CN113962105A - Efficient parameter optimization method for flutter-free finish machining milling process - Google Patents

Efficient parameter optimization method for flutter-free finish machining milling process Download PDF

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CN113962105A
CN113962105A CN202111286179.8A CN202111286179A CN113962105A CN 113962105 A CN113962105 A CN 113962105A CN 202111286179 A CN202111286179 A CN 202111286179A CN 113962105 A CN113962105 A CN 113962105A
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CN113962105B (en
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张星
赵万华
郭卓城
赵钊
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Xian Jiaotong University
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Abstract

A high-efficiency parameter optimization method for a flutter-free finish machining milling process comprises the steps of firstly, establishing a parameter optimization model taking machining efficiency as a target under multiple constraint conditions of parameter feasible region, milling force, milling stability, roughness, machining precision and the like; because the roughness is mainly influenced by the feed amount of each tooth, the feed amount of each tooth of the cutters with different tooth numbers is optimized under the roughness constraint condition by adopting a golden section method; then, numerical iteration optimization is carried out on the rotating speed of the main shaft, the radial width cutting and the axial depth cutting by adopting a random vector search method, and finally the optimal combination of the number of teeth of the cutter, the feed quantity of each tooth, the rotating speed of the main shaft, the radial width cutting and the axial depth cutting is obtained; the invention can greatly improve the milling efficiency under the condition of meeting multiple constraint conditions and realize the flutter-free high-efficiency finish machining.

Description

Efficient parameter optimization method for flutter-free finish machining milling process
Technical Field
The invention belongs to the technical field of numerical control machining, and particularly relates to an efficient parameter optimization method for a flutter-free finish machining milling process.
Background
The aim of the numerical control machining is to realize high-efficiency and high-precision machining, namely to maximize the material removal rate on the premise of ensuring the machining quality and other constraint conditions. In the traditional method, operators mostly use repeated tests and manual experiences as the basis to passively select the processing parameters, but the method is time-consuming and uneconomical, and the selected parameters are mostly conservative, so that the high-efficiency processing in the true sense is difficult to realize. Increasing milling parameters is the most effective method for improving the machining efficiency, but milling vibration is easily caused, even chattering vibration is caused, a cutter and a machine tool are damaged, and the machining quality is deteriorated. Therefore, an effective method for guiding the selection of reasonable processing parameters is urgently needed.
Numerous scholars have studied the problem of optimizing parameters with the objective of roughness and material removal rate. The learners take the surface roughness and the material removal rate as optimization targets, carry out systematic analysis on experimental data, and find that when the roughness characteristics are different, the results obtained by different optimization methods are different, which shows that the influence of parameter levels needs to be considered during optimization. The learners analyze the influence of different processing parameters on the roughness, the cutting force and the material removal rate in the dry turning process, establish four optimization targets of quality, efficiency, energy consumption, cutting force and the like, obtain the optimal processing parameters by adopting a neural network and a response surface method, and show that the roughness is mainly influenced by the feeding speed and obtains the roughness of the grinding grade. Researchers study the parameter optimization problem of the milling process of the thin-wall part, establish three contradictory targets, including the multi-target optimization problem of roughness, milling force and material removal rate, solve the problem through a neural network, and finally obtain the optimal parameter combination of the spindle rotation speed, the feed per tooth and the axial cutting depth. The influence of cutting parameters on roughness, cutting force, machining efficiency and energy consumption in the turning process is studied by scholars in an experiment, and a multi-objective optimization method is provided to obtain the minimum roughness, cutting force, machining efficiency and the maximum material removal rate.
Meanwhile, the researchers have conducted intensive research to obtain a high material removal rate while ensuring the profile accuracy of the part, which is mainly affected by the vibration of the tool and the workpiece during the cutting process. Researchers have studied an optimal selection method of the combination of the radial milling width and the axial milling depth in the stable domain range, and finally the material removal rate in the milling process is improved, and in the given analysis case, the milling time is shortened by about 40%. The learner proposes a multi-objective optimization problem with milling stability and surface position error as objective functions, wherein a certain disturbance amount of spindle rotation speed is introduced when the surface position error is calculated, so that the rapid change of the surface position error caused by a resonance region is avoided, and the robustness of an optimization model is enhanced. On the basis of analyzing milling stability and surface position errors, a learner provides a spindle rotating speed optimization selection method under the condition that the radial milling width and the axial milling depth are determined, researches indicate that the optimal rotating speed is selected on the left side of a resonance area in a high rotating speed area, and an instructive thought is provided for machining parameter optimization. Based on milling dynamics, the learner divides the milling process optimization into two steps, first selecting spindle speed, cut depth and cut width taking into account milling stability, torque and power limitations, then checking milling force, milling stability, torque and power along the tool path after NC program generation, and avoiding overrun by adjusting feed speed and spindle speed. From the viewpoint of improving the machining precision and efficiency of parts, based on statics analysis, a learner provides a parameter optimization method for guaranteeing the surface dimensional precision of thin-wall part milling, and the method establishes a linear relation between the feeding amount of each tooth, the radial milling width and the surface error.
Analysis of the existing method shows that the existing parameter optimization method has two defects: (1) part of the research lacks consideration of the physical properties of the process system, particularly neglecting the dynamic engagement characteristics of the cutter and the workpiece; (2) only partial parameters, such as the rotation speed of the main shaft and the axial cutting depth, can be optimized, and the universality is limited.
In the actual machining process, typical machining parameters include spindle rotation speed, radial cutting width, axial cutting depth, feed per tooth and cutter tooth number, and constraint conditions such as milling stability, profile accuracy, roughness, spindle torque, power and the like, so that how to obtain maximum machining efficiency under the condition of meeting various constraint conditions is an important problem.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide an efficient parameter optimization method for a flutter-free finish machining milling process, which realizes the maximization of the machining efficiency under the condition of ensuring the machining quality and other constraint conditions by establishing a single target-multiple constraint-multivariable problem.
In order to achieve the purpose, the invention adopts the technical scheme that:
an efficient parameter optimization method for a chatter-free finish machining milling process comprises the following steps:
step 1) establishing a parameter optimization model taking machining efficiency as a target under multiple constraint conditions of parameter feasible region, milling force, milling stability, roughness and machining precision;
step 2) optimizing the feed amount of each tooth of the cutters with different tooth numbers under the roughness constraint condition by adopting a golden section method; numerical iteration optimization is carried out on the rotating speed of the main shaft, the radial width cutting and the axial depth cutting by adopting a random vector search method, so that the optimal combination of the number of teeth of the cutter, the feed quantity of each tooth, the rotating speed of the main shaft, the radial width cutting and the axial depth cutting is obtained.
The specific process of the step 1) is as follows:
1.1) establishing an optimization target:
according to the distribution condition of the finishing allowance of the part, two feed modes are adopted for removing: depth first and width first; the parameter optimization objective is to achieve a maximum cutting efficiency, expressed in material removal rate, while satisfying the relevant constraints:
fMRR＝Nt·ft·n·ae·ap/1000(cm3/min) (1)
in the formula: n is a radical oftThe number of teeth of the cutter is shown; f. oftThe feed amount per tooth (mm/tooth); n is the spindle speed (rpm); a iseIs the radial cutting width (mm); a ispAxial depth of cut (mm);
1.2) establishing an optimization variable:
the optimization variables of the machining parameter optimization problem include 5 variable parameters, namely the number of tool teeth NtAnd 4 basic cutting parameters of spindle rotating speed n and radial cutting width aeAxial cutting depth apFeed per tooth ftThe optimization variable is defined as x ═ n, ae,ap,Nt,ft]T；
1.3) establishing multiple constraint conditions:
1.3.1) optimizing the constraints of the variable feasible fields:
limited by the cutting capacity of the main shaft and the cutter, the rotating speed n of the main shaft and the radial cutting width aeAxial cutting depth apAnd feed per tooth ftThe upper limit and the lower limit of the rotation speed of the main shaft are selected, the upper limit of the rotation speed of the main shaft is less than or equal to the maximum allowable rotation speed of the main shaft, the upper limit of the radial cutting width is not more than the diameter of a cutter, the upper limit of the axial cutting depth is less than the length of a cutter tooth segment of the cutter, the cutting capacity of the cutter is required to be considered for the feeding amount of each tooth, and the chip removal capacity of the cutter is required to be considered for the selection of the number of teeth of the cutter; finally, a feasible field for optimizing the variable parameter selection is formed, as shown in the following formula:
Figure BDA0003332916590000031
in the formula: the superscript u is the upper limit of the parameter, and the superscript l is the lower limit of the parameter;
in addition, when the depth is preferred, the row spacing in the width direction should be made uniform as much as possible, and when the width is preferred, the row spacing in the depth direction should be made uniform as much as possible; therefore:
Figure BDA0003332916590000032
in the formula: n is a radical ofwAnd NhThe line spacing discrete number in the width direction and the depth direction is respectively a positive integer;
1.3.2) constraint of milling force:
the magnitude of the milling force needs to be constrained, by the cutting forceThe mechanism model shows that the jth layer of cutting units on the ith cutting edge of the cutter rotate at any angle phii,jThe cutting forces in the tangential, radial and axial directions at (t) are expressed as the sum of the shear and shear forces, i.e.:
Figure BDA0003332916590000041
in the formula: k is a radical ofqs,kqp(q ═ t, r, a) for tangential, radial and axial shear and plow shear force specific coefficients; db is the axial thickness of the j layer cutting unit on the ith cutting edge; phi is ai,j(t) is the rotation angle of the jth layer cutting unit on the ith cutting edge at time t; w is a window function, as follows:
Figure BDA0003332916590000042
in the formula: thetas,i,j,θe,i,jCutting angles of cutter teeth of a j layer of cutting units on an ith cutting edge are set;
in the milling process, the locus of a point P of a tool nose point is a two-dimensional cycloid, the thickness of a cutting layer is equal to the line segment of the intersection part of the connecting line of the point P and the rotation center of the tool and a geometric solid of a workpiece, wherein the point T is a plurality of front tool teeth miAt a certain time τ in the pasti,j(t,mi) Left on the machined surface after cutting, and at t-taui,j(t,mi) At time, the coordinate of the point T in the global reference coordinate system XYZ is:
Figure BDA0003332916590000043
in the formula: ri,jThe actual cutting radius of the j layer cutting unit on the ith cutting edge;
meanwhile, the T point is also expressed as:
Figure BDA0003332916590000044
and according to the feed motion relation of the cutter, neglecting the dynamic displacement response of the cutter, the following can be known:
Figure BDA0003332916590000045
in the formula: f. ofvxThe tool feed speed;
the retardation values obtained by the above formulae (6), (7) and (8) are:
Figure BDA0003332916590000046
in the formula:
Figure BDA0003332916590000047
is the angle between the teeth;
further, the instantaneous cutting layer thickness was obtained as:
Figure BDA0003332916590000048
finally, the cutting layer thickness is the minimum value greater than zero of all cutting layer thicknesses:
hi,j(t)＝max(0,min(hi,j(t,mi)))mi＝1,2,…Nt (11)
under a cutter feeding coordinate system, summing the cutting forces generated by all cutting units participating in cutting at the same moment in an effective cutting depth range to obtain the total cutting force acting on the cutter as follows:
Figure BDA0003332916590000051
in this case, the resultant cutting force acting on the tool is:
Figure BDA0003332916590000052
considering the impact resistance of the tool, the maximum milling force acting on the tool needs to be limited within a certain range, namely:
max(Fc(x,t))≤Fclim (14)
in the formula: fclimThe maximum milling force allowed;
1.3.3) constraints on milling stability:
the restriction of milling stability restricts the upper limit of milling parameter selection; the generation of milling stability is caused by a regeneration mechanism of a flexible process system, and the thickness of a regenerated cutting layer is as follows by considering the regeneration effect of the flexible cutter system in the milling process:
Figure BDA0003332916590000053
further, a milling dynamic model is established, which is shown as the following formula:
Figure BDA0003332916590000054
in the formula:
Figure BDA0003332916590000055
wherein m isx,myModal masses in the x, y directions, respectively, cx,cyModal damping, k, in x, y directions respectivelyx,kyRespectively representing modal stiffness in x and y directions, and X (t) is a vibration displacement vector of the cutter; f0(t)＝[Fcx(t),Fcy(t)]TIs a nominal force;
Figure BDA0003332916590000058
average lag time for regenerative effects; the second term on the right side of the above formula is the milling force regeneration term, where Kc(t) is a coefficient matrix, as shown in the following formula:
Figure BDA0003332916590000056
writing a system equation into a state space model after the discretization method:
Figure BDA0003332916590000059
in the formula:
Figure BDA0003332916590000057
while the time term is discrete, the time-varying time lag term tau is dividedi,j(t) discretizing is also carried out; firstly, the rotation period of the cutter is dispersed into NtEqual minute time period of [ t ]k,tk+1]Represents the kth time period; after the time term and the time lag term are dispersed, the stability of the system is converted from a nonlinear problem to a linear problem; discrete time interval of T/NmAt a minute time period [ t ]k,tk+1]Internally, the solution of the above formula is represented as:
Figure BDA0003332916590000061
in the formula:
Figure BDA0003332916590000062
Figure BDA0003332916590000063
int is a floor function;
here, formula (19) is converted into a discrete graph, as follows:
Vk+1＝ZkVk+Ek (20)
in the formula:
Figure BDA0003332916590000064
Figure BDA0003332916590000065
Figure BDA0003332916590000066
at this time, the state transition relationship of the system over a single time period is represented as:
Figure BDA0003332916590000067
in the formula:
Figure BDA0003332916590000068
according to Floquet theory, if the modulus lambda of all characteristic values of the transformation matrix phi is less than or equal to 1, the system is stable; otherwise, the system is unstable;
thus, the constraints of milling stability are:
|λmax(x)|≤1 (22)
1.3.4) constraints on processing quality:
when the milling process is stable, the system response is obtained by calculating the system stationary point, equation (21)
Figure BDA0003332916590000069
Obtaining:
V*＝(I-Φ)-1G (23)
at this time, the transient displacement response of the tool is substituted into the following formula to obtain the transient locus surface of the cutting point of the tool nose:
Figure BDA00033329165900000610
in the formula:
Figure BDA00033329165900000611
in solving for surface positionDuring error, the track envelope surface of the actual cutter tooth point and the workpiece entity are intersected to obtain the contour of the machined surface, and the contour is used
Figure BDA00033329165900000612
Represents; in this case, the machining error represents the average position of the actual machined surface and the ideal design surface
Figure BDA0003332916590000071
The absolute average of the deviations is shown below:
Figure BDA0003332916590000072
in this case, the constraint conditions of the machining error are:
Figure BDA0003332916590000073
in the formula:
Figure BDA0003332916590000074
is a machining error allowable value;
the roughness is as follows:
Figure BDA0003332916590000075
the constraints of the roughness are:
Figure BDA0003332916590000076
in the formula:
Figure BDA0003332916590000077
the roughness tolerance value is obtained;
1.3.5) mathematical model of the optimization problem:
the multiple constraint conditions are integrated together for consideration, and the efficient milling parameter optimization problem under the multiple constraint conditions is formed, wherein a mathematical model of the efficient milling parameter optimization problem is represented as follows:
min-fMRR(x)
Figure BDA0003332916590000078
the specific process of the step 2) is as follows:
2.1) constraint condition parameter uncertainty processing:
a certain safety margin is required to be given to the constraint condition, and then the formula (29) is improved as follows:
min-fMRR(x)
Figure BDA0003332916590000079
in the formula: lambda [ alpha ]U(U ═ F, S, E, R) is a value less than 1, and the smaller the value, the larger the margin of safety of the constraint, λUThe value range of (1) is 0.7-0.98;
2.2) f based on the golden section methodtOptimizing:
in order to improve the processing efficiency, the feed amount f of each tooth is increased as much as possible on the premise of meeting the ideal surface roughnesstThe roughness constraint is therefore expressed mathematically as follows:
Figure BDA0003332916590000081
in the formula: in the optimization variables [ n, ae,ap,Nt]TSet to a definite value, with only ftTo optimize the variables;
Figure BDA0003332916590000082
is a small amount; judging that the objective function in the formula is a convex function, and optimizing the problem by adopting a golden section method; the optimization process of the golden section method is as follows:
the step (1): determining optimization target and initializing optimization variables
Figure BDA0003332916590000083
Setting the iteration number k to 1, and setting ftSearch interval a of1＝ft l,b1＝ft uAnd convergence accuracy
Figure BDA0003332916590000084
Let η equal to 0.618;
step (2): calculating a coordinate point alpha1＝b1-η(b1-a1) And beta1＝a1+η(b1-a1) Will be alpha1And beta1Is assigned to ftCalculating an objective function
Figure BDA0003332916590000085
Step (3): setting k to k +1, reducing the search interval according to an interval elimination principle: if it is not
Figure BDA0003332916590000086
Then let ak+1＝αk,bk+1＝bk，αk+1＝βk，βk+1＝ak+1+η(bk+1-ak+1) (ii) a Otherwise ak+1＝ak,bk+1＝βk，βk+1＝αkAnd alphak+1＝bk+1-η(bk+1-ak+1)；
Step (4): if it is not
Figure BDA0003332916590000087
F is thent *＝(ak+1+bk+1) 2; otherwise, returning to the step (3) to continue iteration;
2.3) multiple sample random vector search based [ n, a ]e,ap]TOptimizing:
at ftAfter the optimization is complete, the optimization problem is further described by equation (30) in view of the stability constraints described above as:
min-fMRR(x)
Figure BDA0003332916590000088
at the moment, an optimization solving method based on multi-sample random vector search is adopted to solve the above formula; the whole multi-sample random vector search process is as follows:
the step (1): determining an optimized objective function-fMRR(x) Optimizing variables x and constraining conditions gj(x) (ii) a Randomly generating sample initial values of the optimized variables, and judging whether each sample meets the constraint condition gj(x) Finally form NsSample set of samples { x }s}；
Step (2): extracting the s-th sample x in the sample sets；
Step (3): extracting a sample xsStep k variable xs,k＝[ns,k,ae,s,k,ap,s,k]；
Step (4): generating a random vector in the q searching
Figure BDA0003332916590000091
Wherein:
Figure BDA0003332916590000092
for random coefficients, [ -1,1 ] is taken here]A random number of intervals;
step (5): calculating a sample xsThe variable value of the k +1 step:
Figure BDA0003332916590000093
in the formula:
Figure BDA0003332916590000094
for rounding-down the sign of the operation, after rounding-up, the spindle speed ns,k+1Is an integer, radialWidth of cut ae,s,k+1And axial cutting depth ap,s,k+11-bit decimal number is reserved;
step (6): substituting the obtained parameters into the formula (32) to judge, the following parameters are obtained:
Figure BDA0003332916590000095
finally, let the optimization result of the s sample
Figure BDA0003332916590000096
Step (7): let s equal s +1, if s < NsReturning to the step (2); if s is equal to NsIf yes, ending the search; comparing the objective function of all samples
Figure BDA0003332916590000097
Finding out the minimum value, wherein the individual corresponding to the minimum value of the objective function is the optimal individual, and the final variable value of the individual is the optimization result
Figure BDA0003332916590000098
2.4) overall optimization process:
initializing a tool geometric parameter, a tool system dynamic parameter, a tool eccentric parameter and a specific shear force coefficient at the beginning of optimization, and selecting depth priority and width priority; then, parameter optimization is carried out in four layers of circulation, wherein the first layer is as follows: optimizing the margin discrete number when the depth is first and the width is first; a second layer: optimizing the number of teeth of the cutter; and a third layer: optimizing the feeding amount of each tooth by adopting a golden section method; a fourth layer: optimizing the rotation speed of the main shaft, the milling depth and the milling width by adopting a random vector search method; and after the four-layer loop iterative calculation is completed, selecting the milling parameter with the maximum milling efficiency as an optimal result.
The invention has the beneficial effects that:
(1) the method can greatly improve the milling efficiency under the condition of meeting multiple constraint conditions, and realize the flutter-free high-efficiency finish machining.
(2) The invention comprehensively considers multiple constraint conditions such as parameter feasible region, milling force, milling stability, roughness, processing precision and the like, considers uncertainty of model parameters, adopts a safety margin coefficient to enhance the adaptability of the model, and has better applicability compared with the prior method.
(3) In the optimization model of the invention, as the roughness is mainly influenced by the feed amount of each tooth, the optimization of the feed amount parameter of each tooth is firstly carried out, and a golden section method is adopted to solve the problem of single variable optimization, thereby reducing the complexity of the method and having higher convergence.
(4) When the optimization of the remaining variables is solved, the problem that the analytic formulas of the constraint conditions and the variables are difficult to establish is considered, so that the numerical optimization method for random vector search is provided, the fast iteration of an optimization model is ensured, the optimization of the combination of the rotating speed, the radial cutting width and the axial cutting depth of the main shaft is realized, and the high reliability of the optimization method is ensured.
Drawings
Fig. 1 is a schematic diagram of the milling process of the present invention.
Fig. 2 is a schematic diagram of a milling force model according to the present invention.
FIG. 3 is a schematic view of a simulation calculation of a machined surface of the present invention.
FIG. 4 is a diagram illustrating a multi-sample random vector search according to the present invention.
FIG. 5 is a flow chart of parameter optimization according to the present invention.
FIG. 6 is an example of an iterative change of material removal rate for different tooth counts and milling widths, where (a) the result of the MRR iteration (N)t＝1,ae3 mm); (b) iterative result of MRR (N)t＝2,ae3 mm); (c) iterative result of MRR (N)t＝3,ae3 mm); (d) iterative result of MRR (N)t＝4,ae3 mm); (e) iterative result of MRR (N)t＝3,ae1 mm); (f) iterative result of MRR (N)t＝3,ae＝1.5mm)。
FIG. 7 is an iterative variation process of the optimal individual-related parameter according to an embodiment, wherein(a) n and apThe iteration result of (2); (b) n and apThe iterative process of (2); (c) max (F)c) The iterative process of (2); (d) lambda [ alpha ]maxThe iterative process of (2); (e) esThe iterative process of (2); (f) comparison before and after MRR optimization.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
An efficient parameter optimization method for a chatter-free finish machining milling process comprises the following steps:
step 1) establishing a parameter optimization model taking machining efficiency as a target under multiple constraint conditions of parameter feasible region, milling force, milling stability, roughness, machining precision and the like;
1.1) establishing an optimization target:
referring to fig. 1, the thickness of the part finishing allowance in the normal direction of the part surface is often small, and according to the distribution of the allowance, two feed methods are usually adopted for removing: depth first and width first; the goal of parameter optimization is to achieve a maximum cutting efficiency while satisfying the relevant constraints. Milling efficiency can be expressed in terms of material removal rate:
fMRR＝Nt·ft·n·ae·ap/1000(cm3/min) (1)
in the formula: n is a radical oftThe number of teeth of the cutter is shown; f. oftThe feed amount per tooth (mm/tooth); n is the spindle speed (rpm); a iseIs the radial cutting width (mm); a ispAxial depth of cut (mm);
1.2) establishing an optimization variable:
the optimization variables of the machining parameter optimization problem include 5 variable parameters, namely the number of tool teeth NtAnd 4 basic cutting parameters (spindle speed n, radial cut width a)eAxial cutting depth apFeed per tooth ft) The optimization variable is defined as x ═ n, ae,ap,Nt,ft]T；
1.3) establishing multiple constraint conditions:
when the milling parameters are selected, the parameters are restricted by many factors, such as the parameter feasible region, the cutting force, the milling stability, the machining profile precision and the roughness, etc., and then a quantitative model of the constraint conditions is built step by step;
1.3.1) optimizing the constraints of the variable feasible fields:
in the actual processing process, the selection of the 5 optimization variables takes a plurality of constraint conditions into consideration, and firstly, the limitation of the selectable range of the parameters is realized; limited by the cutting capacity of the main shaft and the cutter, the rotating speed n of the main shaft and the radial cutting width aeAxial cutting depth apAnd feed per tooth ftThe upper limit and the lower limit of the parameters are selected, for example, the upper limit of the rotating speed of the main shaft is less than or equal to the maximum rotating speed which can be used by the main shaft, the upper limit of the radial cutting width is less than the diameter of the cutter, the upper limit of the axial cutting depth is less than the length of the cutter tooth segment of the cutter, the cutting capability of the cutter is required to be considered for the feeding amount of each tooth, and the chip removal capability of the cutter is required to be considered for the selection of the number of teeth of the cutter. Finally, a feasible domain for optimizing the parameter selection of the variable is formed, which is also the most basic constraint condition for parameter optimization, and is shown as the following formula:
Figure BDA0003332916590000111
in the formula: the superscript u is the upper limit of the parameter, and the superscript l is the lower limit of the parameter;
in addition, when the depth is preferred, the row spacing in the width direction should be made uniform as much as possible, and when the width is preferred, the row spacing in the depth direction should be made uniform as much as possible; therefore:
Figure BDA0003332916590000121
in the formula: n is a radical ofwAnd NhThe line spacing discrete number in the width direction and the depth direction is respectively a positive integer;
1.3.2) constraint of milling force:
during the milling process, milling force can be generated when the cutter is dynamically engaged with a workpiece, the cutter can deform due to overlarge milling force, and the cutter is impacted to cause cutter deformationThe milling tool is broken or even broken, so that the milling force needs to be restricted; as shown in FIG. 2, according to the cutting force mechanism model, the jth layer of cutting units on the ith cutting edge of the cutter rotates at any angle phii,jThe cutting forces in the tangential, radial and axial directions at (t) can be expressed as the sum of the shear and shear forces, i.e.:
Figure BDA0003332916590000122
in the formula: k is a radical ofqs,kqp(q ═ t, r, a) for tangential, radial and axial shear and plow shear force specific coefficients; db is the axial thickness of the j layer cutting unit on the ith cutting edge; phi is ai,j(t) is the rotation angle of the jth layer cutting unit on the ith cutting edge at time t; w is a window function, as follows:
Figure BDA0003332916590000123
in the formula: thetas,i,j,θe,i,jThe cutting angles of the cutter teeth of the j-th layer of cutting units on the ith cutting edge are the cutting angles.
In the milling process, the locus of the point P of the tool nose is a two-dimensional cycloid, the thickness of the cutting layer is equal to the line segment of the intersection part of the connecting line of the point P and the rotation center of the tool and the geometric solid of the workpiece, namely the line segment in fig. 2
Figure BDA0003332916590000126
Wherein the T point is a plurality of front cutter teeth miAt a certain time τ in the pasti,j(t,mi) Left on the machined surface after cutting; and at t-taui,j(t,mi) At time, the coordinate of the point T in the global reference coordinate system XYZ is:
Figure BDA0003332916590000124
in the formula: ri,jFor cutting elements in the j-th layer on the i-th cutting edgeThe radius of cut.
Meanwhile, the T point may also be expressed as:
Figure BDA0003332916590000125
and according to the feed motion relation of the cutter, neglecting the dynamic displacement response of the cutter, the following can be known:
Figure BDA0003332916590000131
in the formula: f. ofvxThe tool feed speed;
the time lag is represented by the above formulae (6), (7) and (8):
Figure BDA0003332916590000132
in the formula:
Figure BDA0003332916590000133
is the angle between the teeth;
further, the instantaneous cutting layer thickness was obtained as:
Figure BDA0003332916590000134
finally, the cutting layer thickness is the minimum value greater than zero of all cutting layer thicknesses:
hi,j(t)＝max(0,min(hi,j(t,mi)))mi＝1,2,…Nt (11)
under a cutter feeding coordinate system, summing the cutting forces generated by all cutting units participating in cutting at the same moment in an effective cutting depth range to obtain the total cutting force acting on the cutter as follows:
Figure BDA0003332916590000135
in this case, the resultant cutting force acting on the tool is:
Figure BDA0003332916590000136
considering the impact resistance of the tool, the maximum milling force acting on the tool needs to be limited within a certain range, namely:
max(Fc(x,t))≤Fclim (14)
in the formula: fclimThe maximum milling force allowed;
1.3.3) constraints on milling stability:
in order to ensure that the milling process is performed in a stable state, the constraint of milling stability needs to be considered, and the upper limit of milling parameter selection is often constrained; as shown in fig. 2, the generation of milling stability is mainly caused by the regeneration mechanism of the flexible process system, and considering the regeneration effect of the flexible tool system in the milling process, the thickness of the regenerated cutting layer is:
Figure BDA0003332916590000137
further, a milling dynamic model is established, which is shown as the following formula:
Figure BDA0003332916590000138
in the formula:
Figure BDA0003332916590000139
wherein m isx,myModal masses in the x, y directions, respectively, cx,cyModal damping, k, in x, y directions respectivelyx,kyRespectively representing modal stiffness in x and y directions, and X (t) is a vibration displacement vector of the cutter; f0(t)＝[Fcx(t),Fcy(t)]TIs a nominal force;
Figure BDA0003332916590000141
average lag time for regenerative effects; the second term on the right side of the above formula is the milling force regeneration term, where Kc(t) is a coefficient matrix, as shown in the following formula:
Figure BDA0003332916590000142
writing a system equation into a state space model after the discretization method:
Figure BDA0003332916590000143
in the formula:
Figure BDA0003332916590000144
while the time term is discrete, the time-varying time lag term tau is dividedi,j(t) discretizing is also carried out; firstly, the rotation period of the cutter is dispersed into NtEqual minute time period of [ t ]k,tk+1]Represents the kth time period; after the time term and the time lag term are dispersed, the stability of the system is converted from a nonlinear problem to a linear problem; discrete time interval of T/NmAt a minute time period [ t ]k,tk+1]The solution of the above formula can be expressed as:
Figure BDA00033329165900001413
in the formula:
Figure BDA0003332916590000145
Figure BDA0003332916590000146
int is a floor function;
here, formula (19) can be converted into a discrete graph as follows:
Vk+1＝ZkVk+Ek (20)
in the formula:
Figure BDA0003332916590000147
Figure BDA0003332916590000148
Figure BDA0003332916590000149
at this time, the state transition relationship of the system over a single time period can be expressed as:
Figure BDA00033329165900001410
in the formula:
Figure BDA00033329165900001411
according to Floquet theory, if the modulus lambda of all characteristic values of the transformation matrix phi is less than or equal to 1, the system is stable; otherwise, the system is unstable;
thus, the constraints of milling stability are:
|λmax(x)|≤1 (22)
1.3.4) constraints on processing quality:
when the milling process is stable, the system response can be obtained by calculating the system stationary point, namely the equation (21)
Figure BDA0003332916590000151
The following can be obtained:
V*＝(I-Φ)-1G (23)
at this time, the transient displacement response of the tool is substituted into the following formula to obtain the transient locus surface of the cutting point of the tool nose:
Figure BDA0003332916590000152
in the formula:
Figure BDA0003332916590000153
as shown in fig. 3, when the surface position error is solved, the intersection of the trajectory envelope surface of the actual tool tooth point and the workpiece entity is obtained to obtain the contour of the machined surface, and the contour is used
Figure BDA0003332916590000154
Represents; in this case, the machining error may represent the average position of the actual machined surface and the ideal design surface
Figure BDA0003332916590000155
The absolute average of the deviations is shown below:
Figure BDA0003332916590000156
in this case, the constraint conditions of the machining error are:
Figure BDA0003332916590000157
in the formula:
Figure BDA0003332916590000158
is a machining error allowable value;
the roughness is as follows:
Figure BDA0003332916590000159
the constraints of the roughness are:
Figure BDA00033329165900001510
in the formula:
Figure BDA00033329165900001511
the roughness tolerance value is obtained;
1.3.5) mathematical model of the optimization problem:
the multiple constraint conditions are integrated together for consideration, so that the efficient milling parameter optimization problem under the multiple constraint conditions is formed, and a mathematical model of the efficient milling parameter optimization problem can be expressed as follows:
min-fMRR(x)
Figure BDA00033329165900001512
step 2) optimizing the feed amount of each tooth of the cutters with different tooth numbers under the roughness constraint condition by adopting a golden section method; numerical iteration optimization is carried out on the rotating speed of the main shaft, the radial width cutting and the axial depth cutting by adopting a random vector search method so as to obtain the optimal combination of the number of teeth of the cutter, the feed quantity of each tooth, the rotating speed of the main shaft, the radial width cutting and the axial depth cutting;
2.1) constraint condition parameter uncertainty processing:
because the parameters of the actual dynamic model have certain uncertainty, the critical real situation of the actual constraint condition has certain deviation; therefore, a certain margin of safety is required for the constraint conditions, and in this case, equation (29) is modified to:
min-fMRR(x)
Figure BDA0003332916590000161
in the formula: lambda [ alpha ]U(U ═ F, S, E, R) is a value less than 1, and the smaller the value, the larger the margin of safety of the constraint, λUThe value range of (1) is 0.7-0.98;
2.2) f based on the golden section methodtOptimizing:
according to the basic knowledge, the roughness of the machined surface is closely related to the feed per toothOff, and less affected by other optimization variables; in order to improve the machining efficiency, it is often desirable to increase the feed per tooth f as much as possible while satisfying the desired surface roughnesstThe roughness constraint can therefore be expressed mathematically as follows:
Figure BDA0003332916590000162
in the formula: in the optimization variables [ n, ae,ap,Nt]TSet to a definite value, with only ftTo optimize the variables; epsilonRa is a small amount;
the objective function in the above formula can be judged to be a convex function, and the optimization problem can be optimized by adopting a golden section method; the optimization process of the golden section method is as follows:
the step (1): determining optimization target and initializing optimization variables
Figure BDA0003332916590000163
Setting the iteration number k to 1, and setting ftSearch interval of (2)
Figure BDA0003332916590000164
And convergence accuracy
Figure BDA0003332916590000165
Let η equal to 0.618;
step (2): calculating a coordinate point alpha1＝b1-η(b1-a1) And beta1＝a1+η(b1-a1) Will be alpha1And beta1Is assigned to ftCalculating an objective function
Figure BDA0003332916590000166
Step (3): setting k to k +1, reducing the search interval according to an interval elimination principle: if it is not
Figure BDA0003332916590000167
Then let ak+1＝αk,bk+1＝bk，αk+1＝βk，βk+1＝ak+1+η(bk+1-ak+1) (ii) a Otherwise ak+1＝ak,bk+1＝βk，βk+1＝αkAnd alphak+1＝bk+1-η(bk+1-ak+1)；
Step (4): if it is not
Figure BDA0003332916590000171
Then
Figure BDA0003332916590000172
Otherwise, returning to the step (3) to continue iteration;
2.3) multiple sample random vector search based [ n, a ]e,ap]TOptimizing:
at ftAfter the optimization is completed, the optimization problem can be further described by equation (30) in consideration of the stability constraints as follows:
min-fMRR(x)
Figure BDA0003332916590000173
at the moment, an optimization solving method based on multi-sample random vector search is adopted to solve the above formula; as shown in FIG. 4, the idea of the method is to randomly generate a plurality of samples in the parameter feasible region, and for the s-th sample xsStepwise forward search at a random vector step size, at xs,kWhen the step k is iterated, the q search generates a random vector Vs,k,qAnd further obtain a sample xsValue x at step k +1s,k+1＝xs,k+Vs,k,qAt this time, x is judgeds,k+1And judging whether the objective function value is reduced or not on the premise of meeting the constraint condition. If yes, enabling k to be k +1 to continue to search forwards; if not, let q be q +1, continue at xs,kTo generate a random vector Vs,k,q+1. Until the objective function of all samplesConverging to a given precision, and ending the search; the whole multi-sample random vector search process is as follows:
the step (1): determining an optimized objective function-fMRR(x) Optimizing variables x and constraining conditions gj(x) (ii) a Randomly generating sample initial values of the optimized variables, and judging whether each sample meets the constraint condition gj(x) Finally form NsSample set of samples { x }s}；
Step (2): extracting the s-th sample x in the sample sets；
Step (3): extracting a sample xsStep k variable xs,k＝[ns,k,ae,s,k,ap,s,k]；
Step (4): generating a random vector in the q searching
Figure BDA0003332916590000174
Wherein:
Figure BDA0003332916590000175
for random coefficients, [ -1,1 ] is taken here]A random number of intervals;
step (5): calculating a sample xsThe variable value of the k +1 step:
Figure BDA0003332916590000181
in the formula:
Figure BDA0003332916590000182
for rounding-down the sign of the operation, after rounding-up, the spindle speed ns,k+1Is an integer, and has a radial cut width ofe,s,k+1And axial cutting depth ap,s,k+11-bit decimal number is reserved;
step (6): substituting the obtained parameters into the formula (32) to judge, the following parameters are obtained:
Figure BDA0003332916590000183
finally, let the optimization result of the s sample
Figure BDA0003332916590000184
Step (7): let s equal s +1, if s < NsReturning to the step (2); if s is equal to NsIf yes, ending the search; comparing the objective function of all samples
Figure BDA0003332916590000185
Finding out the minimum value, wherein the individual corresponding to the minimum value of the objective function is the optimal individual, and the final variable value of the individual is the optimization result
Figure BDA0003332916590000186
2.4) overall optimization process:
referring to fig. 5, fig. 5 shows the overall optimization flow. In the beginning of optimization, the geometric parameters of the cutter, the dynamic parameters of the cutter system, the eccentric parameters of the cutter and the specific shear force coefficient are initialized, and the depth priority and the width priority are selected. And then, performing parameter optimization in a four-layer cycle. A first layer: optimizing the margin discrete number when the depth is first and the width is first; a second layer: optimizing the number of teeth of the cutter; and a third layer: optimizing the feeding amount of each tooth by adopting a golden section method; a fourth layer: and optimizing the rotating speed of the main shaft, the milling depth and the milling width by adopting a random vector search method. And after the four-layer loop iterative calculation is completed, selecting the milling parameter with the maximum milling efficiency as an optimal result.
The following embodiment shows that the method can greatly improve the milling efficiency under the condition of meeting multiple constraint conditions and realize the flutter-free efficient finish machining.
1) Boundary conditions: the workpiece material in the example is aluminum alloy 7050, and the machining allowance is Lw＝3mm,Lh＝50mm,Ll110mm, and the allowance processing mode is depth-first; the diameter of the cutter is 16mm, the helix angle is 45 degrees, and the overhanging length is longIs 85 mm; the cutting process adopts dry cutting, and the specific shear force coefficients are respectively kts＝999N/mm2,krs＝327N/mm2,kas＝357N/mm2,ktp＝30N/mm,krp＝32N/mm,kap0.4N/mm; the modal masses at the tip point in the X and Y directions were 0.407kg and 0.655kg respectively, the damping ratios were 0.035 and 0.028 respectively, and the natural frequencies were 959.4Hz and 922.1Hz respectively. Within the constraints, the range of feasible ranges of the number of teeth of the tool is
Figure BDA0003332916590000191
The feasible range of milling parameters is [ n ]l,nu]＝[5,10]krpm,
Figure BDA0003332916590000192
The milling mode is forward milling; in the constraint condition, the allowable value of the milling force is 5000N, and the allowable values of the machining error and the roughness are 0.04mm and 0.4 mu m respectively; the safety margin coefficients of milling force, stability, machining error and roughness are 0.95,0.92,0.95 and 0.9 respectively; since the allowance processing mode is depth-first, the width discrete number is selected as N w1,2, 3; the number of samples is 30 and the number of iteration steps is 60.
2) And (4) optimizing the result: firstly, optimizing the feeding amount of each tooth under the constraint of roughness, and obtaining that the feeding amount of each tooth of a cutter is 0.275mm/tooth, the feeding amount of each tooth of a cutter with two teeth is 0.15mm/tooth, the feeding amount of each tooth of a cutter with three teeth is 0.10mm/tooth, and the feeding amount of each tooth of a cutter with four teeth is 0.075 mm/tooth; and further, optimizing milling parameters of different cutter teeth cutters. After the optimization is completed, referring to fig. 6, fig. 6 shows the optimization iteration process of the material removal rate under the condition of different tooth numbers and discrete milling widths, wherein fig. 6(a) - (d) respectively show that the milling width of one-tooth, two-tooth, three-tooth and four-tooth cutters is equal to 3mm (N)w1) the change process of the removal rate of all 30 sample materials in 60 times of iterative calculations; FIGS. 6(e) and (f) respectively three-tooth tool in milling width equal to 1mm (N) respectivelyw3) and 1.5mm (N)w2) the change process of the material removal rate of all 30 samples in 60 times of iterative calculation; can be used forIt is seen that the material removal rate for all samples remained increasing in the iterative process. Wherein the three-tooth tool is equal to 3mm (N) in milling width after the iterative calculation is completedwThe material removal rate of the 28 th individual in 1) reached a maximum of 131.2cm3Min, indicating that the individual is the best individual for all samples.
Referring to fig. 7, fig. 7 shows a three-tooth tool with a milling width equal to 3mm (N)w1) the variation process of the optimal individual-related parameters in the whole iterative calculation; wherein, fig. 7(a) shows initial values and final values of 30 sample spindle rotation speeds and milling depths, and an iterative change process of the 28 th individual, and it can be seen that all samples meet the requirement of stable cutting, the samples before optimization are relatively dispersed, and the samples after optimization have stronger aggregative property; FIG. 7(b) further shows the variation of the 28 th individual spindle speed and milling depth during the optimization iteration, after optimization at spindle speed 9411rpm and milling depth of 15.6mm, respectively; fig. 7(c) - (e) respectively show the change rules of the 28 th individual maximum milling force, the maximum feature value of the milling stability transfer matrix, and the machining error with the number of optimization iterations, and it can be seen that all the three always satisfy the corresponding constraint conditions, where the machining error value and the constraint value are very close to each other, which indicates that the optimization iteration is performed more sufficiently; fig. 7(f) compares the change of the material removal rate before and after the optimization, wherein the average value of the material removal rate of all the samples after the optimization is improved by 216.7% compared with that before the optimization, the maximum value of the material removal rate of all the samples after the optimization is improved by 53.6% compared with that before the optimization, and the maximum value of the material removal rate of the optimal individual after the optimization is improved by 659.2% compared with that before the optimization, which indicates that the parameter optimization process can greatly improve the part processing efficiency.

Claims (3)

1. An efficient parameter optimization method for a chatter-free finish machining milling process is characterized by comprising the following steps of:
step 1) establishing a parameter optimization model taking machining efficiency as a target under multiple constraint conditions of parameter feasible region, milling force, milling stability, roughness and machining precision;
step 2) optimizing the feed amount of each tooth of the cutters with different tooth numbers under the roughness constraint condition by adopting a golden section method; numerical iteration optimization is carried out on the rotating speed of the main shaft, the radial width cutting and the axial depth cutting by adopting a random vector search method, so that the optimal combination of the number of teeth of the cutter, the feed quantity of each tooth, the rotating speed of the main shaft, the radial width cutting and the axial depth cutting is obtained.
2. The method according to claim 1, wherein the specific process of step 1) is as follows:
1.1) establishing an optimization target:
according to the distribution condition of the finishing allowance of the part, two feed modes are adopted for removing: depth first and width first; the parameter optimization objective is to achieve a maximum cutting efficiency, expressed in material removal rate, while satisfying the relevant constraints:
fMRR＝Nt·ft·n·ae·ap/1000(cm3/min) (1)
in the formula: n is a radical oftThe number of teeth of the cutter is shown; f. oftThe feed amount per tooth (mm/tooth); n is the spindle speed (rpm); a iseIs the radial cutting width (mm); a ispAxial depth of cut (mm);
1.2) establishing an optimization variable:
the optimization variables of the machining parameter optimization problem include 5 variable parameters, namely the number of tool teeth NtAnd 4 basic cutting parameters of spindle rotating speed n and radial cutting width aeAxial cutting depth apFeed per tooth ftThe optimization variable is defined as x ═ n, ae,ap,Nt,ft]T；
1.3) establishing multiple constraint conditions:
1.3.1) optimizing the constraints of the variable feasible fields:
limited by the cutting capacity of the main shaft and the cutter, the rotating speed n of the main shaft and the radial cutting width aeAxial cutting depth apAnd feed per tooth ftHas an upper limit and a lower limit, the upper limit of the spindle rotation speed is less than or equal to the maximum allowable spindle rotation speed, and the radial directionThe upper limit of the cutting width does not exceed the diameter of the cutter, the upper limit of the axial cutting depth is smaller than the length of a cutter tooth segment of the cutter, the cutting capacity of the cutter needs to be considered for the feeding amount of each tooth, and the chip removal capacity of the cutter needs to be considered for the selection of the tooth number of the cutter; finally, a feasible field for optimizing the variable parameter selection is formed, as shown in the following formula:
Figure FDA0003332916580000021
in the formula: the superscript u is the upper limit of the parameter, and the superscript l is the lower limit of the parameter;
in addition, when the depth is preferred, the row spacing in the width direction should be made uniform as much as possible, and when the width is preferred, the row spacing in the depth direction should be made uniform as much as possible; therefore:
Figure FDA0003332916580000022
in the formula: n is a radical ofwAnd NhThe line spacing discrete number in the width direction and the depth direction is respectively a positive integer;
1.3.2) constraint of milling force:
the size of the milling force needs to be restrained, and a mechanical model of the cutting force shows that the jth layer of cutting units on the ith cutting edge of the cutter rotates at any angle phii,jThe cutting forces in the tangential, radial and axial directions at (t) are expressed as the sum of the shear and shear forces, i.e.:
Figure FDA0003332916580000023
in the formula: k is a radical ofqs,kqp(q ═ t, r, a) for tangential, radial and axial shear and plow shear force specific coefficients; db is the axial thickness of the j layer cutting unit on the ith cutting edge; phi is ai,j(t) is the rotation angle of the jth layer cutting unit on the ith cutting edge at time t; w is a window function, as follows:
Figure FDA0003332916580000024
in the formula: thetas,i,j,θe,i,jCutting angles of cutter teeth of a j layer of cutting units on an ith cutting edge are set;
in the milling process, the locus of a point P of a tool nose point is a two-dimensional cycloid, the thickness of a cutting layer is equal to the line segment of the intersection part of the connecting line of the point P and the rotation center of the tool and a geometric solid of a workpiece, wherein the point T is a plurality of front tool teeth miAt a certain time τ in the pasti,j(t,mi) Left on the machined surface after cutting, and at t-taui,j(t,mi) At time, the coordinate of the point T in the global reference coordinate system XYZ is:
Figure FDA0003332916580000025
in the formula: ri,jThe actual cutting radius of the j layer cutting unit on the ith cutting edge;
meanwhile, the T point is also expressed as:
Figure FDA0003332916580000031
and according to the feed motion relation of the cutter, neglecting the dynamic displacement response of the cutter, the following can be known:
Figure FDA0003332916580000032
in the formula: f. ofvxThe tool feed speed;
the skew amount is obtained from the above equations (6), (7) and (8):
Figure FDA0003332916580000033
in the formula:
Figure FDA0003332916580000034
is the angle between the teeth;
further, the instantaneous cutting layer thickness was obtained as:
Figure FDA0003332916580000035
finally, the cutting layer thickness is the minimum value greater than zero of all cutting layer thicknesses:
hi,j(t)＝max(0,min(hi,j(t,mi)))mi＝1,2,…Nt (11)
under a cutter feeding coordinate system, summing the cutting forces generated by all cutting units participating in cutting at the same moment in an effective cutting depth range to obtain the total cutting force acting on the cutter as follows:
Figure FDA0003332916580000036
in this case, the resultant cutting force acting on the tool is:
Figure FDA0003332916580000037
considering the impact resistance of the tool, the maximum milling force acting on the tool needs to be limited within a certain range, namely:
max(Fc(x,t))≤Fclim (14)
in the formula: fclimThe maximum milling force allowed;
1.3.3) constraints on milling stability:
the restriction of milling stability restricts the upper limit of milling parameter selection; the generation of milling stability is caused by a regeneration mechanism of a flexible process system, and the thickness of a regenerated cutting layer is as follows by considering the regeneration effect of the flexible cutter system in the milling process:
Figure FDA0003332916580000038
further, a milling dynamic model is established, which is shown as the following formula:
Figure FDA0003332916580000039
in the formula:
Figure FDA00033329165800000310
wherein m isx,myModal masses in the x, y directions, respectively, cx,cyModal damping, k, in x, y directions respectivelyx,kyRespectively representing modal stiffness in x and y directions, and X (t) is a vibration displacement vector of the cutter; f0(t)＝[Fcx(t),Fcy(t)]TIs a nominal force;
Figure FDA0003332916580000041
average lag time for regenerative effects; the second term on the right side of the above formula is the milling force regeneration term, where Kc(t) is a coefficient matrix, as shown in the following formula:
Figure FDA0003332916580000042
writing a system equation into a state space model after the discretization method:
Figure FDA0003332916580000043
in the formula:
Figure FDA0003332916580000044
F(t)＝[02×1M-1F0]T,
Figure FDA0003332916580000045
while the time term is discrete, the time-varying time lag term tau is dividedi,j(t) discretizing is also carried out; firstly, the rotation period of the cutter is dispersed into NtEqual minute time period of [ t ]k,tk+1]Represents the kth time period; after the time term and the time lag term are dispersed, the stability of the system is converted from a nonlinear problem to a linear problem; discrete time interval of T/NmAt a minute time period [ t ]k,tk+1]Internally, the solution of the above formula is represented as:
Figure FDA0003332916580000046
in the formula:
Figure FDA0003332916580000047
Figure FDA0003332916580000048
int is a floor function;
here, formula (19) is converted into a discrete graph, as follows:
Vk+1＝ZkVk+Ek (20)
in the formula:
Figure FDA0003332916580000049
Figure FDA00033329165800000410
Figure FDA00033329165800000411
at this time, the state transition relationship of the system over a single time period is represented as:
Figure FDA00033329165800000412
in the formula:
Figure FDA00033329165800000413
according to Floquet theory, if the modulus lambda of all characteristic values of the transformation matrix phi is less than or equal to 1, the system is stable; otherwise, the system is unstable;
thus, the constraints of milling stability are:
|λmax(x)|≤1 (22)
1.3.4) constraints on processing quality:
when the milling process is stable, the system response is obtained by calculating the system stationary point, equation (21)
Figure FDA0003332916580000051
Obtaining:
V*＝(I-Φ)-1G (23)
at this time, the transient displacement response of the tool is substituted into the following formula to obtain the transient locus surface of the cutting point of the tool nose:
Figure FDA0003332916580000052
in the formula:
Figure FDA0003332916580000053
when the surface position error is solved, the track envelope surface of the actual cutter tooth point and the workpiece entity are intersected to obtain the contour of the machined surface
Figure FDA0003332916580000054
Represents; in this case, the machining error represents the average position of the actual machined surface and the ideal design surface
Figure FDA0003332916580000055
The absolute average of the deviations is shown below:
Figure FDA0003332916580000056
in this case, the constraint conditions of the machining error are:
Figure FDA0003332916580000057
in the formula:
Figure FDA0003332916580000058
is a machining error allowable value;
the roughness is as follows:
Figure FDA0003332916580000059
the constraints of the roughness are:
Figure FDA00033329165800000510
in the formula:
Figure FDA00033329165800000511
the roughness tolerance value is obtained;
1.3.5) mathematical model of the optimization problem:
the multiple constraint conditions are integrated together for consideration, and the efficient milling parameter optimization problem under the multiple constraint conditions is formed, wherein a mathematical model of the efficient milling parameter optimization problem is represented as follows:
Figure FDA00033329165800000512
3. the method according to claim 2, wherein the specific process of step 2) is:
2.1) constraint condition parameter uncertainty processing:
a certain safety margin is required to be given to the constraint condition, and then the formula (29) is improved as follows:
Figure FDA0003332916580000061
in the formula: lambda [ alpha ]U(U ═ F, S, E, R) is a value less than 1, and the smaller the value, the larger the margin of safety of the constraint, λUThe value range of (1) is 0.7-0.98;
2.2) f based on the golden section methodtOptimizing:
in order to improve the processing efficiency, the feed amount f of each tooth is increased as much as possible on the premise of meeting the ideal surface roughnesstThe roughness constraint is therefore expressed mathematically as follows:
Figure FDA0003332916580000062
in the formula: in the optimization variables [ n, ae,ap,Nt]TSet to a definite value, with only ftTo optimize the variables;
Figure FDA0003332916580000063
is a small amount; judging that the objective function in the formula is a convex function, and optimizing the problem by adopting a golden section method; the optimization process of the golden section method is as follows:
the step (1): determining optimization target and initializing optimization variables
Figure FDA0003332916580000064
Setting the iteration number k to 1, and setting ftSearch interval a of1＝ft l,b1＝ft uAnd convergence accuracy
Figure FDA0003332916580000065
Let η equal to 0.618;
step (2): calculating a coordinate point alpha1＝b1-η(b1-a1) And beta1＝a1+η(b1-a1) Will be alpha1And beta1Is assigned to ftCalculating an objective function
Figure FDA0003332916580000066
Step (3): setting k to k +1, reducing the search interval according to an interval elimination principle: if it is not
Figure FDA0003332916580000067
Then let ak+1＝αk,bk+1＝bk，αk+1＝βk，βk+1＝ak+1+η(bk+1-ak+1) (ii) a Otherwise ak+1＝ak,bk+1＝βk，βk+1＝αkAnd alphak+1＝bk+1-η(bk+1-ak+1)；
Step (4): if it is not
Figure FDA0003332916580000068
F is thent *＝(ak+1+bk+1) 2; otherwise, returning to the step (3) to continue iteration;
2.3) multiple sample random vector search based [ n, a ]e,ap]TOptimizing:
at ftAfter the optimization is complete, the optimization problem is further described by equation (30) in view of the stability constraints described above as:
Figure FDA0003332916580000071
at the moment, an optimization solving method based on multi-sample random vector search is adopted to solve the above formula; the whole multi-sample random vector search process is as follows:
the step (1): determining an optimized objective function-fMRR(x) Optimizing variables x and constraining conditions gj(x) (ii) a Randomly generating sample initial values of the optimized variables, and judging whether each sample meets the constraint condition gj(x) Finally form NsSample set of samples { x }s}；
Step (2): extracting the s-th sample x in the sample sets；
Step (3): extracting a sample xsStep k variable xs,k＝[ns,k,ae,s,k,ap,s,k]；
Step (4): generating a random vector in the q searching
Figure FDA0003332916580000072
Wherein:
Figure FDA0003332916580000073
for random coefficients, [ -1,1 ] is taken here]A random number of intervals;
step (5): calculating a sample xsThe variable value of the k +1 step:
Figure FDA0003332916580000074
in the formula:
Figure FDA0003332916580000075
for rounding down the sign of the operation, the rounding operation is performedRear spindle speed ns,k+1Is an integer, and has a radial cut width ofe,s,k+1And axial cutting depth ap,s,k+11-bit decimal number is reserved;
step (6): substituting the obtained parameters into the formula (32) to judge, the following parameters are obtained:
Figure FDA0003332916580000076
finally, let the optimization result of the s sample
Figure FDA0003332916580000077
Step (7): let s equal s +1, if s < NsReturning to the step (2); if s is equal to NsIf yes, ending the search; comparing the objective function of all samples
Figure FDA0003332916580000081
Finding out the minimum value, wherein the individual corresponding to the minimum value of the objective function is the optimal individual, and the final variable value of the individual is the optimization result
Figure FDA0003332916580000082
2.4) overall optimization process:
initializing a tool geometric parameter, a tool system dynamic parameter, a tool eccentric parameter and a specific shear force coefficient at the beginning of optimization, and selecting depth priority and width priority; then, parameter optimization is carried out in four layers of circulation, wherein the first layer is as follows: optimizing the margin discrete number when the depth is first and the width is first; a second layer: optimizing the number of teeth of the cutter; and a third layer: optimizing the feeding amount of each tooth by adopting a golden section method; a fourth layer: optimizing the rotation speed of the main shaft, the milling depth and the milling width by adopting a random vector search method; and after the four-layer loop iterative calculation is completed, selecting the milling parameter with the maximum milling efficiency as an optimal result.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114473651A (en) * 2022-03-02 2022-05-13 广东机电职业技术学院 Intelligent control system for cutting edge grinding
CN115584413A (en) * 2022-09-05 2023-01-10 深圳市万泽中南研究院有限公司 Machining parameter optimization method and nickel-based powder superalloy machine
CN115982887A (en) * 2022-12-30 2023-04-18 恒锋工具股份有限公司 Multi-objective optimization design method for blade arrangement of disc milling cutter for steel rail restoration

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2012107594A1 (en) * 2011-02-11 2012-08-16 Ecole Polytechnique Federale De Lausanne (Epfl) High speed pocket milling optimisation
CN112379637A (en) * 2020-11-04 2021-02-19 华中科技大学 Plunge milling machining parameter optimization method, system, equipment and medium

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2012107594A1 (en) * 2011-02-11 2012-08-16 Ecole Polytechnique Federale De Lausanne (Epfl) High speed pocket milling optimisation
CN112379637A (en) * 2020-11-04 2021-02-19 华中科技大学 Plunge milling machining parameter optimization method, system, equipment and medium

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
周建;杨杰;刘春;董艳超;: "高效加工在普通数控机床上的应用", 水泥技术, no. 02 *
姜彦翠;刘献礼;吴石;李荣义;王洋洋;: "基于铣削稳定性的淬硬钢铣削加工工艺参数优化", 大连交通大学学报, no. 06 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114473651A (en) * 2022-03-02 2022-05-13 广东机电职业技术学院 Intelligent control system for cutting edge grinding
CN115584413A (en) * 2022-09-05 2023-01-10 深圳市万泽中南研究院有限公司 Machining parameter optimization method and nickel-based powder superalloy machine
CN115982887A (en) * 2022-12-30 2023-04-18 恒锋工具股份有限公司 Multi-objective optimization design method for blade arrangement of disc milling cutter for steel rail restoration
CN115982887B (en) * 2022-12-30 2024-01-23 恒锋工具股份有限公司 Multi-objective optimization design method for blade arrangement of disc milling cutter for repairing steel rail

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