CN109145477A

CN109145477A - A kind of cutting parameter optimization method based on SPH cutting Model

Info

Publication number: CN109145477A
Application number: CN201811015465.9A
Authority: CN
Inventors: 莫蓉; 牛伟龙; 韩周鹏; 邓奇; 梅永刚
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2018-08-31
Filing date: 2018-08-31
Publication date: 2019-01-04

Abstract

The invention provides a cutting parameter optimization method based on an SPH cutting model, which belongs to the field of engineering design. Use the SPH algorithm to establish a numerical simulation cutting model to replace the time-consuming, labor-intensive and high-cost cutting Ti-6AL-4V process, and evaluate and calculate the roughness of the workpiece surface after the model is cut, and then use the Taguchi algorithm to first establish The simulation orthogonal test table is used to find a set of cutting parameter combinations that can minimize the surface roughness value of the numerical simulation model through S/N analysis, and this set of cutting parameters is used as the optimal cutting parameter combination under actual machining conditions. The method is easy to implement, suitable for optimization of cutting parameters of expensive metals such as titanium alloys, and helps to save costs, improve production efficiency, and increase the machining accuracy of workpieces.

Description

A kind of cutting parameter optimization method based on SPH cutting Model

Technical field

The present invention relates to SPH Cyomacrotome technical field, specially a kind of cutting parameter optimization based on SPH cutting Model Method, it is thick to reduce workpiece surface come Optimizing Cutting Conditions using numerical simulation model for Ti-6Al-4V titanium alloy material Rugosity.

Background technique

Titanium alloy Ti-6Al-4V is often used as aerospace due to having many advantages, such as low-density, high intensity, corrosion resistance The rapidoprint in equal fields, and in aerospace modern mechanical equipment, the processing quality of titanium alloy components is required very Height, especially the valuing especially to the surface quality of part, and the most important parameter that surface quality is measured is surface Roughness.Suitable one group of cutting parameter how is selected so that workpiece surface roughness is minimum after processing, therefore is directed to workpiece The cutting parameter optimization problem of surface roughness becomes the emphasis for researcher.

Summary of the invention

In order to solve the problems existing in the prior art, the present invention to be to reduce experimentation cost and workpiece surface roughness as target, A kind of cutting parameter optimization method based on SPH cutting Model is proposed, i.e., first establishes a reliable and effective numerical simulation and cuts Model is cut, time-consuming and laborious titanium alloy actual processing process is replaced with the model, is then cut further according to the SPH emulation established Model is cut to assess the surface roughness of part model after processing, and establishes emulation orthogonal test table.Followed by field do a sum orally method, The smallest one group of cutting parameter combination of numerical simulation model surface roughness value can be made by searching out one group by S/N analysis, will This group of cutting parameter is combined as the optimal cutting parameter under actual processing conditions.

The technical solution of the present invention is as follows:

A kind of cutting parameter optimization method based on SPH cutting Model, which comprises the following steps:

Step 1: two-dimensional cutting simulation model is established according to SPH algorithm:

Step 1.1: kernel function is approximate: using integral representation function kernel approximation method to arbitrary function and smoothing kernel function into The integral of row gradually:

Wherein f is the function of three-dimensional coordinate vector x, x_iAnd x_jIt is the function variable of particle i Yu the corresponding position particle j；W is Smoothing kernel function, h is smooth length, for defining the range of smoothing kernel function influence area；

Step 1.2: choose smoothing kernel function:

Wherein α_d=15/ (7 π h²) it is normalization factor, q=r_ij/ h, r_ijIt is the distance between particle i and particle j, h is Smooth length；

Step 1.3: particle is approximate: using the volume delta V of particle_jIt is infinite at particle j in step 1.1 formula to be substituted in Junior unit dx_j, the volume expression of particle j are as follows:

ρ in formula_jFor the density of particle, j=1,2 ... N, N are all total number of particles in particle j support region, to obtain

Step 1.4: the kernel function approximation according to step 1.1 and step 1.3 is approximate with particle, according to Na Wei-Stokes Computational domain is separated into a series of particle, finally obtains the governing equation of material by the conservation of momentum and the conservation of mass in equation Such as following formula:

Wherein N is total number of particles, and α, the direction of β indicates coordinate, m is mass particle, and ρ is particle density, σ^αβFor total stress Tensor, t are the time, and v is particle rapidity, and P is pressure, f^αFor the acceleration as caused by external force, Π_ijFor artificial viscosity；

Step 1.5: choosing constitutive model: when material enters the plastic stage, TANH constitutive equation being selected to close to describe titanium Golden material enters the dynamic mechanical under state of plastic deformation；

Step 1.6: carry out the interactive calculating of particle:

Judge whether two particle contacts: threshold value d is contacted by setting₀, be less than when two distinct types of interparticle distance or Equal to d₀, indicate contact；Tangent vector τ at contact point_pWith normal vector n_pIt is calculated by following formula:

X in formula_k+1=(x_k+1,y_k+1) and x_k+1=(x_k,y_k) be particle k and k+1 coordinate value；

Step 1.7: calculate the contact force between particle:

Power suffered by particle i is divided into two parts, the power F of normal orientation_niWith the power F of tangential direction_τi, according to following public affairs Formula is calculated:

M in formula_iFor particle i mass, v_pi=v_p-v_i, v_pFor tool speed, v_iFor the speed of particle i, μ is cutter and workpiece Between coefficient of friction；

Step 2: the assessment of model surface roughness: according to the built SPH cutting Model machining simulation process of step 1, assessment The roughness of workpiece surface after mould processing:

Step 2.1: numerical simulation is carried out to cutting process according to the SPH cutting Model established, sample length L is set, And the particle on the workpiece surface after processing in sample length L is extracted, the location information of particle is obtained, the seat of invalid particle is rejected Mark；

Step 2.2: calculate the position of center line: the position of center line is subtracted cutting depth by the height of workpiece material and is obtained

f_centerline=H-h

Wherein H is the height of workpiece material, and h is cutting depth；

Step 2.3: each surface particle extracted in sampling length being carried out curve fitting according to coordinate position, by it As the surface profile after work pieces process, and the arithmetic for calculating each particle disalignment vertical range in sample length L is flat Mean value

And as the model surface roughness value after assessment；M is the total number of particles in sample length, y (x_i) it is table Y-coordinate value of the face i particle under coordinate system, | y (x_i)-f_centerline| indicate the vertical range of particle disalignment；

Step 3: optimal cutting parameter is found using field mouthful method:

Step 3.1: selection controllable factors establish factor level allocation list, and are established and imitated according to factor level allocation list True orthogonal test table；

Step 3.2: selecting quality characteristic is to hope small feature, and establishing signal-to-noise ratio S/N calculation formula is

Wherein, n is overall measurement number, y_iThe surface roughness value measured for i-th；

Step 3.3: l-G simulation test being carried out according to l-G simulation test table orthogonal in step 3.1, emulation is repeated as many times every time, and root According to the signal-to-noise ratio of signal-to-noise ratio S/N calculation formula gauging surface roughness in step 3.2；

Step 3.4: according to the data obtained in step 3.3, sorting out the average effect response of controllable factors；

Step 3.5: S/N factorial effect figure is drawn out according to the response of the average effect of the controllable factors in step 3.4, and S/N average value is set to reach maximum controllable factors according to figure selection, using the combination as optimal under the conditions of actual processing Cutting parameter combination.

Further preferred embodiment, a kind of cutting parameter optimization method based on SPH cutting Model, feature exist In: smooth length h takes 1.5 times of interparticle distance in step 1.2.

Further preferred embodiment, a kind of cutting parameter optimization method based on SPH cutting Model, feature exist In: artificial viscosity chooses Monaghan type artificial viscosity in step 1.4.

Beneficial effect

Cutting parameter optimization method proposed by the present invention based on SPH cutting Model, establishes numerical simulation using SPH algorithm Cutting Model replaces the higher cutting Ti-6AL-4V process of time-consuming and laborious and processing cost with this, and to model cutting after Workpiece surface carries out roughness assessment and calculates, and followed by field mental arithmetic method, first establishes emulation orthogonal test table, is analyzed by S/N The smallest one group of cutting parameter combination of numerical simulation model surface roughness value can be made by searching out one group, by this group of cutting parameter As the optimal cutting parameter combination under actual processing conditions.This method is easy to implement, is suitable for the expensive metals such as titanium alloy Cutting parameter optimization, facilitate save the cost, improve production efficiency, increase the machining accuracy of workpiece.

Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description Obviously, or practice through the invention is recognized.

Detailed description of the invention

Above-mentioned and/or additional aspect of the invention and advantage will become from the description of the embodiment in conjunction with the following figures Obviously and it is readily appreciated that, in which:

Fig. 1 SPH emulates cutting Model.

Reciprocation between Fig. 2 SPH particle.

The extraction of Fig. 3 workpiece surface particle.

Fig. 4 coordinate system lower surface particle distribution.

Workpiece surface profile after the fitting of Fig. 5 surface particle.

Average signal-to-noise ratio under Fig. 6 difference corner radius.

Average signal-to-noise ratio under Fig. 7 difference cutting speed.

Average signal-to-noise ratio under Fig. 8 difference cutting depth.

Specific embodiment

The embodiment of the present invention is described below in detail, the embodiment is exemplary, it is intended to it is used to explain the present invention, and It is not considered as limiting the invention.

Cutting parameter optimization method of one of the present embodiment based on SPH cutting Model, comprising the following steps:

Step 1: two-dimensional cutting simulation model being established according to SPH algorithm, as shown in Figure 1:

Step 1.2: smoothing kernel function is chosen, the present embodiment chooses cubic spline smooth function as SPH kernel function:

Wherein α_d=15/ (7 π h²) it is normalization factor, q=r_ij/ h, r_ijIt is the distance between particle i and particle j, h is Smooth length, its size depends on and practical problem, it is excessive it is possible influence computational efficiency, it is too small that will cause precision not high.At this In example, using 1.5 times of interparticle distances as smooth length.

ρ in formula_jFor the density of particle, j=1,2 ... N, N are all total number of particles in particle j support region, to obtain Approximate expression at particle i

Wherein N is total number of particles, and α, the direction of β indicates coordinate, m is mass particle, and ρ is particle density, σ^αβFor total stress Tensor, t are the time, and v is particle rapidity, and P is pressure, f^αFor the acceleration as caused by external force, Π_ijFor artificial viscosity, people here Work viscosity chooses Monaghan type artificial viscosity.

Step 1.5: choosing constitutive model: when material enters the plastic stage, TANH constitutive equation being selected to describe Ti- 6Al-4V material enters the dynamic mechanical under state of plastic deformation:

Wherein ε_effIt is equivalent plastic strain,For equivalent plastic strain rate,For with reference to plastic strain rate, T is practical Temperature, T_meltFor the melt temperature of material, T_roomFor room temperature.A, B, C, M, N are the constant of material, and a, b, c, d, r and tanh are material The corrected parameter of material.Table 1 gives the relevant parameter of Ti-6Al-4V titanium alloy material:

1 constitutive equation of table and material parameter

Step 1.6: carry out the interactive calculating of particle:

As Fig. 2 first determines whether two particle contacts: contacting threshold value d by setting₀, when between two distinct types of particle Away from less than or equal to d₀, indicate contact.

In it is worth noting that, corner radius r is equal with the contact threshold value of point of a knife particle, i.e., here can be by point of a knife Arc radius is dimensioned to the contact threshold value of point of a knife particle.Point p is vertical point of the particle i to tool surface, d_pFor particle i to knife Have the practical vertical range of surface particle, d₀For the contact threshold value of two kinds of particles.Work as d_p≤d₀When, contact occurs.

Tangent vector τ at contact point p point_pWith normal vector n_pIt is calculated by following formula:

X in formula_k+1=(x_k+1,y_k+1) and x_k+1=(x_k,y_k) be particle k and k+1 coordinate value.

Step 1.7: calculate the contact force between particle:

M in formula_iFor particle i mass, v_pi=v_p-v_i, v_pFor the speed at point p, i.e. tool speed, v_iFor the speed of particle i Degree, coefficient of friction of the μ between cutter and workpiece.

SPH cutting simulation model is established by above step.

Step 2: the assessment of model surface roughness: being 240m/min, cutting depth 0.07mm, point of a knife with cutting speed Arc radius is 0.08mm, and for feed speed is 0.1mm/rev, tool orthogonal rake is 0 °, cutting process is emulated, to the mould Surface roughness after type processing is assessed, as shown in Figure 3.

Step 2.1: numerical simulation is carried out to cutting process according to the SPH cutting Model established, sample length L is set, And the particle of model surface in sample length L after processing is extracted, the location information of particle is obtained, the coordinate of invalid particle is rejected (when the vertical range of particle position disalignment is greater than 20 μm, regarding the particle as invalid particle), such as Fig. 4.

f_centerline=H-h

Wherein H is the height of workpiece material, and h is cutting depth；

Step 2.3: each surface particle extracted in sampling length being carried out curve fitting according to coordinate position, by it As the surface profile after work pieces process, such as Fig. 5, and calculate each particle disalignment vertical range in sample length L Arithmetic mean of instantaneous value

Step 3: optimal cutting parameter is found using field mouthful method:

Step 3.1: selection controllable factors, because cutting speed, cutting depth, corner radius are to model in model Surface roughness has a significant impact, and because these three factors can control in simulation process, selects these three factors Three levels are used as controllable factor, while to each factor, establish factor level allocation list 2, and according to factor level Allocation list establishes L₉Emulate orthogonal test table 3.

2 factor level allocation list of table

Table 3L₉Orthogonal l-G simulation test table

Step 3.2: since this experiment is by optimizing that workpiece surface is made to reach the smallest roughness to cutting parameter Value, therefore selecting quality characteristic is to hope small feature, establishing signal-to-noise ratio S/N calculation formula is

Wherein, n is overall measurement number, y_iThe surface roughness value measured for i-th.

Step 3.3: according to L in step 3.1₉Orthogonal l-G simulation test table carries out l-G simulation test, and emulation is repeated as many times every time, and According to the signal-to-noise ratio of signal-to-noise ratio S/N calculation formula gauging surface roughness in step 3.2, obtain such as following table.

4 simulation result of table and surface roughness signal-to-noise ratio

Step 3.4: according to the data obtained in step 3.3, the average effect response of three factors is sorted out, such as table 5.

The response of 5 S/N average effect of table

Step 3.5: S/N factorial effect figure is drawn out according to the table 5 in step 3.4, such as Fig. 6,7,8, and according to will be because of effect Fruit figure selection makes S/N average value reach maximum horizontal factor A3B1C1, using the combination as optimal under the conditions of actual processing Cutting parameter combination.

Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example Property, it is not considered as limiting the invention, those skilled in the art are not departing from the principle of the present invention and objective In the case where can make changes, modifications, alterations, and variations to the above described embodiments within the scope of the invention.

Claims

1. a cutting parameter optimization method based on SPH cutting model, is characterized in that, comprises the following steps:

Step 1: Establish a two-dimensional cutting simulation model according to the SPH algorithm:

Step 1.1: Kernel function approximation: Apply the kernel approximation of the integral representation function to perform stepwise integration of arbitrary functions and smooth kernel functions:

Where f is the function of the three-dimensional coordinate vector x, x _i and x _j are the function variables of the corresponding positions of particle i and particle j; W is the smooth kernel function, h is the smooth length, which is used to define the range of the influence area of the smooth kernel function;

Step 1.2: Select the smooth kernel function:

where α _d =15/(7πh ² ) is the normalization factor, q=r _ij /h, r _ij is the distance between particle i and particle j, and h is the smoothing length;

Step 1.3: Particle approximation: Use the volume ΔV _j of the particle to replace the infinitesimal element dx _j at the particle j in the formula of step 1.1, the volume of the particle j is expressed as:

where ρ _j is the density of particles, j=1, 2...N, N is the total number of all particles in the support domain of particle j, thus obtaining

Step 1.4: According to the kernel function approximation and particle approximation in steps 1.1 and 1.3, according to the conservation of momentum and mass in the Navier-Stokes equation, the computational domain is discretized into a series of particles, and the control equation of the material is finally obtained as follows Mode:

where N is the total number of particles, α, β represent the direction of the coordinates, m is the particle mass, ρ is the particle density, σ ^αβ is the total stress tensor, t is the time, v is the particle velocity, P is the pressure, and f ^α is the external force The acceleration caused, Π _ij is the artificial viscosity;

Step 1.5: Select the constitutive model: When the material enters the plastic stage, select the TANH constitutive equation to describe the dynamic mechanical properties of the titanium alloy material when it enters the plastic deformation state;

Step 1.6: Do the calculation of particle interactions:

Judging whether two particles are in contact: By setting the contact threshold d ₀ , when the distance between two different types of particles is less than or equal to d ₀ , it means that contact occurs; the tangent vector τ _p and the normal vector n _p at the contact point are calculated by the following formula:

where x _k+1 =(x _k+1 , y _k+1 ) and x _k+1 =(x _k , y _k ) are the coordinate values of particles k and k+1;

Step 1.7: Calculate the contact force between particles:

The force on particle i is divided into two parts, the force F _ni in the normal direction and the force F _τi in the tangential direction, which are calculated according to the following formula:

where m _i is the mass of particle i, v _pi =v _p -v _i , v _p is the speed of the tool, v _i is the speed of particle i, and μ is the friction coefficient between the tool and the workpiece;

Step 2: Evaluation of model surface roughness: simulate the machining process according to the SPH cutting model built in step 1, and evaluate the roughness of the workpiece surface after the model is processed:

Step 2.1: Carry out numerical simulation on the cutting process according to the established SPH cutting model, set the sampling length L, and extract the particles on the workpiece surface within the sampling length L after processing, obtain the position information of the particles, and remove the coordinates of the invalid particles;

Step 2.2: Calculate the position of the centerline: The position of the centerline is obtained by subtracting the depth of cut from the height of the workpiece material

f _centerline = Hh

Where H is the height of the workpiece material, and h is the depth of cut;

Step 2.3: Perform curve fitting on each surface particle extracted within the sampling length according to the coordinate position, take it as the surface contour of the workpiece after machining, and calculate the arithmetic mean of the vertical distance of each particle within the sampling length L from the center line

Take it as the surface roughness value of the model after evaluation; M is the total number of particles within the sampling length, y( _xi ) is the y coordinate value of the surface i particle in the coordinate system, |y( _xi )-f _centerline | Indicates the vertical distance that the particle deviates from the centerline;

Step 3: Use Taguchi method to find optimal cutting parameters:

Step 3.1: Select controllable factors, establish a factor level configuration table, and establish a simulation orthogonal test table according to the factor level configuration table;

Step 3.2: Select the quality characteristic as the small characteristic, and establish the S/N calculation formula of the signal-to-noise ratio as

Among them, n is the total number of measurements, y _i is the surface roughness value measured at the i-th time;

Step 3.3: Carry out the simulation test according to the orthogonal simulation test table in Step 3.1, repeat each simulation several times, and calculate the signal-to-noise ratio of the surface roughness according to the S/N calculation formula of the signal-to-noise ratio in Step 3.2;

Step 3.4: According to the data obtained in Step 3.3, sort out the average effect response of the controllable factors;

Step 3.5: Draw the S/N factor effect diagram according to the average effect response of the controllable factors in Step 3.4, and select the controllable factor that maximizes the average S/N value according to the diagram, and use this combination as the actual processing condition. The optimal combination of cutting parameters.

2. A kind of cutting parameter optimization method based on SPH cutting model according to claim 1, is characterized in that: in step 1.2, smooth length h takes 1.5 times the particle spacing.

3. a kind of cutting parameter optimization method based on SPH cutting model according to claim 1, is characterized in that: in step 1.4, artificial viscosity selects Monaghan type artificial viscosity.