CN100533316C - Diamond super precision lathe free curved surface processing path generation method - Google Patents

Abstract

The invention belongs to the technical field of ultra-precise work and complex parts manufacturing, which relates to a path generating method of a curved face processing. The method is utilized on a diamond ultra-precise machine tool with three shafts, which comprises first, establishing a coordinate system of a free curved face model of a processing surface of a workpiece, and establishing conversion relationship between the model coordinate system and a machine tool coordinate system, second, conversing the model coordinate of a processing point on the processed free curved face to a coordinate under the coordinate system of the machine tool, third, solving and processing a normal vector of cutting face of a cutter when the point is processed, fourth, projecting the normal vector of the point of the curved face on the cutting face, and compensating a circular arc radius of the cutter on the projection vector direction, and getting a coordinate of the arc center of the cutting edge under the cutting edge coordinate system, traversing the processing point on the free curved face, at last generating a processing path. The limitation of processing the free curved face on the machine tool with three shafts can be broken by adopting the path generating method which is provided by the invention, the invention can achieve ultra-sophisticated processing of the free curved face.

Description

Method for generating free-form surface machining path of diamond ultra-precision lathe

Technical Field

The invention belongs to the technical field of ultra-precision machining and complex part manufacturing, and relates to a method for generating a curved surface machining path.

Background

At present, machinery and equipment in the fields of aerospace, national defense, biomedicine, optics, communication, microelectronics and the like are continuously developed to ultraprecision and miniaturization while improving performance, and in the process, the system has higher and higher requirements on the shape freedom degree of a tiny key device, so that the free-form surface processing technology with an optical quality surface becomes a key technology for driving the development of the fields.

Ultra-precision machining is a leading-edge field of advanced manufacturing and is a technology capable of realizing optical quality machining of a machined surface, namely the shape precision of a workpiece reaches a submicron level, and the surface roughness reaches a nanometer level. The diamond turning tool is adopted for ultra-precision turning, a certain surface roughness can be achieved without repeated processing like grinding, and one-step forming of the optical quality of the processed surface can be achieved, so that the processing efficiency is very high, and the diamond turning tool is a common processing means in ultra-precision processing.

Due to the special shape of the free-form surface, the machine tool is generally required to have multiple degrees of freedom in diamond ultra-precision turning. In recent years, with the development of driving and control technologies, two machining modes, namely Fast Tool (Fast Tool Servo) and Slow Tool (Slow Tool Servo), appear in the three-axis diamond turning machining, and the Fast Tool (Fast Tool Servo) and the Slow Tool (Slow Tool Servo) add feedback or control to the rotation angle of a main shaft, so that the limitation of machining a free-form surface on a three-axis machine Tool is broken through.

Since these two machining techniques are relatively new, up to now, no pre-and post-processing algorithms or modules for free-form surface machining have been provided by relevant research, including machine tool suppliers, both at home and abroad. The machining path generation method is a key basis of the series of algorithms, so that the development of the machining path generation method for the three-axis diamond ultra-precision lathe is necessary.

Disclosure of Invention

The invention aims to provide a free-form surface ultra-precision machining path generation algorithm suitable for a three-axis machine tool, which breaks through the limitation of machining a free-form surface on the three-axis machine tool and realizes the ultra-precision machining of the free-form surface by using the three-axis machine tool.

Therefore, the invention adopts the following technical scheme:

a method for generating a free-form surface processing path of a diamond ultra-precision lathe is used on a three-axis diamond ultra-precision lathe, a main shaft of the lathe can do rotary motion and move along the X axial direction, an encoder for controlling or feeding back the rotation angle of the main shaft to enable the main shaft to rotate along the C axis is installed on the main shaft, and a diamond cutter does Z-direction motion, and the method comprises the following steps:

(1) establishing a free-form surface model coordinate system of a workpiece machining surface, and establishing a conversion relation between a model coordinate system and a machine tool coordinate system according to a relative motion model which converts the rotary motion of the workpiece into the rotary motion of a cutter around a main shaft on the machining surface;

(2) converting the model coordinates of the processing points on the free-form surface into coordinates under a machine tool coordinate system;

(3) solving a normal vector of the cutting surface of the machining cutter when the point is machined;

(4) projecting the normal vector of the point of the curved surface onto the cutting surface, and performing cutter arc radius compensation in the direction of the projection vector to obtain the coordinate of the center of the blade arc in a machine tool coordinate system;

(5) and (4) according to the steps from (2) to (4), performing machining movement, traversing machining points on the free-form surface, and finally generating a machining path.

The step (4) in the method for generating the free-form surface machining path of the diamond ultra-precision lathe preferably comprises the following steps:

(a) solving a normal vector at a processing point by using partial derivatives of the free-form surface model;

(b) calculating a projection vector of the normal vector of the processing point on the cutting surface by using a vector projection method and using the normal vector of the processing point and the normal vector of the current cutting surface;

(c) solving the direction cosine of the projection vector, performing blade arc radius compensation on the processing point by using the direction cosine, and solving the coordinate of the center of the blade arc under a model coordinate system;

(d) and converting the coordinates of the model coordinate system of the center of the circular arc of the cutting edge into the coordinates of the machine tool coordinate system.

The invention has the following remarkable advantages: the invention utilizes the relativity of motion to convert the rotary motion of a workpiece into the rotary motion of a cutter around a main shaft on the processing surface, and provides a method for generating the free-form surface processing path of the diamond ultra-precision lathe based on the principle.

Drawings

FIG. 1 a diamond tool model;

FIG. 2 is a schematic view of relative movement of the cutters;

FIG. 3 is a spiral path in the xoy plane;

fig. 4 is a schematic view of a processing path.

Detailed Description

The common lathe has 2 degrees of freedom, the main shaft can move along the X axial direction besides rotating, and the turning tool moves along the Z direction. After the coding device is arranged on the rotating main shaft, the rotating angle of the rotating main shaft can be controlled or fed back, so that the lathe has 3 rd freedom degree, namely a C axis. Let the coordinates of any point of the machine tool be expressed asWhere p is the X-axis coordinate,is a C-axis coordinate, and Z is a Z-axis coordinate; the complex free-form surface can be processed by only coordinating and controlling the rotation angle of the main shaft and the feeding amount and cutting depth of the turning tool. FIG. 1 is a top view of a diamond turning tool model, wherein the radius of the arc of the nose of the cutting surface is r₀. The coordinate of the arc center of the tool nose can be controlled and positioned in the machining process, and the part of the cutting edge is actually machined, so the arc radius compensation of the coordinate of the machining point is the key of a machining path generation algorithm.

Assuming that a general expression of the free-form surface to be processed is z ═ f (x, y), and assuming corresponding partial derivatives,

<math> <mrow> <mfrac> <mrow> <mo>&PartialD;</mo> <mi>z</mi> </mrow> <mrow> <mo>&PartialD;</mo> <mi>x</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>f</mi> <mi>x</mi> </msub> </mrow></math> <math> <mrow> <mfrac> <mrow> <mo>&PartialD;</mo> <mi>z</mi> </mrow> <mrow> <mo>&PartialD;</mo> <mi>y</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>f</mi> <mi>y</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow></math>

at any point p on the free-form surface₀(x₀，y₀，z₀) Calculating the machine tool coordinate of the arc center of the tool nose during processing

1. Converting the point model coordinates into coordinates in a machine tool coordinate system

d [. cndot ] is an operation symbol for converting an angle to [0 °, 360 °;

2. by utilizing the relative motion of the machining process, the rotary motion of the workpiece on the main shaft is imagined as that the cutter rotates around the main shaft on the machining surface. As shown in FIG. 2, in machining, the face of the tool faces is perpendicular to the plane of the paper and faces inward, and the normal vector of the cutting face

Can be expressed as a number of times,

3. calculating p₀(x₀，y₀，z₀) Normal vector of point on free-form surface

，

<math> <mrow> <mover> <mi>n</mi> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mrow> <mo>-</mo> <mi>f</mi> </mrow> <mi>x</mi> </msub> <mo>,</mo> <msub> <mrow> <mo>-</mo> <mi>f</mi> </mrow> <mi>y</mi> </msub> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow></math>

The projection vector on the cutting surface can be calculated by vector projection, i.e. vector

Is a vector

In the vector

The projection on the plane is carried out,

$=(a,b,c)$

4. vector projection

Expressed in the form of directional cosines

Wherein,

<math> <mrow> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>cos</mi> <msub> <mi>&alpha;</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mi>a</mi> <msqrt> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> </msqrt> </mfrac> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <msub> <mi>&beta;</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mi>b</mi> <msqrt> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> </msqrt> </mfrac> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <msub> <mi>&gamma;</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mi>c</mi> <msqrt> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> </msqrt> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow></math>

the model coordinate system coordinate o (x) of the arc center of the tool nose_t，y_t，z_t) It can be calculated as,

<math> <mrow> <mrow> <mfenced open='{' close='' separators=','> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mi>cos</mi> <msub> <mi>&alpha;</mi> <mi>p</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mi>cos</mi> <msub> <mi>&beta;</mi> <mi>p</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mi>cos</mi> <msub> <mi>&gamma;</mi> <mi>p</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow></math>

also using equation (2), the corresponding machine coordinates can be calculated

According to a certain mode, for example, a spiral mode in the xoy plane shown in fig. 3, a certain number of points on the free-form surface are traversed to obtain the center coordinates of the circular arc of the tool nose corresponding to each point, and then the generation of the machining path is completed.

Free form surface

According to a series of implementation steps of the invention, a tool radius r is obtained₀A machining path of 1.0mm, as shown in fig. 4; and according to the generated path, a three-axis diamond ultra-precision lathe is used for processing, and an ideal free-form surface shape can be obtained.

The invention is suitable for the free-form surface processing of optical quality by a three-axis diamond ultra-precision lathe, and is also suitable for the free-form surface processing of other lathes in similar processing modes. The equation of the free-form surface can be given by a specific mathematical expression, and for the model of the innumerable mathematical expression, a certain mathematical fitting method is adopted for mathematical description, and the method is also suitable, so that the method has certain universality.

Claims (2)

1. A method for generating a free-form surface processing path of a diamond ultra-precision lathe is used on a three-axis diamond ultra-precision lathe, a main shaft of the lathe can do rotary motion and move along the X axial direction, an encoder for controlling or feeding back the rotation angle of the main shaft to enable the main shaft to rotate along the C axis is installed on the main shaft, and a diamond cutter does Z-direction motion, and the method comprises the following steps:

(1) establishing a free-form surface model coordinate system of a workpiece machining surface, and establishing a conversion relation between a model coordinate system and a machine tool coordinate system according to a relative motion model which converts the rotary motion of the workpiece into the rotary motion of a cutter around a main shaft on the machining surface;

(2) converting the model coordinates of the processing points on the free-form surface into coordinates under a machine tool coordinate system;

(3) solving a normal vector of the cutting surface of the machining cutter when the point is machined;

(4) projecting the normal vector of the point of the curved surface onto the cutting surface, and performing cutter arc radius compensation in the direction of the projection vector to obtain the coordinate of the center of the blade arc in a machine tool coordinate system;

(5) and (4) according to the steps from (2) to (4), performing machining movement, traversing machining points on the free-form surface, and finally generating a machining path.

2. The diamond ultra-precision lathe free-form machining path generation method according to claim 1, wherein the step (4) comprises the steps of:

(a) solving a normal vector at a processing point by using partial derivatives of the free-form surface model;

(b) calculating a projection vector of the normal vector of the processing point on the cutting surface by using a vector projection method and using the normal vector of the processing point and the normal vector of the current cutting surface;

(c) solving the direction cosine of the projection vector, performing blade arc radius compensation on the processing point by using the direction cosine, and solving the coordinate of the center of the blade arc under a model coordinate system;

(d) and converting the coordinates of the model coordinate system of the center of the circular arc of the cutting edge into the coordinates of the machine tool coordinate system.

Images