CN109732401A - A kind of detection method about the unrelated error of five-axle number control machine tool double back rotating shaft position - Google Patents
A kind of detection method about the unrelated error of five-axle number control machine tool double back rotating shaft position Download PDFInfo
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Abstract
The invention discloses a kind of detection methods about the unrelated error of five-axle number control machine tool double back rotating shaft position, it is characterized in that, using ball bar as geometric error (PIGEs) unrelated with position in swinging axle B axle in experimental facilities identification five-axle number control machine tool and rotary shaft C axis, propose a kind of new measurement track, solve aggregate velocity when swinging axle B axle and the rotary shaft C axis coordinated movement of various economic factors and the asynchronism between ball bar acquisition speed, in conjunction with the homogeneous transform matrix in rigid body kinematics, establish simulation model, simulation model is combined with experiment, realize that the identification to five-axle number control machine tool double back shaft geometric error unrelated with position measures, the method of the present invention can rapidly and effectively detect five-axle number control machine tool double back shaft geometric error unrelated with position, precision is high, practicability is good.
Description
Technical field
The invention belongs to numerically-controlled machine tool detection technique fields, in particular to one kind is about five-axle number control machine tool dual AC power axle position
Set the detection method of unrelated error.
Technical background
Five-axle number control machine tool is widely used in the part of processing complex geometry feature, it, which has, improves surface smoothness, improves
The advantages that material remove rate.And under most processing conditions be all the double back shaft by lathe, make cutter relative to workpiece into
Change in orientation occurs when row processing, therefore there is greater flexibility than traditional three axis machining when generating cutter path.But
It is that swinging axle B axle and rotary shaft C axis introduce more geometric error elements in processing, part to be processed is caused flaw occur
And defect.
The constant error for studying swinging axle B axle and rotary shaft C axis is most important for control five-axle number control machine tool precision, mesh
Before there are ball bar, the measuring devices such as laser interferometer and R-test.Due to the features such as ball bar operation is convenient, and time-consuming is few
It is widely adopted.But how to solve aggregate velocity when swinging axle B axle and the rotary shaft C axis coordinated movement of various economic factors and ball bar capture speed
Asynchronism between degree accurately identifies the double back shaft geometric error unrelated with position using ball bar, therefore proposes that one kind can
It is particularly important in the method for quickly and simply detecting the unrelated error of five-axle number control machine tool double back rotating shaft position.
Summary of the invention
To solve the above problems, it is an object of the invention to propose it is a kind of about five-axle number control machine tool double back rotating shaft position without
The detection method for closing error, is examined using the geometric error unrelated with position of the ball bar to swinging axle B axle and rotary shaft C axis
It surveys.The invention can be easy and be accurately measured to error, and then greatlys improve processing quality.Specific measuring process is such as
Under:
Step 1, according to the specific structure and swinging axle B axle of five-axle number control machine tool and the position of rotary shaft C axis, build reality
Test measuring device.
Step 2, Binding experiment device propose 8 Xiang Yuwei of measurement five-axle number control machine tool swinging axle B axle and rotary shaft C axis
Set the track of unrelated geometric error.
Step 3, solve swinging axle B axle and aggregate velocity when the rotary shaft C axis coordinated movement of various economic factors and ball bar acquisition speed it
Between asynchronism
Step 4 carries out error identification in conjunction with lathe multi-body movement Systems Theory and homogeneous coordinate transformation.
According to five shafts numerical controlled machine bed structure and swinging axle B axle and rotary shaft C axis type in step 1, the survey of ball bar is determined
Measure position.Two balls of ball bar are magnetically attracted on two tool cups, the two tool cups are connected to main shaft and are located at workbench
Fixture on, comprising steps of
The coordinate system that step 1.1, setting measure, Z axis are overlapped with the original Z axis of lathe, measure the X-axis and Y-axis of coordinate system
It is parallel to the direction of motion of lathe X-axis and Y-axis.
Step 1.2, rotary shaft C axis tool cup are mounted on the fixture at the top of turntable, and the XOY plane for measuring coordinate system exists
It is lifted on turntable, sets the size of the distance between swinging axle B axle and origin O-XYZ as 400mm, incited somebody to action using touch probe
The center of spindle tools cup to swinging axle B axle is adjusted to 400mm, while the Workpiece tool cup being located on turntable is apart from rotary shaft
C axis center 400mm, ball bar are extended using extension bar, its nominal length is converted to 400mm, and to experimental tool into
Row calibration.
Corresponding program is utilized in step 2, the swinging axle B axle and rotary shaft C axis for controlling five-axle number control machine tool link,
Geometric error unrelated with position of double back shaft of five-axle number control machine tool is measured during this, comprising steps of
It is aligned the axis of ball bar with the Y-axis of O-XYZ in step 2.1, measuring route, one end setting of ball bar exists
The origin of O-XYZ, the other end are arranged at the position 400mm apart from Y-axis.Swinging axle B axle and rotary shaft C axis are rotated from 0 ° respectively
To -90 ° and 90 ° to 0 °.
The distance between two tool cups are not constant in step 2.2, main shaft and turntable, will lead to ball bar from magnetic
Fall down on property centre mount, thus the coordinated movement of various economic factors of swinging axle B axle and rotary shaft C axis should ensure that the point of the P in Fig. 3 and Q point away from
From being held constant at 400mm.
P point in Fig. 3 is projected to XOY plane by step 2.3, Fig. 4, to obtain the rotation of swinging axle B axle and rotary shaft C axis
Relationship between angle:
According to pythagoras of Samos theorem:
In XOY plane according to cosine law:
By measuring device RB=RC=LDBB=400mm, formula (1) and formula (2), the available pass rotated between angle
System:
Solved in step 3 swinging axle B axle and aggregate velocity when the rotary shaft C axis coordinated movement of various economic factors and ball bar acquisition speed it
Between asynchronism.
Step 3.1, swinging axle B axle and rotary shaft C axis rotate to -90 ° and 90 ° from 0 ° respectively and rotate to 0 °, swinging axle B axle
It is rotated with constant speed, step-length is that the position of 0.1 ° of corresponding rotary shaft C shaft angle can provide are as follows:
And the angle position of swinging axle B axle and rotary shaft C axis is:
Step 3.2, each step-length of experiment measurement represent in Fig. 5, form semicircle track.
Step 3.3, Fig. 6 show adjacent step sizes be not it is equidistant, will lead to lathe along the fluctuation of the step-length of track
The problem of movement and ball bar asynchronous sampling, since the acquisition rate of ball bar is constant, thereby, it is ensured that movement is at the uniform velocity
It is also particularly significant, analysis also could be effective.
Step 3.4, track represents tool cup center in Fig. 6.Spindle tools cup is mounted on the main shaft of swinging axle B axle
On shell, therefore tool cup axis and tool cup are centrally formed one and half straight circular cones as shown in fig. 7, cone therefore can be obtained
The bottom radius of circle of parameter, cone isThe aperture of cone is 90 °, and the bus length of cone is 400mm.
Step 3.5, in order to ensure the distance between adjacent step sizes it is constant, cone is deployed on two-dimensional surface, such as Fig. 8
(a) shown in, if distance | | OO ' | | it is r,SchemingIt can also be obtained in expansion planeThe angle of spread can be obtained:
Step 3.6 is expressed as φ by the central angle of OB and BP ' encirclement, can provide are as follows:
Θ can be given by the central angle of OO ' and O ' P ' encirclement in step 3.7, Fig. 8 (c), in the bottom circle of cone
In, it can provide:
Step 3.8, wherein N is in Fig. 8 (c) | | OP ' | | midpoint, be based on triangle relation, following equation can be provided:
Step 3.9, therefore θBIt can be obtained based on equation 5-9 with the relationship of Θ:
As long as step 3.10, tool cup center are evenly distributed in Φ, so that it may realize uniform motion, be selected in centre
900 steps of equidistance are selected, formula equation 5-10 is substituted into, it is as shown in Figure 9 to form equally distributed motion profile.
In step 4, error measure model is established according to theory of multi body system and homogeneous coordinate transformation, although proposed
Method is to put english to carry out on turntable type five-axis machine tool in swinging axle, but can be applied to any have the five of similar topological structure
Axis lathe.In order to simplify modeling process, current multi-axis NC Machine Tools NC system can compensate for linear axis error, it is therefore assumed that all
The geometric error of compensation linear axes only considers the PIGE of rotary shaft before test.
Step 4.1, rotary shaft C axis PIGE according to ISO230-1, each rotary shaft has 4 PIGE, it is contemplated that the zero of CNC
Position compensation function can ignore an error of zero.4 PIGE are two linear position errors in XOY plane in X-axis and Y-axis
Component EXOCAnd EYOC, and two orientation error component E of X-axis and Y-axis are surrounded respectivelyAOCAnd EBOC.It can be based on IOS230-1
Obtain the like error composition of swinging axle B axle.
Step 4.2, the overall error that kinematic axis can be assessed by the sequence multiplication of basic homogeneous transform matrix.According to more bodies
Systems Theory, the eigentransformation matrix from workpiece coordinate system to reference frame can be given below:
Cutting tool branch similar with above-mentioned expression formula can provide:
Ideal transformation matrix from center cutter point to workpiece coordinate system can be given below:
It is influenced by PIGE in contacting, the practical posture of transition matrix indicates are as follows:
Wherein E is 4 × 4 rank unit matrixs, due to there are geometric error,Indicate given deviation matrix:
Then the real transform from cutting tool central point to workpiece can provide:
Wherein letter r, W, T and i indicate the reference frame in the kinematic chain of target lathe, workpiece coordinate system, skiver
Has the coordinate system of coordinate system and the i-th rigid body.DidealAnd DactualIt indicates ideal and actual homogeneous transform matrix, indicates from its left side
Transformation of the lower target coordinate system to one of its pre-super.Rot and Trans respectively describes rotation and translation in homogeneous transform matrix
From its pre-sub coordinate system to the conversion in one of its upper left corner.
The model use pseudoinverse technique proposed in step 4.3, Binding experiment measurement data and step 4 obtains five-shaft numerical control
Eight errors unrelated with geometric position of lathe swinging axle and rotary shaft.
Five-axle number control machine tool double back shaft Error Analysis unrelated with position, including 8 and geometry position are completed above
Set unrelated geometric error.
The identification and inspection of double back shaft geometric error unrelated with position in effective solution of the present invention five-axle number control machine tool
It surveys, propose effective detection path and solves the asynchronism of ball bar in the detection process, finally obtain measurement result.
Detailed description of the invention
Fig. 1 is the structure chart of certain five-axle number control machine tool
Fig. 2 is the schematic diagram of experimental provision position in embodiment of the present invention method
Fig. 3 is by the measuring route that experiment measurement is walked in embodiment of the present invention method
Fig. 4 is the XOY plane perspective view of measuring route in embodiment of the present invention method
Fig. 5 is the semicircle track that each step-length in track is formed in embodiment of the present invention method
Fig. 6 is that measuring route step-length is uneven in embodiment of the present invention method
Fig. 7 be embodiment of the present invention method in B axle measuring route tool cupuliform at semicircle cone
Fig. 8 is that plan view is unfolded in half cone formed in embodiment of the present invention method
Fig. 9 is that measuring route step-length is uniform in embodiment of the present invention method
Specific embodiment
A specific embodiment of the invention is described below with reference to experimental measurement method and attached drawing.
Attached drawing 1 show the structure chart for certain five-axle number control machine tool that the present invention uses, based on this to this measurement method
It is described.
According to five shafts numerical controlled machine bed structure and swinging axle B axle and rotary shaft C axis type in step 1, the survey of ball bar is determined
Measure position.Two balls of ball bar are magnetically attracted on two tool cups, the two tool cups are connected to main shaft and are located at workbench
Fixture on, comprising steps of
Step 1.1, setting meet the measurement coordinate system of this experimental measurement method, by the original Z of the Z axis of coordinate system and lathe
Overlapping of axles, the X-axis and Y-axis of coordinate system are parallel to the direction of motion of lathe X-axis and Y-axis.
Step 1.2, as shown in Fig. 2, the tool cup of rotary shaft C axis is mounted in the top clamp of rotary table,
The XOY plane of measurement coordinate system is lifted on a spinstand, and swinging axle B axle is set as apart from the distance between origin O-XYZ
The center of spindle tools cup to swinging axle B axle is adjusted to 400mm using touch probe, while is located on turntable by 400mm
Workpiece tool cup is extended using extension bar apart from rotary shaft C axis center 400mm, ball bar, its nominal length is converted to
400mm, and experimental tool is calibrated.
Corresponding program is utilized in step 2, the swinging axle B axle and rotary shaft C axis for controlling five-axle number control machine tool link,
Geometric error unrelated with position of five-axle number control machine tool double back shaft is measured during this, comprising steps of
Step 2.1, measuring route are as shown in Fig. 3, are aligned the bar of ball bar with the Y-axis of O-XYZ, ball bar
The origin of O-XYZ is arranged in one end, and the other end is arranged at the position 400mm of distance Y.Swinging axle B axle and rotary shaft C axis difference
- 90 ° and 90 ° to 0 ° are rotated to from 0 °.Ball bar carries out data acquisition simultaneously.
Step 2.2, due between two tool cups on main shaft and in turntable distance be not it is constant, will lead to club
Instrument falls down from non-magnetic center seat, therefore the coordinated movement of various economic factors of swinging axle B axle and rotary shaft C axis should ensure that the point of the P in Fig. 3 and Q
The distance of point is held constant at 400mm.
P point in attached drawing 3 is projected to XOY plane by step 2.3, attached drawing 4, to obtain between B axle and the rotation angle of C axis
Relationship:
According to pythagoras of Samos theorem:
In XOY plane according to cosine law:
By measuring device RB=RC=LDBB=400mm, formula (1) and formula (2), the available pass rotated between angle
System:
Further, it is different that the movement of swinging axle B axle and rotary shaft C axis when carrying out data acquisition is solved in step 3
Step problem.
Step 3.1, swinging axle B axle and rotary shaft C axis rotate to -90 ° and 90 ° from 0 ° respectively and rotate to 0 °, swinging axle B axle
It is rotated with constant speed, step-length is that the position of 0.1 ° of corresponding rotary shaft C shaft angle can provide are as follows:
And the angle position of swinging axle B axle and rotary shaft C axis is:
The semicircle track that each step-length of experiment measurement is formed is illustrated in step 3.2, attached drawing 5.
Step 3.3, attached drawing 6 show adjacent step sizes be not it is equidistant, will lead to machine along the fluctuation of the step-length of track
The problem of bed motion and ball bar asynchronous sampling, since the acquisition rate of ball bar is constant, thereby, it is ensured that movement is even
Fast is also particularly significant, and analysis also could be effective.
Step 3.4, track represents tool cup center in Fig. 6.Spindle tools cup is mounted on the main shaft of swinging axle B axle
On shell, therefore tool cup axis and tool cup are centrally formed one and half straight circular cones as shown in fig. 7, cone therefore can be obtained
The bottom radius of circle of parameter, cone isThe aperture of cone is 90 °, and the bus length of cone is 400mm.
Step 3.5, in order to ensure the distance between adjacent step sizes it is constant, cone is deployed on two-dimensional surface, such as Fig. 8
(a) shown in, if distance | | OO ' | | it is r,SchemingIt can also be obtained in expansion planeThe angle of spread can be obtained:
Step 3.6 is expressed as φ by the central angle of OB and BP ' encirclement, can provide are as follows:
Step 3.7 can be given Θ by the central angle of OO ' in Fig. 8 (c) and O ' P ' encirclement, in the bottom circle of cone
In, it can provide:
Step 3.8, N is in Fig. 8 (c) | | OP ' | | midpoint, be based on triangle relation, following equation can be provided:
Step 3.9, therefore θBIt can be obtained based on equation 5-9 with the relationship of Θ:
Step 3.10, attached drawing 9 show equally distributed motion profile, as long as tool cup center is evenly distributed on Φ
In, so that it may it realizes uniform motion, in 900 steps of intermediate selection equidistance, substitutes into formula equation 5-10, formation is uniformly distributed
Motion profile.
Further, in step 4, error measure model is established according to theory of multi body system and homogeneous coordinate transformation, although institute
The method of proposition is to carry out on " swinging axle B axle and turntable C axis " formula five-axis machine tool, but can be applied to any have
The five-axis machine tool of similar topological structure.In order to simplify modeling process, current multi-axis NC Machine Tools NC system can compensate for linear axes
Error, it is therefore assumed that the geometric error for compensating linear axes before all tests only considers the PIGE of rotary shaft.
Step 4.1, rotary shaft C axis PIGE according to ISO230-1, each rotary shaft has 4 PIGE, it is contemplated that the zero of CNC
Position compensation function can ignore an error of zero.4 PIGE are two linear position errors in XOY plane in X-axis and Y-axis
Component EXOCAnd EYOC, and two orientation error component E of X-axis and Y-axis are surrounded respectivelyAOCAnd EBOC.It can be based on IOS230-1
Obtain the like error composition of swinging axle B axle.
Step 4.2, the overall error that kinematic axis can be assessed by the sequence multiplication of basic homogeneous transform matrix.According to more bodies
Systems Theory, the eigentransformation matrix from workpiece coordinate system to reference frame can be given below:
Cutting tool branch similar with above-mentioned expression formula can provide:
Ideal transformation matrix from center cutter point to workpiece coordinate system can be given below:
It is influenced by PIGE in contacting, the practical posture of transition matrix indicates are as follows:
Wherein E is 4 × 4 rank unit matrixs, due to there are geometric error,Indicate given deviation matrix:
Then the real transform from cutting tool central point to workpiece can provide:
Wherein letter r, W, T and i indicate the reference frame in the kinematic chain of target lathe, workpiece coordinate system, skiver
Has the coordinate system of coordinate system and the i-th rigid body.DidealAnd DactualIt indicates ideal and actual homogeneous transform matrix, indicates from its left side
Transformation of the lower target coordinate system to one of its pre-super.Rot and Trans respectively describes rotation and translation in homogeneous transform matrix
From its pre-sub coordinate system to the conversion in one of its upper left corner.
The model use pseudoinverse technique proposed in step 4.3, Binding experiment measurement data and step 4 obtains five-shaft numerical control
The error unrelated with geometric position of eight of lathe double back shaft is as shown in Table 1:
Claims (5)
1. a kind of detection method about the unrelated error of five-axle number control machine tool double back rotating shaft position, which is characterized in that including as follows
Step:
Step 1, according to the specific structure and swinging axle B axle of five-axle number control machine tool and the position of rotary shaft C axis, build experiment and survey
Measure device.
Step 2, Binding experiment device, propose measurement five-axle number control machine tool swinging axle B axle and 8 of rotary shaft C axis and position without
Close the track of geometric error.
Between aggregate velocity and ball bar acquisition speed when step 3, solution swinging axle B axle and the rotary shaft C axis coordinated movement of various economic factors
Asynchronism
Step 4 carries out error identification in conjunction with lathe multi-body movement Systems Theory and homogeneous coordinate transformation.
2. the detection method according to claim 1 about the unrelated error of five-axle number control machine tool double back rotating shaft position, special
Sign is, in step 1, according to the structure of five-axle number control machine tool and the type of swinging axle B axle and rotary shaft C axis, builds reality
Experiment device, for example, ball bar position and tool cup calibration, comprising steps of
The coordinate system that step 1.1, setting measure, Z axis are overlapped with the original Z axis of lathe, and the X-axis for measuring coordinate system is parallel with Y-axis
In the direction of motion of lathe X-axis and Y-axis.
Step 1.2, rotary shaft C axis tool cup are mounted on the fixture at the top of turntable, and the XOY plane for measuring coordinate system is rotating
It is lifted on platform, sets the size of the distance between swinging axle B axle and origin O-XYZ as 400mm, using touch probe by main shaft
The center of tool cup to swinging axle B axle is adjusted to 400mm, while the Workpiece tool cup being located on turntable is apart from rotary shaft C axis
Center 400mm, ball bar are extended using extension bar, its nominal length are converted to 400mm, and carry out school to experimental tool
It is quasi-.
3. the detection method according to claim 1 about the unrelated error of five-axle number control machine tool double back rotating shaft position,
It is characterized in that, in the step 2, Binding experiment device proposes the 8 of measurement five-axle number control machine tool swinging axle B axle and rotary shaft C axis
The track of item geometric error unrelated with position, comprising steps of
It is aligned the axis of ball bar with the Y-axis of O-XYZ in step 2.1, measuring route, one end of ball bar is arranged in O-
The origin of XYZ, the other end are arranged at the position 400mm apart from Y-axis.Swinging axle B axle and rotary shaft C axis are rotated from 0 ° respectively
To -90 ° and 90 ° to 0 °.
The distance between two tool cups are not constant in step 2.2, main shaft and turntable, will lead to ball bar from magnetism
It falls down on heart seat, therefore the coordinated movement of various economic factors of swinging axle B axle and rotary shaft C axis should ensure that the distance of two pedestal of ball bar keeps permanent
It is set to 400mm.
Measurement track is projected to XOY plane by step 2.3, to obtain between swinging axle B axle and the rotation angle of rotary shaft C axis
Relationship:
According to pythagoras of Samos theorem:
In XOY plane according to cosine law:
By measuring device RB=RC=LDBB=400mm, formula (1) and formula (2), the available relationship rotated between angle:
4. the detection method according to claim 1 about the unrelated error of five-axle number control machine tool double back rotating shaft position,
It is characterized in that in the step 3, solves aggregate velocity and ball bar when swinging axle B axle and the rotary shaft C axis coordinated movement of various economic factors and capture
Asynchronism between speed, comprising steps of
Step 3.1, swinging axle B axle and rotary shaft C axis rotate to -90 ° and 90 ° from 0 ° respectively and rotate to 0 °, and swinging axle B axle is with perseverance
The rotation of constant speed degree, step-length are that the position of 0.1 ° of corresponding rotary shaft C shaft angle can provide are as follows:
And the angle position of B axle and C axis is:
Step 3.2, each step-length of experiment measurement represent discovery and will form semicircle track, and the semicircle track of formation is adjacent
Step-length is not equidistant, the problem of will lead to machine tool motion and ball bar asynchronous sampling along the fluctuation of the step-length of track,
Since the acquisition rate of ball bar is constant, thereby, it is ensured that movement is at the uniform velocity also particularly significant, analysis also could be effective.
Step 3.3, track represent tool cup center.Spindle tools cup is mounted in the main shaft housing of B axle swinging axle, therefore
Tool cup axis and tool cup are centrally formed one and half straight circular cones, therefore can obtain the parameter of cone, the bottom circle half of cone
Diameter isThe aperture of cone is 90 °, and the bus length of cone is 400mm.
Step 3.4, in order to ensure the distance between adjacent step sizes it is constant, centrum is deployed on two-dimensional surface, if distance | |
OO ' | | it is r,It can also be obtained in expansion planeThe angle of spread can be obtained:
Step 3.5 is expressed as φ by the central angle of OB and BP ' encirclement, can provide are as follows:
Step 3.6 can be given Θ by the central angle of OO ' and O ' P ' encirclement, in the bottom circle of cone, can provide:
Step 3.7, wherein N is | | OP ' | | midpoint, be based on triangle relation, following equation can be provided:
Step 3.8, therefore θBIt can be obtained based on equation 5-9 with the relationship of Θ:
As long as step 3.9, tool cup center are evenly distributed in Φ, so that it may realize uniform motion, select phase in centre
Equidistant 900 step substitutes into formula equation 5-10, forms equally distributed motion profile.
5. the detection method according to claim 1 about five-axle number control machine tool dual AC power axis error, which is characterized in that
In the step 4, error identification is carried out in conjunction with lathe multi-body movement Systems Theory and homogeneous coordinate transformation, comprising steps of
Step 4.1, rotary shaft C axis PIGE according to ISO230-1, each rotary shaft has 4 PIGE, it is contemplated that the zero-bit of CNC is mended
An error of zero can be ignored by repaying function.4 PIGE are two linear position error components in XOY plane in X-axis and Y-axis
EXOCAnd EYOC, and two orientation error component E of X-axis and Y-axis are surrounded respectivelyAOCAnd EBOC.It can be obtained based on IOS230-1
The like error of swinging axle B axle forms.
Step 4.2, the overall error that kinematic axis can be assessed by the sequence multiplication of basic homogeneous transform matrix.According to multi-body system
Theory, the eigentransformation matrix from workpiece coordinate system to reference frame can be given below:
Cutting tool branch similar with above-mentioned expression formula can provide:
Ideal transformation matrix from center cutter point to workpiece coordinate system can be given below:
It is influenced by PIGE in contacting, the practical posture of transition matrix indicates are as follows:
Wherein E is 4 × 4 rank unit matrixs, due to there are geometric error,Indicate given deviation matrix:
Then the real transform from cutting tool central point to workpiece can provide:
Wherein letter r, W, T and i indicate that the reference frame in the kinematic chain of target lathe, workpiece coordinate system, cutting element are sat
The coordinate system of mark system and the i-th rigid body.DidealAnd DactualIt indicates ideal and actual homogeneous transform matrix, indicates from its pre-sub
Coordinate system to one of its pre-super transformation.Rot and Trans respectively describe in homogeneous transform matrix rotation and translation from its
Conversion of the pre-sub coordinate system to one of its upper left corner.
The model use pseudoinverse technique proposed in step 4.3, Binding experiment measurement data and step 4 obtains five-axle number control machine tool
The error unrelated with geometric position of eight of double back shaft.
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| CN110837246A (en) * | 2019-11-25 | 2020-02-25 | 天津工业大学 | Method for analyzing geometric error sensitivity of double rotating shafts of five-axis numerical control machine tool |
| CN111872748A (en) * | 2020-07-20 | 2020-11-03 | 天津大学 | Machine tool geometric error measuring method based on ball arm instrument |
| CN111872742A (en) * | 2020-07-20 | 2020-11-03 | 天津大学 | Five-axis machine tool error measurement method based on ball arm instrument |
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| CN114012507A (en) * | 2021-12-09 | 2022-02-08 | 天津工业大学 | Identification method for position-independent errors of double rotating shafts of cradle type five-axis machine tool |
| CN117348518A (en) * | 2023-12-05 | 2024-01-05 | 广东海洋大学 | Numerical control machine tool geometric error identification method and device based on improved nine-line method |
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