CN103831673A - Method for calculating material removal rate for liquid magnetic grinding tool small hole finishing processing - Google Patents

Abstract

The invention relates to a method for calculating a material removal rate for liquid magnetic grinding tool small hole finishing processing. According to magneto-rheological features of a liquid magnetic grinding tool, a material removal mechanism of liquid magnetic grinding tool small hole finishing processing is explained from a microcosmic point of view. A double-blade circle radius model is adopted to serve as a cutting model of a single abrasive particle for research, a mathematical expression of the material removal rate of small hole finishing processing is deduced, theoretical analysis is carried out on influence factors of the mathematical expression, and accordingly it is concluded that the material removal rate of finishing processing is in direct proportion to the square of the diameter of the abrasive particle, shearing stress of the liquid magnetic grinding tool and fluid pressure, and is in inverse proportion to the yield limit of a workpiece material. In a certain range, removal efficiency of the material can be improved by increasing the diameter of abrasive particles, inlet pressure and current intensity, and quality of surfaces obtained after the surfaces are processed for a period of time is correspondingly improved.

Description

A kind of liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods

Technical field

The present invention relates to polishing manufacture field, relate in particular to a kind of liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods.

Background technology

Modern industry is produced hole inner wall surface quality has been proposed to more and more higher requirement, although in recent years, domestic, outer researcher has proposed some non-traditional finishing and Compound Finishing technology, these technology are utilized electric energy, magnetic energy, acoustic energy, luminous energy, chemical energy or adopt the compound action of multiple processing method, have complementary advantages realize the polishing processing to workpiece and process, in some hole surface precision finishings, obtain good effect, but these process technologies have best applications scope separately, at aperture, particularly shoulder hole, cross bore, the polishing processing aspects such as irregularly-shaped hole exist deficiency or certain limitation, be difficult to meet the requirement of modern manufacturing industry to hole precision finishing, liquid-magnetic abrasive tool Finishing can complete the polishing processing to aperture, but owing to there is no quantitative material removing rate computation model, cannot realize quantitative control, the exploitation of special purpose machine tool and applying of this technology are affected.

In view of above-mentioned defect, creator of the present invention has obtained this creation finally through long research and practice.

Summary of the invention

The object of the present invention is to provide a kind of liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods, provide theoretical support for overcoming above-mentioned technological deficiency.

For achieving the above object, the invention provides a kind of liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods, adopt " twolip radius of circle " model to carry out the research of single abrasive grain cutting Model, the material removing rate that draws polishing processing and abrasive grain diameter square, shear stress and fluid pressure be directly proportional, be inversely proportional to the yield limit of workpiece material, the Material Removal Mechanism computational process of aperture polishing processing is:

Known according to Vickers hardness definition:

$F_{r,n}=\frac{1}{2}\mathrm{H\&pi;}{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">X</figure-callout>}}_2\mathrm{\&delta;}---\left(1\right)$

In formula, the Vickers hardness that H is workpiece, X ₂average sword circular diameter while contact with workpiece for abrasive particle, δ is the compression distance of abrasive particle at surface of the work;

Single abrasive grain stress balance in the horizontal direction, F _{r, n}=F _p,

derivation draws:

$\mathrm{\&delta;}=\frac{\mathrm{<figure-callout\; id="1"\; label="p\; X"\; filenames="HSA0000101244970000022.png"\; state="\{\{state\}\}">p</figure-callout>}{X_{}}^{}{{}_1}^2}{2H{X}_2}---\left(2\right)$

In formula, X ₁average sword circular diameter while contact with magnetic particle for abrasive particle;

The suffered fluid pressure of abrasive grain is larger, and abrasive grain particle diameter is larger, and its compression distance at surface of the work can be darker, is pressed into accordingly area larger.

Single abrasive grain in the vertical direction stress balance, F _{r, t}=F _s,

draw:

$A_p=\frac{\mathrm{\&pi;\&tau;}{{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA0000101244970000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1}^2}{4{\mathrm{\&sigma;}}_s}---\left(3\right)$

In formula, σ _sfor the yield limit of workpiece material, the shear stress that τ is liquid-magnetic abrasive tool; Shear stress, the abrasive grain particle diameter yield limit larger, workpiece material of liquid-magnetic abrasive tool is less, and abrasive particle is larger at pressure people's area of surface of the work, and cutting effect is more obvious.

Suppose be pressed into material in area by complete resection unit are on material removing rate VRR be:

VRR=η A _pυ _relatively(4)

In formula, η is the number of abrasive grain in unit are.

Get border

try to achieve

Simultaneous above-mentioned (3), (4), (5) obtain material removal efficiency VRR in unit are:

$\mathrm{VRR}=\mathrm{\&eta;}\frac{\mathrm{\&pi;\&tau;}{{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA0000101244970000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1}^2}{4{\mathrm{\&sigma;}}_s}[{\mathrm{\&upsi;}}_{z0}+\frac{3{{\mathrm{\&tau;}}_0}^2}{{\mathrm{\&eta;}}_0}\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}-(\frac{{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{16{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">D</figure-callout>}}{2{\mathrm{\&eta;}}_0}{\mathrm{\&tau;}}_0)]---\left(6\right)$

Above-mentioned various in, F _pthe fluid pressure that-abrasive particle is suffered; F _{r, t}the tangential resistance that-abrasive particle is suffered, F _{r, n}the normal direction resistance that-abrasive particle is suffered; F _sthe shearing force that-abrasive particle is suffered; A _p-abrasive particle be pressed into area, be pressed into half spherical crown in tangential direction projection.

Further, in the Material Removal Mechanism computational process of above-mentioned aperture polishing processing, make following hypothesis:

The processing of I polishing is mainly to complete by the micro-cutting of abrasive grain, ignores other processing factors;

II abrasive particle is ideal rigid body, ignores the distortion of self in process, and contacting between abrasive grain and workpiece is plasticity contact;

In III Micro cutting Process, abrasive grain is made uniform motion at surface of the work;

IV ignores gravity and the magnetic suspension force effect of particle.

Further, in aperture polishing process, the flow mechanism of liquid-magnetic abrasive tool in circular duct got the thin cylinder of infinitesimal unit centered by axially bored line, and establishing its radius is r, and length is dz; Detailed process is:

Step a, the distribution of shear stress of the thin cylinder of calculating aperture unit;

Step b, the constitutive equation of structure liquid-magnetic abrasive tool;

Step c, the VELOCITY DISTRIBUTION of liquid-magnetic abrasive tool in calculating aperture.

Further, the detailed process of above-mentioned steps a is:

Known according to Newton's second law:

2πrdr[p-(p+dp)]+2πrdz·τ-2π(r+dr)dz(τ+dτ)＝0 (7)

Above formula abbreviation also removes the infinite event of high-order and can obtain:

$\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{1}{r}\&CenterDot;\frac{d\left(\mathrm{\&tau;r}\right)}{\mathrm{dr}}=0---\left(8\right)$

Formula (8) the right and left be multiplied by rdr again integration can obtain

$\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{2}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\mathrm{\&tau;r}=C---\left(9\right)$

Get border r=0, try to achieve constant C=0; Formula (9) distortion arranges and can draw distribution of shear stress formula

$\mathrm{\&tau;}=-\frac{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">r</figure-callout>}}{2}\frac{\mathrm{dp}}{\mathrm{dz}}---\left(10\right)$

Further, in above-mentioned steps b, the character of liquid-magnetic abrasive tool is described by Bingham constitutive equation:

$\left\{\begin{array}{cc}\mathrm{\&tau;}={\mathrm{\&eta;}}_0\mathrm{\&gamma;}+\mathrm{sign}\left(\mathrm{\&gamma;}\right){\mathrm{\&tau;}}_0& (\mathrm{\&tau;}>{\mathrm{\&tau;}}_0)\\ \mathrm{\&gamma;}=0& (\mathrm{\&tau;}<{\mathrm{\&tau;}}_0)\end{array}\right.---\left(11\right)$

In formula, τ ₀for the shear yield stress of grinding tool, η ₀for liquid-magnetic abrasive tool plasticity viscosity coefficient, γ is shear strain rate, the flowing velocity that equals liquid-magnetic abrasive tool along the rate of change of aperture direction, $\mathrm{\&gamma;}=\frac{{\mathrm{d\&upsi;}}_{\mathrm{zr}}}{\mathrm{dr}}.$

Further, the detailed process of above-mentioned steps c is,

Get boundary condition τ=τ ₀, try to achieve " solid-state core " zone radius

$R_0=2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}---\left(12\right)$

To the shear stress τ=η in polishing area ₀γ+τ ₀being out of shape derives can obtain:

$\mathrm{\&gamma;}=\frac{\mathrm{\&tau;}-{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}=\frac{{\mathrm{d\&upsi;}}_{\mathrm{zr}}}{\mathrm{dr}}(\mathrm{\&tau;}>{\mathrm{\&tau;}}_0)---\left(13\right)$

Above formula integration, draws

${\mathrm{\&upsi;}}_{\mathrm{zr}}=-[\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{4{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}r]+C_1(R_0\&le;r\&le;\frac{D}{2})---\left(14\right)$

Get boundary condition: r=R ₀time υ _zr=υ _z0(υ _z0determined by flow), try to achieve so VELOCITY DISTRIBUTION formula of liquid-magnetic abrasive tool in aperture:

$\left\{\begin{array}{cc}{\mathrm{\&upsi;}}_{\mathrm{zr}}={\mathrm{\&upsi;}}_{z0}+\frac{3{{\mathrm{\&tau;}}_0}^2}{{\mathrm{\&eta;}}_0}\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}-[\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{4{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}r]& (2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}\&le;r\&le;\frac{D}{2})\\ {\mathrm{\&upsi;}}_{\mathrm{zr}}={\mathrm{\&upsi;}}_{z0}& (0\&le;\mathrm{\&tau;}<2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1})\end{array}\right.---\left(15\right)$

Work as r=R ₀time, υ _zrfor the speed υ on " solid-state core " border _z0; When

time, υ _zrfor the relative sliding velocity of abrasive grain and surface of the work.

Beneficial effect of the present invention is compared with prior art: the present invention, according to the magnetorheological characteristic of liquid-magnetic abrasive tool, has set forth the Material Removal Mechanism of liquid-magnetic abrasive tool grinding hole polishing processing from microcosmic angle.By the cutting Model research to single abrasive particle, derive the material removing rate mathematic(al) representation of aperture polishing processing and its influence factor has been carried out to theory analysis.Design the processing experimental device of the through-hole parts such as a set of applicable aperture, shoulder hole, cross bore, irregularly-shaped hole and verified by experiment the impacts of factor on material removing rate and surface roughness such as abrasive grain, inlet pressure, current strength.

The present invention proves by Mathematical Modeling, to a certain degree increasing the removal efficiency that abrasive grain diameter, inlet pressure and current strength are conducive to improve material in scope, the corresponding raising of surface quality of aperture inwall after processing a period of time, but in the time that surface roughness value drops to certain numerical value, too high material removing rate likely caused processing, and finally caused surface quality variation.

Accompanying drawing explanation

Fig. 1 is liquid-magnetic abrasive tool aperture inner wall surface integral processing machine reason figure of the present invention;

Fig. 2 is liquid-magnetic abrasive tool element of fluid Z-direction force diagram of the present invention;

Fig. 3 is twolip circle model and the force analysis figure of abrasive grain of the present invention;

Fig. 4 is liquid-magnetic abrasive tool grinding hole Experimental equipment of the present invention;

Fig. 5 is the affect schematic diagram of abrasive grain of the present invention on working (machining) efficiency and surface roughness;

Fig. 6 is the affect schematic diagram of inlet pressure of the present invention on working (machining) efficiency and surface roughness;

Fig. 7 is the affect schematic diagram of current strength of the present invention on working (machining) efficiency and surface roughness.

The specific embodiment

Below in conjunction with accompanying drawing, technical characterictic and the advantage with other above-mentioned to the present invention are described in more detail.

The present invention, take mangneto phase transformation theory as guidance, has set forth the Material Removal Mechanism of liquid-magnetic abrasive tool hole polishing processing from microcosmic angle.Adopt " twolip radius of circle " model to carry out the research of single abrasive grain cutting Model, draw the material removing rate mathematic(al) representation of aperture polishing processing.

Refer to shown in Fig. 1, it is liquid-magnetic abrasive tool aperture inner wall surface integral processing machine reason figure of the present invention, liquid-magnetic abrasive tool is a kind of novel intelligent precision finishing abrasive material proposing based on mangneto phase transformation theory, and it is made up of carrier fluid, magnetic-particle, abrasive grain and stabilizing agent etc.Magnetic-particle in liquid-magnetic abrasive tool forms chain or column structure along magnetic field line direction under magnetic fields, magnetic chain is clamped in abrasive grain between magnetic chain as the binding agent of emery wheel, whole grinding tool can be regarded one " flexible abrasive wheel " as, in the time that " flexible abrasive wheel " clamp-oned from aperture, the abrasive grain and the magnetic-particle that contact with aperture inwall carry out scratching, ploughing, micro-cutting to contact-making surface, thereby reach the object of polishing processing.

As seen from Figure 1, in polishing process, abrasive grain is subject to the chucking power that resistance that workpiece applies and magnetic-particle provide, when the maximum grip power acting on abrasive grain, be the tangential component of the shear stress τ of liquid-magnetic abrasive tool while being less than the resistance that hole wall provides, destroyed under the effect of the resistance that the extruding force that magnetic chain structure provides at power source and hole wall provide; In the time acting on chucking power tangential component on abrasive grain and be greater than the suffered resistance of abrasive grain, abrasive grain produces relative sliding at surface of the work, and surface of the work is carried out to roll extrusion, scratching and cutting.For minute protrusions, the tangential component of the suffered chucking power of abrasive grain is enough to be cut away; For larger projection, although the tangential component of the suffered maximum grip power of abrasive grain can not once be cut away, but can cause surface of the work that small flow occurs or produce fatigue crack, exceed after the flow limit or fatigue crack expansion of material when small flow is added to, bossing generation fatigue fracture strips down from workpiece.

Refer to shown in Fig. 2, it is liquid-magnetic abrasive tool element of fluid Z-direction force diagram of the present invention, in aperture polishing process, for the flow mechanism of Study of Liquid magnetic abrasive tool in circular duct, centered by axially bored line, get the thin cylinder of infinitesimal unit, establishing its radius is r, and length is dz.For simplifying derivation, make following desirable hypothesis:

I at any one time differentiation element makes uniform motion.

II ignores the impact of liquid-magnetic abrasive tool gravity.

In magnetic field, liquid-magnetic abrasive tool is in concretion state, and the kinematic coefficient of viscosity of fluid is very large, and liquid-magnetic abrasive tool is approximate regarding as in laminar condition in aperture, and the force analysis of thin cylinder unit as shown in Figure 2.

Step a, the distribution of shear stress of the thin cylinder of calculating aperture unit;

Known according to Newton's second law:

2πrdr[p-(p+dp)]+2πrdz·τ-2π(r+dr)dz(τ+dτ)＝0 (1)

Above formula abbreviation also removes the infinite event of high-order and can obtain:

$\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{1}{r}\&CenterDot;\frac{d\left(\mathrm{\&tau;r}\right)}{\mathrm{dr}}=0---\left(2\right)$

Formula (2) the right and left be multiplied by rdr again integration can obtain

$\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{2}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\mathrm{\&tau;r}=C---\left(3\right)$

Get border r=0, try to achieve constant C=0; Formula (3) distortion arranges and can draw distribution of shear stress formula

$\mathrm{\&tau;}=-\frac{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">r</figure-callout>}}{2}\frac{\mathrm{dp}}{\mathrm{dz}}---\left(4\right)$

Step b, the constitutive equation of structure liquid-magnetic abrasive tool;

In liquid-magnetic abrasive tool polishing process, under magnetic fields, grinding tool meets Bingham dielectric property.

Therefore,, in process, the character of liquid-magnetic abrasive tool can be described by Bingham constitutive equation:

$\left\{\begin{array}{cc}\mathrm{\&tau;}={\mathrm{\&eta;}}_0\mathrm{\&gamma;}+\mathrm{sign}\left(\mathrm{\&gamma;}\right){\mathrm{\&tau;}}_0& (\mathrm{\&tau;}>{\mathrm{\&tau;}}_0)\\ \mathrm{\&gamma;}=0& (\mathrm{\&tau;}<{\mathrm{\&tau;}}_0)\end{array}\right.---\left(5\right)$

In formula, τ ₀for the shear yield stress of grinding tool, η ₀for liquid-magnetic abrasive tool plasticity viscosity coefficient, γ is shear strain rate, the flowing velocity that equals grinding tool along the rate of change of aperture direction,

Step c, the VELOCITY DISTRIBUTION of liquid-magnetic abrasive tool in calculating aperture;

Known according to Bingham dielectric property, if the liquid-magnetic abrasive tool between different aspects will occur relatively to flow, τ > τ ₀; If τ < is τ ₀, γ=0, the liquid-magnetic abrasive tool between different aspects keeps identical speed, and now Bingham medium forms " solid-state core ".From formula (4), shear stress is directly proportional to radius r, and near axially bored line, τ value is less, now τ < τ ₀, therefore aperture near axis must have solid-state " core " to exist.

Get boundary condition τ=τ ₀, try to achieve " solid-state core " zone radius

$R_0=2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}---\left(6\right)$

To the shear stress τ=η in polishing area ₀γ+τ ₀being out of shape derives can obtain:

$\mathrm{\&gamma;}=\frac{\mathrm{\&tau;}-{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}=\frac{{\mathrm{d\&upsi;}}_{\mathrm{zr}}}{\mathrm{dr}}(\mathrm{\&tau;}>{\mathrm{\&tau;}}_0)---\left(7\right)$

Above formula integration, draws

${\mathrm{\&upsi;}}_{\mathrm{zr}}=-[\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{4{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}r]+C_1(R_0\&le;r\&le;\frac{D}{2})---\left(8\right)$

Get boundary condition: r=R ₀time υ _zr=υ _z0(υ _z0determined by flow), try to achieve

so VELOCITY DISTRIBUTION formula of liquid-magnetic abrasive tool in aperture:

$\left\{\begin{array}{cc}{\mathrm{\&upsi;}}_{\mathrm{zr}}={\mathrm{\&upsi;}}_{z0}+\frac{3{{\mathrm{\&tau;}}_0}^2}{{\mathrm{\&eta;}}_0}\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}-[\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{4{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}r]& (2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}\&le;r\&le;\frac{D}{2})\\ {\mathrm{\&upsi;}}_{\mathrm{zr}}={\mathrm{\&upsi;}}_{z0}& (0\&le;\mathrm{\&tau;}<2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1})\end{array}\right.---\left(9\right)$

Work as r=R ₀time, υ _zrfor the speed υ on " solid-state core " border _z0; When

time, υ _zrfor the relative sliding velocity of abrasive grain and surface of the work.

In order to study better the cutting scheme of micron order irregular polyhedrons structured abrasives particle, adopt " twolip radius of circle " model to carry out the research of single abrasive grain cutting Model.

Refer to shown in Fig. 3, twolip circle model and force analysis figure that it is abrasive grain of the present invention, in figure, F _pthe fluid pressure that-abrasive particle is suffered; F _{r, t}the tangential resistance that-abrasive particle is suffered, F _{r, n}the normal direction resistance that-abrasive particle is suffered; F _sthe shearing force that-abrasive particle is suffered; A _p-abrasive particle be pressed into area, be pressed into half spherical crown in tangential direction projection.

Known according to above-mentioned Analysis on Mechanism process, abrasive grain can be regarded the slip coining process of this rigid ball surface model at surface of the work as to the polishing process of workpiece.For the Material Removal Mechanism of research aperture polishing processing, make following hypothesis:

The processing of I polishing is mainly to complete by the micro-cutting of abrasive grain, ignores other processing factors (as chemical attack).

II abrasive particle is ideal rigid body, ignores the distortion of self in process, and contacting between abrasive grain and workpiece is plasticity contact.

In III Micro cutting Process, abrasive grain is made uniform motion at surface of the work.

IV ignores gravity and the magnetic suspension force effect of particle.

Known according to Vickers hardness definition:

$F_{r,n}=\frac{1}{2}\mathrm{H\&pi;}{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">X</figure-callout>}}_2\mathrm{\&delta;}---\left(10\right)$

In formula, the Vickers hardness that H is workpiece, X ₂average sword circular diameter while contact with workpiece for abrasive particle, δ is the compression distance of abrasive particle at surface of the work;

Single abrasive grain stress balance in the horizontal direction, F _{r, n}=F _p, derivation draws:

$\mathrm{\&delta;}=\frac{\mathrm{<figure-callout\; id="1"\; label="p\; X"\; filenames="HSA0000101244970000022.png"\; state="\{\{state\}\}">p</figure-callout>}{X_{}}^{}{{}_1}^2}{2H{X}_2}---\left(11\right)$

In formula, X ₁average sword circular diameter while contact with magnetic particle for abrasive particle;

The suffered fluid pressure of abrasive grain is larger, and abrasive grain particle diameter is larger, and its compression distance at surface of the work can be darker, is pressed into accordingly area larger.

Single abrasive grain in the vertical direction stress balance, F _{r, t}=F _s,

draw:

$A_p=\frac{\mathrm{\&pi;\&tau;}{{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA0000101244970000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1}^2}{4{\mathrm{\&sigma;}}_s}---\left(12\right)$

In formula, σ _sfor the yield limit of workpiece material, the shear stress that τ is liquid-magnetic abrasive tool;

Shear stress, the abrasive grain particle diameter yield limit larger, workpiece material of liquid-magnetic abrasive tool is less, and abrasive particle is larger at pressure people's area of surface of the work, and cutting effect is more obvious.

Suppose that being pressed into material in area by complete resection, in unit are, material removal efficiency VRR is

VRR=η A _pυ _relatively(13)

In formula, η is the number of abrasive grain in unit are.

Get border

try to achieve

Simultaneous above-mentioned (3), (4), (5) obtain material removing rate VRR in unit are:

$\mathrm{VRR}=\mathrm{\&eta;}\frac{\mathrm{\&pi;\&tau;}{{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA0000101244970000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1}^2}{4{\mathrm{\&sigma;}}_s}[{\mathrm{\&upsi;}}_{z0}+\frac{3{{\mathrm{\&tau;}}_0}^2}{{\mathrm{\&eta;}}_0}\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}-(\frac{{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{16{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HSA0000101244970000022.png,HSA0000101244970000031.png"\; state="\{\{state\}\}">D</figure-callout>}}{2{\mathrm{\&eta;}}_0}{\mathrm{\&tau;}}_0)]---\left(15\right)$

Abrasive grain particle diameter, inlet pressure and liquid-magnetic abrasive tool shear stress are larger, abrasive grain surface of the work to be pressed into area larger, compression distance is darker, material removal efficiency is higher, the line trace processing is darker, the surface roughness value processing is larger.

Refer to shown in Fig. 4, it is liquid-magnetic abrasive tool grinding hole Experimental equipment of the present invention, using pluger type hydraulic pump as power source, promote by hydraulic system that piston rod is reciprocating clamp-ons workpiece hole by liquid-magnetic abrasive tool, the liquid-magnetic abrasive tool that flows through workpiece hole undergoes phase transition and automatically forms flexible grinding layer along hole wall surface in magnetic field, thereby realizes the polishing processing to through-hole parts inner wall surface.In the time moving right under the promotion of piston rod in hydraulic coupling, non-return valve 1,4 opens 2,3 and cuts out, and liquid-magnetic abrasive tool is extruded through ball valve 1 and injected workpiece hole by right accumulator, and the liquid-magnetic abrasive tool in accumulator tank sucks left accumulator through ball valve 4; In the time being moved to the left under the promotion of piston rod in hydraulic coupling, non-return valve 2,3 opens 1,4 and cuts out, liquid-magnetic abrasive tool is extruded through ball valve 3 and is injected workpiece hole by left accumulator, liquid-magnetic abrasive tool in accumulator tank sucks right accumulator through ball valve 2, and periodically iterative cycles like this can be realized polishing processing and carry out incessantly.

Refer to shown in Fig. 5, it is the affect schematic diagram of abrasive grain of the present invention on working (machining) efficiency and surface roughness, aperture shown in Fig. 5 is the aluminum test specimen of 3mm, be under 0.5MP, the current strength condition that is 2.5A in inlet pressure, the law curve figure that after the liquid-magnetic abrasive tool processing that two kinds of different grain size abrasive grains (320 orders and 600 orders) configure, aperture inner wall surface roughness changed with process time.

In figure, can know and find out: when abrasive grain granularity is 600 order, hole part inner wall surface roughness value reduces gradually with the prolongation of process time, the processing 25-30min rear surface roughness value state that tends towards stability, the final surface quality obtaining is higher; When abrasive grain granularity is 320 order, hole part surface roughness value is along with the prolongation of process time first sharply increases after decline gradually, and the surface quality obtaining after processing 30min is poor, and after observation material object can find to process 30min, hole diameter obviously expands.From formula (11), (12), abrasive grain is pressed into square being directly proportional of the degree of depth of workpiece and area and abrasive grain diameter, abrasive grain diameter is larger, abrasive grain is darker at the compression distance of surface of the work, it is larger to be pressed into area, material removal efficiency is also just higher, but abrasive grain diameter is larger, and the compression distance of abrasive grain will be darker, the line trace processing is more obvious, and the final surface roughness value of acquisition is higher.Select the abrasive grain that particle diameter is larger to add man-hour, because working (machining) efficiency is high, surface of the work projection can be fallen by rapid stock-removal, if continue processing, abrasive particle can continue scratching at workpiece inwall, ploughing produced processing phenomenon, made workpiece inwall leave darker cut, and final surface roughness value is higher; While selecting the less abrasive material of particle diameter, abrasive material is more shallow at the cut of surface of the work, and the surface roughness value processing is lower.Therefore,, if when workpiece effects on surface roughness less demanding of processing, should select bulky grain abrasive material to process to improve working (machining) efficiency; If when the workpiece effects on surface roughness of processing has higher requirements, should select granule abrasive material to process.

Refer to shown in Fig. 6, it is the affect schematic diagram of inlet pressure of the present invention on working (machining) efficiency and surface roughness, aperture shown in Fig. 6 is 1mm copper test specimen, be 2.5A at impressed current, abrasive grain 800 orders, under different inlet pressure conditions, the law curve figure that aperture inner wall surface roughness changed with process time.Inlet pressure hour, along with the prolongation of process time, aperture inner wall roughness value slow decreasing; Along with the increase of inlet pressure, material removal effect is obvious, and finally surface roughness value reduces gradually, reaches optimum state in the time that inlet pressure is 2MPa left and right; In the time that inlet pressure is 2.5MPa, along with the prolongation surface roughness value of process time sharply declines, in 10min left and right, surface roughness value reaches optimum state, processes roughness value raise on the contrary if continue.This be because, on the one hand from formula (11), the degree of depth that abrasive grain is pressed into workpiece is directly proportional to abrasive material pressure, pressure is larger, the degree of depth of abrasive material coining is darker, material removal efficiency is higher.Improve on the other hand inlet pressure the pressure reduction at aperture import and export place is increased, barometric gradient increases, and from formula (4), increase barometric gradient can increase the shear stress of liquid-magnetic abrasive tool, improves polishing working (machining) efficiency.In the time that inlet pressure is excessive; abrasive grain produces darker compression distance at surface of the work, and after polishing processing a period of time, the projection of surface of the work can be fallen by rapid stock-removal, if continue processing; abrasive particle can leave darker cut at workpiece inwall, and surface roughness value is increased.Therefore, in polishing process, obtain lower roughness value and higher working (machining) efficiency for guaranteeing, should choose suitable inlet pressure.

Refer to shown in Fig. 7, it is the affect schematic diagram of current strength of the present invention on working (machining) efficiency and surface roughness, be 2MP in inlet pressure, under abrasive grain 800 object conditions, be that 1mm copper test specimen grinds by adjusting the size of current strength to aperture, law curve is as shown in Figure 7 over time for the surface roughness value after processing.As seen from the figure, along with the raising of current strength, the corresponding raising of material removal efficiency of workpiece, the surface quality after grinding 20min also progressively improves.In the time that current strength is 2.5A left and right, working (machining) efficiency and the final surface roughness obtaining reach optimum state; In the time that current strength is 3A, rising after surface roughness value first sharply declines, the surface quality obtaining after processing 20min is poor.This is because magnetic field intensity is determined by current strength, in the time that current strength increases, and the corresponding increase of the shear stress of liquid-magnetic abrasive tool, by the known increase shear stress of formula (15), material removing rate VRR increases, and working (machining) efficiency improves; And the degree of depth that excessive current strength makes abrasive particle be pressed into workpiece increases, abrasive particle depicts darker cut at surface of the work, causes the rear measured roughness grade of processing to decrease.

By micro-unit of liquid-magnetic abrasive tool carried out to mechanical analysis, show that the shear stress of liquid-magnetic abrasive tool is directly proportional to micro-radius, and then derive distributional pattern and the speed distribution regularities of liquid-magnetic abrasive tool in duct.

Adopt " twolip radius of circle " model to carry out the research of single abrasive grain cutting Model, draw material removing rate and abrasive grain diameter that polishing processes square, shear stress and fluid pressure be directly proportional, be inversely proportional to the yield limit of workpiece material.According to the magnetorheological characteristic of liquid-magnetic abrasive tool, design the experimental provision of a set of applicable aperture polishing processing, verify by experiment the impacts of factor on material removing rate and surface roughness such as abrasive grain, inlet pressure and current strength.

Experiment shows: in scope to a certain degree, increase the removal efficiency that abrasive grain diameter, inlet pressure and current strength are conducive to improve material, the corresponding raising of surface quality obtaining after processing a period of time, but in the time that surface roughness value drops to certain numerical value, too high material removing rate likely caused processing, and finally caused surface quality variation.

The foregoing is only preferred embodiment of the present invention, is only illustrative for invention, and nonrestrictive.Those skilled in the art is understood, and in the spirit and scope that limit, can carry out many changes to it in invention claim, revise, and even equivalence, but all will fall within the scope of protection of the present invention.

Claims (6)

1. liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods, it is characterized in that, adopt " twolip radius of circle " model to carry out the research of single abrasive grain cutting Model, the material removing rate that draws polishing processing and abrasive grain diameter square, shear stress and the fluid pressure of liquid-magnetic abrasive tool be directly proportional, be inversely proportional to the yield limit of workpiece material, the Material Removal Mechanism computational process of aperture polishing processing is:

Known according to Vickers hardness definition:

$F_{r,n}=\frac{1}{2}\mathrm{H\&pi;}{X}_2\mathrm{\&delta;}---\left(1\right)$

In formula, the Vickers hardness that H is workpiece, X ₂average sword circular diameter while contact with workpiece for abrasive particle, δ is the compression distance of abrasive particle at surface of the work;

Single abrasive grain stress balance in the horizontal direction, F _{r, n}=F _p,

derivation draws:

$\mathrm{\&delta;}=\frac{p{X_1}^2}{2H{X}_2}---\left(2\right)$

In formula, X ₁average sword circular diameter while contact with magnetic particle for abrasive particle;

The suffered fluid pressure of abrasive grain is larger, and abrasive grain particle diameter is larger, and its compression distance at surface of the work can be darker, is pressed into accordingly area larger;

Single abrasive grain in the vertical direction stress balance, F _{r, t}=F _s,

draw:

$A_p=\frac{\mathrm{\&pi;\&tau;}{X_1}^2}{4{\mathrm{\&sigma;}}_s}---\left(3\right)$

In formula, σ _sfor the yield limit of workpiece material, the shear stress that τ is liquid-magnetic abrasive tool;

Shear stress, the abrasive grain particle diameter yield limit larger, workpiece material of liquid-magnetic abrasive tool is less, and abrasive particle is larger at pressure people's area of surface of the work, and cutting effect is more obvious;

Suppose that being pressed into material in area by complete resection, in unit are, material removing rate VRR is:

VRR=η A _pυ _relatively(4)

In formula, η is the number of abrasive grain in unit are;

Get border

try to achieve

Simultaneous above-mentioned (3), (4), (5) obtain material removal efficiency VRR in unit are:

$\mathrm{VRR}=\mathrm{\&eta;}\frac{\mathrm{\&pi;\&tau;}{X_1}^2}{4{\mathrm{\&sigma;}}_s}[{\mathrm{\&upsi;}}_{z0}+\frac{3{{\mathrm{\&tau;}}_0}^2}{{\mathrm{\&eta;}}_0}\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}-(\frac{D^2}{16{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{D}{2{\mathrm{\&eta;}}_0}{\mathrm{\&tau;}}_0)]---\left(6\right)$

Above-mentioned various in, F _pthe fluid pressure that-abrasive particle is suffered; F _{r, t}the tangential resistance that-abrasive particle is suffered, F _{r, n}the normal direction resistance that-abrasive particle is suffered; F _sthe shearing force that-abrasive particle is suffered; A _p-abrasive particle be pressed into area, be pressed into half spherical crown in tangential direction projection.

2. liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods according to claim 1, is characterized in that, in the Material Removal Mechanism computational process of above-mentioned aperture polishing processing, make following hypothesis:

The processing of I polishing is mainly to complete by the micro-cutting of abrasive grain, ignores other processing factors;

II abrasive particle is ideal rigid body, ignores the distortion of self in process, and contacting between abrasive grain and workpiece is plasticity contact;

In III Micro cutting Process, abrasive grain is made uniform motion at surface of the work;

IV ignores gravity and the magnetic suspension force effect of particle.

3. liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods according to claim 1, it is characterized in that, in aperture polishing process, the flow mechanism of liquid-magnetic abrasive tool in circular duct, centered by axially bored line, get the thin cylinder of infinitesimal unit, if its radius is r, length is dz; Detailed process is:

Step a, the distribution of shear stress of the thin cylinder of calculating aperture unit;

Step b, the constitutive equation of structure liquid-magnetic abrasive tool;

Step c, the VELOCITY DISTRIBUTION of liquid-magnetic abrasive tool in calculating aperture.

4. liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods according to claim 3, is characterized in that, the detailed process of above-mentioned steps a is:

Known according to Newton's second law:

2πrdr[p-(p+dp)]+2πrdz·τ-2π(r+dr)dz(τ+dτ)＝0 (7)

Above formula abbreviation also removes the infinite event of high-order and can obtain:

$\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{1}{r}\&CenterDot;\frac{d\left(\mathrm{\&tau;r}\right)}{\mathrm{dr}}=0---\left(8\right)$

Formula (8) the right and left be multiplied by rdr again integration can obtain

$\frac{r^2}{2}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\mathrm{\&tau;r}=C---\left(9\right)$

Get border r=0, try to achieve constant C=0; Formula (9) distortion arranges and can draw distribution of shear stress formula

$\mathrm{\&tau;}=-\frac{r}{2}\frac{\mathrm{dp}}{\mathrm{dz}}---\left(10\right).$

5. liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods according to claim 3, is characterized in that, in above-mentioned steps b, the character of liquid-magnetic abrasive tool is described by Bingham constitutive equation:

$\left\{\begin{array}{cc}\mathrm{\&tau;}={\mathrm{\&eta;}}_0\mathrm{\&gamma;}+\mathrm{sign}\left(\mathrm{\&gamma;}\right){\mathrm{\&tau;}}_0& (\mathrm{\&tau;}>{\mathrm{\&tau;}}_0)\\ \mathrm{\&gamma;}=0& (\mathrm{\&tau;}<{\mathrm{\&tau;}}_0)\end{array}\right.---\left(11\right)$

In formula, τ ₀for the shear yield stress of grinding tool, η ₀for liquid-magnetic abrasive tool plasticity viscosity coefficient, γ is shear strain rate, equals the flowing velocity of grinding tool along the rate of change of aperture direction

6. liquid-magnetic abrasive tool aperture polishing rapidoprint clearance computational methods according to claim 3, is characterized in that, the detailed process of above-mentioned steps c is:

Get boundary condition τ=τ ₀, try to achieve " solid-state core " zone radius

$R_0=2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}---\left(12\right)$

To the shear stress τ=η in polishing area ₀γ+τ ₀being out of shape derives can obtain:

$\mathrm{\&gamma;}=\frac{\mathrm{\&tau;}-{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}=\frac{{\mathrm{d\&upsi;}}_{\mathrm{zr}}}{\mathrm{dr}}(\mathrm{\&tau;}>{\mathrm{\&tau;}}_0)---\left(13\right)$

Above formula integration, draws

${\mathrm{\&upsi;}}_{\mathrm{zr}}=-[\frac{r^2}{4{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}r]+C_1(R_0\&le;r\&le;\frac{D}{2})---\left(14\right)$

Get boundary condition: r=R ₀time υ _zr=υ _z0(υ _z0determined by flow), try to achieve

so VELOCITY DISTRIBUTION formula of liquid-magnetic abrasive tool in aperture:

$\left\{\begin{array}{cc}{\mathrm{\&upsi;}}_{\mathrm{zr}}={\mathrm{\&upsi;}}_{z0}+\frac{3{{\mathrm{\&tau;}}_0}^2}{{\mathrm{\&eta;}}_0}\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}-[\frac{r^2}{4{\mathrm{\&eta;}}_0}\&CenterDot;\frac{\mathrm{dp}}{\mathrm{dz}}+\frac{{\mathrm{\&tau;}}_0}{{\mathrm{\&eta;}}_0}r]& (2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1}\&le;r\&le;\frac{D}{2})\\ {\mathrm{\&upsi;}}_{\mathrm{zr}}={\mathrm{\&upsi;}}_{z0}& (0\&le;\mathrm{\&tau;}<2{\mathrm{\&tau;}}_0\&CenterDot;{\left(\frac{\mathrm{dp}}{\mathrm{dz}}\right)}^{-1})\end{array}\right.---\left(15\right)$

Work as r=R ₀time, υ _zrfor the speed υ on " solid-state core " border _z0; When

time, υ _zrfor the relative sliding velocity of abrasive grain and surface of the work.

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