CN1290667C - Grinding method for shaping bended surface of workpiece - Google Patents

Abstract

The present invention relates to a bending, shaping and grinding method by a grinding tool, which belongs to the technical field of grinding processing in mechanical processing. The existing shaping and grinding method has the main problems that the grinding working surface of the grinding tool needs to be frequently trimmed to be consistent to the outline shape of a workpiece, and the trimming is even more difficult for the aspheric surface; the grinding tool has no universality, and one grinding tool can only be used for processing one outline-shaped workpiece. Although a strain disc method can solve the problems, the strain disc method has the limitation that the strain disc method can only be used for processing outline shape of the workpiece with big curvature radius and has the problems of softness, complex hardware, theoretical errors, etc. The present invention causes the original state of a beam-shaped grinding tool to be simplified, force with different magnitudes, directions and kinds of is applied to the grinding tool, the same grinding tool can be bent into different curves, and a revolution surface used as a bus bar is consistent to the outline shape of a workpiece which is to be processed. When the grinding tool is trimmed, the grinding tool is restored to the original state, and then, the grinding tool is restored. The present invention is suitable for the grinding of grinding tools with various dimensions and various revolution surfaces.

Description

Grinding tool bending forming polishing

Technical field

The invention belongs to the grinding technology field in the machining, be applicable to the surface of revolution of grinding work-piece, and, be mainly used in the processing aspheric surface.

Background technology

In the grinding technology field, two kinds of forming lapping processing methods related to the present invention are arranged.A kind of beam shape grinding tool forming lapping method that is called as of the first, this is a kind of routine techniques, it is that the grinding working face of a beam shape grinding tool is made the bus cylinder consistent with the bus of the surface of revolution of workpiece to be processed profile in advance.In process of lapping, to often repair grinding tool and grind working face.It two is a kind of processing methods that are called as strain disc forming lapping method, this has been done introduction by " advanced Optical manufacture technology " book (Yang Li chief editor) that Science Press publishes calendar year 2001, see Fig. 1, strain disc 1 is a large scale, have better rigidity, rounded flat basal disc, with it as abrasive disk, at fixing some groups of (as the two groups) rigid cylindricals 2 of its periphery, every group has 3 such cylinders 2, distribute apart from hexagonal angle mutually on same circumference, every group of interior cylinder 2 connected together by one group of flexible steel wire 3.During with this strain disc 1 grinding work-piece surface of revolution, send instruction by computer, control is installed in the driver on the strain disc 1, make and respectively organize steel wire 3 contractions, it is centroclinal to strain disc 1 that each organizes cylinder 2, and bulging deformation takes place strain disc 1, form convex surface, see Fig. 2, control convex surface processing place shape in real time, so that it is consistent with the processing work profile.During the finishing grinding tool, only need steel wire 3 is loosened, counter stress dish 1 grinding working face carries out plane finishing and gets final product.

Summary of the invention

The problem that prior art one exists is the common problem that exists of forming lapping method, the one, because grinding tool weares and teares in process of lapping, need the finishing grinding tool, the finishing of grinding tool is very difficult, and to frequently repair grinding tool, when the workpiece to be processed profile was aspheric surface, not only the finishing of grinding tool was more difficult, and it is very difficult that the making of grinding tool also becomes; The 2nd, the versatility of grinding tool is poor, need all will be equipped with a cover grinding tool to each profile to be processed.The problem one that prior art two exists is the processing that it only is applicable to the larger radius of curvature surface of the work; The 2nd, this method still only is applicable to the processing of concave surface; The 3rd, this method need be equipped with complex control software and hardware; The 4th, because strain disc 1 stressed symmetry can only produce limited distortion, be the surface of revolution of particular curve for bus, also there is theoretical mismachining tolerance in this method.

In order to overcome the shortcoming of prior art, realize that how with, grinding tool finishing easily a grinding tool, can process the concave, convex surface of revolution of various sizes, different shape, simplified control system is eliminated theoretical error, and we have invented a kind of grinding tool bending forming polishing.

The present invention realizes like this, the beam shape thing of getting a cross section and be rectangle is as grinding tool, its bottom surface is for grinding working face, it has two states, be reset condition and case of bending, the use of grinding tool is carried out under case of bending, its grinding working face is the surface that a shape is determined under reset condition, determine constant power when it being imposed in a certain direction one, this grinding tool then transfers one to by reset condition and determines constant case of bending, at this moment, its bottom surface is a bus and the identical cylinder of surface of revolution bus to be processed, and this bus is a curve, this cylinder is for grinding working face, the different reset conditions of grinding tool, the variety classes that is imposed, the power of direction and size, the decision grinding tool is which kind of curve and concrete form thereof at case of bending bottom surface bus, when needs finishing grinding tool, remove applied force, make it return to reset condition, repair again.

Technique scheme integrates the advantage of two kinds of prior aries, simultaneously, has overcome the shortcoming of two kinds of prior aries.In the present invention, though also there are the wearing and tearing of grinding tool,, the reset condition of a grinding tool determines, and usually it is designed to simple shape, as the bottom surface is designed to the plane, this just makes the finishing of grinding tool become very easy.For grinding tool with a certain reset condition, to its power that imposes variety classes, direction and size, can produce different flexural deformation, realized that to a certain extent a grinding tool uses more.The present invention's grinding tool size range broad arrives several meters greatly, and is little of several millimeters, so, processing work size range broad.Grinding tool is imposed power, when this power is a kind of top-down pressure, curved down grinding tool takes place can process concave curved surface, when this power was a kind of pulling force from bottom to top, the grinding tool of bending in generations can be processed convex surface.For obtaining a certain curve, only need impose one determine, constant power get final product, need not the control system of complexity, also do not have theoretical error.

Description of drawings

Fig. 1 is the view before the strain disc distortion.Fig. 2 is the view after the strain disc distortion.Fig. 3 is that reset condition is that master highly constant, that width becomes grinding tool looks, vertical view.Fig. 4 is that reset condition is a stereogram highly constant, that width becomes grinding tool.Fig. 5 imposes the moment of flexure schematic diagram.Fig. 6 imposes moment of flexure apparatus structure schematic diagram.Fig. 7 is that reset condition is that highly constant, width becomes the form schematic diagram in coordinate system after the grinding tool bending.Fig. 8 be reset condition be highly become, the master of the constant grinding tool of width looks, vertical view.Fig. 9 be reset condition be highly become, the stereogram of the constant grinding tool of width.Figure 10 imposes the concentrfated load schematic diagram.Figure 11 imposes concentrfated load apparatus structure schematic diagram.Figure 12 imposes the distributed load schematic diagram.Figure 13 imposes distributed load apparatus structure schematic diagram.

The specific embodiment

As the beam shape thing with square-section of grinding tool, its reset condition can be designed as 4 kinds of situations, 1, highly constant, width is constant; 2, highly constant, width becomes; 3, highly become, width is constant; 4, highly change, width become.Highly constantly be meant that upper and lower bottom surface is parallel this situation of plane.Equally, the constant two sides that are meant of width are parallel this situation of plane.Highly become in two kinds of situation, one is meant two ends height value maximum, reduces intermediate altitude value minimum gradually along horizontal axis to the centre-height value from two ends; Two are meant two ends height value minimum, increase intermediate altitude value maximum gradually along horizontal axis to the centre-height value from two ends.Equally, the width change also is divided into two kinds of situations, and one is meant two ends width value maximum, reduces intermediate width value minimum gradually along horizontal axis to the center width value from two ends; Two are meant two ends width value minimum, increase intermediate width value maximum gradually along horizontal axis to the centre-height value from two ends.The original-shape of these beam shape thing two sides and upper and lower bottom surface has decisive influence to the grinding tool bottom surface because of the curve that stressed bending produces.

The power that imposes has 3 types, and 1, moment of flexure; 2, concentrfated load; 3, distributed load.Wherein, can impose load, promptly press from top to bottom, or draw from bottom to top from both direction; And applying of moment of flexure also is divided into curved down and upward curved two kinds.

Illustrate the present invention below, example 1, setting grinding tool 4 is highly constant, width becomes (first kind of situation), sees Fig. 3, shown in Figure 4.Impose moment M, and, see Fig. 5, shown in Figure 6 for curved down.Grinding tool 4 is the simply supported beam state, by precession bolt 5,6, screws out bolt 7,8, pulls the end plate 9,10 that is connected as a single entity with grinding tool 4, makes grinding tool 4 be subjected to moment M, and wherein 11 is bracing frame.Grinding tool 4 is bent downwardly distortion, sees shown in Figure 7ly, and the mid point when not being out of shape with simply supported beam is the origin of coordinates, and its axis is an X-axis, sets up rectangular coordinate system.The curve that produces for making is a parabola, does following derivation:

Parabolical normal equation is:

$y=\frac{1}{2p}{x}^2$

For making distortion consistent with parabola, following formula can be write as:

$y+k=\frac{x^2}{2p}$

For obtaining k, establish the stressed symmetry of simply supported beam, distortion symmetry, half of simply supported beam longly is l, when x=± 1, y=0, so have:

$k=\frac{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="C20041000618100071.png"\; state="\{\{state\}\}">l</figure-callout>}}^2}{2p}$

The parabolic equation that is produced is:

$y+\frac{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="C20041000618100071.png"\; state="\{\{state\}\}">l</figure-callout>}}^2}{2p}=\frac{x^2}{2p}$

Just:

$y=\frac{1}{2p}(x^2-l^2),-l\&le;x\&le;l$

For realizing this curve, to calculate through mechanics, higher mathematics, the width B of grinding tool 4 satisfies following formula and gets final product:

$B=\frac{12M}{p^{2}E{h}^3}\sqrt{{({\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="C20041000618100071.png"\; state="\{\{state\}\}">p</figure-callout>}}^2+x^2)}^3}$

Wherein, h is the height of grinding tool 4, and E is the elastic modelling quantity of grinding tool 4 materials; When x=0, B=B ₀

According to same calculating process, when:

$B=\frac{12M\sqrt{{(a^4-a^2{x}^2+b^2{x}^2)}^3}}{a^4\mathrm{<figure-callout\; id="3"\; label="bE\; h"\; filenames="C20041000618100071.png"\; state="\{\{state\}\}">bE</figure-callout>}{h}^{}{}^3}$

The deformation curve of grinding tool 4 is oval:

$\frac{x^2}{a^2}+\frac{{(y-k)}^2}{b^2}=1,-l\&le;x\&le;l$

According to same calculating process, when:

$B=\frac{12M\sqrt{{[a^2(a^2+x^2)+b^2{x}^3]}^3}}{a^4\mathrm{<figure-callout\; id="3"\; label="bE\; h"\; filenames="C20041000618100071.png"\; state="\{\{state\}\}">bE</figure-callout>}{h}^{}{}^3}$

The deformation curve of grinding tool 4 is a hyperbola:

$-\frac{x^2}{a^2}+\frac{{(y+k)}^2}{b^2}=1,-l\&le;x\&le;l$

Example 2, setting grinding tool 4 highly becomes (first kind of situation), width is constant, sees Fig. 8, shown in Figure 9.Set up rectangular coordinate system by example 1.Consider the symmetry of simply supported beam, right half part only is discussed is got final product, impose down winding square, it is identical with example 1 that it applies mode.Through mechanics, higher mathematics analysis, h satisfies following formula when height:

$h=\frac{1}{x}\sqrt[3]{\frac{12M}{\mathrm{EB}(20a+30\mathrm{bx})}}$

When x=0, h=h ₀,

The deformation curve that is produced is one 6 curves:

y＝ax ⁵+bx ⁶+c 0≤x≤l

Wherein, a, b, c will satisfy boundary condition.

Example 3, set that grinding tool 4 is highly constant, width is constant, considers the symmetry of simply supported beam, right half part only is discussed get final product, the mode that applies of 2 kinds of different power of branch is inquired into respectively below,

1, impose concentrfated load pressure, see Figure 10, shown in Figure 11, bolt 12 contacts for point with grinding tool 4.Precession bolt 12 can impose concentrfated load P to grinding tool 4.Through mechanics, higher mathematics analysis, the deformation curve that is produced is one 3 curves:

$y=\frac{P}{12\mathrm{EJ}}(3l{x}^2-x^3-2l^3),0\&le;x\&le;l$

Wherein, J is the cross sectional moment of inertia of simply supported beam.

2, impose distributed load pressure, see Figure 12, shown in Figure 13, bolt 13 contacts for face with grinding tool 4.Precession bolt 13 can impose distributed load q to grinding tool 4.Through mechanics, higher mathematics analysis, the deformation curve that is produced is one 4 curves:

$y=\frac{q}{24\mathrm{EJ}}(6l^{2}x-x^4-5l^4),0\&le;x\&le;l$

Claims (9)

1, a kind of forming lapping method, the bottom surface of grinding tool is for grinding working face, it is characterized in that, the beam shape thing of getting a cross section and be rectangle is as grinding tool, it has two states, be reset condition and case of bending, the use of grinding tool is carried out under case of bending, its grinding working face is the face that a shape is determined under reset condition, determine constant power when it being imposed in a certain direction one, this grinding tool then transfers one to by reset condition and determines constant case of bending, at this moment, its bottom surface is a bus and the identical cylinder of surface of revolution bus to be processed, this bus is a curve, and this cylinder is for grinding working face, the different reset conditions of grinding tool, the variety classes that is imposed, the power of direction and size, the decision grinding tool is which kind of curve and concrete form thereof at case of bending bottom surface bus, when needs finishing grinding tool, removes applied force, make it return to reset condition, repair again.

2, forming lapping method according to claim 1 is characterized in that, the reset condition of grinding tool for highly constant, width is constant, upper and lower bottom surface is a parallel plane, two sides are parallel plane.

3, forming lapping method according to claim 1 is characterized in that, the reset condition of grinding tool becomes for highly constant, width, upper and lower bottom surface is a parallel plane, two ends width value maximum reduces along horizontal axis to the center width value gradually from two ends, intermediate width value minimum.

4, forming lapping method according to claim 1 is characterized in that, the reset condition of grinding tool becomes for highly constant, width, upper and lower bottom surface is a parallel plane, two ends width value minimum increases along horizontal axis to the center width value gradually from two ends, intermediate width value maximum.

5, forming lapping method according to claim 1 is characterized in that, the reset condition of grinding tool is that highly change, width are constant, two sides are parallel plane, two ends height value maximum reduces along horizontal axis to the centre-height value gradually from two ends, intermediate altitude value minimum.

6, forming lapping method according to claim 1 is characterized in that, the reset condition of grinding tool is that highly change, width are constant, two sides are parallel plane, two ends height value minimum increases along horizontal axis to the centre-height value gradually from two ends, intermediate altitude value maximum.

7, forming lapping method according to claim 1 is characterized in that, the power that is imposed is moment of flexure.

8, forming lapping method according to claim 1 is characterized in that, the power that is imposed is concentrfated load.

9, forming lapping method according to claim 1 is characterized in that, the power that is imposed is distributed load.

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