the blade curve is in smooth transition in Matlab, and checking the correctness of the blade curve model. In this embodiment, the mathematical model simulation software used is Matlab, which not only has a strong numerical operation capability, but also has a strong drawing function, and can conveniently visualize data as a multidimensional graph. In a workpiece coordinate system, mathematical expressions of three sections of blade curves are programmed in software by using functions, and after a code is run, a three-dimensional simulation schematic diagram of the blade curve with circular arc transition can be seen. Reference may be made in particular to fig. 5.
In the fourth step, a grinding point P is defined as a point of the edge of the grinding surface of the grinding wheel, and a local coordinate system X is established based on the grinding point PLYLZLThe local coordinate system is obtained by the rotation transformation and the translation transformation of a workpiece coordinate system; the origin O of the local coordinate system is positioned on the edge line, the cutting plane of the edge is taken through the point, the plane must pass through the center of the grinding wheel, and the radius of the diameter of the grinding wheel on the cutting plane is the real radius R of the grinding wheelg(ii) a Defining the tangential direction of the edge curve as coordinate system XLCoordinate axis YLIs in the direction of the normal to the edge curve, the coordinate axis ZLIs on the edge face; the local coordinate system is used for determining the relative positions of different parts of the grinding wheel machining tool and solving the grinding track of the grinding wheel when the cutting edge is ground, and the coordinate system moves along with the grinding point on the cutting edge curve.
Grinding the grinding wheel used for grinding the ultrasonic cutter into a CBN bowl-shaped grinding wheel, wherein the grinding method is to grind and machine the edge surface by using the large end surface of the bowl-shaped grinding wheel, and the upper edge surface and the lower edge surface naturally form a blade; the center of the grinding wheel is defined as the geometric center of the grinding surface of the grinding wheel, the attitude of the grinding edge surface of the grinding wheel is defined through a specific grinding process method, and the position of the center of the grinding wheel under a normal section coordinate system is solved based on the grinding attitude.
In the sixth step, an expression of the center of the grinding wheel in the workpiece coordinate system is obtained through coordinate conversion calculation between the local coordinate system and the workpiece coordinate system, and the grinding track expression of the grinding wheel in smooth transition with respect to the cutting edge of the ultrasonic knife is obtained as follows:
(1) grinding track of parallel blade face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t is3Is a rotation transformation matrix; [ x ] ofLSyLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the parallel blade edge surface is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TThe expression of the grinding wheel axis vector under a local coordinate system is shown;
(2) grinding track of arc edge face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t'2、T3Is a rotation transformation matrix; [ x ] ofLS yLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the circular-arc blade edge surface is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TThe expression of the grinding wheel axis vector under a local coordinate system is shown;
(3) grinding track of end edge face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t is2、T3Is a rotation transformation matrix; [ x ] ofLS yLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the edge face of the end cutting edge is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TIs the expression of the grinding wheel axis vector in a local coordinate system.
As shown in fig. 7, the system for improving the structure and innovatively designing the grinding track of the ultrasonic straight-edged blade of the embodiment comprises the following modules:
the model extraction module of smooth transition of the cutting edge extracts a model of smooth transition of the cutting edge on the basis of analyzing the structure of the cutter body of the ultrasonic straight-edge cutter; specifically, the ultrasonic straight-blade knife body has a structural shape: the upper part, the lower part and the left part are respectively symmetrical, the included angle of two edge lines on one side is 170 degrees, and smooth transition does not exist between corresponding edge surfaces; after the improved design, the knife edge can be smoothly transited.
The model establishing module of smooth transition of the cutting edge establishes a workpiece coordinate system XYZ at the center of the root of the straight-edged knife, and establishes a model of smooth transition of the cutting edge under the coordinate system, wherein the model comprises mathematical models of a parallel cutting edge curve, an arc cutting edge curve and an end straight-edged curve; specifically, a workpiece coordinate system is established and fixed on the workpiece, a coordinate axis X is coincident with the axis of the workpiece, the direction of the coordinate axis Y, Z is determined by adopting a right-hand rule, and the coordinate system is used for describing the geometric parameters of the tool and the geometric shape of the tool; the smooth transition edge curve established based on the workpiece coordinate system is as follows:
(1) parallel edge curve:
(2) arc blade curve:
(3) end straight edge curve:
defining the geometrical parameters of the cutter after the arc transition, wherein L1 is the length of the parallel cutting edge, L1＝H1-c；RtThe radius is the self-defined radius of the arc blade; c is RtSine value of (c ═ R)tTan (. alpha./2); theta is a central angle corresponding to the arc section of the cutter, namely an included angle between a tangent line of the arc blade and the X-axis direction, and theta is more than or equal to 0 and less than or equal to 10 degrees; l2 is the linear distance from the origin of the workpiece coordinate system to the end point of the circular arc blade, L2＝H1+ c · cos (α); alpha is an included angle between the curve of the end straight blade and the X axis, namely, half of the included angle of the two straight blades at the end, and alpha is 10 degrees; a is half of the width of the knife edge, and a is b/2- (L-H)1)·tan(α)。
The verification module is used for verifying whether the blade curve is in smooth transition in Matlab and verifying the correctness of the blade curve model;
a coordinate system establishing module for establishing a local coordinate system X based on the grinding point P according to the processing technique of the ultrasonic straight-edged knifeLYLZL(ii) a Specifically, a grinding point P is defined as a point of the edge of a grinding surface of the grinding wheel, and a local coordinate system X is established based on the grinding point PLYLZLThe local coordinate system is obtained by the rotation transformation and the translation transformation of a workpiece coordinate system; the origin O of the local coordinate system is located on the edge line, and the cutting plane of the edge is taken through the point and passes through the middle of the grinding wheelThe radius of the diameter of the grinding wheel on the tangent plane surface is the real radius R of the grinding wheelg(ii) a Defining the tangential direction of the edge curve as coordinate system XLCoordinate axis YLIs in the direction of the normal to the edge curve, the coordinate axis ZLIs on the edge face; the local coordinate system is used for determining the relative positions of different parts of the grinding wheel machining tool and solving the grinding track of the grinding wheel when the cutting edge is ground, and the coordinate system moves along with the grinding point on the cutting edge curve.
The position calculating module calculates the position of the center of the grinding wheel under a local coordinate system according to the grinding attitude of the grinding wheel, wherein the position comprises the center position of the grinding wheel and a grinding wheel shaft vector; specifically, the grinding wheel used for grinding the ultrasonic cutter is a CBN bowl-shaped grinding wheel, the grinding method is to grind and process the edge surface by using the large end surface of the bowl-shaped grinding wheel, and the upper edge surface and the lower edge surface naturally form a blade; the center of the grinding wheel is defined as the geometric center of the grinding surface of the grinding wheel, the attitude of the grinding edge surface of the grinding wheel is defined through a specific grinding process method, and the position of the center of the grinding wheel under a normal section coordinate system is solved based on the grinding attitude.
And outputting a grinding track module for the smooth transition of the ultrasonic knife edge, and obtaining an expression of the center of the grinding wheel in a workpiece coordinate system through coordinate conversion to obtain the grinding track of the grinding wheel in the smooth transition of the ultrasonic knife edge. Specifically, an expression of the center of the grinding wheel in the workpiece coordinate system is obtained through coordinate conversion calculation between the local coordinate system and the workpiece coordinate system, and the grinding track expression of the grinding wheel in smooth transition with respect to the cutting edge of the ultrasonic knife is obtained as follows:
(1) grinding track of parallel blade face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t is3Is a rotation transformation matrix; [ x ] ofLSyLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the parallel blade edge surface is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TThe expression of the grinding wheel axis vector under a local coordinate system is shown;
(2) grinding track of arc edge face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t'2、T3Is a rotation transformation matrix; [ x ] ofLS yLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the circular-arc blade edge surface is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TThe expression of the grinding wheel axis vector under a local coordinate system is shown;
(3) grinding track of end edge face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t is2、T3Is a rotation transformation matrix; [ x ] ofLS yLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the edge face of the end cutting edge is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TIs the expression of the grinding wheel axis vector in a local coordinate system.
The invention carries out deep research aiming at the structural improvement and the grinding track solving of the ultrasonic straight-edged knife, and provides a sufficient theoretical basis for the actual production and processing of the cutter.
Claims (8)
1. The structure improvement and grinding track innovative design method of the ultrasonic straight-edged knife is characterized by comprising the following steps of:
firstly, providing a model with a smooth transition blade on the basis of analyzing the structure of a cutter body of an ultrasonic straight-blade cutter;
establishing a workpiece coordinate system XYZ at the center of the root part of the straight-edged knife tool, and establishing a model of smooth transition of the knife edge under the coordinate system, wherein the model comprises mathematical models of a parallel knife edge curve, an arc knife edge curve and an end straight-edged curve;
step three, verifying whether the blade curve is in smooth transition or not, and checking the correctness of the blade curve model;
step four, establishing a local coordinate system X based on the grinding point P according to the processing technology of the ultrasonic straight-edged knifeLYLZL；
Calculating the position of the center of the grinding wheel under a local coordinate system according to the grinding attitude of the grinding wheel, wherein the position comprises the center position of the grinding wheel and a grinding wheel shaft vector;
and step six, obtaining an expression of the center of the grinding wheel under a workpiece coordinate system through coordinate conversion, and obtaining a grinding track of the grinding wheel in smooth transition relative to the cutting edge of the ultrasonic knife.
2. The ultrasonic straight-blade knife structure improvement and grinding track innovative design method according to claim 1, characterized in that: in the first step, the structural shape of the ultrasonic straight-blade knife body is as follows: the upper part, the lower part and the left part are respectively symmetrical, the included angle of two edge lines on one side is 170 degrees, and smooth transition does not exist between corresponding edge surfaces.
3. The ultrasonic straight-blade knife structure improvement and grinding track innovative design method according to claim 1 or 2, characterized in that: establishing a workpiece coordinate system fixed on the workpiece, wherein a coordinate axis X is coincident with the axis of the workpiece, the direction of the coordinate axis Y, Z is determined by adopting a right-hand rule, and the coordinate system is used for describing the geometric parameters and the geometric shape of the tool; the smooth transition edge curve established based on the workpiece coordinate system is as follows:
(1) parallel edge curve:
(2) arc blade curve:
(3) end straight edge curve:
defining the geometrical parameters of the cutter after the arc transition, wherein L1 is the length of the parallel cutting edge, L1＝H1-c；RtThe radius is the self-defined radius of the arc blade; c is RtSine value of (c ═ R)tTan (. alpha./2); theta is a central angle corresponding to the arc section of the cutter, namely an included angle between a tangent line of the arc blade and the X-axis direction, and theta is more than or equal to 0 and less than or equal to 10 degrees; l2 is the linear distance from the origin of the workpiece coordinate system to the end point of the circular arc blade, L2＝H1+ c · cos (α); alpha is an included angle between the curve of the end straight blade and the X axis, namely, half of the included angle of the two straight blades at the end, and alpha is 10 degrees; a is half of the width of the knife edge, and a is b/2- (L-H)1)·tan(α)。
4. The ultrasonic straight-blade knife structure improvement and grinding track innovative design method according to claim 3, characterized in that: and in the third step, verifying whether the blade curve is in smooth transition in Matlab, and checking the correctness of the blade curve model.
5. The ultrasonic straight-blade knife structure improvement and grinding track innovative design method according to claim 4, characterized in that: in the fourth step, a grinding point P is defined as a point of the edge of the grinding surface of the grinding wheel, and a local coordinate system X is established based on the grinding point PLYLZLThe local coordinate system is obtained by the rotation transformation and the translation transformation of a workpiece coordinate system; the origin O of the local coordinate system is positioned on the edge line, the cutting plane of the edge is taken through the point, the plane must pass through the center of the grinding wheel, and the radius of the diameter of the grinding wheel on the cutting plane is the real radius R of the grinding wheelg(ii) a Defining the tangential direction of the edge curve as coordinate system XLCoordinate axis YLIs in the direction of the normal to the edge curve, the coordinate axis ZLIs on the edge face; the local coordinate system is used for determining the relative positions of different parts of the grinding wheel machining tool and solving the grinding track of the grinding wheel when the cutting edge is ground, and the coordinate system moves along with the grinding point on the cutting edge curve.
6. The ultrasonic straight-blade knife structure improvement and grinding track innovative design method according to claim 5, characterized in that: grinding the grinding wheel used for grinding the ultrasonic cutter into a CBN bowl-shaped grinding wheel, wherein the grinding method is to grind and machine the edge surface by using the large end surface of the bowl-shaped grinding wheel, and the upper edge surface and the lower edge surface naturally form a blade; the center of the grinding wheel is defined as the geometric center of the grinding surface of the grinding wheel, the attitude of the grinding edge surface of the grinding wheel is defined through a specific grinding process method, and the position of the center of the grinding wheel under a normal section coordinate system is solved based on the grinding attitude.
7. The ultrasonic straight-blade knife structure improvement and grinding track innovative design method according to claim 6, characterized in that: in the sixth step, an expression of the center of the grinding wheel in the workpiece coordinate system is obtained through coordinate conversion calculation between the local coordinate system and the workpiece coordinate system, and the grinding track expression of the grinding wheel in smooth transition with respect to the cutting edge of the ultrasonic knife is obtained as follows:
(1) grinding track of parallel blade face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t is3Is a rotation transformation matrix; [ x ] ofLS yLSzLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the parallel blade edge surface is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TThe expression of the grinding wheel axis vector under a local coordinate system is shown;
(2) grinding track of arc edge face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t'2、T3Is a rotation transformation matrix; [ x ] ofLSyLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the circular-arc blade edge surface is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TThe expression of the grinding wheel axis vector under a local coordinate system is shown;
(3) grinding track of end edge face:
wherein T is1A translation transformation matrix for translating the workpiece coordinate system to a local coordinate system; t is2、T3Is a rotation transformation matrix; [ x ] ofLSyLS zLS]TThe position of the center of the grinding wheel under a local coordinate system;
the expression of the grinding wheel axis vector in the workpiece coordinate system during grinding of the edge face of the end cutting edge is as follows:
wherein [ X ]tw2 Ytw2 Ztw2]TIs the expression of the grinding wheel axis vector in a local coordinate system.
8. The structure improvement and grinding track innovation design system of supersound straight sword is characterized in that, includes the following module:
the model extraction module of smooth transition of the cutting edge extracts a model of smooth transition of the cutting edge on the basis of analyzing the structure of the cutter body of the ultrasonic straight-edge cutter;
the model establishing module of smooth transition of the cutting edge establishes a workpiece coordinate system XYZ at the center of the root of the straight-edged knife, and establishes a model of smooth transition of the cutting edge under the coordinate system, wherein the model comprises mathematical models of a parallel cutting edge curve, an arc cutting edge curve and an end straight-edged curve;
the verification module is used for verifying whether the blade curve is in smooth transition or not and verifying the correctness of the blade curve model;
a coordinate system establishing module for establishing a local coordinate system X based on the grinding point P according to the processing technique of the ultrasonic straight-edged knifeLYLZL；
The position calculating module calculates the position of the center of the grinding wheel under a local coordinate system according to the grinding attitude of the grinding wheel, wherein the position comprises the center position of the grinding wheel and a grinding wheel shaft vector;
and outputting a grinding track module for the smooth transition of the ultrasonic knife edge, and obtaining an expression of the center of the grinding wheel in a workpiece coordinate system through coordinate conversion to obtain the grinding track of the grinding wheel in the smooth transition of the ultrasonic knife edge.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114986268A (en) * | 2022-05-16 | 2022-09-02 | 北京博海康源医疗器械有限公司 | Precise grinding device and micro-blade grinding method |
| CN115194831A (en) * | 2022-08-10 | 2022-10-18 | 杭州电子科技大学 | Novel wedge-shaped edge ultrasonic vibration cutting knife |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114986268A (en) * | 2022-05-16 | 2022-09-02 | 北京博海康源医疗器械有限公司 | Precise grinding device and micro-blade grinding method |
| CN114986268B (en) * | 2022-05-16 | 2023-09-29 | 北京博海康源医疗器械有限公司 | Precise grinding device and micro-blade grinding method |
| CN115194831A (en) * | 2022-08-10 | 2022-10-18 | 杭州电子科技大学 | Novel wedge-shaped edge ultrasonic vibration cutting knife |
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