CN110807254A - Constant-force-based feeding speed optimization method in five-axis side milling process - Google Patents
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Abstract
The invention provides a constant force-based feed speed optimization method in a five-axis side milling process, which comprises the following steps of: step 1: determining a fitting expression of the instantaneous undeformed chip thickness based on a preset first feed speed and a tool rotation angle; step 2: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula, and analyzing the moment of the peak cutting force to obtain a peak cutting force expression at any moment; and step 3: reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the entry angle; and 4, step 4: calculating a second feeding speed according to the arbitrarily set constant peak force, the set cut-in angle and a preset expression; and 5: and saving the second feeding speed to the cutter position file. The constant-force-based feed speed optimization method in the five-axis side milling process accurately and efficiently realizes the feed speed optimization process, ensures the stability in the cutting process, reduces the vibration and protects the cutter.
Description
Technical Field
The invention relates to the technical field of contour extraction, in particular to a constant force-based feed speed optimization method in a five-axis side milling process.
Background
The feed speed is an important physical parameter in the cutting process and is an essential important factor in the research of the metal processing process, the constant feed speed shows variable cutting force under different workpiece curvatures, and the variable cutting force can cause processing vibration, tool abrasion and poor surface quality. Therefore, the constant force-based feeding speed optimization process has important practical significance for reducing vibration, protecting the cutter and improving the surface quality.
Milling force modeling is a prerequisite for constant force feed rate optimization. The low precision milling force model reduces the effect of constant force feed rate optimization, and the low efficiency milling force model wastes a large amount of optimization time. Therefore, the high-precision milling force model is also a necessary link for constant force feed speed optimization.
Document 1 "s.elk, Erdim H, Lazoglu i.off force control and feedback procedure for complex free force surfaces in 5-axis milling [ J ]. Procedia Cirp,2012,1: 96-101" discloses a constant force-based feed speed optimization method for a five-axis machine tool, including a calculation method for five-axis milling force. And the effectiveness of the method is verified by comparing the feeding speed before and after optimization. The effectiveness of the milling force model is verified through the simulation and experimental comparison of the milling force. However, the method adopts the Newton iteration method to optimize the feeding speed, and a great deal of optimization time is wasted. In addition, the method adopts a low-precision milling force model, and the optimization effect needs to be improved.
Document 2 "Park HS, Qi B, Dang DV, et al, development of machining strategies to machining time [ J ] Journal of computational Design and Engineering,2018,5(3): 299-304" discloses an automated machining system and optimization strategy to predict and improve milling performance operations. The method uses an intelligent algorithm for feed speed optimization, and the process is a complex process which is continuously adjusted and needs to consume a large amount of optimization time.
Disclosure of Invention
The invention provides a constant-force-based feed speed optimization method in a five-axis side milling process, aiming at accurately and efficiently realizing a constant-force feed speed optimization process, ensuring the stability in a cutting process, reducing vibration and protecting a cutter.
The embodiment of the invention provides a constant force-based feed speed optimization method in a five-axis side milling process, which comprises the following steps:
step 1: determining a fitting expression of the instantaneous undeformed chip thickness based on a preset first feed speed and a tool rotation angle;
step 2: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula, and analyzing the moment of the peak cutting force to obtain a peak cutting force expression at any moment;
and step 3: reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the entry angle;
and 4, step 4: calculating a second feeding speed according to the arbitrarily set constant peak force, the set cut-in angle and the preset expression;
and 5: and saving the second feeding speed to the cutter position file.
Optionally, step 1: determining a fitting expression of the instantaneous undeformed chip thickness based on a preset first feed speed and a tool rotation angle, comprising:
step 11: and determining an expression of the instantaneous undeformed chip thickness according to the fitting constant, the feed per tooth and the tool rotation angle as follows:
wherein the content of the first and second substances,
representing the instantaneous undeformed chip thickness of the jth infinitesimal layer of the ith tooth at the time t; f. ofzThe feed amount per tooth is taken;
the tool rotation angle of the jth infinitesimal layer of the ith tooth at the moment t; k is a radical of0,k1,k2,...,kn+1,kn+2Is the fitting constant;
step 12: establishing a fitting error function with a constant for fitting the instantaneous undeformed chip thickness as a parameter; the fitting error function is as follows:
wherein, W (k)0,k1,k2,...,kn+1,kn+2) Is a fitting error function; j is the feed per tooth data volume participating in the fitting; k is the tool rotation angle data quantity participating in fitting; f. ofz,pFor the pth feed speed value participating in the fitting;for a feed speed of fzWhen the angle of cut is
Instantaneous undeformed cut thickness of the time fit;
is the jth cutting element of the ith tooth at tqThe cut-in angle of the fitting is participated in at any moment; k is a radical of0,k1,k2,...,kn+1,kn+2Fitting a constant for the instantaneous undeformed chip thickness;
step 13: the fitting error function calculates a partial derivative of each fitting constant and makes the partial derivative equal to 0, and then solves the values of the fitting constants by combining a plurality of partial derivative equations, wherein the equation of the partial derivative is as follows:
step 14: substituting the value of the fitting constant, the relation of the first feeding speed and the feeding amount of each tooth into an instantaneous undeformed chip thickness expression, and determining an instantaneous undeformed chip thickness fitting expression;
the first feeding speed and the feeding amount per tooth are in the following relation:
v1＝Nfznz，
wherein N is the number of teeth, v1At a first feed speed, fzFor feed per tooth, nzThe main shaft rotating speed;
the fitting expression of the instantaneous undeformed chip thickness is as follows:
optionally, step 2: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula, and analyzing the moment of the peak cutting force to obtain the peak cutting force expression at any moment, wherein the peak cutting force expression comprises the following steps:
step 21: and determining the rotation angle of the cutter according to the cutting angle of the cutter, wherein the calculation formula is as follows:
wherein E is the cutting angle of the cutter,
the rotation angle of a cutter of the jth infinitesimal layer of the ith tooth at the time t, β is the spiral angle of the cutter, D (i, j) is the diameter of the jth cutting infinitesimal of the ith tooth, apIs the axial cutting depth of the tool; j is the jth infinitesimal layer; e1The rotation angle of the tool when the first cutting element is first cut, M is the number of layers of the cutting element, and the relationship between them can be represented by the following formula:
step 22: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula:
wherein dz represents the thickness of each cutting infinitesimal layer after the tool is axially discretized; ktc，KrcAnd KacRespectively representing the tangential, radial and axial shear force coefficients; kte，KreAnd KaeRespectively representing tangential, radial and axial cutting edge force coefficients;and
respectively represents the j cutting micro-element of the ith tooth at the cutting angle of
Tangential, radial and axial cutting forces;
the system is used for indicating whether the jth cutting element of the ith tooth participates in cutting at the moment t or not;
the force in the x-direction of the tool coordinate system can be expressed as:
wherein, Fc,x(t) is the force applied in the x direction of the tool coordinate system,
the tool rotation angle for the jth infinitesimal layer of the ith tooth at time t,
and
respectively representing the tangential force and the radial force of the jth infinitesimal layer of the ith tooth at the moment tIt can be expressed as:
the force in the y direction of the tool coordinate system can be obtained by substituting the instantaneous undeformed chip thickness into the following formula:
the z-direction force of the tool coordinate system can be obtained by substituting the instantaneous undeformed chip thickness into the following formula:
step 23: judging whether the current cutting belongs to single-tooth cutting or multi-tooth cutting according to the cutter parameters and the processing parameters;
when the cutting mode is single-tooth cutting, the peak cutting force exists when the maximum tooth completely cuts into a workpiece for the first time;
when the cutting mode is multi-tooth cutting, the peak cutting force exists when the maximum cutting infinitesimal is firstly cut into the workpiece;
calculating a cutter rotation angle at the moment when the peak force is maximum according to the cutting conditions and the cut-in angle, and substituting the cutter rotation angle into a cutting force formula to obtain the peak cutting force;
when the number of axially divided infinitesimal layers tends to infinity, the peak cutting force can be expressed as:
wherein the content of the first and second substances,and
the cutting thickness and the tool rotation angle are expressed by the following formula
Where u is an integral variable, D (i)max) Is the radius at which the largest tooth actually participates in cutting;
the shape of u is generated in the simplification processncosudu and unThe integral process of sinudu can be calculated by the following formula:
∫uncosudu＝sinu((-1)2un+(-1)3n(n-1)un-2…)+cosu((-1)2nun-1+(-1)3n(n-1)(n-2)un-3…)
∫unsinudu＝cosu((-1)1un+(-1)2n(n-1)un-2…)+sinu((-1)2nun-1+(-1)3n(n-1)(n-2)un-3…)
step 24: the x, y and z forces in the tool coordinate system are reduced as a function of the peak cutting force with respect to the cut-in angle and feed speed as follows:
wherein f is1，f2And f3Are all functional relationships, Fc,x,max、Fc,y,max、Fc,z,maxThe component forces of the peak cutting force in the x, y and z directions under the tool coordinate system,
according to the formula of the resultant force:
the peak cutting force to which the cutter is subjected can be obtained as follows:
wherein, Fc,x,max(t)、Fc,y,max(t)、Fc,z,max(t) the x-, y-and z-direction component forces of the peak cutting force at time t in the tool coordinate system, Fc,max(t) is the peak cutting force at time t;
then, the formula can be simplified according to the peak value cutting force borne by the cutter to obtain:
a0fz 2+b0fz+c0＝0
wherein, a0，b0And c0Are all constant parameters; can be obtained from a simplified peak cutting force formula.
Optionally, step 3: reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the entry angle; the method comprises the following steps:
according to the formula of peak cutting force and formula v2＝NfznzObtaining a preset expression as follows:
wherein N is the number of teeth, NzThe main shaft rotating speed; a is0，b0And c0Respectively, parameters confirmed by the first feed speed and the cut-in angle; v. of2Is the second feed rate.
Optionally, step 4: calculating a second feeding speed according to the arbitrarily set constant peak force, the set cut-in angle and a preset expression, wherein the second feeding speed comprises the following steps:
step 41: a proper constant peak force is set according to the actual cutting condition,
step 42: generating a cutter position file according to a part to be processed and calculating the cutting angle of each cutter position point;
step 43: and substituting the constant peak force and the cut-in angle of each cutter point into a preset expression to calculate a second feeding speed of each cutter point.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram of a constant force-based feed rate optimization method during five-axis side milling machining according to an embodiment of the invention;
FIG. 2 is a software flow chart of a constant force based feed rate optimization method for a five-axis side milling process according to an embodiment of the present invention;
FIG. 3 is a software flow diagram of a conventional feed rate optimization method;
FIG. 4 illustrates the feed rate for each tool location prior to optimization in an embodiment of the present invention;
FIG. 5 is a graph illustrating the optimized feed rate for each tool location in an embodiment of the present invention;
FIG. 6 is a graph showing the trend of the resultant force applied to the optimized front cutter along with the change of the cutting time in the embodiment of the invention;
fig. 7 shows the trend of the resultant force applied to the tool after optimization according to the embodiment of the invention, which is changed along with the cutting time.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
The embodiment of the invention provides a constant-force-based feed speed optimization method in a five-axis side milling process, which comprises the following steps of:
step 1: determining a fitting expression of the instantaneous undeformed chip thickness based on a preset first feed speed and a tool rotation angle;
step 2: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula, and analyzing the moment of the peak cutting force to obtain a peak cutting force expression at any moment;
and step 3: reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the entry angle;
and 4, step 4: calculating a second feeding speed according to the arbitrarily set constant peak force, the set cut-in angle and a preset expression;
and 5: and saving the second feeding speed to the cutter position file.
The working principle and the beneficial effects of the technical scheme are as follows:
firstly, determining a fitting expression of the instantaneous undeformed chip thickness based on a preset first feed speed (feed speed in an original cutter position file) and a cutter rotation angle; substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula, and analyzing the moment of the peak cutting force to obtain a peak cutting force expression at any moment; reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the entry angle; calculating a second feeding speed (optimized feeding speed) according to the arbitrarily set constant peak force, the set cut-in angle and a preset expression; and saving the second feeding speed in a cutter position file to finish the process of optimizing the feeding speed.
The method of the invention adjusts the feeding speed to ensure that the peak cutting force borne by the cutter is kept constant. The instantaneous undeformed chip thickness is represented in a fitting manner, and the feed speed expression is obtained by reversely solving the cutting force model. The iterative calculation process in the traditional constant force feeding speed optimization process is avoided. The constant force feeding speed optimization efficiency is greatly improved, and meanwhile, the optimization precision is considered. The method is particularly suitable for stabilizing the machining process in five-axis machining, protecting the cutter and reducing vibration. The method is convenient to integrate with a CAM system and is used for the feed speed optimization process under the constant force condition.
In one embodiment, step 1: determining a fitting expression of the instantaneous undeformed chip thickness based on a preset first feed speed and a tool rotation angle, comprising:
step 11: and determining an expression of the instantaneous undeformed chip thickness according to the fitting constant, the feed per tooth and the tool rotation angle as follows:
in the formula (I), the compound is shown in the specification,
represents the instantaneous undeformed chip thickness, f, of the jth microlayer of the ith tooth at time tzFor the amount of feed per tooth,
the tool rotation angle, k, of the j infinitesimal layer for the ith tooth at time t0,k1,k2,...,kn+1,kn+2Is the fitting constant;
axially dispersing the cutter into a plurality of infinitesimal layers; starting from the bottom end of the cutter, the 1 st infinitesimal layer, the 2 nd infinitesimal layer, … … the jth infinitesimal layer, … … are respectively arranged.
Step 12: establishing a fitting error function with a constant for fitting the instantaneous undeformed chip thickness as a parameter; the fitting error function is as follows:
wherein, W (k)0,k1,k2,...,kn+1,kn+2) J is the data quantity of feed quantity of each tooth participating in fitting, and K is the data quantity of the rotation angle of the cutter participating in fitting; f. ofz,pFor the pth feed speed value participating in the fitting;
for a feed speed of fzWhen the angle of cut is
Instantaneous undeformed cut thickness of the time fit;
is the jth cutting element of the ith tooth at tqThe cut-in angle of the fitting is participated in at any moment; k is a radical of0,k1,k2,...,kn+1,kn+2Fitting a constant for the instantaneous undeformed chip thickness;
step 13: the fitting error function calculates a partial derivative of each fitting constant and makes the partial derivative equal to 0, and then solves the values of the fitting constants by combining a plurality of partial derivative equations, wherein the equation of the partial derivative is as follows:
step 14: substituting the value of the fitting constant, the relation of the first feeding speed and the feeding amount of each tooth into an instantaneous undeformed chip thickness expression, and determining an instantaneous undeformed chip thickness fitting expression;
the first feeding speed and the feeding amount per tooth are in the following relation:
v1＝Nfznz，
wherein N is the number of teeth, v1At a first feed speed, fzFor feed per tooth, nzThe main shaft rotating speed;
the fitting expression of the instantaneous undeformed chip thickness is as follows:
in one embodiment, step 2: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula, and analyzing the moment of the peak cutting force to obtain the peak cutting force expression at any moment, wherein the peak cutting force expression comprises the following steps:
step 21: and determining the rotation angle of the cutter according to the cutting angle of the cutter, wherein the calculation formula is as follows:
wherein E is the cutting angle of the cutter,
the rotation angle of a cutter of the jth infinitesimal layer of the ith tooth at the time t, β is the spiral angle of the cutter, D (i, j) is the diameter of the jth cutting infinitesimal of the ith tooth, apIs the axial cutting depth of the tool; j is the jth infinitesimal layer; e1The rotation angle of the tool when the first cutting element is first cut, M is the number of layers of the cutting element, and the relationship between them can be represented by the following formula:
step 22: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula:
wherein dz represents the thickness of each cutting infinitesimal layer after the tool is axially discretized; ktc，KrcAnd KacRespectively representing the tangential, radial and axial shear force coefficients; kte，KreAnd KaeRespectively representing tangential, radial and axial cutting edge force coefficients;
and
respectively represents the j cutting micro-element of the ith tooth at the cutting angle of
Tangential, radial and axial cutting forces;the system is used for indicating whether the jth cutting element of the ith tooth participates in cutting at the moment t or not;
the force in the x-direction of the tool coordinate system can be expressed as:
wherein, Fc,x(t) is the force applied in the x direction of the tool coordinate system,the tool rotation angle for the jth infinitesimal layer of the ith tooth at time t,
and
the tangential force and the radial force of the jth micro-element layer of the ith tooth at the moment t are respectively expressed as follows:
the force in the y direction of the tool coordinate system can be obtained by substituting the instantaneous undeformed chip thickness into the following formula:
the z-direction force of the tool coordinate system can be obtained by substituting the instantaneous undeformed chip thickness into the following formula:
step 23: judging whether the current cutting belongs to single-tooth cutting or multi-tooth cutting according to the cutter parameters and the processing parameters; when the cutting mode is single-tooth cutting, the peak cutting force exists when the maximum tooth completely cuts into a workpiece for the first time;
when the cutting mode is multi-tooth cutting, the peak cutting force exists when the maximum cutting infinitesimal is firstly cut into the workpiece;
calculating a cutter rotation angle at the moment when the peak force is maximum according to the cutting conditions and the cut-in angle, and substituting the cutter rotation angle into a cutting force formula to obtain the peak cutting force;
when the number of axially divided infinitesimal layers tends to infinity, the peak cutting force can be expressed as:
wherein the content of the first and second substances,
andthe cutting thickness and the tool rotation angle are expressed by the following formula
Where u is an integral variable, D (i)max) Is the radius at which the largest tooth actually participates in cutting.
The shape of u is generated in the simplification processncosudu and unThe integral process of sinudu can be calculated by the following formula:
∫uncosudu＝sinu((-1)2un+(-1)3n(n-1)un-2…)+cosu((-1)2nun-1+(-1)3n(n-1)(n-2)un-3…)
∫unsinudu＝cosu((-1)1un+(-1)2n(n-1)un-2…)+sinu((-1)2nun-1+(-1)3n(n-1)(n-2)un-3…)
step 24: the x, y and z forces in the tool coordinate system are reduced as a function of the peak cutting force with respect to the cut-in angle and feed speed as follows:
wherein f is1，f2And f3Are all functional relationships, Fc,x,max、Fc,y,max、Fc,z,maxThe component forces of the peak cutting force in the x, y and z directions under the tool coordinate system,
according to the formula of the resultant force:
the peak cutting force to which the cutter is subjected can be obtained as follows:
wherein, Fc,x,max(t)、Fc,y,max(t)、Fc,z,max(t) the x-, y-and z-direction component forces of the peak cutting force at time t in the tool coordinate system, Fc,max(t) is the peak cutting force at time t;
then, the formula can be simplified according to the peak value cutting force borne by the cutter to obtain:
a0fz 2+b0fz+c0＝0
wherein, a0，b0And c0Are parameters identified by the first feed rate and the cut-in angle, and can be obtained from a simplified peak cutting force formula.
In one embodiment, step 3: reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the entry angle; the method comprises the following steps:
according to the formula of peak cutting force and formula v2＝NfznzObtaining a preset expression as follows:
wherein N is the number of teeth, NzThe main shaft rotating speed; a is0，b0And c0Is a parameter identified by the first feed rate and the cut-in angle; v. of2A second feed rate;
a0,b0and c0The values of these three parameters are specifically identified as follows:
the expression of the x-direction component with respect to the feed speed and the cut-in angle can be obtained from the formula in the text:
wherein L isa,1,La,2,...La,n,Lb,1,Lb,2,...Lb,nCan be expressed as follows:
similarly, Fc,y,maxAnd Fc,z,maxCan be expressed as follows:
wherein L isc,1,Lc,2,...Lc,n,Ld,1,Ld,2,...Ld,nCan be according to La,1The solution process of (2) is similar to the solution.
Wherein L ise,1,Le,2,...Le,nCan be expressed as follows:
combining the above equations can be transformed into:
wherein M is1,M2,M3,M4,M5And M6Are parameters relating to the angle of entry, which can be expressed as follows:
(Krc)(k1Lb,1+k2Lb,2+…+knLb,n-kn+1)cos(E+2tanβ/D(imax)ap)
M2＝k0sin(E+2tanβ/D(imax)ap)(D(imax)/(2aptanβ)(-Ktc)(k1La,1+k2La,2+…+knLa,n+kn+2)+(D(imax))/(2aptanβ)(Krc)(k1Lb,1+k2Lb,2+…+knLb,n-kn+2)-(D(imax))/(2aptanβ)(Ktesin(E+2tanβ/D(imax)ap+Krecos(E+2tanβ/D(imax)ap))
M3＝cos(E+2tanβ/D(imax)ap)(D(imax)/(2aptanβ)(-Ktc)(k1La,1+k2La,2+…+knLa,n+kn1+)+D(imax)/(2aptanβ)(-Krc)(k1Lb,1+k2Lb,2+…+knLb,n-kn+1)sin(E+2tanβ/D(imax)ap)
thus, according to the equation:
this is a quadratic equation, and a is solved0，b0And c0。
In one embodiment, step 4: calculating a second feeding speed according to the arbitrarily set constant peak force, the set cut-in angle and a preset expression, wherein the second feeding speed comprises the following steps:
step 41: setting a proper constant peak force according to the actual cutting condition;
step 42: generating a cutter position file according to a part to be processed and calculating the cutting angle of each cutter position point;
step 43: and substituting the constant peak force and the cut-in angle of each cutter point into a preset expression to calculate a second feeding speed of each cutter point.
Firstly, dispersing a cutter into a plurality of cutting microelements along the axial direction; fig. 2 is a flow chart of software to which the method of the present invention is applied. Fig. 3 shows a software flowchart applied to a conventional constant force feed speed optimization method. This process, which requires constant adjustments to bring the cutting force close to the target cutting force, is time consuming and becomes more complex as the accuracy of the optimization increases. The invention avoids iterative calculation of the traditional method by directly calculating the feeding speed under the constant cutting force. The calculation result of the method keeps higher precision, greatly improves optimization efficiency and has wide application prospect. The method has important significance for optimizing the feed speed under the constant force condition, and the method for optimizing the feed speed based on the constant force in the five-axis side milling process is explained by specific numerical values
For example: firstly, selecting a hard alloy end mill with the cutter radius R of 6mm, the cutter tooth number N of 4 and the cutter helix angle of 30 degrees, wherein the feed speed is 200mm/min, the main shaft rotation speed is 1000R/min, and the workpiece material is 7075 aluminum alloy. The feed per tooth is recorded as fzThe tool rotation angle of the jth infinitesimal layer of the ith tooth at the time t is recorded as
Then the instantaneous undeformed chip thickness of the jth microlayer of the ith tooth at time t is expressed as:
in the formula
Represents the instantaneous undeformed chip thickness, k, of the jth infinitesimal layer of the ith tooth at time t0,k1,k2,...,kn+1,kn+2Is the constant parameter to be solved. Counting the number of teeth as N, the feeding speed as v, NzThe relation v between the feeding speed and the feeding amount per tooth is Nf for the main shaft rotating speedznzSubstituting the formula to obtain a fitting expression of the instantaneous undeformed chip thickness based on the feed speed and the tool rotation angle; the fitting expression is:
cutting microelements: the tool is axially divided into n (which may be considered as defining numerical values) halves, each of which is a cutting element (layer of elements).
Secondly, determining an unknown constant in fitting expression according to the existing simulation result of the instantaneous undeformed chip thickness:
firstly, establishing a function of a constant parameter to be solved in the first step and the second step:
in the formula, W (k)0,k1,k2,...,kn+1,kn+2) The method comprises the following steps that a fitting error function about a constant to be obtained is obtained, J is data quantity of feed quantity of each tooth participating in fitting, and K is data quantity of a tool rotation angle participating in fitting; f. ofz,pFor the pth feed speed value participating in the fitting;for a feed speed of fzWhen the angle of cut is
The instantaneous undeformed cut thickness of the fit.
Is the jth cutting element of the ith tooth at tqThe entry angle at which the moment participates in the fitting. To maximize the fit, according to the formula:
and solving a partial derivative of each parameter in the parameter function to be solved to be equal to 0, and then solving a plurality of partial derivative equation sets to obtain each parameter value. Substituting the solved parameter values into an instantaneous undeformed chip thickness expression to obtain an instantaneous undeformed chip thickness fitting expression, selecting 1500 groups of existing simulation data, substituting the simulation data into a formula, selecting a polynomial fitting series n to be 4, and obtaining a parameter to be solved as k0＝0.0048，k1＝-0.4708，k3＝0.0259，k4＝0.0241，k50.99 and k6＝0.0009。
Substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force formula, wherein each milling force coefficient in the milling force calculation formula is Ktc＝974.13N/mm2,Ktc＝219N/mm2,Ktc＝87.6N/mm2,Ktc＝37.8N/mm,Ktc＝53.2N/mm,Ktc20.17N/mm. Analyzing the time of the peak force to obtain a peak cutting force display expression at any time:
if E is the cutter entry angle, the cutter rotatesCan be expressed as:
wherein β is the helix angle of the cutter, D (i, j) is the diameter of the jth cutting element of the ith tooth, apIs the axial cutting depth of the tool; j is the jth infinitesimal layer; e1The rotation angle of the tool when the first infinitesimal layer is cut in for the first time, and M is the number of infinitesimal layers, the relationship between them can be expressed as follows:
and then substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula:
where dz represents the thickness of each cutting infinitesimal layer after the tool has been axially discretized. Ktc，KrcAnd KacThe shear force coefficients in the tangential direction, the radial direction and the axial direction are respectively expressed. Kte，KreAnd KaeRespectively representing tangential, radial and axial cutting edge force coefficients;
and
respectively represents the j cutting micro-element of the ith tooth at the cutting angle of
Tangential, radial and axial cutting forces;
the system is used for indicating whether the jth cutting element of the ith tooth participates in cutting at the moment t or not;
the force in the x-direction of the tool coordinate system can be expressed as:
in the formula (I), the compound is shown in the specification,
wherein, Fc,x(t) is recorded as the force applied in the x-direction of the tool coordinate system,and
the tangential force and the radial force of the jth micro-element layer of the ith tooth at the moment t are respectively expressed as follows:
and similarly, the stress in the y direction and the z direction of the tool coordinate system can be obtained by substituting the instantaneous undeformed chip thickness into the following formula:
firstly, analyzing the moment when the peak force exists, and judging whether the current cutting belongs to single-tooth cutting or multi-tooth cutting according to the cutter parameters and the processing parameters; when the cutter is used for cutting, the cutter jumps, so that different cutting edges actually participate in different cutting radii, and the largest tooth is recorded as the tooth with the largest actual cutting radius; recording the maximum cutting element as an axial element layer with the maximum actual cutting radius;
when the cutting mode is single-tooth cutting, the peak cutting force exists when the maximum tooth completely cuts into a workpiece for the first time;
when the cutting mode is multi-tooth cutting, the peak cutting force exists when the maximum cutting infinitesimal first cuts into the workpiece.
Calculating a cutter rotation angle at the moment when the peak force is maximum according to the cutting conditions and the cut-in angle, and substituting the cutter rotation angle into a cutting force formula to obtain the peak cutting force;
considering the moment when the peak force occurs, when the number of axially divided infinitesimal layers tends to infinity, the peak cutting force can be expressed as:
in the formula
And
the cutting thickness and the tool rotation angle are expressed by the following formula
Where u is an integral variable, D (i)max) Is the radius at which the largest tooth actually participates in cutting.
The shape of u is generated in the simplification processncosudu and unThe integral process of sinudu can be calculated by the following formula:
∫uncosudu＝sinu((-1)2un+(-1)3n(n-1)un-2…)+cosu((-1)2nun-1+(-1)3n(n-1)(n-2)un-3…)
∫unsinudu＝cosu((-1)1un+(-1)2n(n-1)un-2…)+sinu((-1)2nun-1+(-1)3n(n-1)(n-2)un-3…)
the x, y and z forces in the tool coordinate system are then reduced as a function of peak cutting force with respect to the cut-in angle and feed rate as follows:
in the formula f1，f2And f3Are all functional relationships according to the formula of the resultant force:
the peak cutting force to which the cutter is subjected can be obtained as follows:
then, the formula can be simplified according to the peak value cutting force borne by the cutter to obtain:
a0fz 2+b0fz+c0＝0
in the formula a0，b0And c0Are all thatThe parameters determined by the original feed speed (first feed speed) and the cut-in angle can be obtained from a simplified peak cutting force formula.
And fourthly, reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the cutting angle:
according to the formula of peak cutting force and formula v ═ NfznzObtaining a preset expression as follows:
and fifthly, calculating the feeding speed of each cutter location point according to the arbitrarily set constant peak force, the set cut-in angle and a preset expression:
and generating a cutter position file according to the part to be machined and calculating the cutting-in angle of each cutter position by taking 273N peak force (constant peak force) of the horizontal cutting area as constraint according to the actual cutting condition.
And then calculating the feed speed of each tool location point through a preset expression in the step four, generating a new tool location file by using the calculated feed speed, and finishing the feed speed optimization process based on constant force in the five-axis side milling process.
The feed rates before and after optimization are shown in fig. 4 and 5, respectively, and the feed rate before optimization is a constant 200 mm/min. The milling force obtained using this feed rate is plotted against the machining time as shown in fig. 6. It can be seen that the cutting force is not uniform because at a constant feed rate, the magnitude of the cutting force varies with the curvature of the workpiece.
The optimized feed rate is shown in fig. 5, and it can be seen that in the region of high milling force, the feed rate must be reduced in order to achieve the target milling force. In the region of low milling forces, the feed rate must be increased in order to achieve the target milling force.
The same workpiece was re-machined using the optimized feed rate and the resulting cutting force versus time was shown in fig. 7, which shows that the peak force experienced by the tool was essentially constant. Thereby achieving the result of optimizing the feeding speed under the condition of constant force.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (5)
1. A constant-force-based feeding speed obtaining method in a five-axis side milling process is characterized by comprising the following steps:
step 1: determining a fitting expression of the instantaneous undeformed chip thickness based on a preset first feed speed and a tool rotation angle;
step 2: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula, and analyzing the moment of the peak cutting force to obtain a peak cutting force expression at any moment;
and step 3: reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the cutting angle;
and 4, step 4: calculating the second feeding speed according to any set constant peak force, a set cut-in angle and the preset expression;
and 5: and saving the second feeding speed to a cutter position file.
2. The constant force-based feed speed optimization method in the five-axis side milling process according to claim 1, characterized in that the step 1: determining a fitting expression of the instantaneous undeformed chip thickness based on a preset first feed speed and a tool rotation angle, comprising:
step 11: and determining an expression of the instantaneous undeformed chip thickness according to the fitting constant, the feed per tooth and the tool rotation angle as follows:
wherein the content of the first and second substances,
representing the instantaneous undeformed chip thickness of the jth infinitesimal layer of the ith tooth at the time t; f. ofzThe feed amount per tooth is taken;
the tool rotation angle of the jth infinitesimal layer of the ith tooth at the moment t; k is a radical of0,k1,k2,...,kn+1,kn+2Is the fitting constant;
step 12: establishing a fitting error function with a constant for fitting the instantaneous undeformed chip thickness as a parameter; the fitting error function is as follows:
wherein, W (k)0,k1,k2,...,kn+1,kn+2) Is a fitting error function; j is the feed per tooth data volume participating in the fitting; k is the data quantity of the rotation angle of the tool participating in fitting; f. ofz,pFor the pth feed speed value participating in the fitting;
for a feed speed of fzWhen the angle of cut is
Instantaneous undeformed cut thickness of the time fit;
is the jth cutting element of the ith tooth at tqThe cut-in angle of the fitting is participated in at any moment;
step 13: the fitting error function calculates a partial derivative of each fitting constant and makes the partial derivative equal to 0, and then solves the values of the fitting constants by combining a plurality of partial derivative equations, wherein the equation of the partial derivative is as follows:
step 14: substituting the value of the fitting constant, the relation of the first feeding speed and the feeding amount of each tooth into an instantaneous undeformed chip thickness expression, and determining an instantaneous undeformed chip thickness fitting expression;
the first feeding speed and the feeding amount per tooth are in the following relation:
v1＝Nfznz，
wherein N is the number of teeth, v1At a first feed speed, fzFor feed per tooth, nzThe main shaft rotating speed;
the fitting expression of the instantaneous undeformed chip thickness is as follows:
3. the constant force based feed speed optimization method in the five-axis side milling process according to claim 1, characterized in that the step 2: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula, and analyzing the moment of the peak cutting force to obtain the peak cutting force expression at any moment, wherein the peak cutting force expression comprises the following steps:
step 21: and determining the rotation angle of the cutter according to the cutting angle of the cutter, wherein the calculation formula is as follows:
wherein E is the cutting angle of the cutter,
the rotation angle of a cutter of the jth infinitesimal layer of the ith tooth at the time t, β is the spiral angle of the cutter, D (i, j) is the diameter of the jth cutting infinitesimal of the ith tooth, apIs the axial cutting depth of the tool; j is the jth infinitesimal layer; e1For the first cutting of the first cutting elementThe rotation angle, M, is the number of cutting micro-elements, and the relationship between them can be represented by the following formula:
step 22: substituting the determined fitting expression of the instantaneous undeformed chip thickness into a cutting force calculation formula:
wherein dz represents the thickness of each cutting infinitesimal layer after the tool is axially discretized; ktc，KrcAnd KacRespectively representing the tangential, radial and axial shear force coefficients; kte，KreAnd KaeRespectively representing tangential, radial and axial cutting edge force coefficients;
and
respectively represents the j cutting micro-element of the ith tooth at the cutting angle ofTangential, radial and axial cutting forces;
the system is used for indicating whether the jth cutting element of the ith tooth participates in cutting at the moment t or not;
the force in the x-direction of the tool coordinate system can be expressed as:
wherein, Fc,x(t) is the force applied in the x direction of the tool coordinate system,
the tool rotation angle for the jth infinitesimal layer of the ith tooth at time t,
and
the tangential force and the radial force of the jth micro-element layer of the ith tooth at the moment t are respectively expressed as follows:
the force in the y direction of the tool coordinate system can be obtained by substituting the instantaneous undeformed chip thickness into the following formula:
the z-direction force of the tool coordinate system can be obtained by substituting the instantaneous undeformed chip thickness into the following formula:
step 23: judging whether the current cutting belongs to single-tooth cutting or multi-tooth cutting according to the cutter parameters and the processing parameters;
when the cutting mode is single-tooth cutting, the peak cutting force exists when the maximum tooth completely cuts into a workpiece for the first time;
when the cutting mode is multi-tooth cutting, the peak cutting force exists when the maximum cutting infinitesimal is firstly cut into the workpiece;
calculating a cutter rotation angle at the moment when the peak force is maximum according to the cutting conditions and the cut-in angle, and substituting the cutter rotation angle into a cutting force formula to obtain the peak cutting force;
when the number of axially divided infinitesimal layers tends to infinity, the peak cutting force can be expressed as:
wherein the content of the first and second substances,andthe cutting thickness and the tool rotation angle are expressed by the following formula
Where u is an integral variable, D (i)max) Is the radius at which the largest tooth actually participates in cutting;
the shape of u is generated in the simplification processncosudu and unThe integral process of sinudu can be calculated by the following formula: integral multiple of uncosudu＝sinu((-1)2un+(-1)3n(n-1)un-2…)+cosu((-1)2nun-1+(-1)3n(n-1)(n-2)un-3…)∫unsinudu＝cosu((-1)1un+(-1)2n(n-1)un-2…)+sinu((-1)2nun-1+(-1)3n(n-1)(n-2)un-3…)
Step 24: the x, y and z forces in the tool coordinate system are reduced as a function of the peak cutting force with respect to the cut-in angle and feed speed as follows:
wherein f is1，f2And f3Are all functional relationships, Fc,x,max、Fc,y,max、Fc,z,maxThe component forces of the peak cutting force in the x, y and z directions under the tool coordinate system,
according to the formula of the resultant force:
the peak cutting force to which the cutter is subjected can be obtained as follows:
wherein, Fc,x,max(t)、Fc,y,max(t)、Fc,z,max(t) the x-, y-and z-direction component forces of the peak cutting force at time t in the tool coordinate system, Fc,max(t) is the peak cutting force at time t;
then, the formula can be simplified according to the peak value cutting force borne by the cutter to obtain:
a0fz 2+b0fz+c0＝0
wherein, a0，b0And c0Are parameters determined based on the first feed speed and the cut-in angle; can be obtained from a simplified peak cutting force formula.
4. The constant force based feed speed optimization method in the five-axis side milling process according to claim 1, characterized in that step 3: reversely solving the expression of the peak cutting force to obtain a preset expression among the feeding speed, the peak cutting force and the entry angle; the method comprises the following steps:
according to the formula of peak cutting force and formula v2＝NfznzObtaining a preset expression as follows:
wherein N is the number of teeth, NzThe main shaft rotating speed; a is0，b0And c0Are parameters identified based on the first feed rate and the cut-in angle; v. of2Is the second feed rate.
5. The constant force based feed speed optimization method in the five-axis side milling process according to claim 1, characterized in that step 4: calculating a second feeding speed according to the arbitrarily set constant peak force, the set cut-in angle and a preset expression, wherein the second feeding speed comprises the following steps:
step 41: a proper constant peak force is set according to the actual cutting condition,
step 42: generating a tool position file according to a part to be processed and calculating the cutting-in angle;
step 43: and substituting the constant peak force and the cut-in angle into the preset expression to calculate a second feeding speed of each cutter location point.
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| CN103955169A (en) * | 2014-04-11 | 2014-07-30 | 上海交通大学 | Method for predicting milling force of five-axis numerical control side milling |
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| CN103955169A (en) * | 2014-04-11 | 2014-07-30 | 上海交通大学 | Method for predicting milling force of five-axis numerical control side milling |
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