CN113885432B - Cutter path planning method for few-axis numerical control machining face gear - Google Patents
Cutter path planning method for few-axis numerical control machining face gear Download PDFInfo
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- CN113885432B CN113885432B CN202111249337.2A CN202111249337A CN113885432B CN 113885432 B CN113885432 B CN 113885432B CN 202111249337 A CN202111249337 A CN 202111249337A CN 113885432 B CN113885432 B CN 113885432B
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Classifications
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/35—Nc in input of data, input till input file format
- G05B2219/35349—Display part, programmed locus and tool path, traject, dynamic locus
Abstract
The invention relates to a cutter path planning method for a few-axis numerical control machining face gear, which mainly comprises the following steps: the method comprises the steps of establishing a face gear universal machining tool radius optimization method by analyzing the change conditions of chord length deviation and residual height in the machining process of the universal tool; and (3) establishing a face gear universal cutter processing path planning method by analyzing the tracks of the face gears processed by the universal processing cutters. The cutter selection and path generation planning method provided by the invention can effectively avoid blindly searching the maximum allowed machining cutter and a proper machining area in numerical control machining software, so that the numerical control machining process of the face gear can be circulated, the accurate selection of the face gear machining cutter based on few-axis numerical control machining and the reasonable planning of the machining path are realized, the machining precision of the high-order bearing curved surface of the face gear can be effectively improved, and the efficient machining of the tooth surface is realized.
Description
Technical Field
The invention relates to the technical field of precise depiction and processing of gears, in particular to a tool path planning method for a few-axis numerical control processing face gear.
Background
The face gear transmission has the characteristics of simple structure, low vibration and noise, insensitivity to installation errors, power split, high interchangeability and the like, and has wide application prospect in the fields of intersecting shaft power and motion transmission. However, since the face gear is a high-order complex curved surface with a variable tooth thickness, special processing equipment is required for processing and manufacturing the face gear, and a final precise profile correction processing procedure based on meshing performance is not available at all. And domestic research on face gear processing technology does not have a generalized program, and a generalized face gear numerical control processing technology is not established at present. Therefore, the research on the general processing method of the face gear with few shafts realizes the accurate depiction and efficient processing of the high-order bearing curved surface of the face gear, and has important theoretical significance and engineering application value for improving the precision manufacturing level of the high-performance face gear in China and improving the development capability of the high-performance power transmission element in China.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a tool path planning method for processing a face gear by few-axis numerical control, so as to realize accurate depiction and efficient processing of a high-order bearing curved surface of the face gear.
The technical scheme adopted by the invention is as follows:
the invention provides a cutter path planning method for a few-axis numerical control machining face gear, which specifically comprises the following steps:
s1: establishing a face gear universal machining tool radius optimization method by analyzing interference conditions between the universal tool and a tooth surface in the machining process;
s2: the universal cutter processing path planning method for the face gear is established by analyzing the variation condition of chord length deviation and residual height in the cutter processing process and the processing cutter processing face gear track.
Further, in the step S1, interference conditions with the tooth surface during the machining process of the tool are summarized as follows:
first case: the interference between the cutter and the non-processing surface is that the selection condition of the cutter radius is:
r b ≤min{||o r p i，j ||，(i＝1，...m；j＝1，...n)} (1)
wherein r is b For the few-axis numerical control machining tool radius, m represents the number of discrete curves of the tooth surface of the face gear, n represents the number of discrete points on each discrete curve, o r Is the center point of a cutting fillet of a cutter, p i，j Discrete points of tooth surfaces of the face gears;
second case: the constraint conditions of the cutter and the interference of the tooth groove bottom are as follows:
r b ≤d r1 (2)
wherein r is b For few-axis numerical control machining tool radius d r1 The vertical distance from the center of the machining tool to the tooth bottom line is controlled for a few axes;
third case: the local interference near the tool contact point, the selection condition of the tool radius is:
wherein, kappa max Is the maximum principal curvature of the tooth surface at the point of contact of the tool.
Further, the specific process of step S2 is as follows:
the cutter path problem is that on the basis of cutter radius selection and processing area division, the cutter radius selection is developed on the basis of three interference calculation methods mentioned in the step S1, and the distance between the center of the cutter and each tooth surface discrete point is calculated, so that the tooth surface of the face gear is divided into different processing areas according to the cutter radius; meanwhile, considering the existence of curved surface machining errors in the actual machining process, introducing the concept of residual height and chord length deviation in the step, wherein the residual height and chord length deviation can be regulated and controlled through the number of cutter contact paths;
when the maximum residual height is smaller than the allowable value, the minimum number of tool contact paths may be determined, and then a tool contact point is generated for each tool contact path; for each tool contact path, when the maximum chord length deviation is smaller than the allowable value, the number of tool contact points can be increased or decreased to determine the minimum value of the tool contact points, thereby determining the minimum number of tool contact paths meeting the residual height chord length deviation;
thus, the tool vertex coordinate calculation formula can be obtained as follows:
O c ＝q+r b ·N q -r b ·l c (4)
wherein O is c Is the tool vertex, l c Is the axis of the tool, N q Represents the normal direction at the q point, r b The radius of the machining tool is controlled for a few axes;
based on the tool path planning algorithm set forth above, a tool path on one side of the tooth surface can be obtained.
Compared with the prior art, the invention has the following beneficial effects:
the cutter selection and path generation planning method provided by the invention can effectively avoid blindly searching the maximum allowed machining cutter and a proper machining area in numerical control machining software, so that the numerical control machining process of the face gear can be circulated, the accurate selection of the face gear machining cutter based on few-axis numerical control machining and the reasonable planning of the machining path are realized, the machining precision of the high-order bearing curved surface of the face gear can be effectively improved, and the efficient machining of the tooth surface is realized.
Drawings
FIG. 1 is a schematic diagram of a case-interference;
FIG. 2 is a schematic diagram of a second interference scenario;
FIG. 3 is a case three interference schematic;
FIG. 4 is a schematic diagram of residual height and bias;
FIG. 5 is a schematic diagram of tooth surface discrete point chord deviation and residual height;
FIG. 6 is a tool path plan at a contact point;
fig. 7 is a final tool path plan for one side of the tooth face.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
The invention provides a cutter path planning method for a few-axis numerical control machining face gear, which comprises the following specific implementation steps:
s1: establishing a face gear universal machining tool radius optimization method by analyzing interference conditions between the universal tool and a tooth surface in the machining process;
in the cutter machining process, the selection of the cutter radius is crucial, the cutter radius is increased blindly, the number of cutter contact paths is reduced, but the interference risk is increased, the tooth surface of the face gear is a complex curved surface with high-order variable curvature, the change of the tooth surface is complex, and the machining interference condition is easy to generate. The possible interference situations are now summarised as follows:
first case: interference between tool and non-machined surface
During the processing of the cutter, interference with the non-processed surface may occur; to avoid this, it is necessary to further define the distance between the tool and the non-machined surface; as shown in fig. 1, when the radius of the few-axis numerically controlled tool is larger than the distance between the center of the tool and the adjacent non-machined surface, an interference phenomenon occurs; because the tooth surface of the face gear is formed by fitting discrete points, the phenomenon can be avoided by calculating the distance between the discrete points of the tooth surface and the center of the cutter; if the calculation finds interference, the tool radius needs to be reduced until interference is no longer occurring.
Let p be i，j The selection conditions for obtaining the cutter radius for the discrete points of the tooth surface of the face gear are as follows:
r b ≤min{||o r p i，j ||，(i＝1，...m；j＝1，...n)} (1)
wherein m represents the number of discrete curves of the tooth surface of the face gear, and n represents the number of discrete points on each discrete curve. The values of m and n are near the possible critical points and can be as large as possible in order to obtain more accurate results.
Second case: interference of cutter and tooth slot bottom
When machining face gear tooth surface transitions using a few axis numerical control machining tool as shown in fig. 2, the tool may interfere with the face gear tooth bottom. In order to avoid this, it is necessary to constrain the distance between the tool tip and the tooth bottom line, i.e. to further limit the tool radius.
Assuming that the vertical distance from the center of the few-axis numerical control machining tool to the tooth bottom line is d r1 The constraint conditions of the cutter radius are:
r b ≤d r1 (2)
third case: localized interference of tool contact point attachments
As shown in fig. 3, the local interference generally occurs when the tool working surface is concave, and the vicinity of the convex tool contact point does not contact the rest of the contact points. When the radius of the tool is larger than that of the concave curved surface, a local interference situation occurs. In order to avoid this local interference, the tool radius is selected as follows:
wherein, kappa max Is the maximum principal curvature of the tooth surface at the point of contact of the tool.
By analyzing the three conditions, the required few-axis numerical control machining tool radius of each discrete point on the tooth surface of the face gear can be determined. For each discrete curve, a minimum value of the discrete point on the curve corresponding to the radius of the tool can be selected. And forming a corresponding processing area by using the dispersion curves with the same tool radius. Thus, the classified tooth surface machining area can be optimally selected and planned.
S2: the method comprises the steps of establishing a universal cutter processing path planning method of the face gear by analyzing the change conditions of chord length deviation and residual height in the cutter processing process and processing the face gear track of the cutter;
the method comprises the steps of firstly determining discrete tooth surface points, discretizing the tooth surface of a face gear into n rows of tooth surface points according to the discrete curved surface digital meshing principle of the face gear, wherein the m rows refer to the tooth surface point rows in the tooth width direction of the face gear, and the n rows refer to the tooth surface point columns in the tooth height direction of the face gear; then selecting a cutter radius, wherein the cutter radius is mainly selected by expanding according to the interference calculation methods mentioned in the previous step, and calculating the distance between the center of the cutter and each tooth surface discrete point, so that the tooth surface of the face gear is divided into different processing areas according to the cutter radius; and finally, planning a tool path of the machining area.
Firstly introducing the introduction of the residual height and chord length deviation, and in the process of the face gear few-axis numerical control machining, taking the face gear curved surface which is fitted by using the discrete numerical curved surface meshing theory as a final machining target, and carrying out forming cutting on a face gear blank. Theoretically, if the cutting point on the cutter can be in tangential contact with each point of the discrete curved surface of the face gear, the discrete curved surface of the face gear is obtained without curved surface machining errors.
In the process of processing the tool to approach the designed curved surface, the residual height is controlled. Symbol delta for residual height s Two adjacent contact directions are denoted by the symbol L i And L i+1 And (3) representing. As shown in fig. 4, N i，j Is the point q i，j Normal vector of unit tooth surface on the upper surface, residual height is in vector N i，j And q i，j q i+1，j The formed in-plane calculation and the residual height calculation formula are as follows:
wherein l s Is the distance between the contact directions of two adjacent cutters; r is (r) b The radius of the machining tool is controlled by the number of small shafts; kappa (kappa) s Is the local curvature along a direction perpendicular to the tool contact direction, the signs corresponding to convex and concave surfaces, respectively. If the residual height is greater than acceptableThe value will need to be increased by the number of total tool contact paths until the condition is met.
The concept of tool tooth face chord deviation needs to be introduced below. In the actual machining process, a series of sample points are selected as actual contact points of the tools, and the actual contact points of the tools form a contact path of the tools. In the processing of sample points, chord length deviation between adjacent sample points, which is the maximum deviation in the straight line distance connecting two adjacent cutter contact points in the cutter contact direction, is inevitably generated. Symbol delta for chord length deviation c As shown in FIG. 4, two adjacent tool contact points are shown with q i,j And q i+1,j Representation, where q i,j The j-th tool contact point representing the i-th tool contact direction. The calculation formula of the chord length deviation is as follows:
wherein, kappa c Is the local curvature of the corresponding part of the contact direction of the cutter; l (L) c Representing the distance between two consecutive tool contact points. If the chord deviation is calculated to be greater than the acceptable value, the total number of points of contact in the tool contact direction needs to be increased until the chord deviation reaches the acceptable range.
The tool path is planned by contacting the adjacent tools in the direction of the distance l s Radius r of tool b And tooth surface surrounding q i，j q i+1，j Local curvature of part κ s An approximation of the residual height can be obtained.
B i，j Is composed of vector N i，j And q i，j q i+1，j The direction vector of the determined plane is calculated as follows:
B i，j ＝N i，j ×(N i，j ×q i，j q i+1，j ) (6)
along with calculating the direction vector B i，j Along B i，j Tooth surface at q i，j The upper normal curvature can be calculated according to equation (5); also, κ i+1 May also be calculated. Thereafter, the process (r e ，l s ，κ s ) Sum (r) e ，l s ，κ i+1，j ) Substituting formula (4) to calculate two residual heights, and the larger one after calculation is recorded asConsidering j=1, 2,3, …, n is in all +.>The maximum residual height obtained in (1) is designated->
Taking all adjacent tool contact paths into consideration as one area, maximum valueThe maximum residual height of this region, denoted +.>If->Too large, the number of tool contact paths can be increased by Δm each time until +.>The condition is satisfied. If->The number of tool contact paths may also be reduced by reducing Δm, initially less than the allowable value. Based on the above considerations, when the maximum residual height is smaller than the allowable value, the minimum number of tool contact paths may be determined. In addition, the minimum value should be selected as an approximation, and if Δm is larger than 1, it is unnecessary to take too much calculation time.
Generating a tool contact point for each tool contact path; for each tool contact path, when the maximum chord deviation is less than the allowable value, the number of tool contact points may be increased or decreased to determine a minimum value of tool contact points. As shown in FIG. 5, in tangential direction T i，j Calculate q i，j Local curvature of the point. T (T) i，j Is a hypothetical direction vector not only in the tangential plane q i，j Also on vector N i，j And q i，j q i+1，j On the plane formed. Thus, it is possible to obtain:
T i，j ＝N i，j ×(N i，j ×q i，j q i+1，j ) (7)
and generating tool coordinate data. As shown in FIG. 6, the radius is r b The fewer-axis numerical control machining tool of (2) is contacted with one side tooth surface of the face gear at a point q, O c Is the tool vertex, l c Is the axis of the tool, O r Is the center point of the cutting fillet of the cutter passing through the q point; symbol N for normal direction at q point q The tangential direction at point q is denoted by the symbol T assuming that the normal direction of the contact points are all directed to the outside of the face gear tooth face q And (3) representing.
Thus, the tool vertex coordinate calculation formula can be obtained as follows:
O c ＝q+r b ·N q -r b ·l c (8)
the result of the obtained tool path on the tooth surface side based on the tool path planning algorithm set forth above is shown in fig. 7.
The above examples are only illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the scope of protection defined by the claims of the present invention without departing from the spirit of the design of the present invention.
Claims (1)
1. A tool path planning method for a few-axis numerically controlled machined face gear, characterized by comprising the steps of:
s1: establishing a face gear universal machining tool radius optimization method by analyzing interference conditions between the universal tool and a tooth surface in the machining process;
s2: the method comprises the steps of establishing a universal cutter processing path planning method of the face gear by analyzing the change conditions of chord length deviation and residual height in the cutter processing process and processing the face gear track of the cutter;
in the step S1, interference conditions with the tooth surface during the tool machining are summarized as follows:
first case: the interference between the cutter and the non-processing surface is that the selection condition of the cutter radius is:
r b ≤min{||o r p i，j ||，(i＝1，...m；j＝1，...n)} (1)
wherein r is b For the few-axis numerical control machining tool radius, m represents the number of discrete curves of the tooth surface of the face gear, n represents the number of discrete points on each discrete curve, o r Is the center point of a cutting fillet of a cutter, p i,j Discrete points of tooth surfaces of the face gears;
second case: the constraint conditions of the cutter and the interference of the tooth groove bottom are as follows:
r b ≤d r1 (2)
wherein r is b For few-axis numerical control machining tool radius d r1 The vertical distance from the center of the machining tool to the tooth bottom line is controlled for a few axes;
third case: the local interference near the tool contact point, the selection condition of the tool radius is:
wherein, kappa max Is the maximum principal curvature of the tooth surface at the tool contact point;
the specific process of the step S2 is as follows:
the cutter path problem is that on the basis of cutter radius selection and processing area division, the cutter radius selection is developed on the basis of three interference calculation methods mentioned in the step S1, and the distance between the center of the cutter and each tooth surface discrete point is calculated, so that the tooth surface of the face gear is divided into different processing areas according to the cutter radius; meanwhile, considering the existence of curved surface machining errors in the actual machining process, introducing the concept of residual height and chord length deviation in the step S2, wherein the residual height and chord length deviation can be regulated and controlled through the number of cutter contact paths;
when the maximum residual height is smaller than the allowable value, the minimum number of tool contact paths may be determined, and then a tool contact point is generated for each tool contact path; for each tool contact path, when the maximum chord length deviation is smaller than the allowable value, the number of tool contact points can be increased or decreased to determine the minimum value of the tool contact points, thereby determining the minimum number of tool contact paths meeting the residual height chord length deviation;
thus, the tool vertex coordinate calculation formula can be obtained as follows:
O c ＝q+r b ·N q -r b ·l c (4)
wherein O is c Is the tool vertex, l c Is the axis of the tool, N q Represents the normal direction at the q point, r b The radius of the machining tool is controlled for a few axes;
based on the cutter path planning algorithm, a cutter path on one side of the tooth surface can be obtained;
the calculation formula of the chord length deviation is as follows:
wherein, kappa c Is the local curvature of the corresponding part of the contact direction of the cutter; l (L) c Representing the distance between two consecutive tool contact points; if the calculated chord deviation is greater than the acceptable value, the total number of contact points in the contact direction of the cutter needs to be increased until the chord deviation reaches the acceptable range;
the residual height calculation formula is:
wherein l s Is the distance between the contact directions of two adjacent cutters; r is (r) b The radius of the machining tool is controlled by the number of small shafts; kappa (kappa) s Is the local curvature along a direction perpendicular to the tool contact direction, the signs corresponding to convex and concave surfaces, respectively; if the residual height is greater than acceptable, the number of total tool contact paths needs to be increased until the condition is met.
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