CN113199647B - Method and device for determining brittle-plastic transition critical cutting thickness - Google Patents
Method and device for determining brittle-plastic transition critical cutting thickness Download PDFInfo
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- B28D1/00—Working stone or stone-like materials, e.g. brick, concrete or glass, not provided for elsewhere; Machines, devices, tools therefor
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Abstract
The method comprises the steps of firstly, carrying out pre-cutting treatment on a workpiece, and then calculating to obtain a relational expression between the maximum undeformed chip thickness and the radial distance according to the relation between the linear speed and the rotating speed of a machine tool spindle, the relation between the feeding amount and the feeding speed of each rotation of the spindle and the relation between the feeding amount and the radial distance of the geometric center of the workpiece; then processing and measuring the workpiece with the determined cutting area, determining a brittle-plastic transformation point and calculating to obtain the radial distance from the brittle-plastic transformation point to the transformation point of the geometric center of the workpiece; and finally, calculating the brittle-plastic transition critical cutting thickness according to the radial distance of the transition point and the relational expression. The invention utilizes the contourgraph to detect the machined surface, and calculates the critical cutting thickness of the material under the parameter through the detection result.
Description
Technical Field
The invention relates to the technical field of brittle optics, in particular to a method and a device for determining brittle-plastic transition critical cutting thickness.
Background
With the continuous development of the photoelectric technology, brittle optical materials are increasingly required in space detection, national defense safety and civil optical elements nowadays. However, these optical materials have high brittleness and high hardness, and the surface roughness of the optical elements is low, the surface shape is generally complex, and the conventional processing method is difficult to meet the surface precision requirement of these optical elements. The single-point diamond turning adopts an ultra-precision machine tool with an air hydrostatic spindle and a hydrostatic guide rail and a diamond cutter with a nanoscale blunt-edge round radius to remove the ultra-thin cutting of the part, so that the machined surface can reach nanoscale roughness. Thus, single point diamond turning provides a good solution for ultra-precision machining of these optical elements.
The brittle material is easy to generate cracks in the processing process due to poor processing performance, and the surface quality is reduced. Studies have shown that when the cut thickness is less than a certain critical value, the material is removed in a plastic manner and the machined surface is free from cracks and pits. This critical value is called the brittle-to-ductile transition critical cut thickness. The premise for realizing the cutting of the brittle optical element with the nano-scale surface roughness is to enable the material to be processed in a plastic domain all the time in the processing process. Therefore, the determination of the brittle-to-plastic transition critical cutting thickness has great significance for improving the surface quality and the processing efficiency.
The current methods for determining critical cutting thickness mainly include: indentation, scoring, fly-cutting and spiral scoring. The indentation method extrudes a material through a pressure head, and observes the surface appearance to determine the critical cutting thickness, but the method belongs to quasi-static loading and cannot reflect the influence of the change of various parameters on the critical cutting thickness in the actual processing process; the scratching method determines the critical cutting thickness by changing the cutting depth and scratching, but the scratching speed is lower and has a larger difference with the actual linear speed of turning; the fly-cutting method has a cutting linear velocity faster than that of a scratching method, but the front angle of the cutter is continuously changed in the material removing process, and the front angle is not consistent with the actual turning condition; the spiral line scribing method determines the critical cutting thickness by performing a variable-cutting-depth spiral line scribing method on the surface of the part, but the critical cutting thickness cannot be accurately influenced by the anisotropy of the material due to different scribing depths at different circumferential positions in the scribing process.
Disclosure of Invention
In order to solve the problems of the critical cutting thickness determination method in the prior art, the embodiment of the invention provides a method for determining the brittle-plastic transition critical cutting thickness. The machined surface is detected by using a contourgraph, the critical cutting thickness of the material under the parameter is calculated through the detection result, and compared with the traditional method, the method is closer to the critical cutting thickness value under the actual machining condition. The specific technical scheme is as follows:
the method for determining the brittle-plastic transition critical cutting thickness provided by the embodiment of the invention comprises the following steps:
mounting a diamond cutter, and performing pre-cutting treatment on the workpiece;
calculating a relational expression between the maximum undeformed chip thickness and the radial distance according to the relation between the linear speed and the rotating speed of a machine tool spindle, the relation between the feeding amount per rotation of the spindle and the feeding speed, and the relation between the feeding amount and the radial distance of the geometric center of the workpiece;
determining a cutting area of a workpiece after pre-cutting, and performing constant linear velocity single-point diamond turning on the workpiece in the cutting area;
acquiring a radial profile curve of the workpiece, determining a brittle-ductile transition point, and calculating the radial distance from the brittle-ductile transition point to the transition point of the geometric center of the workpiece according to the brittle-ductile transition point;
and calculating the brittle-ductile transition critical cutting thickness according to the relation among the radial distance of the transition point, the maximum undeformed chip thickness and the radial distance.
Further, the relationship between the maximum undeformed chip thickness and the radial distance is:
in the formula: r is the arc radius of the tool nose, ap is the back bite, v is the linear velocity, F is the feed speed, and R is the radial distance.
Further, the cutting area of the workpiece after pre-cutting is a circular ring belt area.
Further, the obtaining a radial profile curve of the workpiece, determining a brittle-plastic transition point, and calculating a radial distance from the brittle-plastic transition point to a transition point of a geometric center of the workpiece according to the brittle-plastic transition point includes:
measuring the machined workpiece by using a contourgraph, and obtaining a profile curve of the workpiece according to a measurement result;
searching a discontinuity point of a roughness value existing on the contour curve, and taking the discontinuity point as a brittle-plastic transition point;
measuring the measuring distance between the brittle-plastic transition point and the contour starting point behind the cutting area;
and calculating the radial distance of the transition point from the brittle-plastic transition point to the geometric center of the workpiece according to the relation between the measured distance and the radial distance.
A second aspect of the present invention provides an apparatus for determining a critical cut thickness for brittle-to-plastic transition, including:
the pre-cutting module is used for mounting a diamond cutter and performing pre-cutting treatment on a workpiece;
the relation obtaining module is used for calculating a relation between the maximum undeformed chip thickness and the radial distance according to the relation between the linear speed and the rotating speed of the main shaft of the machine tool, the relation between the feeding amount per rotation of the main shaft and the feeding speed, and the relation between the feeding amount and the radial distance of the geometric center of the workpiece;
the determining module is used for determining a cutting area of the workpiece after pre-cutting and processing the workpiece in the cutting area;
the brittle-plastic transition point determining module is used for acquiring profile curves of the plastic region and the brittle region of the workpiece, determining a brittle-plastic transition point, and calculating the radial distance from the brittle-plastic transition point to the transition point of the geometric center of the workpiece according to the brittle-plastic transition point;
and the cutting thickness calculation module is used for calculating the brittle-plastic transition critical cutting thickness according to the calculated relational expression among the radial distance of the transition point, the maximum undeformed chip thickness and the radial distance.
Further, the relationship between the maximum undeformed chip thickness and the radial distance is:
in the formula: r is the arc radius of the tool nose, ap is the back bite, v is the linear velocity, F is the feed speed, and R is the radial distance.
Further, the brittle transition point determining module includes:
the profile curve module is used for measuring the machined workpiece by adopting a profiler and obtaining a profile curve of the workpiece according to a measurement result;
the system comprises a discontinuity point searching module, a shape memory module and a shape memory module, wherein the discontinuity point searching module is used for searching a discontinuity point of a roughness value existing on a contour curve and taking the discontinuity point as a brittle transition point;
the measuring module is used for measuring the measuring distance between the brittle-plastic transition point and the contour starting point behind the cutting area;
and the radial distance calculation module of the transition point is used for calculating the radial distance from the brittle transition point to the transition point of the geometric center of the workpiece according to the relation between the measured distance and the radial distance.
Further, the cutting area of the workpiece after pre-cutting is a circular ring belt area.
According to the method and the device for determining the critical cutting thickness of brittle-plastic transition, provided by the embodiment of the invention, firstly, a workpiece is subjected to pre-cutting treatment, and then a relational expression between the maximum undeformed chip thickness and the radial distance is calculated according to the relation between the linear speed and the rotating speed of a machine tool spindle, the relation between the feeding amount and the feeding speed of each rotation of the spindle and the relation between the feeding amount and the radial distance of the geometric center of the workpiece; then processing and measuring the workpiece with the determined cutting area, determining a brittle-plastic transformation point and calculating to obtain the radial distance from the brittle-plastic transformation point to the transformation point of the geometric center of the workpiece; and finally, calculating the brittle-plastic transition critical cutting thickness according to the radial distance of the transition point and the relational expression. According to the invention, the machined surface is detected by using the contourgraph, the critical cutting thickness of the material under the parameter is calculated according to the detection result, and compared with the traditional method, the method is closer to the critical cutting thickness value under the actual machining condition.
Drawings
FIG. 1 is a flow chart of a method for determining a critical cutting thickness for brittle-to-plastic transition according to the present invention.
FIG. 2 is a schematic view of the ultra-precision machining structure under a T-shaped layout guide rail lathe;
FIG. 3 is a model diagram of maximum undeformed cut thickness;
FIG. 4 is a schematic illustration of the dynamic variation of the maximum undeformed cut thickness during machining;
FIG. 5 is a view of a processing area, with a hatched portion being the processing area;
FIG. 6 is a distribution diagram of a brittle-plastic worked area of a worked part;
FIG. 7a is a profile curve after profilometer measurement;
FIG. 7b is a process diagram of extracting regions using a reference after profilometer measurement;
FIG. 8 is a graph showing the measured distance change between the abrupt change point and the contour start point after the cutting region;
in the figure: 1-machine tool spindle, 2-vacuum chuck, 3-workpiece to be processed, 4-diamond tool, 5-tool rest, 6-machine tool Z-axis guide rail and 7-machine tool X-axis guide rail.
Detailed Description
The present invention is described below with reference to the accompanying drawings, but the present invention is not limited thereto.
Referring to fig. 1, a flow chart of a method for determining a critical cutting thickness for brittle-to-plastic transition according to the present invention includes:
s1: and mounting a diamond cutter, and performing precutting treatment on the workpiece.
Clamping a workpiece material on a machining main shaft of an ultra-precision machine tool, and mounting a designed diamond cutter on a cutter frame of the ultra-precision machine tool; as shown in fig. 2, 1 is a machine tool spindle, 2 is a vacuum chuck, 3 is a workpiece to be machined, 4 is a diamond tool, 5 is a tool rest, 6 is a machine tool Z-axis guide rail, and 7 is a machine tool X-axis guide rail.
In order to avoid uneven back bite ap of a lathe plane caused by factors such as vertical error of a machine tool guide rail during subsequent cutting, in the embodiment of the invention, a workpiece needs to be subjected to one-time micro-cutting before a workpiece material is cut, and a cutting area is the whole plane.
S2: and calculating a relational expression between the maximum undeformed chip thickness and the radial distance according to the relation between the linear speed and the rotating speed of the machine tool spindle, the relation between the feeding amount per revolution of the spindle and the feeding speed, and the relation between the feeding amount and the radial distance of the geometric center of the workpiece.
The linear velocity of the machine spindle is indicated by the letter v, the rotational speed is indicated by S, the feed per revolution of the spindle is indicated by F, and the feed rate is indicated by F.
The relationship between the above linear velocity v and the spindle rotational speed S is given by equation (1):
where r is the radial distance from the cutting point of the tool to the geometric center of the workpiece.
The relationship between the feed amount F per revolution during cutting and the feed speed F is given by equation (2):
the relation between the feed amount f per revolution in the cutting process and the radial position r from the cutting point to the geometric center of the workpiece can be obtained by combining the formula (1) and is shown as a formula (3):
in the ordinary machining, the value of the maximum undeformed cutting thickness tmax is equal to the back bite ap, but in the ultra-precision machining, since the material removal amount is extremely small, the value of the feed amount f is low, and f is satisfied<
When the cutting is finished (wherein R is the radius of the circular arc of the nose), the cutting model is shown in FIG. 3, the value of the maximum undeformed cutting thickness tmax is no longer equal to ap, and the expression is shown in formula (4):
formula (5) can be obtained by combining formula (4) with formula (3):
from the formula (5), on the premise that the arc radius R of the tool nose, the back bite ap, the linear velocity v and the feeding speed F are constant, the maximum undeformed cutting thickness in the cutting process only changes with the change of R, that is, the maximum undeformed cutting thickness tmax dynamically changes in the process that the tool is fed in the X direction, as shown in fig. 4.
S3: determining a cutting area of the workpiece after pre-cutting, and processing the workpiece in the cutting area.
In the practice of the invention, the cutting area of the pre-cut workpiece does not cover the entire face, but takes only one annular band area near the outer circumference side, as shown in FIG. 5. The use of the cutting in the ring belt region results from the following advantages: the influence on the dynamic balance caused by overlarge main shaft rotating speed due to an excessively small r value close to the center is avoided; the abrasion of the cutter caused by long-distance cutting of the diamond cutter is avoided; when the contourgraph is used for measurement, the geometric central point is not easy to find due to plane measurement, and the middle circular ring step provides a reference for position calculation for measurement. In the embodiment of the present invention, the processed workpiece is as shown in fig. 6, in which the black portion is a plastic processed region, the roughness value is small, the white portion is a brittle processed region, and the roughness value is large, so that a sudden change in roughness occurs at the boundary between the black portion and the white portion. The material has anisotropy, and r values of brittle-plastic transition points in all directions are different, so that the intersection line of the black area and the white area presents a petal shape.
S4: and acquiring a radial profile curve of the workpiece, determining a brittle-ductile transition point, and calculating the radial distance from the brittle-ductile transition point to the transition point of the geometric center of the workpiece according to the brittle-ductile transition point.
In the embodiment of the invention, a profile instrument is adopted to measure the machined workpiece, and the profile curve of the workpiece is obtained according to the measurement result, the profile curve is shown in figure 7a, for the convenience of measurement, the measurement starting point is a position on a center circle, which is 1-2mm away from a step in the direction of the circle center, and the measurement is carried out along the radial direction to the outer circle. After obtaining the measurement results, the area behind the step is manually extracted and analyzed as shown in fig. 7 b. The discontinuity of the roughness values, which is the brittle-to-plastic transition point, which is present on the contour curve is sought, the cause of the discontinuity of the roughness values being the propagation of a crack right up to the machined surface.
S5: and calculating the brittle-ductile transition critical cutting thickness according to the relation among the radial distance of the transition point, the maximum undeformed chip thickness and the radial distance.
The roughness value discontinuity on the profile curve is found, and the distance measurement function is used to measure the distance between the discontinuity and the starting point of the profile after the cutting area, as shown in fig. 8. The r value of the brittle-plastic transition point can be calculated by the formula (6):
wherein r represents the radial distance of the brittle transition point, r0 represents the radial distance of the measurement starting point, the obtained r value is substituted into the formula (5), and the obtained tmax is the brittle transition critical cutting thickness tc of the workpiece under the parameter. The minimum critical cutting thickness in each typical crystal orientation is obtained, and when cutting is performed under the parameters, the full plastic domain cutting can be realized by selecting the maximum undeformed cutting thickness smaller than the critical cutting thickness.
The contour starting point is the contour starting point after the cutting area, namely the center circle step position.
In an alternative embodiment of the present invention, the method further comprises optimizing cutting parameters, wherein the cutting parameters include: during the process of cutting a workpiece, cutting parameters are changed at intervals of preset time to obtain a change rule of the critical cutting thickness along with each parameter, and a proper cutting parameter is selected based on the change rule, so that the brittle-plastic transition critical cutting thickness can be accurately determined.
Although the invention has been described in detail above with reference to a general description and specific examples, it will be apparent to one skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (8)
1. A method for determining a critical cutting thickness for brittle-to-plastic transition is characterized by comprising the following steps:
mounting a diamond cutter, and performing precutting treatment on the workpiece;
calculating a relational expression between the maximum undeformed chip thickness and the radial distance according to the relation between the linear speed and the rotating speed of a machine tool spindle, the relation between the feeding amount per rotation of the spindle and the feeding speed, and the relation between the feeding amount and the radial distance of the geometric center of the workpiece;
determining a cutting area of a workpiece after pre-cutting, and performing constant linear velocity single-point diamond turning on the workpiece in the cutting area;
acquiring a radial profile curve of the workpiece, determining a brittle-ductile transition point, and calculating the radial distance from the brittle-ductile transition point to the transition point of the geometric center of the workpiece according to the brittle-ductile transition point;
and calculating the brittle-ductile transition critical cutting thickness according to the relation among the radial distance of the transition point, the maximum undeformed chip thickness value and the radial distance.
2. The method for determining a brittle-plastic transition critical cutting thickness as claimed in claim 1, characterized in that the relation between the maximum undeformed chip thickness value and the radial distance is:
in the formula: r is the arc radius of the tool nose, ap is the back bite, v is the linear velocity, F is the feed speed, and R is the radial distance.
3. The method for determining the critical cutting thickness for brittle-ductile transition as claimed in claim 1, wherein the cutting area of the pre-cut workpiece is a circular ring belt area.
4. The method of determining a brittle transition critical cutting thickness as claimed in claim 1, wherein the step of obtaining a workpiece radial profile curve, determining a brittle transition point, and calculating a radial distance of the brittle transition point to a transition point of a geometric center of the workpiece based on the brittle transition point comprises:
measuring the machined workpiece by using a profile instrument, and obtaining a profile curve of the workpiece according to a measurement result;
searching a discontinuity point of a roughness value existing on the contour curve, and taking the discontinuity point as a brittle-plastic transition point;
measuring the measuring distance between the brittle-plastic transition point and the contour starting point behind the cutting area;
and calculating the radial distance from the brittle-plastic transition point to the transition point of the geometric center of the workpiece according to the relation between the measured distance and the radial distance.
5. An apparatus for determining a critical cut thickness for brittle-to-plastic transition, comprising:
the pre-cutting module is used for mounting a diamond cutter and performing pre-cutting treatment on a workpiece;
the relational expression obtaining module is used for calculating a relational expression between the maximum undeformed chip thickness value and the radial distance according to the relation between the linear speed and the rotating speed of the spindle of the machine tool, the relation between the feeding amount per rotation of the spindle and the feeding speed, and the relation between the feeding amount and the radial distance of the geometric center of the workpiece;
the determining module is used for determining a cutting area of a workpiece after pre-cutting and performing constant linear velocity single-point diamond turning on the workpiece in the cutting area;
the brittle-plastic transition point determining module is used for acquiring profile curves of the plastic region and the brittle region of the workpiece, determining a brittle-plastic transition point, and calculating the radial distance from the brittle-plastic transition point to the transition point of the geometric center of the workpiece according to the brittle-plastic transition point;
and the cutting thickness calculation module is used for calculating the brittle-plastic transition critical cutting thickness according to the calculated relational expression among the radial distance of the transition point, the maximum undeformed chip thickness and the radial distance.
6. The apparatus for determining a brittle-ductile transition critical cutting thickness according to claim 5, wherein the relationship between the maximum undeformed chip thickness and the radial distance is:
in the formula: r is the arc radius of the tool nose, ap is the back bite, v is the linear velocity, F is the feed speed, and R is the radial distance.
7. The brittle transition critical cutting thickness determining apparatus according to claim 5, wherein the brittle transition point determining module includes:
the profile curve module is used for measuring the machined workpiece by adopting a profiler and obtaining a profile curve of the workpiece according to a measurement result;
the system comprises a discontinuity searching module, a shape memory module and a shape memory module, wherein the discontinuity searching module is used for searching a roughness value discontinuity point existing on a contour curve and taking the discontinuity point as a brittle-plastic transition point;
the measuring module is used for measuring the measuring distance between the brittle-plastic transition point and the contour starting point behind the cutting area;
and the transition point radial distance calculation module is used for calculating the radial distance from the brittle and plastic transition point to the geometric center of the workpiece according to the relation between the measured distance and the radial distance.
8. The apparatus for determining a brittle-brittle transition critical cutting thickness as claimed in claim 5, characterized in that the cutting area of the pre-cut workpiece is a ring belt area.
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