A forward design method of a five-axis machine tool rotary shaft configuration

Abstract

The application discloses a kind of positive design method of five-axis machine tool rotary shaft configuration, comprising: the numerical control tool path of the machining part to be analyzed is obtained to obtain tool shaft posture vector sequence;For each adjacent posture vector, calculate the base element motion axis and motion weight to realize ideal single-axis rotation therebetween, and form weighted base element motion axis distribution on unit sphere;Structural tensor is constructed and eigenvalue decomposition is carried out, and the distribution type is distinguished by direction concentration index and the direction of the first rotary shaft is determined;The base element motion axis is transformed to the second rotary shaft zero position coordinate system by accompanying inverse mapping and residual weighting is carried out, and the second rotary shaft zero position direction is determined by constructing secondary structural tensor;The angle between the shafts is calculated and the configuration parameters are output after reachability check. By using the application, the whole process calculation complexity is O (N), which can make the direction speed gain of the whole process far away from zero, and reduce the risk of approaching kinematic singularity.

Description

Technical Field

[0001] This invention relates to the field of five-axis CNC machine tool configuration design technology, and in particular to a forward design method for the rotary axis configuration of a five-axis machine tool. Background Technology

[0002] Five-axis machine tools, as core industrial machines for machining complex curved surface parts such as aero-engine blades, marine propellers, and integral impellers, are the foundation of high-end equipment manufacturing. Five-axis machine tools achieve arbitrary tool orientation relative to the workpiece through the linkage of three translational axes and two rotary axes. The directions of the two rotary axes and their inter-axis angles (collectively referred to as rotary axis configuration) directly determine the nonlinear errors, kinematic singularities, and dynamic performance of the rotary axes during machining.

[0003] In traditional five-axis machine tool design, rotary axes are typically orthogonally arranged (with an inter-axis angle of 90°) and designed according to standardized principles. However, for a given complex surface machining task, the standardized rotary axis direction often mismatches with the actual rotary motion direction required by the toolpath. When the required change direction of the tool axis posture tends to be perpendicular to the machine tool's rotary axis direction, the machine tool approaches a kinematically singular configuration. To achieve the required posture change, the rotary axis must move at extremely high speeds and accelerations, causing not only severe dynamic shocks but also amplifying nonlinear errors due to the noncommutativity of the finite rotation of the two rotary axes, resulting in significant redundancy in the rotary axis stroke. These three types of problems—nonlinear errors, kinematic singularities, and deterioration of rotary axis dynamics—are usually addressed separately in existing research, lacking a unified design standard.

[0004] In terms of configuration design, current practices mainly rely on design experience or select one from several typical configurations after kinematic calibration. There is a lack of means to directly determine the direction of the rotation axis and the inter-axis angle from the machining task. The few existing methods that determine the configuration based on the toolpath rely on the distribution of the tool axis posture itself on the spherical surface, that is, based on the criterion of "whether the posture can be covered and reached". They do not characterize the direction and intensity requirements of the rotational motion during the machining process, and it is difficult to distinguish machining tasks with the same posture set but completely different motion processes. Moreover, most of them give a feasible range of inter-axis angles for specific configurations, without dealing with the coupling caused by the rotation of the second rotation axis with the first rotation axis when two rotation axes are arranged in series, and without giving a definite optimal configuration parameter. It is still necessary to manually select points within the range.

[0005] In summary, the traditional five-axis machine tool rotary axis configuration design has the following shortcomings: (1) The three types of problems, namely nonlinear error, kinematic singularity and deterioration of rotary shaft dynamics, are dealt with separately, and there is a lack of a unified design criterion to reveal their common root cause; the generalized orthogonal configuration is mismatched with the specific machining task, and the rotary shaft is prone to singularity during machining, which causes a sharp increase in rotational speed and acceleration and an increase in nonlinear error; (2) There is a lack of a method to directly determine the direction of the rotation axis and the angle between the axes from the machining toolpath. The configuration design relies on experience or checks each candidate configuration one by one, which is inefficient and difficult to guarantee the optimal. (3) Existing methods for defining the configuration based on the toolpath are based on the distribution of the tool axis posture itself. They do not characterize the rotary motion requirements of the machining process, cannot distinguish machining tasks with the same posture set but different motion processes, and do not handle the coupling when two rotary axes are arranged in series. (4) The existing method outputs the feasible range of interaxial angles, but manual point selection is still required, and no definite optimal configuration parameters are given. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention provides a forward design method for the rotary axis configuration of a five-axis machine tool. Using the ideal rotary axis of the toolpath adjacent posture pair as the design input, it can deterministically synthesize the directions and inter-axis angles of the two rotary axes from the machining task, and keep the directional velocity gain far from zero throughout the machining process.

[0007] A forward design method for a five-axis machine tool rotary axis configuration, wherein the five-axis machine tool includes three translational axes and two rotary axes arranged in series, and the instantaneous axial direction of the second rotary axis changes with the rotation of the first rotary axis; the method includes the following steps: (1) Obtain and parse the CNC machining toolpath file of the part to be machined to obtain... Each tool position data point contains tool position coordinates and a unit tool axis posture vector. , ; (2) Tool axis attitude vector for each pair of adjacent tool positions and Calculate the elementary motion axis of the ideal single-axis rotation during this period. and the corresponding motion weights A weighted distribution of the motion axes of the primitives is formed on a unit sphere; (3) Construct the structure tensor from all the motion axes of the primitives and their motion weights. Then, feature decomposition is performed to calculate the directional concentration index. ; (4) Using the directional concentration index Determine the type of weighted element motion axis distribution and determine the direction of the first rotation axis. ; (5) According to the tool axis attitude vector of each tool position point and the direction of the first rotation axis Based on the geometric relationships, the motion axes of each elementary element are transformed to the zero coordinate system of the second rotation axis, residual weighting is performed, and a quadratic structure tensor is constructed. Calculate its directional concentration index Determine the zero position direction of the second rotating shaft. ; (6) Calculate the interaxial angles After reachability verification, the first rotation axis direction is output. Second rotating shaft zero position direction and interaxial angle , which serves as the layout configuration parameter for the two rotary axes of the five-axis machine tool.

[0008] Furthermore, the two tandemly arranged rotary shafts can be implemented in any of the following ways: (a) both the first and second rotary shafts are located on the motion chain carrying the workpiece, forming a double-rotor-type rotary structure, with the second rotary shaft bearing on the first rotary shaft and carrying the workpiece to be processed; (b) both the first and second rotary shafts are located on the motion chain carrying the cutting tool, forming a double-swing-head rotary structure, with the second rotary shaft bearing on the first rotary shaft and carrying the tool spindle; (c) the first rotary shaft is located on the motion chain carrying the workpiece, and the second rotary shaft is located on the motion chain carrying the cutting tool, or vice versa, forming a rotary-swing composite structure; in any of the above implementations, the instantaneous axial direction of the second rotary shaft changes with the rotation of the first rotary shaft according to... Changes, among which To bypass The corner is The rotation matrix.

[0009] The specific process of step (2) is as follows: Tool axis attitude vector for each pair of adjacent tool positions and The computation is implemented by Transformed by single-axis rotation to The ideal rotation axis direction serves as the basic motion axis. and the spatial rotation angle between two adjacent attitude vectors. The motion weights of this basic element's motion axis; From the motion axes of all basic elements and its motion weights The weighted primitive motion axis distribution representing the rotary motion requirements of the processing task is obtained on a unit sphere.

[0010] The specific process of step (3) is as follows: Construct a third-order real symmetric structure tensor from all primitive motion axes and their motion weights. ,right Perform eigenvalue decomposition to obtain eigenvalues ​​arranged in descending order. , , and its corresponding unit eigenvector , , ; Calculate the directional concentration index .

[0011] The structural tensor quadratic form Characterizing the direction of a single candidate rotation axis The weighted sum of squares of the projections of all elementary motions, i.e., the weighted velocity transmission capacity in the direction of that single axis; after the two rotary axes of the machine tool are arranged, along the first... The directional velocity gain of each element's motion direction is defined as... , , representing the square of the angular velocity output by the machine tool along this direction under a unit joint angular velocity input, where For the direction of the first rotation axis of the machine tool, The instantaneous direction of the second rotation axis at the tool position point; the weighted sum of the velocity gains in the above direction along all elementary motion directions equals the motion weights. ;when At that time, the machine tool is in a kinematically singular configuration in the direction of motion of the basic element.

[0012] Furthermore, the specific process of step (4) is as follows: Directional Concentration Index With preset threshold Compare; when When determining that the weighted primitive motion axis distribution has a unique optimal direction, the direction of the first rotation axis is taken. ; when At that time, it was determined that the weighted primitive motion axis distribution exhibited a banded distribution and that a near-equivalent optimal family of directions existed. Using the initial values, iteratively update the auxiliary weights according to the degree of deviation between the current rotation axis direction and the motion axes of each primitive; then re-solve for the maximum eigenvector of the reweighted structure tensor, iterating until convergence to obtain the first rotation axis direction. .

[0013] The preset threshold according to Confirmed, among which To maintain the preset performance level, ;when When, the second eigenvalue Greater than The first eigenvalue of times That is, the difference between the weighted velocity transfer capability of the second characteristic direction and that of the principal characteristic direction is... Within this range, it is determined that a near-equivalent optimal family of directions exists; the aforementioned The preferred value is 0.95, corresponding to .

[0014] when At that time, the direction of the first rotation axis is obtained. The iterative process is as follows: (4.1) Set initial values ​​for iteration Iteration number ; (4.2) Update the auxiliary weights of each element's motion axis using the following formula: ,in To prevent the regularity constant with a denominator of zero, take ; (4.3) Constructing the reweighted structural tensor Take the unit eigenvector corresponding to its largest eigenvalue as ; (4.4) If the weighted sinusoidal objective function of two consecutive iterations The change is less than the convergence threshold, or the iteration number If the preset maximum number of iterations is reached, then let And end the iteration; otherwise, let And return to step (4.2). Wherein, the convergence threshold is taken as... The maximum number of iterations is 50.

[0015] In step (5), the tool axis attitude vector at each tool position point is aligned with the direction of the first rotation axis. The geometric relationships are used to transform the motion axes of each element to the zero coordinate system of the second rotation axis, specifically including: According to the tool axis attitude vector at each tool position point and the direction of the first rotation axis The geometric relationship is used to pre-calculate the rotation angle of the first rotation axis at each tool point in a closed loop. ;in, To bypass Align the preset initial reference attitude vector to the angle required by the tool axis attitude vector at the tool position point; The motion axes of each element are rotated around Reverse rotation Transform to the zero coordinate system of the second rotation axis to obtain the basic motion axes in the zero coordinate system. .

[0016] The rotation angle of the first rotation axis at each tool point Pre-calculation using the following closed-form formula: ; in, For the first The tool axis attitude vector at each tool position point The preset initial reference attitude vector, The direction of the first rotation axis, The function is the arctangent function in the four quadrants; the motion axis of each element is rotated around... Reverse rotation Transform to the second rotation axis zero coordinate system to apply a rotational force around the element's motion axis. The corner is The rotational transformation, i.e., the accompanying inverse mapping , This represents a rotation matrix about a given axis and a rotation angle.

[0017] In step (5), residual weighting is performed and a quadratic structure tensor is constructed. Determine the zero position direction of the second rotating shaft. Specifically, it includes: Using residual weights Weight the motion axes of the transformed primitives, where For focusing parameters, and Thus, a quadratic structure tensor is constructed. ; For the secondary structure tensor Perform eigenvalue decomposition to obtain the top two eigenvalues ​​in descending order. , and its corresponding eigenvectors; calculate its directional concentration index. and with preset threshold Compare; when At that time, take the zero position direction of the second rotating shaft. For the quadratic structure tensor The largest eigenvector; when At that time, the re-weighted quadratic structure tensor is re-solved. The largest eigenvector is iterated until convergence to obtain the zero-position direction of the second rotation axis. .

[0018] Specifically, when At that time, the iterative process described in steps (4.1) to (4.4) is applied to... Perform reweighted refinement, where the initial value for iteration is taken as... The largest eigenvector, and the basic motion axis in the iterative equation. Replace with zero coordinate system Motion weights Replace with residual weights .

[0019] In step (6), the specific process of reachability verification is as follows: Calculate interaxial angles According to the direction of the first rotation axis Second rotating shaft zero position direction and interaxial angle The determined two-axis cascaded kinematic chain is used to perform inverse kinematic reachability checks on all tool positions; if any tool positions are unreachable, the zero-position direction of the second axis is adjusted. Towards the deviation from the first axis of rotation The direction is gradually deflected according to the preset angle step size, so that the inter-axis angle After increasing the value accordingly, re-perform the reachability check until all tool positions are reachable, and then take the minimum adjustment amount that meets the reachability condition.

[0020] Preferably, the preset angle step size is taken as follows: In the inverse kinematics reachability verification, if the inverse kinematics of a certain tool position point has no real solution, or if the obtained rotation angle of the rotary axis exceeds the travel limit of the machine tool rotary axis, the tool position point is determined to be unreachable. Furthermore, while performing the reachability verification, the interference between the tool and the workpiece and the fixture is verified at the tool position point. If interference exists, the tool position point is also determined to be unreachable.

[0021] In step (6), the interaxial angle With tolerance range The output is in the form of, where, It is the tolerance half-width.

[0022] Tolerance half-width Select the zero position direction of the candidate second rotation axis Second and third eigenvectors Azimuth in the plane The near-dominant half-angle at that location, i.e. ,in To maintain a level of performance The corresponding near-optimal region half-angle; the near-optimal region half-angle Calculate using the closed-form formula: ; in, The candidate rotation axis direction is in the second and third eigenvectors Azimuth in the plane (in) Direction is ,Towards (Direction measurement) To maintain the aforementioned performance level; where , , and , All are taken from the quadratic structure tensor The eigenvalues ​​and eigenvectors; when the value inside the square root in the above equation is greater than 1. Pick .

[0023] Preferably, the design method of the present invention further includes a configuration verification and selection step: calculating the projection efficiency and directional velocity gain of the synthetic configuration determined by the configuration parameters output in step (6) and several preset standard configurations respectively, wherein the projection efficiency is... , The first rotation axis direction of the standard configuration; the minimum value of the velocity gain along the toolpath in the direction mentioned above. A value greater than zero is used as a criterion for kinematic singularity, based on the aforementioned projection efficiency. The average value of the directional velocity gain along the toolpath The efficiency of speed transmission is used as the basis for ranking, and the best option is selected for machine tool manufacturing.

[0024] Preferably, it further includes a part family configuration design step: for the part family... A family of parts composed of different parts is constructed by constructing the structural tensor of each part according to steps (1) to (3). , ,according to Weighted aggregation yields the component family structure tensor, where For the first The weighting coefficients of each component; the tensor of the component family structure. Perform feature decomposition in step (3) and steps (4) to (6) to obtain common rotary shaft configuration parameters applicable to the entire part family.

[0025] Compared with the prior art, the present invention has the following beneficial effects: First, this invention reveals that the directional mismatch between the physical rotation axis and the toolpath element motion axis is the common kinematic root of three types of problems in machining: nonlinear error, kinematic singularity, and deterioration of rotation axis dynamics. It uses directional velocity gain as a unified design criterion to align the designed physical rotation axis with the element motion axis of the machining task as much as possible. When the physical axis and the element motion axis are aligned, the coupling error caused by the noncommutativity of the finite rotation of the two rotation axes can be reduced simultaneously (suppressing nonlinear error), the directional velocity gain can be moved away from zero (avoiding singularity), and the joint displacement required to achieve the required posture change can be reduced (improving the kinematic and dynamic burden of the rotation axis). Thus, it improves the three types of performance with a single criterion, overcoming the shortcomings mentioned in the background technology (1), that is, the existing technology treats the three separately and it is difficult to take all three into account. This is the technical effect of this invention compared with the existing toolpath-based configuration method that is based on the distribution of the tool axis posture set itself and only gives the feasible interval of the inter-axis angle.

[0026] Second, this invention starts from the rotary motion requirements of the machining toolpath, and uses the closed-form synthesis of the eigenvalue decomposition of the structural tensor to determine the rotation axis direction and inter-axis angle (point solution). The computational complexity of the entire process is [missing information]. This eliminates the need for simulation verification of each candidate configuration, overcoming the shortcomings of the background technology (2) and (4).

[0027] Third, this invention uses the primitive motion axes of adjacent posture pairs to characterize the first-order rotary motion requirements of the machining process, which can distinguish machining tasks with the same posture set but different motion processes; and by using the accompanying inverse mapping to handle the coupling of the second rotary axis direction with the rotation of the first rotary axis when the two rotary axes are arranged in series, this method is applicable to various configurations such as double turntables, double swing heads, and rotary-swing composites, overcoming the shortcomings of the prior art (3). This accompanying inverse mapping transforms the design of the second rotary axis rotating with the first rotary axis into a definite point solution in the zero coordinate system, which is also the technical effect of this invention compared to the above-mentioned existing methods.

[0028] Fourth, this invention, under reachability verification, makes the velocity gain in the entire processing path direction as far away from zero as possible, and significantly improves the singular margin relative to the general reference configuration. The singular margin refers to the minimum velocity gain in the entire path direction. The greater the distance from zero, the further the machine tool's motion state is from the kinematic singular configuration (except for geometrically unavoidable singularities where the elementary motion axis is perpendicular to both rotation axes simultaneously, which cannot be eliminated by any configuration). It also reduces the joint angular velocity and angular acceleration (kinematic dynamic burden) required by the rotation axis to achieve the desired posture change. For machining tasks where the elementary motion axes are distributed in a strip, the direction concentration index is automatically diagnosed and iterative refinement is triggered to eliminate the arbitrariness of the optimal direction under the strip distribution. The inter-axis angle is output in the form of a tolerance zone, which is convenient for manufacturing and assembly. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 This is a flowchart of a forward design method for a five-axis machine tool rotary axis configuration according to the present invention.

[0031] Figure 2 This is a schematic diagram of the configuration of the series motion chain of two rotary axes of a five-axis machine tool, which is the subject of this invention.

[0032] Figure 3 This is a schematic diagram of the geometric structure of the motion axis of the basic element in this invention.

[0033] Figure 4 This is a schematic diagram comparing the two types of distribution patterns of the weighted element motion axis in this invention: a banded pattern and a concentrated pattern.

[0034] Figure 5 This is a schematic diagram comparing the energy distribution of the spectral solution (before refinement) under the banded distribution and the iterative refinement solution in this invention.

[0035] Figure 6 This is a schematic diagram illustrating the determination of the second rotation axis using inverse mapping and residual weighting in this invention.

[0036] Figure 7 This is a schematic diagram of the energy distribution of the main and secondary rotating shafts and the near-optimal domain boundary and standard configuration markings in this invention.

[0037] Figure 8 This is a comparison diagram of the directional velocity gain along the processing path between the synthetic configuration and the reference configuration in this embodiment of the invention.

[0038] Figure 9 This is a comparison diagram of the nonlinear error between the synthesized configuration and the reference configuration in the embodiments of the present invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] It should be noted that, unless otherwise specified, the features in the following embodiments and implementation methods can be combined with each other.

[0041] like Figure 1 As shown, a forward design method for the rotary axis configuration of a five-axis machine tool is proposed, according to... Figure 1 The steps shown can be synthesized from the CNC machining toolpath of the part to be machined in a forward direction, as follows: Figure 2 The directions of the two rotary axes of the five-axis machine tool shown , and interaxial angle Key configuration parameters, etc.

[0042] like Figure 2 As shown, the five-axis machine tool includes a bed 1 and translational axes arranged in three mutually perpendicular directions (i.e., axis, axis, (Axis), first rotating shaft 2 and second rotating shaft 3; the second rotating shaft 3 is arranged in series on the kinematic chain where the first rotating shaft 2 is located, when the first rotating shaft 2 rotates by an angle At that time, the instantaneous axial direction of the second rotating shaft 3 deflects accordingly. ,in, To bypass The corner is The rotation matrix; the direction of the first rotation axis is denoted as... The zero position direction of the second rotating shaft is denoted as The angle between the two axes of rotation is the inter-axis angle. .

[0043] The series arrangement of two rotary axes can be implemented in various ways, including but not limited to: a double-rotary-table rotary structure where both rotary axes are located on the kinematic chain carrying the workpiece (the second rotary axis carries the workpiece, as in this embodiment); a double-swing-head rotary structure where both rotary axes are located on the kinematic chain carrying the tool (the second rotary axis carries the tool spindle); and a rotary-swing composite structure where one rotary axis is located on the workpiece side and the other on the tool side. The configuration synthesis method of this invention is applicable to all of the above implementations; the difference between different implementations lies only in the specific kinematic model used for reachability verification, while the synthesis process for the rotary axis directions is exactly the same. This embodiment uses a double-rotary-table rotary structure as an example, with the tool 5 mounted on the spindle 4.

[0044] In this invention, all vectors are three-dimensional column vectors, with superscripts... Indicates transpose. For vector cross product, The magnitude of the vector. Represents the result of the vector outer product matrix.

[0045] The present invention specifically includes the following steps: Step (1): Obtain and parse the toolpath.

[0046] The CNC machining toolpath for the part to be machined is generated using computer-aided manufacturing (CAM) software. The toolpath consists of multiple tool points, each represented as follows: This includes two parts of information: the spatial coordinates of the tool tip in the machine tool coordinate system. and the tool's attitude vector Attitude vector The direction of the tool axis is represented by a unit vector, satisfying the following conditions: Extract the attitude portion of each tool position point in the toolpath to form a tool axis attitude vector sequence. , This represents the number of toolpath points. The toolpath file can be a CLS format text file or other file formats that record the coordinates and orientation of toolpath points.

[0047] Step (2): Extract the weighted primitive motion axis distribution.

[0048] Tool axis attitude vector for each pair of adjacent tool positions and Calculate the motion axes and motion weights of the primitives (the geometric construction of the motion axes of the primitives is as follows). Figure 3 (as shown) ; ; In the formula, the basic motion axis It is to achieve by arrive The unique unit axis of rotation around which the ideal geodesic (single-axis) rotation revolves, i.e., the direction of the normalized cross product of the two attitude vectors; motion weights. The spatial rotation angle between two adjacent attitude vectors represents the amplitude of the elementary motion segment. For elements containing... Toolpaths at each tool position point were extracted. Each of the elementary motion axes is a unit sphere. A point on the graph constitutes a weighted distribution of primitive motion axes (i.e., primitive motion manifold) that characterizes the rotational motion requirements of the processing task.

[0049] It should be noted that, by As a premise; in actual toolpaths, when the attitude vectors of adjacent tool axes are approximately parallel (such as rapid positioning segments or continuous segments with the same attitude), the modulus of the cross product is... tending to zero Undefined. Regarding this, when Less than the preset threshold (take) When the segment is determined to be a degenerate segment, its basic motion axis is set to follow the basic motion axis direction of the previous effective segment (any fixed direction is taken when it is the first segment). Simultaneously, due to the motion weight of this segment... Its contribution to the subsequent structural tensor is naturally suppressed, and it does not affect the configuration synthesis result.

[0050] Step (3): Construct the structural tensor and perform eigenvalue decomposition.

[0051] Construct a third-order real-symmetric structure tensor from all the primitive motion axes and their motion weights: ; right Perform eigenvalue decomposition to obtain eigenvalues ​​arranged in descending order. and the corresponding unit eigenvector , , Any candidate rotation axis direction quadratic form It equals the weighted sum of squares of the projections of the rotation axis along all the motion axes of the elementary elements, representing the arrangement of the rotation axis in the direction. The ability to transfer weighted velocity across all elementary motions; therefore, enabling The direction with the largest value is the optimal principal axis of rotation. By the extremum property (Rayleigh quotient property) of the quadratic form of a real symmetric matrix, this direction is the direction with the largest eigenvalue. corresponding feature vector .

[0052] Regarding directional velocity gain: After the two rotary axes of the machine tool are arranged, along any elementary element's motion direction... Directional velocity gain is defined as ,in For the return of Jacobi; unfolded , That is, the sum of the squares of the projections of the two physical axes of rotation onto the motion direction of the elementary element. Directional velocity gain characterizes the square of the angular velocity output by the machine tool along that direction under a unit joint angular velocity input: The larger the value, the smaller the joint velocity required to achieve an attitude change in that direction; when At that time, both rotating shafts were in contact with If the joint is perpendicular, the machine tool cannot generate an output angular velocity in that direction, meaning it is in a kinematically singular configuration. In this case, the joint velocity will follow... tending towards infinity (in the formula) The joint angular velocity vectors of the two rotating axes. To achieve the angular velocity required for attitude change in this direction, the nonlinear error and dynamic impact are amplified. Therefore, maximizing the weighted directional velocity gain across the entire path (i.e., maximizing...) This invention can simultaneously suppress nonlinear errors, avoid kinematic singularities, and improve the dynamic performance of the rotating shaft—this is the theoretical basis for classifying three types of problems into the same kinematic root and solving them with a single criterion.

[0053] Step (4): Manifold type diagnosis and condition refinement determine the first rotation axis (comparison of the two distribution patterns of the weighted elementary motion axis, namely the banded and concentrated types, such as...). Figure 4 (As shown).

[0054] Calculate the directional concentration index: ; Will With preset threshold Compare, Preferred Right now ; when At that time, the distribution of the weighted primitive motion axis is determined along The directions are concentrated, and there exists a unique optimal direction. Therefore, the direction of the first rotation axis is directly taken. ; when hour, and near( This indicates that the axis of motion of the elementary element is in the direction of... , Zhang Cheng's large circular band is approximately uniformly distributed (band-shaped distribution). In this case, the largest eigenvector is not unique within the band and can be directly taken. This will yield arbitrary solutions; therefore, with Using the initial values, refine them using an iterative reweighting process: ; in To prevent the regularity constant with a denominator of zero, take ; Each iteration constructs a reweighted structure tensor And take its largest eigenvector as Repeat until the weighted sinusoidal objective function is applied. (i.e., direction) The change in the weighted sinusoidal deviation of all elementary motion axes is less than the convergence threshold. If the number of iterations reaches 50, output the direction of the first rotation axis. Each step of this iterative reweighting process is still... Eigenvalue decomposition of the structure tensor has low complexity, maintaining near-linear complexity throughout the process. (Under banded distribution) Comparison of energy distributions of spectral solutions and iterative refinement solutions, for example Figure 5 As shown.

[0055] Step (5): Determine the second axis of rotation by combining the inverse mapping and residual weighting (e.g., Figure 6 (As shown).

[0056] Since the second rotating shaft rotates with the first rotating shaft, its instantaneous axial direction changes with the rotation angle of the first rotating shaft. The deflection design variable is the zero-position direction of the second rotation axis. The zero-position coordinate system of the second rotation axis is the same as the rotation angle of the first rotation axis. The coordinate system corresponding to the initial configuration of the machine tool has its origin aligned with the machine tool coordinate system, and its coordinate axes are set to... The fixed direction of the second rotary shaft unit. To decouple the design of the second rotary shaft from the motion state of the first rotary shaft, the rotation angle of the first rotary shaft at each tool position point is first pre-calculated using the following closed-form formula: ; In the formula, The preset initial reference attitude vector is (take the tool axis attitude vector at the first tool position point of the toolpath, or take the weighted average direction of all attitude vectors). That's around Reference posture Align to current pose The required first rotation angle of the axis of rotation. Then, rotate each element's motion axis around... Reverse rotation Transform to the second rotation axis zero coordinate system (accompanied by inverse mapping): ; in, To bypass The corner is - The rotation matrix; around the unit vector The corner is The rotation matrix can be obtained according to the Rodriguez formula. Calculation, where It is a third-order identity matrix. for The cross product of the antisymmetric matrix, the positive direction of the rotation is based on the direction of the rotation. The right-hand rule is used to determine this. Then, the transformed primitive motion axes are weighted using residual weights: ; in For focusing parameters, and Preferred ; As the axis of motion of the basic element With the first rotating shaft The angle between the residual weights. The role of the residual weights is to: Parallel elementary motion (the first rotating axis can already handle this efficiently) because And suppressed, with The vertical residual motion (which the first rotation axis cannot achieve) is highlighted, thus allowing the second rotation axis to specifically handle the residual motion that the first rotation axis cannot perform, achieving a deterministic division of labor between the two axes. A quadratic structure tensor is constructed from the residual-weighted primitive motion axes: ; right Perform eigenvalue decomposition and take the largest eigenvector as the zero-position direction of the second rotation axis. Furthermore, regarding Similarly, calculate And determine whether to refine it according to the criterion in step (4). The energy distribution of the main and secondary rotation axes and the near-optimal domain boundary of the synthetic configuration of this invention and each standard configuration are as follows: Figure 7 As shown.

[0057] Step (6): Calculation of inter-axis angle and accessibility verification.

[0058] Calculate the interaxial angle: ; according to , , A defined two-axis cascaded kinematic chain is used to establish forward and inverse kinematic models corresponding to specific configurations (double rotary table / double swivel head / compound). The inverse kinematic reachability of all tool positions is verified: if the inverse kinematics of a tool position has no real solution, or the obtained rotary axis rotation angle exceeds the travel limit, or there is interference between the tool and the workpiece / fixture, that tool position is determined to be unreachable. If an unreachable tool position exists, the zero-position direction of the second rotary axis is adjusted. Towards the deviation from the first axis of rotation Direction, according to preset angle step size (take Gradually deflect, making the interaxial angle After increasing the value accordingly, the reachability check is performed again until all tool points are reachable. The minimum adjustment amount that satisfies the reachability condition is taken to minimize the disruption to the optimality of the primary and secondary axis spectra.

[0059] Step (7): Output configuration parameters.

[0060] Output the direction of the first rotation axis Second rotating shaft zero position direction and interaxial angle As a layout parameter for the two rotating shafts. Furthermore, the inter-shaft angle can be determined according to a tolerance range. Output in format, tolerance half-width Take the zero position direction of the second rotating shaft exist Azimuth in the plane The near-dominant half-angle at that location, i.e. ( See the following formula, in which , , and , Take the quadratic structure tensor (Eigenvalues ​​and eigenvectors) ; Based on the aforementioned configuration parameters, the layout design and machine tool manufacturing of the two rotary axis units are carried out: according to , , Determine the spatial arrangement and structural component interfaces of the two rotating axes. The inter-axis angle is given an assembly tolerance according to the tolerance zone. After assembly, the deviation of the rotating axis direction is checked using standard testing methods.

[0061] Example 1 (Propeller blades, strip-shaped distribution, triggered iterative refinement). Taking the five-axis machining toolpath (using a double rotary table structure) of a marine propeller blade as an example, the toolpath includes... Each knife point. Construct the structural tensor and perform eigenvalue decomposition according to steps (1) to (3), and obtain , , Calculate according to step (4). The distribution is determined to be banded, triggering iterative refinement to obtain the direction of the first rotation axis. Comparing the largest eigenvector The deflection is 23.44°, and its weighted velocity transfers energy. The decrease is only 0.10%, thus eliminating the directional arbitrariness under the banded distribution. Following step (5), through the adjoint inverse mapping and residual weighting ( ) Construction ,That Without triggering refinement, the zero-position direction of the second rotation axis is obtained. Calculate according to step (6). All tool positions are accessible without adjustment. The resulting synthetic configuration has the minimum directional velocity gain across the entire path. (Greater than zero, no singularity), the average directional velocity gain is based on the CA reference configuration (i.e., the first rotation axis along the machine tool). towards The second rotary axis along the machine tool towards The RMS attitude nonlinearity error of the commonly used orthogonal double rotary table configuration (for the axis) is increased from 0.5426 to 0.8496; compared with the commonly used CA reference configuration, the RMS attitude nonlinearity error throughout the toolpath is reduced by approximately 96.5%. For comparison, the commonly used CA configuration on this toolpath... A value of zero (indicating a singularity, confirmed by calculation) indicates that the synthesized configuration of this invention possesses a singularity margin for this task that the CA configuration lacks. A comparison of the directional velocity gain along the machining path between the synthesized configuration and the reference configuration is provided. Figure 8 As shown, the nonlinear error pair is as follows: Figure 9 As shown.

[0062] Example 2 (Cavity side milling, non-strip distribution, direct extraction) (Do not trigger refinement). Taking the side milling toolpath of a certain cavity part as an example, the toolpath includes... Each blade location. The eigenvalues ​​are obtained through eigendecomposition in steps (1) to (3). , , Calculate according to step (4). If a unique optimal direction exists, the direction of the first rotation axis is directly selected. (relatively A deflection of 0.00°, i.e., no iterative refinement is triggered (as opposed to the strip branch in Example 1). The second rotation axis zero-position direction is obtained according to step (5). (That (Does not trigger refinement). Calculate according to step (6). All tool positions are reachable. The minimum velocity gain of the resulting synthetic configuration along the entire path is... (Greater than zero, no singularity), the average directional velocity gain is increased from 0.3551 in the CA baseline configuration to 0.8180; compared with the CA baseline configuration, the RMS attitude nonlinearity error is reduced by about 96.6% throughout the entire range.

[0063] Examples 1 and 2 demonstrate that the method of the present invention uses the directional concentration index Automatically identify the distribution type and select the solution branch—banded distribution (Example 1, Triggering iterative refinement to eliminate directional arbitrariness, non-banded distribution (Example 2, ) Spectral analysis is used directly. For machining tasks with highly concentrated attitude changes (such as deep hole machining with twist drills), actual measurements... The directional concentration threshold can reach 0.99. The elementary motion manifold degenerates into a near-single-point distribution. At this point, the first rotation axis can handle almost all rotational motion, and the contribution of the second rotation axis to velocity transmission becomes secondary. Its zero-position direction is mainly determined by reachability constraints. The method of this invention still provides definite configuration parameters in this extreme case. It has been verified that the directional concentration threshold... exist When taking values ​​within the range, the above branch determination is consistent with the obtained first rotation axis direction; focusing parameters exist When the value is taken within the range, the change in the direction of the second rotation axis falls within its near-optimal range, indicating that this method is not sensitive to the value of the above-mentioned preset parameters.

[0064] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A forward design method for the rotary axis configuration of a five-axis machine tool, characterized in that, Includes the following steps: (1) Obtain and parse the CNC machining toolpath file of the part to be machined to obtain... Each tool position data point contains tool position coordinates and a unit tool axis posture vector. , ; (2) Tool axis attitude vector for each pair of adjacent tool positions and Calculate the elementary motion axis of the ideal single-axis rotation during this period. and the corresponding motion weights A weighted distribution of the motion axes of the primitives is formed on a unit sphere; (3) Construct the structure tensor from all the motion axes of the primitives and their motion weights. Then, feature decomposition is performed to calculate the directional concentration index. ; (4) Using the directional concentration index Determine the type of weighted element motion axis distribution and determine the direction of the first rotation axis. ; (5) According to the tool axis attitude vector of each tool position point and the direction of the first rotation axis Based on the geometric relationships, the motion axes of each elementary element are transformed to the zero coordinate system of the second rotation axis, residual weighting is performed, and a quadratic structure tensor is constructed. Calculate its directional concentration index Determine the zero position direction of the second rotating shaft. ; (6) Calculate the interaxial angles After reachability verification, the first rotation axis direction is output. Second rotating shaft zero position direction and interaxial angle , which serves as the layout configuration parameter for the two rotary axes of the five-axis machine tool.

2. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 1, characterized in that, The specific process of step (2) is as follows: Tool axis attitude vector for each pair of adjacent tool positions and The computation is implemented by Transformed by single-axis rotation to The ideal rotation axis direction serves as the basic motion axis. and the spatial rotation angle between two adjacent attitude vectors. The motion weights of this basic element's motion axis; From the motion axes of all basic elements and its motion weights The weighted primitive motion axis distribution representing the rotary motion requirements of the processing task is obtained on a unit sphere.

3. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 1, characterized in that, The specific process of step (3) is as follows: Construct a third-order real symmetric structure tensor from all primitive motion axes and their motion weights. ,right Perform eigenvalue decomposition to obtain eigenvalues ​​arranged in descending order. , , and its corresponding unit eigenvector , , ; Calculate the directional concentration index .

4. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 3, characterized in that, The specific process of step (4) is as follows: Directional Concentration Index With preset threshold Compare; when When determining that the weighted primitive motion axis distribution has a unique optimal direction, the direction of the first rotation axis is taken. ; when At that time, it was determined that the weighted primitive motion axis distribution exhibited a banded distribution and that a near-equivalent optimal family of directions existed. The initial values ​​are used to iteratively update the auxiliary weights according to the degree of deviation between the current rotation axis direction and the motion axis of each element; Then, recalculate the maximum eigenvector of the reweighted structure tensor, iterating until convergence, to obtain the direction of the first rotation axis. .

5. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 4, characterized in that, when At that time, the direction of the first rotation axis is obtained. The iterative process is as follows: (4.1) Set initial values ​​for iteration Iteration number ; (4.2) Update the auxiliary weights of each element's motion axis using the following formula: ,in To prevent the regularity constant with a denominator of zero, take ; (4.3) Constructing the reweighted structural tensor Take the unit eigenvector corresponding to its largest eigenvalue as ; (4.4) If the weighted sinusoidal objective function of two consecutive iterations The change is less than the convergence threshold, or the iteration number If the preset maximum number of iterations is reached, then let And end the iteration; otherwise, let Then return to step (4.2).

6. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 1, characterized in that, In step (5), the tool axis attitude vector at each tool position point is aligned with the direction of the first rotation axis. The geometric relationships are used to transform the motion axes of each element to the zero coordinate system of the second rotation axis, specifically including: According to the tool axis attitude vector at each tool position point and the direction of the first rotation axis The geometric relationship is used to pre-calculate the rotation angle of the first rotation axis at each tool point in a closed loop. ;in, To bypass Align the preset initial reference attitude vector to the angle required by the tool axis attitude vector at the tool position point; The motion axes of each element are rotated around Reverse rotation Transform to the zero coordinate system of the second rotation axis to obtain the basic motion axes in the zero coordinate system. .

7. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 6, characterized in that, In step (5), residual weighting is performed and a quadratic structure tensor is constructed. Determine the zero position direction of the second rotating shaft. Specifically, it includes: Using residual weights Weight the motion axes of the transformed primitives, where For focusing parameters, and Thus, a quadratic structure tensor is constructed. ; For the secondary structure tensor Perform eigenvalue decomposition to obtain the top two eigenvalues ​​in descending order. , and its corresponding eigenvectors; calculate its directional concentration index. and with preset threshold Compare; when At that time, take the zero position direction of the second rotating shaft. For the quadratic structure tensor The largest eigenvector; when At that time, the re-weighted quadratic structure tensor is re-solved. The largest eigenvector is iterated until convergence to obtain the zero-position direction of the second rotation axis. .

8. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 1, characterized in that, In step (6), the specific process of reachability verification is as follows: Calculate interaxial angles According to the direction of the first rotation axis Second rotating shaft zero position direction and interaxial angle The determined two-axis cascaded kinematic chain is used to perform inverse kinematic reachability checks on all tool positions; if any tool positions are unreachable, the zero-position direction of the second axis is adjusted. Towards the deviation from the first axis of rotation The direction is gradually deflected according to the preset angle step size, so that the inter-axis angle After increasing the value accordingly, re-perform the reachability check until all tool positions are reachable, and then take the minimum adjustment amount that meets the reachability condition.

9. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 8, characterized in that, The preset angle step size is taken .

10. The forward design method for the rotary axis configuration of a five-axis machine tool according to claim 1, characterized in that, In step (6), the interaxial angle With tolerance range The output is in the form of, where, It is the tolerance half-width.

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