CN105512400A - Cutting process simulation process for brittle materials - Google Patents

Abstract

The invention provides a cutting process simulation process for brittle materials, belongs to the field of micro-nano ultraprecision machining numerical simulation and relates to a three-dimensional micro-nano cutting machining simulation method based on an SPH (smoothed particle hydrodynamics) method. According to the simulation method, dimensions of a cutter and a workpiece material are set firstly; then a three-dimensional cutter finite element model is established in ANSYS, an SPH model of the workpiece material is established in LS-PrePost, parameters of contact, boundary, the material and the like are set, and calculation is performed in LS-DYNA; finally, a simulation result is analyzed, and whether the result meets the actual machining condition is judged. The simulation method has the advantages that data including stress, strain, density and the like in a cutting machining process can be obtained more clearly and more accurately, the brittle materials are removed from a ductile region through control of cutting depth, and acquisition of more ideal surface quality is more facilitated. A large quantity of labor cost, experimental cost and economic cost is saved, and the problem of on-line observation difficulty of an experimental method is solved.

Description

A kind of hard brittle material cutting process simulation method

Technical field

The present invention relates to micro-nano Ultra-precision Turning numerical simulation field, relate to the three-dimensional micro-nano cutting process simulation method of a kind of employing based on Smoothed Particle Hydrodynamics Method.

Background technology

The hard brittle materials such as optical glass, because of the physical property of its excellence, are widely used in the fields such as space flight, information, the energy, chemical industry, microelectronics.The classic method of work brittleness material is mainly removed as the grinding of main ground, grinding, polishing with fragility territory, loads and easily produces micro-crack in process.These micro-cracks more easily cause brittle fracture when following process, are difficult to obtain nano level finished surface, have a strong impact on the application of hard brittle material.At present, determining hard brittle material by the experiment such as impression, cut can remove with plastic manner on nanoscale, now can not crack, collapse the behavior reducing surface quality such as broken.Such as, TAMAKIJ etc. Japanese 11thInternationalSymposiumonAdvancesinAbrasiveTechnology meeting was delivered in 2009 " Experimentalanalysisofelasticandplasticbehaviorinductile-regimemachiningofglassquartzutilizingadiamondtool ", collection of thesis 235 – 240 pages.Relevant scholar, again from the angle of the actual processing technology such as grinding and single point diamond cutting, demonstrates the Machinability Evaluation that hard brittle material realizes plastic region removal, and have studied the correlative factor that some affect crudy.But due to processing and observation condition restriction, experiment only can observe part processing result, can not show well for the material behavior on micro/nano-scale in processing.The research of ultra precision cutting relates to numerous subjects such as mechanics, calorifics, tribology, materialogy, mechanical kinetics, and have strong non-linear, process is complicated.Therefore, traditional research mode wants human and material resources and the financial resources of at substantial, and the test period is long.And developing rapidly of computer technology, numerical computation technology makes researchist can simulate metal cutting process by numerical evaluation instrument.Fact proved: cutting simulation test can not only shorten the test period greatly, save ample resources, the more important thing is by emulating the test that can complete in a lot of actual conditions and be difficult to or be inconvenient to carry out, obtaining the data being difficult in a lot of actual tests obtain, thus Guiding Practice.Cutting simulation, in production, all has important practical significance in scientific research, discloses materials processing mechanism from another angle, can capture the such as experiment such as ess-strain, material separation process in real time exactly and not allow facile data.

At present, be suitable for the Johnson-HolmquistCeramics material constitutive model of hard brittle material High-speed machining, be called for short JH-2 model, refer to JOHNSONGR, HOLMQUISTTJ.Animprovedcomputationalconstitutivemodelforb rittlematerials [C] //High-PressureScienceandTechnology, ColoradoSprings, USA, 1994:981 – 4, is applicable to simulating high-speed work brittleness material.And Smoothed Particle Hydrodynamics Method (SmoothedParticleHydrodynamics, SPH) as a kind of emulation mode of emerging mesh free, solve Finite Element Method problem such as mesh distortion when processing large sstrain, large strain rate, hard brittle material detachment process can be simulated well, but seldom have report to use SPH method to carry out the research of quartz glass cutting mechanisms.

Summary of the invention

The object of the invention is to, overcome the deficiency in existing process technology, invent a kind of fragile material ultraprecise cutting simulation method based on SPH.By setting up the SPH particle model of machined material, virtual particle method is adopted to retrain the border of SPH particle, the judgement that contacts and calculating is carried out with symmetric penalized-function method, selective erosion contacts as contact type and arranges correlation parameter, adopt the JH-2 cast material constitutive model being suitable for hard brittle material High-speed machining, and calculate in LS-DYNA, simulation result is analyzed.This emulation mode more clearly can obtain the data such as stress in cutting process, strain, density exactly, by controlling cutting-in, hard brittle material being removed at plastic region, being more conducive to obtaining ideal surface quality.Save a large amount of human costs, experimental cost and financial cost.

The technical scheme that the present invention takes is a kind of hard brittle material cutting process simulation method, it is characterized in that, first emulation mode determines the size of cutter and workpiece material, then, sets up three-dimensional cutter finite element model in ANSYS, the SPH model of workpiece material is set up in LS-PrePost, the parameters such as contact, border, material are set again, and calculate in LS-DYNA, finally, the whether realistic processing situation of judged result, analyzes simulation result; Emulation mode concrete steps are as follows:

Step 1: the size determining cutter and part model

A) yardstick emulated as required, to limit workpiece and tool dimension, gets 10 times that part model length is back engagement of the cutting edge, and height is 5 times of back engagement of the cutting edge;

B) according to the shape determination cutter parameters of actual cutter, size to be mated with workpiece size;

Step 2: set up three-dimensional cutter finite element model in ANSYS, set up cutter model in FEM-software ANSYS, material model selects rigid body, and material parameter adopts adamantine parameter;

Step 3: the SPH model setting up workpiece material in LS-PrePost

A) by the smooth function method of approximation of SPH method, particle approximate function is defined as:

∏ ^hf(x)＝∫f(y)W(x-y,h)dy(1)

Wherein, W is smooth function (or kernel function), and f is the function of three-dimensional coordinate vector x, y, and h is smooth length, by the domain of influence deciding smooth function.The condition of smooth function demand fulfillment comprises: 1. regular conditions; 2. when smooth length goes to zero, there is Dirac function character; 3. compact sup-port condition; 4. value non-negative; 5. must be symmetrical; 6. interparticle distance is from monotone decreasing during increase.

Smooth function W represents through conventional auxiliary function θ:

$W(x,h)=\frac{1}{h{\left(x\right)}^d}\mathrm{\θ}\left(x\right)---\left(2\right)$

Wherein, d is space dimensionality;

In numerical evaluation, smooth length h requires to arrange minimum value and maximal value,

HMIN*h ₀＜h＜HMAX*h ₀(3)

Wherein, h ₀for initial smooth length, HMIN and HMAX is respectively minimum value coefficient and maximal value coefficient.

SPH method, by the integral representation made for completing function of smooth function, is similar to the effective measure for fulfill in a series of arbitrfary point, adopts cubic B-spline function:

$\mathrm{\&theta;}\left(u\right)=C\&times;\left\{\begin{array}{cc}1-1.5u^2+0.75u^3& \left|u\right|\&le;1\\ 0.25(2-u^3)& 1<\left|u\right|\&le;2\\ 0& \left|u\right|>2\end{array}\right.---\left(4\right)$

Wherein, C is normaliztion constant, is determined by space dimensionality;

B) particle is similar to and neighborhood search:

The realistic model adopted is by having independent mass, and limited the particle occupying separate space represents, the continuous integration form of any point superior function is converted into the discrete form of all particles stacked summations in neighborhood;

Neighborhood search adopts bucket algorithm; Each SPH particle periphery radius is the spheric region of 2h is its domain of influence, and the whole territory that solves is divided into several subdomains, searches in adjacent subarea territory afterwards in boss region and with it to each particle;

Step 4: boundary constraint, contact type are set, and calculate in LS-DYNA

A) in finite element model, boundary constraint is generally by defining the constraint of boundary node.And in SPH model, apply virtual particle principle, virtual particle is the mirror image of particle in the 2h distance range of border, each particle around border, automatically the virtual particle corresponded is created by mapping self, virtual particle has the quality identical with real particle, pressure, speed etc., therefore can produce approximate effect to other particles;

B) part model adopts the JH-2 constitutive model being applicable to simulation hard brittle material High-speed machining, wherein,

The strength of materials is described by following formula: σ ^*=σ ^* _i-D (σ ^* _i-σ ^* _f) (5)

Wherein: ${\mathrm{\&sigma;}}_i^{*}=A{(P^{*}+T^{*})}^N(1+C\&times;ln{\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}^{*})---\left(6\right)$

${\mathrm{\&sigma;}}_f^{*}=B{\left(P^{*}\right)}^M(1+C\&times;ln{\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}^{*})---\left(7\right)$

In formula (5) ~ (7): σ ^*for standardization equivalent stress; for non-injury criterion equivalent stress; for injury criterion equivalent stress; P ^*for standardization hydrostatic force; T ^*for standardization maximum hydrostatic pressure; for standardization rate of strain; D is Damage coefficient; A, B, C, M, N are material parameter, determine according to concrete material;

The semi-invariant of damage is determined by following formula:

$D=\mathrm{\&Sigma;}\frac{{\mathrm{\&Delta;\&epsiv;}}_p}{D_1{(P^{*}+T^{*})}^{D_2}}---\left(8\right)$

Wherein, △ ε _pfor the plastic strain increment in single cycle; D ₁, D ₂for material parameter, determine according to concrete material;

Can the judgement c) adopting symmetric penalized-function method to carry out contacting and calculating, do corresponding inspection at each time step in computation process, first will test and occur penetrating from node and main interface; If penetration phenomenon occurs, so need at this from setting an interracial contact power between node and main interface, the value of this contact force is comparatively large, is specifically directly proportional to contact stiffness and penetration depth, is called penalty function value; Spring contact power equals the product of contact stiffness K and the amount of penetrating δ; The amount of the penetrating δ of two objects is relevant with contact stiffness K, and contact stiffness K is relevant with the relative rigidity of contact, for:

$K=\frac{f_s\&times;S^2\&times;k}{V}---\left(9\right)$

Wherein, S is surface area, V is volume, k is the bulk modulus of osculating element; F in formula _sfor penalty factor, in the present invention, be set to 0.1;

D) contact type adopted corrodes contact; The parameter arranged is needed to have friction factor parameter, contacting search method, the contact degree of depth and other additional parameters;

The friction factor of the present invention's contact is by coefficient of static friction F _s, kinetic friction coefficient F _dto form with exponential damping coefficient DC, and think coefficientoffrictionμ _cwith the relative velocity V of surface in contact _relrelevant; Relation is expressed as:

${\mathrm{\&mu;}}_c=F_d+(F_s-F_d)e^{-DC\&times;V_{rel}}---\left(10\right)$

Step 5: reasonable evaluation analysis is carried out to simulation result, the time history of being processed by analysis, Stress distribution, Crack Extension, cutting force, particle density disclose fragile material ultraprecise working angles, if realistic processing situation, terminates, otherwise returns step 3.

The invention has the beneficial effects as follows based on dynamic analysis software LS-DYNA, application SPH method carries out hard brittle material cutting process simulation method, this emulation mode more clearly can obtain the data such as stress in cutting process, strain, density exactly, by controlling cutting-in, hard brittle material being removed at plastic region, being more conducive to obtaining ideal surface quality.Save a large amount of human costs, experimental cost and financial cost, and avoid the difficult problem that experimental technique is difficult to online observation.

Accompanying drawing explanation

Fig. 1 is a kind of process flow diagram of hard brittle material cutting process simulation analogy method.

Tangentially trying hard to when Fig. 2 is different cutting-in in embodiment.Wherein, abscissa representing time process, unit microsecond; Ordinate represents tangential force size, unit milli ox; The curve that when curve 1,2,3 represents that cutting depth is 0.15 μm, 0.3 μm, 0.5 μm respectively, transverse and longitudinal coordinate is corresponding.

Normal direction when Fig. 3 is different cutting-in in embodiment is tried hard to.Wherein, abscissa representing time process, unit microsecond; Ordinate represents normal force size respectively, unit milli ox; The curve that when curve 1,2,3 represents that cutting depth is 0.15 μm, 0.3 μm, 0.5 μm respectively, transverse and longitudinal coordinate is corresponding.

Embodiment

Specific embodiment of the invention example is described in detail below in conjunction with accompanying drawing and technical scheme.

Accompanying drawing 1 is the process flow diagram of the invention process process, and for quartz glass, explaination is based on the hard brittle material cutting process simulation method of SPH algorithm in detail.Concrete steps are as follows:

Step 1: the size of setting cutter and workpiece material.Cutter material is adamas, density 3.51g/cm ³, elastic modulus 1141GPa, Poisson ratio 0.07, tool orthogonal rake 10 °, relief angle 10 °, cutting speed 10m/s.Quartz glass workpiece is designed to 5 × 3 × 0.5 μm ³cube.

Step 2: set up three-dimensional cutter finite element model in ANSYS.Because diamond hardness is far above quartz glass, and research emphasis is quartz glass processing characteristics, and therefore diamond cutter is reduced to ideal rigid body and adopts mesh modeling mode.In working angles, cutter only carries out horizontal one direction and moves, therefore limits the degree of freedom in other directions.Cutter blunt round radius is the influence factor very important to Ultra-precision machining, is set to 0.1 μm here.

Step 3: the SPH model setting up workpiece material in LS-PrePost.

According to above-mentioned steps 1 quartz glass workpiece size, and take into account simulation efficiency and precision, arranging SPH number of particles is 96000, application smooth function method of approximation, uses formula (1) above and formula (2) and adopts cubic B-spline function formula (4) to calculate.In numerical evaluation, smooth length h requires to arrange minimum value and maximal value, is set as 0.2 and 2 times of initial smooth length value under normal circumstances, that is: 0.2*h ₀< h < 2*h ₀, wherein, h ₀for initial smooth length.

SPH method is by the integration made for completing function of smooth function, the continuous integration form of any point superior function, by having independent mass and limited the particle occupying separate space represents, is converted into the discrete form of all particles stacked summations in neighborhood by the realistic model adopted.Require parameters according to smooth function, cubic B-spline, Neighborhood-region-search algorithm, the length etc. that polishes, complete the foundation of SPH model.

Neighborhood search adopts bucket algorithm; Each SPH particle periphery radius is the spheric region of 2h is its domain of influence, and the whole territory that solves is divided into several subdomains, searches in adjacent subarea territory afterwards in boss region and with it to each particle.

Step 4: boundary constraint, contact type are set, and calculate in LS-DYNA.

A) adopt virtual particle method to retrain the border of SPH particle, " virtual particle method " may retrain by moving direction workpiece.Virtual particle is set out within the scope of SPH particle edges place 2h.For the SPH particle near border, by the mapping to self, automatically create the virtual particle with equal in quality, pressure, absolute velocity, make true particle normally can carry out neighborhood search, to reach the object of restrained boundary.Notice that virtual particle interface is arranged to be connected with SPH particle edges, can not overlap or have space.

B) for the selection of part model, the material constitutive model being suitable for hard brittle material High-speed machining is adopted to be JH-2 model; Be applicable to simulating high-speed work brittleness material.Real material intensity formula (5) ~ (7) calculate, and the semi-invariant of damage can pass through formula (8) statement.

C) carry out the judgement that contacts and calculating with symmetric penalized-function method, in Symmetric Penalty Function algorithm, each time step first checks respectively whether penetrate first type surface from node, does not penetrate, is left intact to this node; If penetrated, then at this node and penetrated and to introduce a larger interracial contact power between first type surface, its size is directly proportional to penetration depth, main leaf rigidity, be called penalty function value, its physical significance is equivalent to from node with penetrated between first type surface and place a normal direction spring, to limit from node penetrating first type surface.Symmetric penalized-function method is simultaneously again to host node process one time, and its algorithm is the same with from node.Particularly, spring contact power equals the product of contact stiffness K and the amount of penetrating δ.The amount of the penetrating δ of two objects is relevant with contact stiffness K, ideally, should not penetrate, but this means K=∞, and numerical evaluation will be caused unstable, and usually allow the small amount of penetrating to exist, it is controlled by contact stiffness.Contact stiffness K is relevant with the relative rigidity of contact, utilizes formula (9) to calculate, wherein, and penalty factor f _sbe set to 0.1.

C) selective erosion contact is as contact type, and arranges correlation parameter,

The friction factor of the present invention's contact is by coefficient of static friction F _s, kinetic friction coefficient F _dto form with exponential damping coefficient DC, and think coefficientoffrictionμ _cwith the relative velocity V of surface in contact _relrelevant, utilize formula (10) to calculate.Untrue contact when contacting the degree of depth and being excessive produces the instability that corresponding excessive contact force can cause calculating.Therefore will define a Maximum Contact degree of depth, contact penetrates and is no more than this value, can ignore to it.

Step 5: carry out reasonable evaluation to simulation result, if realistic processing situation, is further analyzed, and guides processing, otherwise returns step (3).

Interpretation of result is made to embodiment below: the tangential force that when Fig. 2, Fig. 3 are respectively 10 ° of anterior angles, different cutting-ins, cutting force decomposes and normal force.As shown in Figure 2, along with cutting depth increases, the material that in the unit interval, cutter is removed increases, and then tangential force increases, and plastic strain increases, and when plastic strain is concentrated and reached a certain critical value, material produces micro-crack, and removing method changes brittle removal into.When entering fragility territory, because material is that discontinuous bulk is removed, causes again tangential force that comparatively serious fluctuation occurs, see Fig. 3.Initial incision positions of materials tangential force has a spike sharply risen.During different cutting-in, normal force is numerically much smaller than tangential force, and after entering fragility territory, along with cutting-in increases, normal force fluctuation is more obvious.In material removal process, stable cutting force is particularly important to the surface quality improving finished surface, and less cutting force more contributes to realizing plastic removal, therefore shows, by controlling cutting-in, hard brittle material being removed at plastic region, being more conducive to obtaining ideal surface quality.

The present invention's application SPH method carries out hard brittle material cutting process simulation, more clearly obtain the data such as stress in cutting process, strain, density exactly, pattern removed by the material studying different cutting depth hard brittle material, obtain hard brittle material and mould crisp transformation critical cutting depth, for the Ultra-precision Turning of the hard brittle materials such as such as quartz glass provides Research foundation, save a large amount of human costs, experimental cost and financial cost, and avoid the difficult problem that experimental technique is difficult to online observation.

Claims (1)

1. a hard brittle material cutting process simulation method, it is characterized in that, first emulation mode sets the size of cutter and part model, then, three-dimensional cutter finite element model is set up in ANSYS, the SPH model of workpiece material is set up in LS-PrePost, virtual particle method is adopted to retrain the border of SPH particle, the judgement that contacts and calculating is carried out with symmetric penalized-function method, selective erosion contacts as contact type and arranges correlation parameter, adopt the JH-2 cast material constitutive model being suitable for hard brittle material High-speed machining, and calculate in LS-DYNA; Finally, simulation result is analyzed; Emulation mode concrete steps are as follows:

Step 1: the size of setting cutter and part model;

The yardstick emulated as required, to set part model and tool dimension, gets 10 times that part model length is back engagement of the cutting edge, and height is 5 times of back engagement of the cutting edge; According to the shape of actual cutter, select cutter parameters;

Step 2: set up three-dimensional cutter finite element model in ANSYS, assuming that part model is rigid body, material parameter adopts adamantine parameter;

Step 3: the SPH model setting up part model in LS-PrePost

A) by the smooth function method of approximation of SPH method, particle approximate function is defined as:

∏ ^hf(x)＝∫f(y)W(x-y,h)dy(1)

Wherein, W is smooth function, and f is the function of three-dimensional coordinate vector x, y, and h is smooth length, by the domain of influence deciding smooth function; Smooth function W represents through conventional auxiliary function θ:

Wherein, d is space dimensionality;

In numerical evaluation, smooth length h requires to arrange minimum value and maximal value,

HMIN*h ₀<h<HMAX*h ₀(3)

Wherein, h ₀for initial smooth length, HMIN and HMAX is respectively minimum value coefficient and maximal value coefficient;

SPH method, by the integral representation made for completing function of smooth function, is similar to the effective measure for fulfill in a series of arbitrfary point, adopts cubic B-spline function:

Wherein, C is normaliztion constant, is determined by space dimensionality;

B) particle is similar to and neighborhood search:

The realistic model adopted is by having independent mass, and limited the particle occupying separate space represents, the continuous integration form of any point superior function is converted into the discrete form of all particles stacked summations in neighborhood;

Neighborhood search adopts bucket algorithm; Each SPH particle periphery radius is the spheric region of 2h is its domain of influence, and the whole territory that solves is divided into several subdomains, searches in adjacent subarea territory afterwards in boss region and with it to each particle;

Step 4: boundary constraint, contact type are set, and calculate in LS-DYNA;

A) adopt virtual particle method to retrain the border of SPH particle, " virtual particle method " may retrain by moving direction workpiece; Virtual particle is set out within the scope of SPH particle edges place 2h; For the SPH particle near border, by the mapping to self, automatically create the virtual particle with equal in quality, pressure, absolute velocity, make true particle normally can carry out neighborhood search, to reach the object of restrained boundary; Notice that virtual particle interface is arranged to be connected with SPH particle edges, can not overlap or have space;

B) for the selection of part model, the JH-2 model being suitable for hard brittle material High-speed machining is adopted;

The strength of materials is described by following formula: σ ^*=σ ^* _i-D (σ ^* _i-σ ^* _f) (5)

Wherein:

In formula (5) ~ (7), σ ^*for standardization equivalent stress; for non-injury criterion equivalent stress;

for injury criterion equivalent stress; P ^*for standardization hydrostatic force; T ^*for standardization maximum hydrostatic pressure;

for standardization rate of strain; D is Damage coefficient; A, B, C, M, N are material parameter, determine according to concrete material;

The semi-invariant of damage is determined by following formula:

Wherein, Δ ε _pfor the plastic strain increment in single cycle; D ₁, D ₂for material parameter, determine according to concrete material;

C) carry out the judgement that contacts and calculating with symmetric penalized-function method, in Symmetric Penalty Function algorithm, each time step first checks respectively whether penetrate first type surface from node, does not penetrate, is left intact to this node; If penetrated, then at this node and penetrated and to introduce a larger interracial contact power between first type surface, its size is directly proportional to penetration depth, main leaf rigidity, be called penalty function value, its physical significance is equivalent to from node with penetrated between first type surface and place a normal direction spring, to limit from node penetrating first type surface; Symmetric penalized-function method is simultaneously again to host node process one time, and its algorithm is the same with from node; Spring contact power equals the product of contact stiffness K and the amount of penetrating δ; The amount of the penetrating δ of two objects is relevant with contact stiffness K, and contact stiffness K is relevant with the relative rigidity of contact, for:

Wherein, S is surface area, V is volume, k is the bulk modulus of osculating element; F in formula _sfor penalty factor, in the present invention, be set to 0.1;

D) contact type selective erosion contact, and correlation parameter is set

The friction factor of the present invention's contact is by coefficient of static friction F _s, kinetic friction coefficient F _dto form with exponential damping coefficient DC, and think coefficientoffrictionμ _cwith the relative velocity V of surface in contact _relrelevant; Relation is expressed as:

Step 5: reasonable evaluation analysis is carried out to simulation result, the time history of being processed by analysis, Stress distribution, Crack Extension, cutting force, particle density disclose fragile material ultraprecise working angles, if realistic processing situation, terminates, otherwise returns step 3.