CN107480354A - A kind of turnery processing parameter optimization method for considering uncertain parameter - Google Patents
A kind of turnery processing parameter optimization method for considering uncertain parameter Download PDFInfo
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Abstract
The present invention provides a kind of turnery processing parameter optimization method for considering uncertain parameter, including：According to the vibration primary condition and system Critical Stability status information of the turnery processing system of setting, limit of stability function of state is obtained；And the RELIABILITY INDEX for evaluation system stability is obtained using AFOSM；Using MRR as optimization aim, default constraints, the Optimized model of turning process parametric reliability in system is established；Constraints includes：Reliability constraint and Random Design variable boundary constraint；Optimization processing Optimized model, obtain optimization convergence and meet the target function value of Reliability Constraint, now the turnery processing parameter of deterministic parameter, Random Design variable and random parameter corresponding to target function value as output.The above method can be using reliability as measurement index as optimal conditions, influence of the analysis uncertain factor to turning process, to obtain optimal turning machined parameters.
Description
Technical Field
The invention relates to a turning parameter optimization technology, in particular to a turning parameter optimization method considering uncertain parameters.
Background
High-speed and high-precision machining is the development trend of modern manufacturing, and stable cutting is the premise of realizing high-performance cutting. The regenerative chatter vibration in the turning process seriously affects the processing efficiency and precision of the machine tool and the service life of the cutter. Therefore, the turning parameters optimization must take into account the turning chatter factor.
Regenerative flutter is considered to be the most widely studied mechanism at present. In recent years, scholars at home and abroad propose various methods for avoiding regenerative chatter and optimizing turning parameters. The industry proposes to apply variable parameters such as variable rotating speed and inclination angle to restrain regenerative flutter. In addition, the industry has also proposed to use variable spindle speed machining to study fast tool servo-assisted turning systems to suppress regenerative chatter.
In addition, in the aspect of turning parameter optimization, the skilled person also provides a multi-target turning parameter optimization method and a thin-wall cylindrical shell turning parameter optimization method based on an artificial bee colony algorithm, wherein workpiece deformation and cutter vibration are considered in the thin-wall cylindrical shell turning parameter optimization method. ,
in the method, the turning parameters are considered to be deterministic, but are influenced by load and environmental conditions, and the turning parameters are random in practical engineering, so that the research has certain limitations.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a turning parameter optimization method considering uncertain parameters, which can analyze the influence of uncertain factors on a turning process by taking reliability as a measurement index as an optimization condition so as to obtain the optimal turning parameters.
In a first aspect, the present invention provides a turning parameter optimization method considering uncertainty parameters, comprising:
step S1, processing a dynamic model of the turning system according to a set vibration initial condition of the turning system and the stability critical state information of the turning system to obtain a stability limit state function of the turning system, wherein the stability limit state function comprises the following steps: the minimum value of the limit cutting depth, the spindle rotating speed corresponding to the limit cutting depth and the mechanical cutting width;
s2, based on the stability limit state function, acquiring a reliability index for evaluating the stability of the turning system by adopting AFOSM (automatic frequency of modulation);
s3, establishing an optimization model of the reliability of the turning technological parameters in the turning system by taking the material removal rate in unit time as an optimization target and preset constraint conditions;
the constraint conditions include: reliability constraints and random design variable boundary constraints.
Wherein the reliability constraints include: reliability constraint, turning system stability constraint, cutting force constraint, surface roughness constraint, cutting power constraint and the like;
the random design variable boundary constraints include: cutting depth constraint, cutting processing system vibration angular frequency constraint, feed amount constraint and the like.
And S4, optimizing the optimization model by adopting an SORA method and combining the reliability index to obtain an objective function value which is optimized and converged and accords with reliability constraint, wherein at the moment, a deterministic parameter, a random design variable and a random parameter which correspond to the objective function value are used as output turning parameters.
Optionally, step S1 comprises:
s11, establishing a dynamic model of the turning system according to a regenerative flutter mechanism;
s12, acquiring an expression of dynamic cutting force according to the set cutting thickness variation;
s13, integrating the expression of the dynamic cutting force with the dynamic model, and performing Laplace transform on the integrated expression when the initial vibration condition is zero;
s14, applying the stable critical state information of the turning system to an expression after Laplace transformation to obtain the minimum value of the limit cutting depth, the spindle rotating speed corresponding to the limit cutting depth and the mechanical cutting width;
and S15, establishing a stability limit state function according to the limit cutting depth and the minimum value of the spindle rotating speed and the mechanical cutting width corresponding to the limit cutting depth.
Alternatively,
the vibration differential equation of the dynamic model of the turning system in sub-step S11 is:
wherein m is equivalent mass; c is equivalent damping; k is the equivalent stiffness;shows dynamic cutting force Δ F d (t) forming an included angle with the vibration direction of the cutter; alpha represents the included angle between the main vibration direction q (t) of the cutter and the vibration direction;
the expression of the dynamic cutting force in the substep S12 is:
ΔF d (t)＝k c a p a(t)＝k c a p [ηy(t-T)-y(t)]
wherein a (T) = eta y (T-T) -y (T), the overlapping coefficient of two times of processing before and after turning is eta, y (T) is the vibration displacement of the tool, T is the rotation period of the main shaft, k is c Is the cutting stiffness coefficient; a is a p Is the cutting depth;
the expression after laplace transformation in substep S13 is:
the limit depth of cut in the sub-step S14 is:
the spindle rotating speed corresponding to the limit cutting depth is as follows:
when the overlap coefficient η =1, the minimum value of the machine cutting width is:
the stability limit state function in substep S15 is:
wherein, a p Is the cutting depth; a is a plim Is the limit cutting depth; x is a random parameter, g(x)&0 represents stable turning cutting; g (x)&0 represents that the turning has flutter; g (x) =0 indicates that the turning is in the limit stable cutting state.
Optionally, step S2 includes:
s21, converting each random design variable related to the stability limit state function into a standard normal form
μ i And σ i Are each X i Mean and variance of (2), X i For x in the stability limit state function i Random parameters of (a);
s22, obtaining a reliability index beta which represents the shortest distance from the original point to the approximate failure curved surface in the normal space mapped by the original point in the AFOSM;
s23, obtaining the reliability P according to the reliability index S ；
S24, determining the reliability P S If the reliability is greater than the minimum reliability in the reliability constraint condition, executing the step S3, otherwise, acquiring the reliability P again S 。
Optionally, in step S3,
the optimization model of the turning process parameter reliability comprises the following steps:
wherein d, V and P respectively represent a deterministic parameter, a random design variable and a random parameter; mu.s V ，μ P Are the mean values of V and P, respectively; g θ (. Cndot.) refers to the extreme state function at the theta failure mode; r is θ A given reliability threshold; q. q.s ξ (. Is) an inequality constraint matrix; m and N are reliability constraint and inequality constraint quantity respectively; reliability P { g θ (d, V, P). Ltoreq.0 byDetermining;
the objective function in the optimization model of reliability is: f (x) = f MRR ＝1/(πa p f·Ω(ω)·D)；
Wherein D is the cutting diameter of the workpiece, and omega (omega) is the rotating speed of the main shaft;
the preset constraint conditions comprise:
reliability constraint, P (g) θ (x)≤0)≥R θ θ＝1,…,4；
Wherein the target reliability is R θ Is a preset value;
turning processThe stability of the system is restricted, and the stability of the system is limited,
restraining the cutting force:
k n a and b are constant coefficients; f c Is the instantaneous cutting force; f cmax Is the maximum cutting force;
surface roughness constraint: g 3 (x)＝R a -R amax ＝f 2 /(8r CT )-R amax ≤0；
R a Instantaneous surface roughness; r is CT The radius of the arc of the turning tool nose; r is amax Maximum theoretical surface roughness;
cutting power constraint: g 4 (x)＝P c -P cmax ＝F c Ω(ω)/60000-P cmax ≤0；
P c Instantaneous cutting power; p is cmax The maximum cutting power;
and randomly designing variable boundary constraint conditions.
Optionally, the boundary constraints of the random design variables include:
0＜a p ＜2、560＜ω＜750、0.1＜f＜0.9；
depth of cut a p The stable vibration frequency omega and the stable feed amount f of the turning system.
Optionally, step S4 includes:
s41, selecting initial values of random design variables and random parameters, and obtaining a maximum failure probability point MPP through an optimization model;
s42, reliability evaluation is carried out by adopting an inverse MPP search method, an inverse MPP point is obtained based on an AFORM method, the inverse MPP point is optimized, and whether the optimized inverse MPP point is larger than the value of the inverse MPP point in the reliability index obtaining process in the step S2 is judged;
and if the target function value is larger than the preset target function value, taking the certainty parameter, the random design variable and the random parameter corresponding to the optimized target function value as the output turning parameter.
Optionally, step S4 further includes:
if the random design variable and the random parameter are not more than the preset motion vector, redefining the random design variable and the random parameter through a preset motion vector, and repeating the step S2 to the step S4.
Optionally, sub-step S42 comprises:
reliability evaluation is carried out by applying an inverse MPP search method, reliability optimization constraint equivalent transformation is carried out, and an optimization model after the equivalent transformation is as follows:
wherein, g R Is the R percentage of the constraint g (d, V, P) and is defined as
Prob{g(d,V,P)≤g R }＝R；
Based on AFORM, reliability index beta = Φ -1 (R)；
Wherein phi is -1 (. Cndot.) represents an inverse cumulative distribution function of a standard normal distribution;
by passingObtaining an inverse MPP point;
wherein u = [ ] V ；u P ]，u V 、u P Standard forms for v and p, respectively;
optimizing an inverse MPP point, and determining an R percentage point according to the optimized inverse MPP point;
and substituting the determined R percentage point into a reliability constraint to check whether the inverse MPP point meets the reliability constraint condition.
Optionally, redefining the random design variables and the random parameters by presetting the motion vectors, and repeating the steps S2 to S4, including:
if constraining g (. Mu.) V ,μ P ) Inverse MPP point ofOut of reliabilityWithin the constraint conditions, the reliability constraints before the optimization model is established will be modified, including:
a motion vector s is set, and,
and modifying the deterministic optimization constraints of the next loop to
g(μ V -s)≤0
Similarly, the optimization model of the loop in step T +1 is
min f(d,μ V ,μ p )
Wherein, the first and the second end of the pipe are connected with each other,
and when the objective function value is kept stable and the reliability constraint reaches a given value, the iteration is terminated, and the reliability optimization is completed.
The invention has the following beneficial effects:
the invention provides a turning parameter optimization method considering uncertain parameters. And then analyzing the influence of uncertain factors on the turning process, and establishing an optimization model based on reliability so as to obtain the optimal turning parameters.
In the reliability optimization model, the maximum removal rate of materials is used as an objective function, the turning stability, the surface roughness, the cutting force and the like which meet the requirements are used as constraint functions, and the reliability of constraint conditions is calculated by applying the reliability to the AFSOM for the reliability analysis of the mechanical structure. A serial single-loop SORA method is applied to solve the reliability-based optimization model. Compared with the traditional turning parameter optimization, the method considers the influence of uncertain parameters and has more practical application value.
Drawings
FIG. 1 is a diagram of a dynamic model of a regenerative vehicle flutter system in accordance with one embodiment of the present invention;
FIGS. 2A and 2B are flow charts of a turning parameter optimization method considering uncertain parameters according to an embodiment of the present invention;
FIG. 3 is a flowchart of a method for sequence optimization and reliability assessment according to an embodiment of the present invention;
FIG. 4 is a view of a turning system stability lobe in one embodiment of the present invention;
fig. 5 is a diagram of the R percentile of the constraint function.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
All technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
In the embodiments of the present invention, the uncertain parameter is not a definite value but fluctuates over a numerical value, and the random design variables and the random parameters in the following embodiments are uncertain parameters, such as those listed in table 1 below.
The parameters given in the following examples have known mean and coefficient of variation (i.e., variance), as shown in fig. 1, i.e., representing uncertainty parameters. For example, the given parameter f-means is 0.5 and the coefficient of variation is 0.05, i.e. the given parameter is 0.5 with a fluctuation of 0.0025.
As shown in fig. 2A, the present embodiment provides a turning parameter optimization method considering uncertain parameters, which includes the following steps:
s1, processing a dynamic model of the turning system according to the set vibration initial condition of the turning system and the stability critical state information of the turning system, and acquiring a stability limit state function of the turning system.
The stability limit state function in this embodiment may include: and the minimum value of the limit cutting depth, the spindle rotating speed corresponding to the limit cutting depth and the mechanical cutting width.
For example, the step S1 may include the following sub-steps not shown in the figure:
s11, establishing a dynamic model of the turning system according to a regenerative flutter mechanism;
s12, acquiring an expression of dynamic cutting force according to the set cutting thickness variation;
s13, integrating the expression of the dynamic cutting force with the dynamic model, and performing Laplace transform on the integrated expression when the initial vibration condition is zero;
s14, applying the stable critical state information of the turning system to an expression after Laplace transformation to obtain the minimum value of the limit cutting depth, the spindle rotating speed corresponding to the limit cutting depth and the mechanical cutting width;
and a substep S15 of establishing a stability limit state function according to the limit cutting depth and the minimum value of the spindle rotating speed and the mechanical cutting width corresponding to the limit cutting depth.
And S2, based on the stability limit state function, acquiring a reliability index for evaluating the stability of the turning system by adopting AFOSM.
S3, establishing an optimization model of the reliability of the turning technological parameters in the turning system by taking the material removal rate in unit time as an optimization target and preset constraint conditions;
the constraint conditions in this embodiment may include: reliability constraints and random design variable boundary constraints.
Wherein the reliability constraints include: reliability constraint, turning system stability constraint, cutting force constraint, surface roughness constraint, cutting power constraint and the like;
the random design variable boundary constraints include: cutting depth constraint, cutting processing system vibration angular frequency constraint, feed amount constraint and the like.
And S4, optimizing the optimization model by adopting an SORA method and combining the reliability index to obtain an objective function value which is optimized and converged and accords with reliability constraint, wherein at the moment, a deterministic parameter, a random design variable and a random parameter which correspond to the objective function value are used as output turning parameters.
In the embodiment, a turning regeneration chatter vibration mechanical model is established, a cutting depth expression is deduced, and the cutting limit depth is predicted. And then analyzing the influence of uncertain factors on the turning process, and establishing an optimization model based on reliability so as to obtain the optimal turning parameters.
The following is described in detail with reference to fig. 1, 2B, 3, and 4.
In the present embodiment, a general turning chatter system model is taken as an example, as shown in fig. 1, and is simplified as follows: (1) the workpiece system has good rigidity, and the analysis research object mainly aims at a lathe tool system; (2) the chatter system is linear, the elastic restoring force of the cutter system is in direct proportion to the vibration displacement, and the damping force is in direct proportion to the vibration speed of the cutter system; (3) the regenerative chatter vibration is caused only by dynamic variation of the cutting thickness, and does not consider factors such as hard particles of the machined workpiece.
In this embodiment, the turning parameter optimization method considering the uncertain parameters is shown in fig. 2B, a sequence optimization and reliability assessment method (SORA) is applied to solve the reliability optimization problem, the method flowchart is shown in fig. 3, and fig. 4 shows a turning stability lobe graph formed by the spindle rotation speed and the cutting depth.
Step 01, establishing a turning system dynamic model according to a regenerative flutter mechanism, and establishing a vibration differential equation:
wherein m is the equivalent mass of the turning system; c is equivalent damping of the turning system; k is the equivalent stiffness of the turning system;shows dynamic cutting force Δ F d (t) forming an included angle with the vibration direction of the cutter; alpha represents the included angle between the main vibration direction q (t) of the cutter and the vibration direction.
The dynamic cutting force is caused by dynamic variation of the cutting thickness, thus F d (t) is expressed as a vibrational displacement. The overlap coefficient of the two processing before and after turning is set as eta, and 0 is satisfied<η&1, the variation of the cutting thickness in the current machining is expressed as
a(t)＝ηy(t-T)-y(t) (2)
Wherein y (t) is the vibration displacement of the cutter at the time, and y (t) = q (t) cos alpha is met; and y (T-T) is the vibration displacement of the previous cutter. T is the rotation period of the main shaft and meets the condition that T = 60/omega; omega is the spindle speed.
Two machining operations before and after turning can be understood as cutting at a certain point in time and cutting before this point in time in the same machining operation, such as y (T) and y (T-T) in fig. 1.
Dynamic cutting force Δ F d (t) can be expressed by the change in cut thickness as
ΔF d (t)＝k c a p a(t)＝k c a p [ηy(t-T)-y(t)] (3)
Wherein k is c Is the cutting stiffness coefficient; a is p Is the depth of cut.
By integrating the formulas (1) and (3) and analyzing the relationship between the vibration displacement and the system characteristic parameters, the method can be obtained
Wherein, ω is n Is the natural frequency of the system, and satisfies omega n 2 ＝k/m；Is a damping ratio, satisfiesCoefficient K = - ω n 2 ·k c a p U/k; u is a directional coefficient, satisfiesAnd omega is the system vibration frequency.
Step 02, keeping the initial vibration condition to be zero and carrying out Laplace transformation on the formula (4)
And (3) taking a stable critical state of the turning processing system, and further obtaining the limit cutting depth of stable turning:
the corresponding main shaft rotating speed is as follows:
when the cutting overlap coefficient η =1, the vibration is most intense, and the minimum value of the limit cutting width can be obtained:
and 03, establishing a limit state equation, namely a stability limit state function, and analyzing the reliability of the turning stability.
Substep 3-1, establishing a stability limit state function of the turning:
wherein, a p Is the cutting depth; a is a plim The specific expression is shown in formula (6) for the limit cutting depth; x is a random parameter, and x is a random parameter,
g (x) <0 denotes a stable turning cut; g (x) >0 represents the turning chatter; g (x) =0 indicates that the turning is in the limit stable cutting state.
And 3-2, calculating the reliability of the stability of the turning process by applying an improved first second moment method (AFOSM).
Firstly, introducing standard normal random design variables, and converting each random design variable into a standard normal form:
wherein, mu i And σ i Are each X i Mean and variance of (2), X i Is related to x in formula (9) i The random parameter of (2).
Through orthogonal transformation, the mean point in X space is mapped to the origin of normal space (U space), and the failure surface g (X) =0 in X space is mapped to the corresponding failure surface g (U) =0 in U space.
And a substep 3-3 of obtaining a reliability index β (reliability index for evaluating reliability) in the AFOSM, which represents the shortest distance from the origin to the origin in the U space to the approximate failure surface g (U) =0. Most probable point of failure (MPP) u for g (u) MPP This can be obtained by solving the following optimization problem:
corresponding reliability P S Can be obtained.
Step 04, establishing a turning parameter reliability optimization mathematical model:
wherein d, V and P respectively represent a deterministic parameter, a random design variable and a random parameter; mu.s V ，μ P Are the mean values of V and P, respectively; g θ (. Cndot.) refers to the extreme state function at the theta failure mode; r is θ A given reliability threshold; q. q of ξ (. Is) an inequality constraint matrix; m and N are reliability constraint and inequality constraint quantity respectively. Reliability P { g) in equation (12) θ The calculation of (d, V, P). Ltoreq.0 } can be converted into an optimization problem by AFOSM in step 3-2, for example, can be solved by equation (11).
Substep 4-1 of turning the process parameter (depth of cut a) of the machining system p Feed f and system vibration frequency omega) as random design variables, assuming that the random design variables are mutually independent and obey normal distribution, and regarding performance parameters and geometric parameters of other turning systems as random parameters.
And substep 4-2, adopting maximum production efficiency as an optimization target. Specific production efficiency is expressed as the material removal rate per unit time MRR = pi a p F Ω D, the objective function is:
f(x)＝f MRR ＝1/(πa p f·Ω(ω)·D) (13)
wherein D is the cutting diameter of the workpiece, and omega (omega) is the rotating speed of the main shaft.
And a substep 4-3 of establishing a reliability constraint condition. In the turning process, factors influencing the material removal rate are many, and it is necessary to add reliability constraints under complex conditions, and the reliability constraints are considered from the aspects of stability, cutting force, surface roughness and cutting power respectively, so that the following requirements are met:
P(g θ (x)≤0)≥R θ θ＝1,…,4 (14)
wherein the target reliability is R θ ＝0.99。
And a substep 4-3-a, establishing stability constraints. In turning, if the cutting parameters are not selected properly, chatter vibration is highly likely to occur. The turning stability constraints should therefore guarantee:
wherein the content of the first and second substances,for the limit depth of cut, the expression refers to equation (6).
Substep 4-3-b, establishing a cutting force constraint. The cutting force is influenced by workpiece materials, cutting parameters, cutter parameters and the like, and constraint conditions are obtained according to a simplified empirical formula of the cutting force:
wherein k is n A and b are constant coefficients; f c Is the instantaneous cutting force; f cmax Is the maximum cutting force.
And substep 4-3-c, establishing a surface roughness constraint. The surface roughness has important influence on the wear resistance, fatigue resistance and corrosion resistance of workpieces, and plays an important role in the working performance, assembly quality, service life, vibration, noise and the like of mechanical equipment. The theoretical turning roughness is influenced by the feed amount and the arc radius of the tool nose, and is specifically limited as follows:
g 3 (x)＝R a -R amax ＝f 2 /(8r CT )-R amax ≤0 (17)
wherein R is a Instantaneous surface roughness; r is CT The radius of the arc of the turning tool nose; r amax The maximum theoretical surface roughness.
Substep 4-3-d, establishing a cutting power constraint. The cutting power is determined by the cutting force and the spindle speed, so the constraint conditions are:
g 4 (x)＝P c -P cmax ＝F c Ω(ω)/60000-P cmax ≤0 (18)
wherein, P c Instantaneous cutting power; p is cmax Is the maximum cutting power.
And a substep 4-4 of establishing random design variable boundary constraints.
And substep 4-4-a, establishing a cut depth constraint. Depth of cut a p The cutting depth is limited by the rigidity of the machine tool, the cutting depth is as large as possible under the condition that the rigidity of the machine tool allows, and if the cutting depth is not limited by the machining precision, the cutting depth can be equal to the machining allowance of the part. The constraint may be expressed as:
0＜a p ＜2 (19)
and a substep 4-4-b, establishing a system vibration angular frequency constraint. And the stable vibration frequency omega of the turning system is equal to the vibration source frequency and can be estimated according to the rotating speed of the main shaft. The spindle speed is limited by the machine tool and can therefore be expressed as
560＜ω＜750 (20)
And substep 4-4-c, establishing a feed constraint. The feed amount f needs to meet the requirements of the maximum and minimum feed amounts of the machine tool, and the constraint condition is that
0.1＜f＜0.9 (21)
And step 05, reliability optimization is a nested optimization problem with the inner layer for reliability analysis and the outer layer for structure optimization. By applying the SORA method of the serial single loop, the stability and the high efficiency of the problem solving can be ensured by decoupling the structure optimization and the reliability analysis. And (4) applying an inverse MPP (maximum power point) searching method in each iteration, and evaluating the reliability after multiple times of loop optimization convergence. And when the objective function value is kept stable and the reliability constraint reaches a given value, the iteration is terminated, and the reliability optimization is completed. The specific flow chart is shown in fig. 3.
Substep 5-1, initial deterministic optimization. In the first step, MPP point information is lacked, and the mean value v of variables and random parameters is randomly designed MPPθ And p MPPθ As an initial point. The optimization model is as follows
Through the optimization model, a new MPP point can be obtained and used for the reliability evaluation of the next step.
And a substep 5-2 of evaluating the reliability by applying an inverse MPP search method. Here, the reliability optimization constrains the equivalent transformation, and the optimization model is as follows:
wherein, g R Is the R percentile of the constraint g (d, V, P), defined as:
Prob{g(d,V,P)≤g R }＝R (24)
based on AFORM, the reliability index can be calculated by the required reliability R, as follows
β＝Φ -1 (R) (25)
Wherein phi -1 (. Cndot.) represents the inverse cumulative distribution function of a standard normal distribution.
The inverse MPP point problem can be solved by the following model:
wherein u = [ ] V ；u P ]，u V 、u P Standard forms for v and p, respectively.
After the optimized inverse MPP point is determined through a formula (26), the R percentage point can be obtained;
g R ＝g(u MPP )＝g(v MPP ,p MPP ) (27)
and verifying whether the calculated inverse MPP point can be satisfied with the reliability requirement. If not, the next operation is needed.
That is, after the inverse MPP point is optimized, whether the optimized inverse MPP point is greater than the value of the inverse MPP point in the process of obtaining the reliability index is determined, and if so, the certainty parameter, the random design variable and the random parameter corresponding to the optimized objective function value are used as the output turning parameter. If less than or equal to, the following substep 5-3 is performed.
The above percentage R is explained as follows: the equivalent transformation of the percentage R can be illustrated in connection with fig. 5, where the shaded area in fig. 5 equals the required reliability R, if g R 0 or less, i.e. Prob g i And (d, X, P) is less than or equal to 0} and is more than or equal to R, so that the conversion is equivalent, and the reliability constraint inequality is converted into equivalent constraint containing R percentage points.
And step 5-3, redefining the deterministic optimization constraint through the motion vector. Reliability fails to meet the requirement, which states the constraint g (mu) V ,μ P ) Inverse MPP point ofNot within the deterministic feasibility domain, i.e., the reliability constraint. In order to ensure the effectiveness of the reliability constraint, the constraint is corrected to meet the requirement that the inverse MPP point at least reaches the constraint boundary before the establishment of the next equivalent deterministic optimization model. Where s denotes a motion vector, which satisfies
Wherein u is v (1) This can be understood as a deterministic optimization design point for the first step loop.
So that the deterministic optimization constraints of the next loop can be modified to
g(μ V -s)≤0 (29)
Similarly, the optimization model of the loop in step T +1 is
Wherein, the first and the second end of the pipe are connected with each other,
and when the objective function value is kept stable and the reliability constraint reaches a given value, the iteration is terminated, and the reliability optimization is completed. That is, the random design variables (design points) are continually moved closer to the optimal optimization point, marking the random design variables to meet the reliability requirements when the loop terminates.
In this embodiment, in the reliability optimization model, the maximum removal rate of the material is used as an objective function, the reliability that the turning stability, the surface roughness, the cutting force and the like meet is used as a constraint function, and the reliability of the constraint condition is calculated by applying the AFSOM for the reliability analysis of the mechanical structure. A serial single-loop SORA method is applied to solve the reliability-based optimization model. Compared with the traditional turning parameter optimization, the method has the advantages that the influence of uncertain parameters is considered, and the method has more practical application value.
Example 1
The design variable parameters and the random parameter probability distribution characteristics of a numerically controlled lathe are shown in table 1.
TABLE 1 probability distribution characteristics of basic parameters
Substituting the turning dynamics parameters into the formulas (6), (7) and (8), and obtaining a turning stability lobe graph by corresponding different rotation speeds omega to different limit cutting depths aplim, as shown in fig. 4. The curve divides the space into an unstable region and a stable region, if a value-taking point is above the curve, the flutter phenomenon can occur, and the point on the lobe curve is in a critical state.
The SORA method in step 05 is applied to solve the reliability optimization problem. The objective function of the example is nonlinear, an MATLAB programming language can be applied in programming optimization, and the deterministic optimization link in the deterministic optimization and the reliability optimization uniformly uses an fmincon function of nonlinear programming in the MATLAB for comparison.
The results before and after optimization are shown in table 2.
TABLE 2 comparison of optimization results
As can be seen from table 2, the two optimization methods greatly improve the material removal rate per unit time (MRR) before optimization, but the reliability of the constraint after deterministic optimization is generally low, while the material removal rate per unit time, the feed amount, and the depth of cut after reliability optimization by the SORA method are reduced, but the reliability of the constraint is greatly improved, and the required reliability R =0.99 can be satisfied.
In order to improve the processing efficiency to the maximum extent while ensuring the processing quality of a workpiece, the method firstly establishes a dynamic model of regenerative chatter in the turning process and deduces a limit cutting depth expression. And analyzing the influence of uncertain factors on the turning process, and establishing an optimization model based on reliability so as to obtain the optimal turning parameters. In the reliability optimization model, the maximum removal rate of the material is used as an objective function, and the reliability of the turning stability, the surface roughness, the cutting force and the like which meet the requirements is used as a constraint function. And calculating the reliability of the constraint condition by using the AFSOM widely applied to the reliability analysis of the mechanical structure. A serial single-loop SORA method is applied to solve the reliability-based optimization model. As can be seen from the example 1, the turning parameters obtained by the method meet the reliability requirement, and the machining efficiency is improved by about 80%. For other turning processes, the method proposed by the present invention is still effective.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive.
Finally, it should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. A method for optimizing turning parameters in consideration of uncertain parameters, comprising:
s1, processing a turning system dynamic model according to a set vibration initial condition of the turning system and the turning system stability critical state information to obtain a stability limit state function of the turning system, wherein the stability limit state function comprises: the minimum value of the limit cutting depth, the spindle rotating speed corresponding to the limit cutting depth and the mechanical cutting width;
s2, based on the stability limit state function, acquiring a reliability index for evaluating the stability of the turning system by adopting AFOSM;
s3, establishing an optimization model of the reliability of the turning technological parameters in the turning system by taking the material removal rate in unit time as an optimization target and preset constraint conditions;
the constraint conditions include: reliability constraint conditions and random design variable boundary constraints;
and S4, optimizing the optimization model by adopting an SORA method and combining the reliability index to obtain an objective function value which is optimized and converged and accords with reliability constraint, wherein a deterministic parameter, a random design variable and a random parameter corresponding to the objective function value are used as output turning parameters.
2. The method according to claim 1, wherein step S1 comprises:
s11, establishing a dynamic model of the turning system according to a regenerative flutter mechanism;
s12, acquiring an expression of dynamic cutting force according to the set cutting thickness variation;
s13, integrating the dynamic cutting force expression and the dynamic model, and performing Laplace transform on the integrated expression when the initial vibration condition is zero;
s14, applying the stable critical state information of the turning system to the expression after Laplace transformation to obtain the limit cutting depth and the minimum value of the spindle rotating speed and the mechanical cutting width corresponding to the limit cutting depth;
and S15, establishing a stability limit state function according to the limit cutting depth and the minimum value of the spindle rotating speed and the mechanical cutting width corresponding to the limit cutting depth.
3. The method of claim 2,
the vibration differential equation of the dynamic model of the turning system in the substep S11 is:
wherein m is equivalent mass; c is equivalent damping; k is the equivalent stiffness;shows dynamic cutting force Δ F d (t) forming an included angle with the vibration direction of the cutter; alpha represents the included angle between the main vibration direction q (t) of the cutter and the vibration direction;
the expression of the dynamic cutting force in the substep S12 is:
ΔF d (t)＝k c a p a(t)＝k c a p [ηy(t-T)-y(t)]
wherein a (T) = eta y (T-T) -y (T), the overlapping coefficient of two times of processing before and after turning is eta, y (T) is the vibration displacement of the tool, T is the rotation period of the main shaft, k is c Is the cutting stiffness coefficient; a is a p Is the cutting depth;
the expression after the laplace transform in sub-step S13 is:
the limit cutting depth in the substep S14 is:
the spindle rotating speed corresponding to the limit cutting depth is as follows:
when the overlap coefficient η =1, the minimum value of the machine cutting width is:
the stability limit state function in substep S15 is:
wherein, a p Is the cutting depth; a is plim Is the limit depth of cut; x is a random parameter, g(x)&0 represents turning stable cutting; g (x)&0 represents the turning flutter; g (x) =0 indicates that the turning is in the limit stable cutting state.
4. A method according to claim 2 or 3, characterized in that step S2 comprises:
s21, converting each random design variable related to the stability limit state function into a standard normal form
μ i And σ i Are each X i Mean and variance of (2), X i For x in the stability limit state function i Random parameters of (a);
s22, obtaining a reliability index beta which represents the shortest distance from the original point to the approximate failure curved surface in the normal space mapped by the original point in the AFOSM;
s23, obtaining the reliability P according to the reliability index S ；
S24, if the reliability P S If the reliability is greater than the minimum reliability in the reliability constraint, executing the step S3, otherwise, re-acquiring the reliability P S 。
5. The method according to claim 4, characterized in that, in step S3,
the optimization model of the turning process parameter reliability comprises the following steps:
2
wherein d, V and P respectively represent a deterministic parameter, a random design variable and a random parameter; mu.s V ，μ P Are the mean values of V and P, respectively; g θ (. Cndot.) refers to the extreme state function at the theta failure mode; r θ A given reliability threshold; q. q.s ξ (. Is) an inequality constraint matrix; m and N are reliability constraint and inequality constraint quantity respectively; reliability P { g θ (d, V, P). Ltoreq.0 byDetermining;
the objective function in the optimization model of reliability is: f (x) = f MRR ＝1/(πa p f·Ω(ω)·D)；
Wherein D is the cutting diameter of the workpiece, and omega (omega) is the rotating speed of the main shaft;
the reliability constraints include: reliability constraint, turning system stability constraint, cutting force constraint, surface roughness constraint and cutting power constraint;
reliability constraint expression, P (g) θ (x)≤0)≥R θ θ＝1,…,4；
Wherein the target reliability is R θ Is a preset value;
the stability constraint expression of the turning system is expressed,
cutting force constraint expression:
k n a and b are constant coefficients; f c Is the instantaneous cutting force; f cmax Is the maximum cutting force;
surface roughness constraint expression: g 3 (x)＝R a -R amax ＝f 2 /(8r CT )-R amax ≤0；
R a Instantaneous surface roughness; r is CT The radius of the arc of the turning tool nose; r amax Maximum theoretical surface roughness;
cutting power constraint expression: g is a radical of formula 4 (x)＝P c -P cmax ＝F c Ω(ω)/60000-P cmax ≤0；
P c Instantaneous cutting power; p cmax The maximum cutting power;
the random design variable boundary constraints include: cutting depth constraint, cutting processing system vibration angular frequency constraint and feed quantity constraint.
6. The method of claim 5, wherein randomly designing the boundary constraints for the variables comprises:
0＜a p ＜2、560＜ω＜750、0.1＜f＜0.9；
depth of cut a p The stable vibration frequency omega and the stable feed amount f of the turning system.
7. The method of claim 6, wherein step S4 comprises:
s41, selecting initial values of random design variables and random parameters, and obtaining a maximum failure probability point MPP through an optimization model;
s42, reliability evaluation is carried out by adopting an inverse MPP searching method, an inverse MPP point is obtained based on an AFORM method, the inverse MPP point is optimized, and whether the optimized inverse MPP point is larger than the value of the inverse MPP point in the reliability index obtaining process in the S2 is judged;
and if so, taking the certainty parameter, the random design variable and the random parameter corresponding to the optimized objective function value as the output turning parameter.
8. The method of claim 7, wherein step S4 further comprises:
if the random design variable and the random parameter are not more than the preset motion vector, redefining the random design variable and the random parameter through a preset motion vector, and repeating the step S2 to the step S4.
9. The method according to claim 1, characterized in that sub-step S42 comprises:
reliability evaluation is carried out by applying an inverse MPP search method, reliability optimization constraint equivalent transformation is carried out, and min f (d, mu) V ,μ P )
The optimization model after equivalent transformation is as follows:
wherein, g R Is the R percentile of the constraint g (d, V, P), defined as
Prob{g(d,V,P)≤g R }＝R；
Based on AFORM, reliability index beta = Φ -1 (R)；
Wherein phi -1 (. Cndot.) represents an inverse cumulative distribution function of a standard normal distribution;
by passingObtaining an inverse MPP point;
wherein u = [ u = V ；u P ]，u V 、u P Standard forms for v and p, respectively;
optimizing the inverse MPP point, and determining the R percentage point according to the optimized inverse MPP point
And substituting the determined R percentage point into the reliability constraint condition, and checking whether the inverse MPP point meets the reliability constraint condition.
10. The method of claim 8, wherein the step S2 to step S4 are repeated by redefining the random design variables and the random parameters by the predetermined motion vectors, comprising:
if constraining g (. Mu.), V ,μ P ) Inverse MPP point ofIf not, the reliability constraint condition before the optimization model is built is corrected, and the reliability constraint condition comprises the following steps:
a motion vector s is set and, in this case,
and revising the deterministic optimization constraints of the next loop to
g(μ V -s)≤0
Similarly, the optimization model of the loop in step T +1 is
minf(d,μ V ,μ p )
Wherein the content of the first and second substances,
and when the objective function value is kept stable and the reliability constraint reaches a given value, the iteration is terminated, and the reliability optimization is completed.
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