CN107703744A - Consider the Digit Control Machine Tool Kinematic Chain Design method of nonlinearity erron and generalized Modal - Google Patents
Consider the Digit Control Machine Tool Kinematic Chain Design method of nonlinearity erron and generalized Modal Download PDFInfo
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Abstract
The invention discloses a kind of Digit Control Machine Tool Kinematic Chain Design method for considering nonlinearity erron and generalized Modal.Structure Kinematic Chain Design computation model, to minimize accumulation nonlinearity erron and minimize the inverse of generalized Modal as solution target；Generation motion chain configuration population, to wherein each moving chain configuration, demarcates workpiece coordinate system, rotation transformation of the cutting location data through destroked constraint and straight line is converted to obtain obtaining N group lathe postures；Whether judge to move chain configuration with realizing that the machine tool motion needed for component shaping is consistent, kinematic chain reconstruct is carried out if not being inconsistent；Generalized Modal is calculated using neural network model, accumulation nonlinearity erron is calculated using the differential method；Solve Kinematic Chain Design computation model and obtain Pareto disaggregation, optimal motion chain configuration is obtained using TOPSIS methods.Instant invention overcomes conventional motion chain design method rely on experience, only consider part forming feature, applicability is not strong the shortcomings that, improve kinematics, the dynamics of lathe, improve the machining accuracy of lathe.
Description
Technical Field
The invention relates to the field of numerical control machine tools, in particular to a numerical control machine tool kinematic chain design method considering nonlinear errors and generalized modes.
Background
The scheme design of the complete machine of the numerical control machine guides the subsequent design work and plays a decisive role in the performance of the machine tool. The design of the kinematic chain is the first task of the design of the whole machine scheme, and the traditional analogy and empirical design method is restricted by experience. At present, the individuation and customization of products become a great trend of the design and manufacture of mechanical equipment, and numerical control machine tool kinematic chains obtained by analogy and experience methods cannot meet the processing requirements of individuation and customization, particularly processing parts with complex free curved surfaces such as an aerospace engine impeller.
The field focuses on the research of the classification and the comprehensive problems of the multi-axis numerical control machine kinematic chain, and a scientific and systematic numerical control machine kinematic chain design method is lacked. At present, a creative kinematic chain design method based on a position posture matrix between an analytic tool and a workpiece can only aim at simple parts, and has too many creative schemes, and more importantly, the kinematic, dynamic and precision performances of the kinematic chain cannot be considered, and only the forming characteristics of the parts are considered. When the same processing task is completed, the inherent defects of some kinematic chains cause the consequences of large processing error, low kinematic efficiency, large occupied working space, singular point generation, interference generation and the like. These defects can be reduced by the associated optimization algorithms in subsequent designs, but cannot be completely eliminated.
Disclosure of Invention
The invention provides a numerical control machine tool kinematic chain design method considering nonlinear errors and generalized modes in order to solve the problems in the background art, and aims to obtain an optimal numerical control machine tool kinematic chain meeting the machining requirements of complex curved surface workpieces by constructing and solving a numerical control machine tool kinematic chain design calculation model, improve the kinematics and dynamics characteristics of a machine tool and improve the machining precision of the machine tool.
In order to achieve the above purpose, as shown in fig. 1, the present invention adopts the technical scheme that:
step (1): building a kinematic chain design computation model to minimize the cumulative nonlinear error ∑ ε non And minimizing the reciprocal M of the generalized mode -1 Initializing a kinematic chain configuration population algebra g for solving a target, and enabling g =1;
step (2): generating a g-th generation of kinematic chain configuration population, taking the kinematic chain configuration KC as a population individual, and obtaining an individual serial number p in the kinematic chain configuration population, namely the serial number of the kinematic chain configuration, wherein p =1;
in the step 2), when g =1, a g-th generation of the kinematic chain configuration population is randomly generated, and the individual serial number P of the kinematic chain configuration population is initialized, so that P =1,2,3 \8230, and P, P represents the total number of the individuals in the kinematic chain configuration population.
And (3): aiming at the p-th kinematic chain configuration KC in the g-th generation kinematic chain configuration population, calibrating a workpiece coordinate system relative to a machine tool coordinate system on the p-th kinematic chain configuration KC, determining XYZ axes of the machine tool coordinate system after calibration, and then obtaining N groups of machine tool postures D by carrying out stroke-constraint-free rotation transformation and linear transformation on tool position data of a complex curved surface workpiece to be processed t ；
Wherein each group of machine tool postures D t ＝(x t ,y t ,z t ,r 1,t ,r 2,t )，x t Data representing the X-axis of the machine coordinate system, y t Data representing the Y-axis, z t Data representing the Z axis, r 1,t Represents R 1 Data of axes r 2,t Represents R 2 Data of axes, R 1 、R 2 Each being one of an axis of rotation about the X-axis derived from kinematic chain configuration KC, an axis of rotation about the Y-axis derived from kinematic chain configuration KC, and an axis of rotation about the Z-axis derived from kinematic chain configuration KC, and R 1 Is not equal to R 2 T represents the serial number of the machine tool attitude, t =1,2,3 \8230, N, N represents the total number of the machine tool attitudes;
and (4): judging whether the p-th kinematic chain configuration KC is consistent with the machine tool motion required for realizing the forming of the complex curved surface workpiece to be processed or not according to the N groups of machine tool postures, if not, correcting the kinematic chain configuration, and if so, keeping the kinematic chain configuration;
and (5): aiming at the pth kinematic chain configuration, a neural network model is used for calculating a generalized mode M, and a differentiation method is used for calculating an accumulated nonlinear error sigma epsilon non ；
And (6): repeating the steps (3) to (5) for each of the kinematic chain configuration populationsProcessing the population individuals to obtain the generalized mode M and the accumulated nonlinear error sigma epsilon of each population individual non ；
And (7): solving a kinematic chain design calculation model by adopting an NSGA-II algorithm, enabling g = g +1, repeating the steps (2) to (6) to obtain various generations of kinematic chain configuration populations, and when g >1, selecting, crossing and mutating the g-1 generation populations to generate g generation kinematic chain configuration populations; until G is equal to the maximum kinematic chain configuration population generation G, obtaining a Pareto optimal solution set;
and (8): and solving the Pareto optimal solution set by using a TOPSIS multi-standard decision analysis method to obtain the optimal kinematic chain configuration.
The kinematic chain design calculation model in the step (1) is specifically expressed by the following formula and is minimized by f 1 And minimize f 2 To solve the objective:
M≥M p
Σε non ≤ε p
x imin ≤x i ≤x imax
x＝[x 1 ，x 2 ，x 3 ，x 4 ，x 5 ]∈R 5
in the formula (f) 1 Representing the accumulated non-linear error e non As a first objective function; f. of 2 Reciprocal M representing generalized mode -1 As a second objective function; sigma epsilon non Representing accumulated nonlinear error, M representing generalized mode;representing the connected t-th group of machine tool attitude D t Corresponding tool position vector and t +1 set of machine tool attitude D t+1 The vector formed by the corresponding tool position vector,representing the connected t-th group of machine tool attitude D t Corresponding tool location vector sumT denotes a machine tool attitude serial number, t =1,2,3 \8230, N denotes a total number of machine tool attitudes, m denotes a total number of machine tool attitudes, andk denotes the number of the differential machine tool attitudeThe total number of differential machine tool poses of (2); f. of t,k The method comprises the steps of representing the kth order natural frequency corresponding to the t set of machine tool postures, wherein t represents the serial number of the machine tool postures, t =1,2,3 \8230, N and N represent the total number of the machine tool postures, k represents the order of the natural frequency, and k =1,2,3; m p Is a minimum allowable value of a generalized mode, epsilon p Is the maximum allowable value of the accumulated nonlinear error; x is the number of imin Represents the minimum value, x, of the ith design variable value imax Represents the maximum value of the ith design variable value, i represents the serial number of the design variable, and i =1,2,3,4,5; r is 5 Representing a five-dimensional design variable solution space.
In a specific implementation, variable X is designed i All possible values depend on the number of axes of the kinematic chain, where i denotes the serial number of the design variable, i =1,2,3,4,5.
In the step (2), the kinematic chain configuration population consists of P kinematic chain configurations KC, wherein P represents the total number of individuals in the kinematic chain configuration population, one individual is one kinematic chain configuration KC, and the kinematic chain configuration KC is represented by KC = { X = 1 ,X 2 ,X 3 ,X 4 ,X 5 H, five design variables are respectivelyConfiguring type X for a rotating shaft 1 Translational shaft configuration type X 2 Spindle layout type X 3 The workpiece clamping direction X 4 And bed position X 5 (ii) a Rotation axis configuration type X 1 Showing the distribution and combination of the rotary shafts, the type X of the arrangement of the translation shafts 2 Showing the arrangement combination form of three translational axes under a three-axis coordinate system and the main shaft layout type X 3 Divided into vertical and horizontal, the workpiece clamping direction X 4 Indicating the positive direction of the Z axis of the workpiece coordinate system in the machine tool coordinate system, the bed position X 5 Indicating the position of the bed in the kinematic chain.
In the step (3), the calibration of the workpiece coordinate system relative to the machine tool coordinate system is carried out on the pth kinematic chain configuration KC, which specifically comprises the following steps: firstly, the type X of the main shaft layout in the obtained kinematic chain configuration KC 3 Establishing a coordinate system by using a national standard JB 3051-1999-T numerical control machine tool coordinate system and the name of the motion direction as a virtual machine tool coordinate system; then clamping the workpiece in the direction X by the kinematic chain configuration KC 4 Determining the offset of each axis of the workpiece coordinate system relative to the virtual machine tool coordinate system by using the workpiece coordinate system of the complex curved surface workpiece to be processed; and then, according to the axis offset of the workpiece coordinate system and the virtual machine tool coordinate system, the workpiece coordinate system is transformed to the virtual machine tool coordinate system in a same time to finish the calibration.
In the step (3), the tool position data is obtained by performing pre-processing on model data of the complex curved surface workpiece to be processed by the CAM software.
And (3) firstly setting the number of the kinematic chain shafts to be constructed as the total number of the shafts, namely 5, processing once according to the step (4), removing the non-conforming kinematic chain shafts, and reconstructing the kinematic chain configuration.
The specific process of the step (4) is as follows:
to N groups of machine tool postures D t The attitude of each two adjacent machine tools is calculated and judged by adopting the following formula:
max|D t+1(l) -D t(l) |≤ε
in the formula, D t(l) Denotes the firstt sets of data of the ith dimension of the machine tool attitude, wherein l represents the dimension number of the machine tool attitude, and represents data of the X axis when l =1,2,3,4,5,l =1, represents data of the Y axis when l =2, represents data of the Z axis when l =3, and represents data of the R axis when l =4 1 Data on axes, i =5 denotes R 1 Data of the axis; r 1 、R 2 Each being one of an axis of rotation about the X-axis derived from kinematic chain configuration KC, an axis of rotation about the Y-axis derived from kinematic chain configuration KC, and an axis of rotation about the Z-axis derived from kinematic chain configuration KC, and R 1 Is not equal to R 2 T represents the serial number of the machine tool attitude, t =1,2,3 \8230, N, N represents the total number of the machine tool attitudes;
if the formula is not established, considering that the kinematic chain configuration KC does not accord with the machine tool motion required by realizing the forming of the complex curved surface workpiece to be processed, removing the currently calculated motion axis, and correcting each design variable to obtain the reconstructed kinematic chain configuration;
if the formula is established, the kinematic chain configuration KC is considered to be in accordance with the machine tool motion required by realizing the forming of the complex curved surface workpiece to be processed, and the kinematic chain configuration KC is reserved.
In the step (4), the design variables are corrected, specifically: keeping the serial number of each design variable value in the current calculation unchanged, and aiming at the serial number of each design variable value, performing the following judgment: and if the serial number of the design variable value is larger than the total number of all possible design variable values of the design variable under the current shaft number, reducing the serial number until the serial number is equal to the total number of all possible design variable values of the design variable under the current shaft number.
The generalized mode M in the step (5) is specifically the minimum value of the average values of the dynamic natural frequencies of the first three orders of the machine tool corresponding to all the tool positions. The tool location point refers to a combination of a group of tool location vectors and cutter axis vectors in the tool location data.
The generalized mode M is obtained by calculation of a neural network model by adopting the following processes:
i construction with KC, D t ,s x ,s y ,s z For input, s x ,s y ,s z Respectively representing kinematic chain mechanismsThe BP neural network model takes the dynamic natural frequency of the front three orders of the machine tool as output according to the X-axis, Y-axis and Z-axis strokes of the machine tool corresponding to the type KC;
II, obtaining N sample sets through a test method, and training a BP neural network model;
iii, for a kinematic chain configuration KC, calculating each set of KC and D by using a neural network model t ,s x ,s y ,s z Corresponding first three-order natural frequency f t,k T represents the serial number of the machine tool attitude, t =1,2,3 \8230, N, N represents the total number of the machine tool attitude, k represents the order of the natural frequency, k =1,2,3, and the generalized mode M is calculated by adopting the following formula:
the X-axis, Y-axis and Z-axis strokes s of the machine tool corresponding to the kinematic chain configuration KC x ,s y ,s z Is calculated in the same way as the X-axis stroke s x For the sake of example:
upper limit of travel s of X axis x(max) The calculation is as follows:
lower limit of travel s of X-axis x(min) The calculation is as follows:
the stroke s of the X axis x The calculation is as follows:
s x ＝s x(max) -s x(min)
t denotes a serial number of machine tool postures, t =1,2,3 \8230, and N, N denotes a total number of machine tool postures.
The specific implementation can adopt the same method to obtain the stroke of each other shaft.
Said accumulated nonlinear error ∑ ε non Specifically, the following formula differential method is adopted for solving:
i, for machine attitude, from t-th set of machine attitude D t ＝(x t ,y t ,z t ,r 1,t ,r 2,t ) To t +1 th group of machine tool attitude D t+1 ＝(x t+1 ,y t+1 ,z t+1 ,r 1,t+1 ,r 2,t+1 ) And performing K equal division differentiation on the variable quantity of each axis to obtain:
Δ m ＝(Δx,Δy,Δz,Δr 1 ,Δr 2 )m,m＝1,2,3,…,K
in the formula,. DELTA. m Representing the amount of change in the attitude of the machine tool, m representingThe number of the differential machine tool attitude of (1),representing the vector formed by connecting the t-th set of machine tool poses and the t + 1-th set of machine tool poses, Δ x, Δ y, Δ z, Δ r 1 ,Δr 2 Respectively represent X, Y, Z, R 1 ,R 2 The amount of change of the axis, i.e. from (x) t ,y t ,z t ,r 1,t ,r 2,t ) To (x) t+1 ,y t+1 ,z t+1 ,r 1,t+1 ,r 2,t+1 ) The respective corresponding change amounts, K representsThe total number of differential machine tool attitudes in D t +Δ m As slave machine attitude D t To the machine attitude D t+1 The mth differential machine tool attitude of (1);
ii, sequentially changing the machine tool posture D t ,D t +Δ m ,D t+1 Substituting into the linear transformation in step (3) to respectively obtain corresponding tool position vectors (x) t(w) ,y t(w) ,z t(w) )、(x t+m (w ) ,y t+m(w) ,Z t+m(w) )、(x t+1(w) ,y t+1(w) ,z t+1(w) ) Wherein x is t(w) ,y t(w) ,z t(w) Respectively representing machine tool attitude D t Data of the corresponding tool position vector in the workpiece coordinate system along the X, Y, Z axes, Z t+m(w) ,y t+m(w) ,z t+m(w) Respectively representing machine tool attitude D t +Δ m Data of the corresponding tool position vector in the workpiece coordinate system along the X, Y and Z axes, X t+1(w) ,y t+1(w) ,z t+1(w) Respectively representing machine tool attitude D t+1 Data of the corresponding tool position vector in the workpiece coordinate system along X, Y and Z axes;
then, machine attitude D t To D t+1 Of non-linear error e non(t) Calculated as follows using the following formula:
in the formula (I), the compound is shown in the specification,representing a vector formed by connecting a tool position vector corresponding to the t-th group of machine tool postures with a tool position vector corresponding to the t + 1-th group of machine tool postures:
representing the sum of the tool position vectors associated with the poses of the machine tool of the connected t-th groupThe m-th differential machine tool attitude of (2) is a vector consisting of tool position vectors corresponding to:
wherein, tA serial number indicating the attitude of the machine tool, t =1,2,3 \ 8230, N, N indicates the total number of machine tool attitudes, and m indicatesThe serial number of the corresponding differential machine tool attitude, m =1,2,3, \8230;, K, K representsThe total number of differential machine tool poses of (1);
and finally, calculating the accumulated nonlinear error in the whole processing process by adopting the following formula:
the method has the advantages that through reducing the accumulated nonlinear error in the machining process, the meaningless curvilinear motion caused by the rotating shaft in the interpolation process can be reduced, the motion efficiency of the machine tool is improved, the working space required by realizing the same machining task is reduced, meanwhile, the simple deviation between the actual machined curved surface and the ideal machined curved surface is reduced, and the machining precision is improved; by adding the generalized mode, the inherent frequency in the machining process of the machine tool can be improved, and the dynamic characteristics such as vibration resistance and the like are improved; through the rotation transformation and the linear transformation without stroke constraint, the value of the rotation amount can be optimized, and the interference and singular points are reduced.
The invention has the beneficial effects that:
1. the invention introduces inverse machine tool kinematic transformation in the post-processing process into the design process of the kinematic chain, lays a foundation for quantitatively analyzing the kinematic chain in various heterogeneous forms, and solves the problem that the prior method depends on prior knowledge.
2. The method comprehensively considers the kinematics, dynamics and precision performances of the kinematic chain, improves the kinematic efficiency, the dynamic characteristics and the processing precision of the machine tool at the design stage of the complete machine scheme of the machine tool, optimizes the space utilization rate and reduces interference and singular points.
3. The method provided by the invention aims at the process characteristics of complex parts to be processed, the optimal kinematic chain is obtained from various heterogeneous forms, a design basis is provided for developing a special machine tool when specific parts are produced in large batch, a machine tool model selection basis is provided when specific parts are produced in medium and small batch, the scientificity of kinematic chain design is increased, and the design cycle is shortened.
Drawings
FIG. 1 is a general flow chart of the method of the present invention.
FIG. 2 is a composition diagram of design variables of the kinematic chain configuration of the present invention.
Fig. 3 is a flow chart of a method of calibrating a workpiece coordinate system relative to a machine coordinate system in accordance with the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and examples.
As shown in fig. 1, the embodiment of the present invention and its implementation are as follows:
step (1): building a kinematic chain design computation model to minimize the cumulative nonlinear error ∑ ε non And minimizing the reciprocal M of the generalized mode -1 Initializing a kinematic chain configuration population algebra g for solving a target, and enabling g =1; model to minimize f 1 And minimize f 2 To solve the objective.
Step (2): when g =1, randomly generating a g-th generation kinematic chain configuration population, and initializing an individual serial number p of the kinematic chain configuration population, so that p =1; when g is larger than 1, selecting, crossing and mutating the g-1 generation population to generate a g generation kinematic chain configuration population;
each population consists of P kinematic chain configurations KC, P denoting the size of the kinematic chain configuration population, P in a particular implementation may be 5.
As shown in fig. 2, the kinematic chain configuration KC = { X) in the step (2) 1 ,X 2 ,X 3 ,X 4 ,X 5 Wherein five design variables are respectively the rotating shaft configuration type X 1 Translational shaft configuration type X 2 Spindle clothOffice type X 3 Workpiece clamping direction X 4 And bed position X 5 (ii) a Wherein the rotation axis configuration type X 1 Showing the distribution and combination form of the rotating shafts, and the type X of the translational shaft configuration 2 Showing the arrangement combination form of three translational axes in a three-axis coordinate system, the main axis layout type X 3 Divided into vertical and horizontal, the workpiece clamping direction X 4 Indicating the direction of the Z-axis of the workpiece coordinate system in the machine tool coordinate system, the bed position X 5 Indicating the position of the bed in the kinematic chain.
In a specific implementation, variable X is designed i All possible values are based on the number of axes of the kinematic chain, where i denotes the serial number of the design variable, i =1,2,3,4,5;
if the number of axes of the kinematic chain is 5, and there are 3 translational axes, then translational axis configuration type X 2 Comprises the following steps:
X 2 ＝{x 2 |XYZ,XZY,YXZ,YZX,ZXY,ZYX}
when the number of axes of the kinematic chain is 4 and only two translational axes of X and Y are provided, the translational axis configuration type X 2 Comprises the following steps:
X 2 ＝{x 2 |XY，YX}
and (3): taking out the p-th kinematic chain configuration KC in the g-th generation kinematic chain configuration population, calibrating a workpiece coordinate system relative to a machine tool coordinate system, and then obtaining N groups of machine tool postures D by carrying out rotation transformation and linear transformation without stroke constraint on tool position data corresponding to the complex curved surface workpiece to be processed t (ii) a Each set of machine poses is denoted as D t ＝(x t ,y t ,Z t ,r 1,t ,r 2,t )。
If the positive direction of the Z axis of the workpiece coordinate system is along the positive direction of the X axis in the established virtual machine tool coordinate system, the workpiece coordinate system needs to be rotated by 90 degrees clockwise along the Y axis of the machine tool coordinate system.
And (3) firstly setting the number of the kinematic chain shafts to be constructed as the total number of the shafts, namely 5, processing once according to the step (4), removing the non-conforming kinematic chain shafts, and reconstructing the kinematic chain configuration.
And (4): according to N groups of machine tool postures D t Judging whether the kinematic chain configuration KC is consistent with the machine tool motion required for realizing the forming of the complex curved surface workpiece to be processed, if not, correcting the kinematic chain configuration and reconstructing the kinematic chain configuration, and if so, keeping the kinematic chain configuration;
and calculating the dimensional data of the N groups of machine tool postures by adopting the following formulas respectively:
max|D t+1(l) -D t(l) |≤ε
if the formula is not satisfied, considering that the kinematic chain configuration KC does not conform to the machine tool motion required for realizing the forming of the complex curved surface workpiece to be processed, removing the corresponding motion axis, and correcting each design variable: and keeping the serial numbers of the values of the current design variables unchanged, and if the serial number of one design variable is greater than the total number of all possible values of the design variable under the current shaft number, correspondingly reducing the serial number until the serial number is equal to the total number of all possible values of the design variable under the current shaft number. And obtaining the reconstructed kinematic chain configuration after correction.
If the formula is established, the kinematic chain configuration KC is considered to be in accordance with the machine tool motion required by realizing the forming of the complex curved surface workpiece to be processed, and the kinematic chain configuration KC is reserved.
For example, when the number of axes of the kinematic chain is 5, the type X of the translational axis configuration 2 All possible values are:
X 2 ＝{x 2 |XYZ,XZY,YXZ,YZX,ZXY,ZYX}
the current value is a value No. 3, namely YXZ;
if the Z axis needs to be removed at this time, the actual number of axes of the kinematic chain is 4, and only two translational axes X and Y are provided, and the translational axis is configured to be type X 2 All possible values are:
X 2 ＝{x 2 |XY，YX}
translational axis arrangement type X 2 The value of 2 with the correction of 4 axes is YX.
And (5): calculating the accumulated nonlinear error ∑ ε using a differential method non Specifically, the following are adoptedSolving by a formula differential method:
i from D for the attitude of the machine tool t ＝(x t ,y t ,z t ,r 1,t ,r 2,t ) To D t+1 ＝(x t+1 ,y t+1 ,z t+1 ,r 1,t+1 ,r 2,t+1 )，x t Data representing the X-axis, y t Data representing the Y-axis, z t Data representing the Z-axis, r 1t Represents R 1 Data of axes r 2t Represents R 2 Data of axes, R 1 、R 2 The machine tool attitude control method comprises the following steps of (1) possibly obtaining an A axis rotating around an X axis, a B axis rotating around a Y axis, one of C axes rotating around a Z axis, t represents the serial number of the machine tool attitude, t =1,2,3 \8230, N, N represents the total number of the machine tool attitude, and the variation of each axis is subjected to K equal differential to obtain:
Δ m ＝(Δx，Δy，Δz，Δr 1 ，Δr 2 ) m ，m＝1，2，3，..·，K
in the formula,. DELTA. m Representing the amount of change in the attitude of the machine tool, m representsThe number of the differential machine tool attitude of (1),representing the vector formed by connecting the t-th set of machine tool poses and the t + 1-th set of machine tool poses, Δ x, Δ y, Δ z, Δ r 1 ,Δr 2 Respectively represent X, Y, Z, R 1 ,R 2 The amount of change of the axis, K representsThe total number of differential machine tool poses of (2);
ii, sequentially changing the machine tool posture D t ,D t +Δ m ,D t+1 Substituting into the linear transformation in the step (3) to respectively obtain corresponding tool position vectors (x) t(w) ,y t(w) ,z t(w) )、(x t+m(w) ,y t+m(w) ,z t+m(w) )、(x t+1(w) ,y t+1(w) ,z t+1(w) ) Wherein x is t(w) ,y t(w) ,z t(w) Respectively representing machine tool attitude D t Data of the corresponding tool position vector in the workpiece coordinate system along the X, Y, Z axes, X t+m(w) ,y t+m(w) ,z t+m(w) Respectively representing machine tool attitude D t +Δ m Data of the corresponding tool position vector in the workpiece coordinate system along the X, Y and Z axes, X t+1(w) ,y t+1(w) ,z t+1(w) Respectively representing machine tool attitude D t+1 Data of the corresponding tool position vector in the workpiece coordinate system along the X, Y and Z axes;
machine tool attitude D t ＝(x t ,y t ,z t ,r 1,t ,r 2,t ) To D t+1 ＝(x t+1 ,y t+1 ,z t+1 ,r 1,t+1 ,r 2,t+1 ) Of non-linear error e non(t) Comprises the following steps:
in the formula (I), the compound is shown in the specification,representing the vector formed by connecting the t-th group of machine tool postures and the t + 1-th group of machine tool postures:
representing the attitude of the connected t-th group of machines andthe m-th differential machine attitude of (2):
t denotes the number of machine tool attitude, t=1,2,3 \8230n, N represents the total number of machine tool poses, m represents the total number of machine tool posesM =1,2,3, \ 8230;, K, K denotes the number of the differential machine tool attitude of (1)The total number of differential machine tool poses of (2);
the cumulative nonlinear error during the entire process is calculated as:
then, the generalized mode M is calculated using a neural network model, which is calculated by using the following procedure:
i construction with (KC, D) t ,s x ,s y ,s z ) For input, s x ,s y ,s z Respectively representing X-axis, Y-axis and Z-axis strokes of a machine tool corresponding to the kinematic chain configuration KC, and taking the dynamic natural frequency of the first three orders of the machine tool as an output BP neural network model;
II, obtaining N sample sets through a test method, and training a BP neural network model;
iii, for a kinematic chain configuration KC, calculating each group thereof (KC, D) by using a neural network model t ,s x ,s y ,s z ) Corresponding first third order natural frequency f t,k T represents the serial number of the machine tool attitude, t =1,2,3 \8230, N, N represents the total number of the machine tool attitude, k represents the order of the natural frequency, k =1,2,3, and the generalized mode M is calculated by the following formula:
and (6): judging whether the sequence number P of the population individual is equal to the size P of the kinematic chain configuration population, if not, enabling P = P +1, repeating the steps (3) and (5), and if not, entering the step (7);
and (7): solving a kinematic chain design calculation model by adopting an NSGA-II algorithm, enabling G = G +1, repeating the step (2) to the step (6) until G is equal to a maximum kinematic chain configuration population generation G, wherein G can be 15 in specific implementation, and obtaining a Pareto optimal solution set;
and (8): and solving the Pareto optimal solution set by using a TOPSIS multi-standard decision analysis method to obtain the optimal kinematic chain configuration.
If the obtained Pareto optimal solution set is { KC 1 ,KC 2 ,KC 3 ,KC 4 ,KC 5 The optimal kinematic chain configuration obtained by the TOPSIS multi-standard decision analysis method is KC 3 。
Therefore, the implementation of the invention can overcome the defects that the traditional kinematic chain design method depends on experience, only considers the part forming characteristics and has poor applicability, improve the kinematics and the dynamic characteristics of the machine tool and improve the processing precision of the machine tool.
Claims (9)
1. A numerical control machine tool kinematic chain design method considering nonlinear errors and generalized modes is characterized by comprising the following steps:
step (1): building a kinematic chain design computation model to minimize the cumulative nonlinear error ∑ ε non And minimizing the reciprocal M of the generalized mode -1 Solving the target;
step (2): generating a g generation kinematic chain configuration population, and taking a kinematic chain configuration KC as a population individual;
and (3): aiming at the p-th kinematic chain configuration KC in the g-th generation kinematic chain configuration population, calibrating a workpiece coordinate system relative to a machine tool coordinate system on the p-th kinematic chain configuration KC, and then performing stroke-constraint-free rotation transformation and linear transformation on tool position data of a complex curved surface workpiece to be machined to obtain N groups of machine tool postures D t ；
Wherein each group of machine tool attitude D t ＝(x t ,y t ,z t ,r 1,t ,r 2,t )，x t Data representing the X-axis in the machine coordinate system，y t Data representing the Y-axis, z t Data representing the Z-axis, r 1,t Represents R 1 Data of axes r 2,t Represents R 2 Data of axes, R 1 、R 2 Each being one of an axis of rotation about the X-axis derived from kinematic chain configuration KC, an axis of rotation about the Y-axis derived from kinematic chain configuration KC, and an axis of rotation about the Z-axis derived from kinematic chain configuration KC, and R 1 Is not equal to R 2 T represents the serial number of the machine tool attitude, t =1,2,3 \8230, N, N represents the total number of the machine tool attitudes;
and (4): judging whether the p-th kinematic chain configuration KC is consistent with the machine tool motion required for realizing the forming of the complex curved surface workpiece to be processed or not according to the N groups of machine tool postures, if not, correcting the kinematic chain configuration, and if so, keeping the kinematic chain configuration;
and (5): aiming at the pth kinematic chain configuration, a neural network model is used for calculating a generalized mode M, and a differentiation method is used for calculating an accumulated nonlinear error sigma epsilon non ；
And (6): repeating the step (3) to the step (5), and processing each population individual in the kinematic chain configuration population to obtain the generalized mode M and the accumulated nonlinear error sigma epsilon of each population individual non ；
And (7): solving a kinematic chain design calculation model by adopting an NSGA-II algorithm, enabling g = g +1, repeating the steps (2) to (6) to obtain various generations of kinematic chain configuration populations, and when g >1, selecting, crossing and mutating the g-1 generation populations to generate g generation kinematic chain configuration populations; until G is equal to the maximum kinematic chain configuration population algebra G, obtaining a Pareto optimal solution set;
and (8): and solving the Pareto optimal solution set by using a TOPSIS multi-standard decision analysis method to obtain the optimal kinematic chain configuration.
2. The method for designing the numerical control machine tool kinematic chain considering the nonlinear error and the generalized mode according to claim 1, wherein the method comprises the following steps: the kinematic chain design calculation model in the step (1) is specifically expressed by the following formula and is minimized by f 1 And minimize f 2 To solve the objective:
M≥M p
∑ε non ≤ε p
x imin ≤x i ≤x imax
x＝[x 1 ,x 2 ,x 3 ,x 4 ,x 5 ]∈R 5
in the formula (f) 1 Representing the accumulated nonlinear error ∑ epsilon non As a first objective function; f. of 2 Reciprocal M representing generalized mode -1 As a second objective function; sigma epsilon non Representing cumulative nonlinear error, M representing generalized mode;representing the attitude D of the machine tool in the t-th group of connections t Corresponding tool position vector and t +1 set of machine tool attitude D t+1 The vector formed by the corresponding tool position vector,representing the attitude D of the machine tool in the t-th group of connections t Corresponding tool location vector sumT denotes a machine tool attitude serial number, t =1,2,3 \8230, N denotes a total number of machine tool attitudes, m denotes a total number of machine tool attitudes, andk denotes the number of the differential machine tool attitudeThe total number of differential machine tool poses of (2); f. of t,k The method comprises the steps of representing a kth order natural frequency corresponding to a tth group of machine tool postures, wherein t represents a serial number of the machine tool postures, and t =1,2,3 \8230; m p Is the minimum allowable value of the generalized mode, ∈ p Is the maximum allowable value of the accumulated nonlinear error; x is the number of imin Represents the minimum value, x, of the ith design variable value imax Represents the maximum value of the ith design variable value, i represents the serial number of the design variable, and i =1,2,3,4,5; r 5 Representing a five-dimensional design variable solution space.
3. The method for designing the kinematic chain of the numerical control machine considering the nonlinear error and the generalized mode according to claim 1, wherein the method comprises the following steps: in the step (2), the kinematic chain configuration population consists of P kinematic chain configurations KC, wherein P represents the total number of individuals in the kinematic chain configuration population, one individual is one kinematic chain configuration KC, and the kinematic chain configuration KC is represented by KC = { X = 1 ,X 2 ,X 3 ,X 4 ,X 5 H, five design variables are respectively rotation axis configuration types X 1 Translational shaft configuration type X 2 Spindle layout type X 3 The workpiece clamping direction X 4 And bed position X 5 (ii) a Rotation axis configuration type X 1 Showing the distribution and combination of the rotary shafts, the type X of the arrangement of the translation shafts 2 Showing the arrangement combination form of three translational axes under a three-axis coordinate system and the main shaft layout type X 3 Divided into vertical and horizontal, the workpiece clamping direction X 4 Indicating the positive direction of the Z axis of the workpiece coordinate system in the machine tool coordinate system, the bed position X 5 Indicating the position of the bed in the kinematic chain.
4. The method for designing the numerical control machine tool kinematic chain considering the nonlinear error and the generalized mode according to claim 1, wherein the method comprises the following steps: in the step (3), the p-th kinematic chain configuration KC is subjected to the processing of the workpiece coordinate system relative to the machine tool coordinate systemThe calibration specifically comprises the following steps: firstly, the type X of the main shaft layout in the obtained kinematic chain configuration KC 3 Establishing a coordinate system by using a national standard JB 3051-1999-T numerical control machine tool coordinate system and the name of the motion direction as a virtual machine tool coordinate system; then clamping the workpiece in the direction X by the kinematic chain configuration KC 4 Determining the offset of each axis of the workpiece coordinate system relative to the virtual machine tool coordinate system by using the workpiece coordinate system of the complex curved surface workpiece to be processed; and then, according to the axis offset of the workpiece coordinate system and the virtual machine tool coordinate system, the workpiece coordinate system is transformed to the virtual machine tool coordinate system in a same time to finish the calibration.
5. The method for designing the numerical control machine tool kinematic chain considering the nonlinear error and the generalized mode according to claim 1, wherein the method comprises the following steps: the specific process of the step (4) is as follows:
to N groups of machine tool postures D t The attitude of each two adjacent machine tools is calculated and judged by adopting the following formula:
max|D t+1(l) -D t(l) |≤ε
in the formula D t(l) Data indicating the ith dimension of the t-th set of machine tool postures, wherein l indicates the dimension number of the machine tool posture, and indicates the X-axis data when l =1,2,3,4,5,l =1, the Y-axis data when l =2, the Z-axis data when l =3, and the R-axis data when l =4 1 Data on axis, where l =5 represents R 1 Data of the axis; r is 1 、R 2 Each being one of an axis of rotation about the X-axis derived from a kinematic chain configuration KC, an axis of rotation about the Y-axis derived from a kinematic chain configuration KC, and an axis of rotation about the Z-axis derived from a kinematic chain configuration KC, and R 1 Is not equal to R 2 T represents the serial number of the machine tool attitude, t =1,2,3 \8230, N, N represents the total number of the machine tool attitudes;
if the formula is not satisfied, considering that the kinematic chain configuration KC does not conform to the machine tool motion required for realizing the forming of the complex curved surface workpiece to be processed, removing the currently calculated motion axis, and correcting each design variable to obtain the reconstructed kinematic chain configuration;
if the formula is established, the kinematic chain configuration KC is considered to be in accordance with the machine tool motion required by realizing the forming of the complex curved surface workpiece to be processed, and the kinematic chain configuration KC is reserved.
6. The method for designing the kinematic chain of the numerical control machine considering the nonlinear error and the generalized mode according to claim 1, wherein the method comprises the following steps: the generalized mode M in the step (5) is specifically the minimum value of the average values of the dynamic natural frequencies of the first three orders of the machine tool corresponding to all the tool positions.
7. The method for designing a kinematic chain of a numerically controlled machine tool considering nonlinear error and generalized mode according to claim 1 or 6, wherein: the generalized mode M in the step (5) is obtained by calculation of a neural network model by adopting the following process:
i construction with KC, D t ,s x ,s y ,s z As input s x ,s y ,s z Respectively representing X-axis, Y-axis and Z-axis strokes of a machine tool corresponding to the kinematic chain configuration KC, and taking the dynamic natural frequency of the first three orders of the machine tool as an output BP neural network model;
II, obtaining N sample sets through a test method, and training a BP neural network model;
iii, calculating each set of KC and D by using a neural network model for a motion chain configuration KC t ,s x ,s y ,s z Corresponding first three-order natural frequency f t,k T represents the serial number of the machine tool attitude, t =1,2,3 \8230, N, N represents the total number of the machine tool attitude, k represents the order of the natural frequency, k =1,2,3, and the generalized mode M is calculated by adopting the following formula:
8. the method for designing a kinematic chain of a numerically controlled machine tool considering nonlinear error and generalized mode according to claim 7, wherein the method comprises the following steps: the X-axis, Y-axis and Z-axis strokes of the machine tool corresponding to the kinematic chain configuration KCs x ,s y ,s z Is calculated in the same way as for the X-axis stroke s x For illustration purposes:
upper limit of travel s of X-axis x(max) The calculation is as follows:
lower limit of travel s of X-axis x(min) The calculation is as follows:
the stroke s of the X axis x The calculation is as follows:
s x ＝s x(max) -s x(min)
t denotes a serial number of machine tool postures, t =1,2,3 \8230, and N, N denotes a total number of machine tool postures.
9. The method for designing the kinematic chain of the numerical control machine considering the nonlinear error and the generalized mode according to claim 1, wherein the method comprises the following steps: the accumulated nonlinear error ∑ ε in the step (5) non Specifically, the following formula differential method is adopted for solving:
i, for machine attitude, from t-th set of machine attitude D t ＝(x t ,y t ,z t ,r 1,t ,r 2,t ) To t +1 set of machine tool attitude D t+1 ＝(x t+1 ,y t+1 ,z t+1 ,r 1,t+1 ,r 2,t+1 ) And performing K equal division differentiation on the variable quantity of each axis to obtain:
Δ m ＝(Δx,Δy,Δz,Δr 1 ,Δr 2 ) m ,m＝1,2,3,…,K
in the formula,. DELTA. m Representing the amount of change in the attitude of the machine tool, m representsThe number of the differential machine tool attitude of (1),represents the vector formed by connecting the t-th set of machine tool postures and the t + 1-th set of machine tool postures, deltax, deltay, deltaz, deltar 1 ,Δr 2 Respectively represent X, Y, Z, R 1 ,R 2 The amount of change of the axis, i.e. from (x) t ,y t ,z t ,r 1,t ,r 2,t ) To (x) t+1 ,y t+1 ,z t+1 ,r 1，t+1 ,r 2，t+1 ) The respective corresponding change amounts, K representsThe total number of differential machine tool attitudes in D t +Δ m As slave machine attitude D t To the machine attitude D t+1 The mth differential machine tool attitude of (1);
ii, sequentially changing the machine tool posture D t ,D t +Δ m ,D t+1 Substituting into the linear transformation in step (3) to respectively obtain corresponding tool position vectors (x) t(w) ,y t(w) ,z t(w) )、(x t+m(w) ,y t+m(w) ,z t+m(w) )、(x t+1(w) ,y t+1(w) ,z t+1(w) ) Wherein x is t(w) ,y t(w) ,z t(w) Respectively representing machine tool attitude D t Data of the corresponding tool position vector in the workpiece coordinate system along the X, Y and Z axes, X t+m(w) ,y t+m(w) ,z t+m(w) Respectively representing machine tool attitude D t +Δ m Data of the corresponding tool position vector in the workpiece coordinate system along the X, Y, Z axes, X t+1(w) ,y t+1(w) ,z t+1(w) Respectively representing machine tool attitude D t+1 Data of the corresponding tool position vector in the workpiece coordinate system along the X, Y and Z axes;
then, the machine tool attitude D t To D t+1 Non-linear error of (e) non(t) Calculated as follows using the following formula:
in the formula (I), the compound is shown in the specification,representing a vector formed by connecting a tool position vector corresponding to the t-th group of machine tool postures with a tool position vector corresponding to the t + 1-th group of machine tool postures:
representing the sum of the tool position vectors associated with the poses of the machine tool of the connected t-th groupThe m-th differential tool attitude of (2) is a vector consisting of tool position vectors corresponding to:
wherein t represents the number of machine tool poses, t =1,2,3 \8230, N, N represents the total number of machine tool poses, m represents the total number of machine tool posesThe serial number of the corresponding differential machine tool attitude, m =1,2,3, \8230;, K, K representsThe total number of differential machine tool poses of (1);
and finally, calculating the accumulated nonlinear error in the whole processing process by adopting the following formula:
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