CN109798854A - The scaling method and system of lathe yaw - Google Patents
The scaling method and system of lathe yaw Download PDFInfo
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Abstract
The invention discloses the scaling methods and system of a kind of lathe yaw.The calibration system includes: standard ball component, probe assembly, control module and computing module;The standard ball component is fixed on the workbench;The probe assembly is fixed on the yaw;The control module rotates at least three angles for controlling the rotary shaft;Wherein, an angle at least three angle is 0 °;The computing module is used to calculate the target mechanical coordinate of lathe identification point under each angle by the standard ball component and the probe assembly, and demarcates the rotation center of the rotary shaft and/or the direction of rotary shaft according at least three target mechanical coordinates.Not only algorithm is simple, accuracy is higher for the scaling method of lathe yaw of the invention, and has general applicability.
Description
Technical field
The present invention relates to a kind of scaling method of lathe, in particular to the scaling method of a kind of five-axis machine tool yaw and it is
System.
Background technique
Lathe can be realized the processing and measurement of complex parts high-accuracy high-efficiency, reflect a state to a certain extent
The power of family's equipment manufacturing ability is an important indicator for measuring a national manufacturing industry level height.And in order to ensure machine
The machining accuracy of bed, needs to demarcate the yaw of lathe.In the prior art, very multiple for the calibration of yaw or calculating
Miscellaneous or accuracy is lower.
Summary of the invention
The technical problem to be solved by the present invention is to overcome in the prior art to the calibration of yaw or calculating complexity
The lower defect of accuracy provides the scaling method and system of a kind of lathe yaw.
The present invention is to solve above-mentioned technical problem by following technical proposals:
A kind of scaling method of lathe yaw, the lathe includes workbench and yaw;The yaw includes rotary shaft, institute
Stating scaling method includes:
S1, standard ball component is fixed on the workbench, probe assembly is fixed on the yaw;
S2, control rotary shaft rotate at least three angles, and by the standard ball component and the probe assembly calculating
The target mechanical coordinate of lathe identification point under each angle;
Wherein, an angle at least three angle is 0 °;
S3, according at least three target mechanical coordinates demarcate the rotation center of the rotary shaft and/or the direction of rotary shaft.
Preferably, step S3In, the step of demarcating the direction of rotary shaft, specifically includes:
Based on least square method and according at least three targets machinery coordinate fitting plane, by the normal direction of the plane
It is determined as the direction of the rotary shaft.
Preferably, the probe assembly includes: probe ball;The standard ball component includes standard ball;
Step S2In, the mesh of lathe identification point under each angle is calculated by the standard ball component and the probe assembly
The step of marking mechanical coordinate specifically includes:
S21, the driving yaw do relative motion relative to the standard ball so that the probe ball is from least three directions
Lathe identification point close to the standard ball until contacted with the standard ball, and when the probe ball and the standard ball are contacted
Coordinate be determined as initial mechanical coordinate;
S22, according at least three initial mechanical coordinates calculate the target mechanical coordinate.
In the present solution, the target mechanical coordinate being calculated be equivalent to probe ball the centre of sphere and standard ball the centre of sphere be overlapped when
The coordinate of lathe identification point.
Preferably, if the quantity of the initial mechanical coordinate is three, step S22It is middle calculate the target mechanical coordinate (X,
Y, Z) formula, it is as follows:
(X-x1)2+(Y-y1)2+(Z-z1)2=(Rb+Rq)2;
(X-x2)2+(Y-y2)2+(Z-z2)2=(Rb+Rq)2;
(X-x3)2+(Y-y3)2+(Z-z3)2=(Rb+Rq)2;
Wherein, x1, x2 and x3 are respectively coordinate of three initial mechanical coordinates in x-axis, and y1, y2 and y3 are respectively three
The coordinate of initial mechanical coordinate on the y axis, z1, z2 and z3 are respectively coordinate of three initial mechanical coordinates in z-axis;RbIt indicates
The radius of standard ball;RqIndicate the radius of probe ball.
Preferably, if the quantity of the initial mechanical coordinate is four, step S22It is middle calculate the target mechanical coordinate (X,
Y, Z) formula, it is as follows:
(X-x1)2+(Y-y1)2+(Z-z1)2=α;
(X-x2)2+(Y-y2)2+(Z-z2)2=α;
(X-x3)2+(Y-y3)2+(Z-z3)2=α;
(X-x4)2+(Y-y4)2+(Z-z4)2=α;
Wherein, x1, x2, x3 and x4 are respectively coordinate of four initial mechanical coordinates in x-axis, y1, y2, y3 and y4 difference
For the coordinate of four initial mechanical coordinates on the y axis, z1, z2, z3 and z4 are respectively seat of four initial mechanical coordinates in z-axis
Mark;α indicates unknown constant.
Preferably, if the quantity of the initial mechanical coordinate is greater than four, step S22It is middle to calculate the target mechanical coordinate
The step of (X, Y, Z), specifically includes:
The initial mechanical coordinate fitting is sat the centre of sphere of first spherical surface at the first spherical surface using least square method
Mark is determined as target mechanical coordinate (X, Y, Z).
Preferably, step S3In, demarcate rotation center the step of specifically include:
S3-1a, three coordinate Q are arbitrarily chosen from at least three targets mechanical coordinatem、QpAnd Qq;
S3-2a, calculate line segment QmQpMiddle vertical plane M1, line segment QpQqMiddle vertical plane M2 and M1 and M2 intersection L;
S3-3a, calculate the intersecting point coordinate of the intersection L and the plane, according to the intersecting point coordinate and when the angle of rotary shaft
The target mechanical coordinate that degree obtains when being 0 ° calculates the rotation center;
Or, S3-1b, the normal vector of the plane is labeled as
S3-2b, calculate target mechanical coordinate QjProjection coordinate Q ' on the planej;
S3-3b, willThe spin matrix R of Z axis forward direction is rotated to be, and spin matrix R is applied to projection coordinate Q 'jOn, it obtains
To postrotational coordinate Q "j;
S3-4b, using least square method by Q "jIt is fitted to circle, equation of a circle is (x-a)2+(y-b)2=R2, by (a, b, z0) really
It is set to initial center of circle O;
z0Indicate Q "jCoordinate on Z axis;
S3-5b, calculate Z axis rotate in the forward direction forSpin matrix R ', spin matrix R ' is applied on initial center of circle O, is obtained
To the coordinate of postrotational center of circle O ';
S3-6b, according to the coordinate of postrotational center of circle O ' and the target mechanical coordinate obtained when the angle of rotary shaft is 0 °
Calculate the rotation center;
Or, S3-1c, using least square method by target mechanical coordinate QjIt is fitted to the second spherical surface, the equation of the second spherical surface is
(x-d)2+(y-e)2+(z-c)2=R2, (d, e, c) is determined as initial centre of sphere S;
S3-2c, calculate the subpoint S ' of initial centre of sphere S on the plane;
S3-2c, the target mechanical coordinate that obtains when being 0 ° of the coordinate according to subpoint S ' and the angle when rotary shaft calculate institute
State rotation center;
J is the integer greater than 0.
In the present solution, in order to improve the accuracy of calculating, can be obtained multiple when demarcating rotation center using first method
Target mechanical coordinate arbitrarily chooses three point Qm、QpAnd QqAn intersection point, Q can be calculatedm、Qp、QqThere are several combinations
Several intersection points can be found out, the average coordinates value of all intersection points is calculated, using this average coordinates value as final intersecting point coordinate, meter
Final intersecting point coordinate and step S2In the difference of target mechanical coordinate that is obtained when rotation shaft angle is 0 °, as rotate
Center.
The present invention also provides a kind of calibration system of lathe yaw, lathe includes workbench and yaw;The yaw includes
Rotary shaft, the calibration system include: standard ball component, probe assembly, control module and computing module;
The standard ball component is fixed on the workbench;
The probe assembly is fixed on the yaw;
The control module rotates at least three angles for controlling the rotary shaft;
Wherein, an angle at least three angle is 0 °;
The computing module is used to calculate lathe mark under each angle by the standard ball component and the probe assembly
Know the target mechanical coordinate of point, and demarcates rotation center and/or the rotation of the rotary shaft according at least three target mechanical coordinates
The direction of shaft.
In the present solution, the target mechanical coordinate being calculated be equivalent to probe ball the centre of sphere and standard ball the centre of sphere be overlapped when
The coordinate of lathe identification point.
Preferably, the computing module specifically includes the first computing unit;
First computing unit is used for based on least square method and according at least three targets machinery coordinate fitting
Plane, and the normal direction of the plane is determined as to the direction of the rotary shaft.
Preferably, the probe assembly includes: probe ball;The standard ball component includes standard ball;
The control module includes: driving unit;
The computing module further include: the second computing unit;
The driving unit for driving the yaw to do relative motion relative to the standard ball so that the probe ball from
Until contact with the standard ball, and second computing unit is called close to the standard ball at least three directions;
The coordinate that second computing unit is used for lathe identification point when contacting the probe ball with the standard ball is true
It is set to initial mechanical coordinate, and calculates the target mechanical coordinate according at least three initial mechanical coordinates.
Preferably, second computing unit passes through following formula meter if the quantity of the initial mechanical coordinate is three
It calculates target mechanical coordinate (X, Y, Z):
(X-x1)2+(Y-y1)2+(Z-z1)2=(Rb+Rq)2;
(X-x2)2+(Y-y2)2+(Z-z2)2=(Rb+Rq)2;
(X-x3)2+(Y-y3)2+(Z-z3)2=(Rb+Rq)2;
Wherein, x1, x2 and x3 are respectively coordinate of three initial mechanical coordinates in x-axis, and y1, y2 and y3 are respectively three
The coordinate of initial mechanical coordinate on the y axis, z1, z2 and z3 are respectively coordinate of three initial mechanical coordinates in z-axis;RbIt indicates
The radius of standard ball;RqIndicate the radius of probe ball.
Preferably, second computing unit passes through following formula meter if the quantity of the initial mechanical coordinate is four
It calculates target mechanical coordinate (X, Y, Z):
(X-x1)2+(Y-y1)2+(Z-z1)2=α;
(X-x2)2+(Y-y2)2+(Z-z2)2=α;
(X-x3)2+(Y-y3)2+(Z-z3)2=α;
(X-x4)2+(Y-y4)2+(Z-z4)2=α;
Wherein, x1, x2, x3 and x4 are respectively coordinate of four initial mechanical coordinates in x-axis, y1, y2, y3 and y4 difference
For the coordinate of four initial mechanical coordinates on the y axis, z1, z2, z3 and z4 are respectively seat of four initial mechanical coordinates in z-axis
Mark;α indicates unknown constant.
Preferably, second computing unit is specifically used for using if the quantity of the initial mechanical coordinate is greater than four
The sphere centre coordinate of first spherical surface at the first spherical surface, is determined as target by the initial mechanical coordinate fitting by least square method
Mechanical coordinate (X, Y, Z).
Preferably, the computing module further include: third computing unit;
The third computing unit from least three target mechanical coordinates for arbitrarily choosing three coordinate Qm、QpAnd Qq,
Calculate line segment QmQpMiddle vertical plane M1, line segment QpQqMiddle vertical plane M2 and M1 and M2 intersection L, calculate the intersection L and institute
The intersecting point coordinate of plane is stated, and according to the intersecting point coordinate and the target mechanical coordinate meter obtained when the angle of rotary shaft is 0 °
Calculate the rotation center;
Or, the third computing unit is for the normal vector of the plane to be labeled asCalculate target mechanical coordinate Qj?
Projection coordinate Q ' in the planej, willThe spin matrix R of Z axis forward direction is rotated to be, and spin matrix R is applied to projection
Coordinate Q 'jOn, obtain postrotational coordinate Q "j;The third computing unit is also used to utilize least square method by Q "jFitting
Cheng Yuan, equation of a circle are (x-a)2+(y-b)2=R2, by (a, b, z0) be determined as initial center of circle O, and calculate Z axis rotate in the forward direction for
Spin matrix R ', spin matrix R ' is applied on initial center of circle O, obtains the coordinate of postrotational center of circle O ', and according to rotation
The coordinate of center of circle O ' after turning and the target mechanical coordinate obtained when the angle of rotary shaft is 0 ° calculate the rotation center;Its
In, z0Indicate Q "jCoordinate on Z axis;
Or, the third computing unit is used to use least square method by target mechanical coordinate QjIt is fitted to the second spherical surface,
Second spherical equation is (x-d)2+(y-e)2+(z-c)2=R2, (d, e, c) is determined as initial centre of sphere S, and calculate the initial centre of sphere
The subpoint S ' of S on the plane;The third computing unit is also used to according to the coordinate of subpoint S ' and when rotary shaft
The target mechanical coordinate that angle obtains when being 0 ° calculates the rotation center;
J is the integer greater than 0.If there is m target mechanical coordinate, one sequence number of each target mechanical coordinate, institute are given
With j=1,2 ..., m.
In the present solution, in order to improve the accuracy of calculating, can be obtained multiple when demarcating rotation center using first method
Target mechanical coordinate arbitrarily chooses three point Qm、QpAnd QqAn intersection point, Q can be calculatedm、Qp、QqThere are several combinations
Several intersection points can be found out, the average coordinates value of all intersection points is calculated, using this average coordinates value as final intersecting point coordinate, meter
Final intersecting point coordinate and step S2In the difference of target mechanical coordinate that is obtained when rotation shaft angle is 0 °, as rotate
Center.
The positive effect of the present invention is that: not only algorithm is simple, accurate for the scaling method of lathe yaw of the invention
Degree is higher, and has general applicability.
Detailed description of the invention
Fig. 1 is the partial structure diagram of the calibration system of the lathe yaw of the embodiment of the present invention 1.
Fig. 2 is the part of module schematic diagram of the calibration system of the lathe yaw of the embodiment of the present invention 1.
Fig. 3 is the structural schematic diagram of the standard ball component in the calibration system of the lathe yaw of the embodiment of the present invention 1.
Fig. 4 is the structural schematic diagram of the probe assembly in the calibration system of the lathe yaw of the embodiment of the present invention 1.
Fig. 5 is the first shape when the probe ball in the calibration system of the lathe yaw of the embodiment of the present invention 1 is contacted with standard ball
State schematic diagram.
Fig. 6 is the second shape when the probe ball in the calibration system of the lathe yaw of the embodiment of the present invention 1 is contacted with standard ball
State schematic diagram.
Fig. 7 is the third shape when probe ball in the calibration system of the lathe yaw of the embodiment of the present invention 1 is contacted with standard ball
State schematic diagram.
Fig. 8 is the first pass figure of the scaling method of the lathe yaw of the embodiment of the present invention 2.
Fig. 9 is the initial flowchart of the scaling method of the lathe yaw of the embodiment of the present invention 2.
Specific embodiment
The present invention is further illustrated below by the mode of embodiment, but does not therefore limit the present invention to the reality
It applies among a range.
Embodiment 1
The calibration system of the present embodiment for realizing lathe yaw calibration, as shown in Figure 1, lathe include workbench 1, pendulum
First 2 and linear axis (X, Y, Z axis) (not shown), yaw 2 includes main shaft 21 and rotary shaft 22.As shown in Figs. 1-2, this implementation
The calibration system of example includes: standard ball component 3, probe assembly 4, control module 5 and computing module 6.Wherein, control module 5 is wrapped
It includes: driving unit 51.Computing module 6 includes the first computing unit 61, the second computing unit 62 and third computing unit 63.
Specifically, as shown in figure 3, standard ball component 3 includes: standard ball 31, standard ball strut 32 and standard ball pedestal 33.
Standard ball 31 and standard ball pedestal 33 are connected by standard ball strut 32.As shown in figure 4, probe assembly 4 includes: probe ball 41, visits
Bar 42 and probe base 43.Probe ball 41 and probe base 43 are connected by feeler lever 42.
Before being demarcated, system building is first carried out, as shown in Figure 1, standard ball component 3 is fixed by standard ball pedestal 33
In on workbench 1, probe assembly 4 is fixed on main shaft 21 by probe base 43.When calibration, control module 5 controls rotary shaft
22 rotate at least three angles, and one of angle at least three angles is 0 °.Computing module 6 by standard ball component and
Probe assembly calculates the target mechanical coordinate of the lathe identification point under each angle, and according at least three target mechanical coordinate marks
Determine the rotation center of rotary shaft and/or the direction of rotary shaft.It should be noted that user can voluntarily set lathe mark on lathe
Know point, selected identification point should not be by the Effect of Rotation of rotary shaft, such as can be the point at the top of yaw.
Calibration system introduced below obtains the specific implementation side of target mechanical coordinate by standard ball component and probe assembly
Formula:
Control module adjusts the angle of rotary shaft, it is made to go to 0 ° of position, and driving unit 51 drives yaw 2 relative to standard
Ball do relative motion (by drive tri- linear axis of X, Y, Z movement so that yaw relative to standard ball along X-axis, Y-axis and Z axis
It is mobile) so that probe ball 41 is contacted close to standard ball 31 up to standard ball 31 from least three directions, referring to shown in Fig. 53
The position of a probe ball being represented by dashed line, yaw 2 stop relative motion.When contacting standard ball 31 and probe ball 41, driving is single
Member 51 calls the second computing unit 62.The coordinate of lathe identification point when second computing unit 62 contacts probe ball with standard ball is true
It is set to initial mechanical coordinate.To which when rotary shaft is at 0 °, the second computing unit can get probe ball 41 from different directions close to mark
At least three initial mechanical coordinates of the quasi- ball 31 when being contacted with standard ball 31.Second computing unit is then according at the beginning of at least three
A target mechanical coordinate is calculated in beginning mechanical coordinate.The target mechanical coordinate is equivalent to the centre of sphere of probe ball and the ball of standard ball
The coordinate of lathe identification point when the heart is overlapped.
Rotary shaft is rotated to different angles, and repeats aforesaid operations step at least twice, as shown in fig. 6, so as to obtain
Obtain at least three target mechanical coordinates of the rotary shaft in different rotary angle.
It should be noted that the quantity of the initial mechanical coordinate obtained is more, determining target mechanical coordinate will be more smart
Really, theoretically need to only obtain three initial mechanical coordinates can obtain a target mechanical coordinate by calculating.
In order to make it easy to understand, referring to Fig. 7, provide following explanation: probe ball 41 is from different directions close to standard ball 31, not Tongfang
To the probe ball 41 for touching standard ball 31 the centre of sphere on a spherical surface, the centre of sphere of the spherical surface is overlapped with the standard ball centre of sphere, radius
For the sum of probe ball and the standard radius of a ball Rq+Rb.If only obtaining 3 groups of initial mechanical coordinates, it is also necessary to obtain the radius R of probe ballqWith
The radius R of standard ballb, target mechanical coordinate could be calculated;If obtaining 4 groups or more initial mechanical coordinates and corresponding coordinate points
It is non-coplanar, then require no knowledge about the radius R of probe ballqWith the radius R of standard ballb, target mechanical coordinate can be calculated.Specifically,
The possible implementation for calculating target mechanical coordinate is illustrated below:
If the quantity of the initial mechanical coordinate obtained is three, and obtains the radius R of probe ballqWith the radius R of standard ballb,
Then the second computing unit calculates target mechanical coordinate (X, Y, Z) by following formula:
(X-x1)2+(Y-y1)2+(Z-z1)2=(Rb+Rq)2;
(X-x2)2+(Y-y2)2+(Z-z2)2=(Rb+Rq)2;
(X-x3)2+(Y-y3)2+(Z-z3)2=(Rb+Rq)2;
Wherein, x1, x2 and x3 are respectively coordinate of three initial mechanical coordinates in x-axis, and y1, y2 and y3 are respectively three
The coordinate of initial mechanical coordinate on the y axis, z1, z2 and z3 are respectively coordinate of three initial mechanical coordinates in z-axis.By asking
Solving above-mentioned equation group can be obtained target mechanical coordinate (X, Y, Z).
If the quantity of the initial mechanical coordinate obtained is four, the second computing unit calculates target machine by following formula
Tool coordinate (X, Y, Z):
(X-x1)2+(Y-y1)2+(Z-z1)2=M;
(X-x2)2+(Y-y2)2+(Z-z2)2=M;
(X-x3)2+(Y-y3)2+(Z-z3)2=M;
(X-x4)2+(Y-y4)2+(Z-z4)2=M;
Wherein, x1, x2, x3 and x4 are respectively coordinate of four initial mechanical coordinates in x-axis, y1, y2, y3 and y4 difference
For the coordinate of four initial mechanical coordinates on the y axis, z1, z2, z3 and z4 are respectively seat of four initial mechanical coordinates in z-axis
Mark;M indicates unknown constant.Target mechanical coordinate (X, Y, Z) can be obtained by solving above-mentioned equation group.
If the quantity of the initial mechanical coordinate obtained is greater than four, the second computing unit will be initial using least square method
Mechanical coordinate is fitted to the first spherical surface, and the sphere centre coordinate of the first spherical surface is determined as target mechanical coordinate (X, Y, Z), specific:
Assuming that obtaining n group (n >=5) initial mechanical coordinate, it is expressed as (Xi, Yi, Zi), i=1,2 ..., n.Based on most
Small square law and according to n group initial mechanical coordinate fitting spherical surface, it is assumed that the radius of the ball is R, and D is a unknown constant, is enabled:
A=-2X;
B=-2Y;
C=-2Z;
D=X2+Y2+Z2-R2;
According to the principle of least square method, available following equation group:
(n∑Xi2-∑Xi∑Xi)A+(n∑Xi Yi-∑Xi∑Yi)B+(n∑Xi Zi-∑Xi∑Zi)C+N∑Xi3+N
∑XiYi2+N∑XiZi2-∑(Xi2+Yi2+Zi2) ∑ Xi=0;
(n∑XiYi-∑Xi∑Yi)A+(n∑Yi2-∑Yi∑Yi)B+(n∑Yi Zi-∑Yi∑Zi)C+N∑Xi2Yi+N
∑Yi3+N∑YiZi2-∑(Xi2+Yi2+Zi2) ∑ Yi=0;
(n∑XiZi-∑Xi∑Zi)A+(n∑YiZi-∑Yi∑Zi)B+(n∑Zi2-∑Zi∑Zi)C+N∑Xi2Zi+N
∑Yi2Zi+N∑Zi3-∑(Xi2+Yi2+Zi2) ∑ Xi=0;
It is thus possible to solve A, B, C, and then sphere centre coordinate (X, Y, Z) is obtained, sphere centre coordinate at this time is standard ball
Target mechanical coordinate (X, Y, Z) when being overlapped with the centre of sphere of probe ball.
In the present embodiment, the first computing unit of computing module is used to demarcate the direction of rotary shaft, specifically, first calculates
Unit is based on least square method and according at least three mechanical coordinate fit Plane, and the normal direction of plane is determined as to the side of rotary shaft
To.To complete the calibration of the rotation center of rotary shaft and the direction of rotary shaft.
In the present embodiment, any one determination rotation in following three kinds of methods is may be selected in the third computing unit of computing module
Turn center:
(1) third computing unit arbitrarily chooses three coordinate Q from least three target mechanical coordinatesm、QpAnd Qq, calculate
Line segment QmQpMiddle vertical plane M1, line segment QpQqMiddle vertical plane M2 and M1 and M2 intersection L, calculate intersection L and plane (the first meter
Calculate the plane that is fitted of unit) intersecting point coordinate, and according to intersecting point coordinate and the mesh obtained when the angle of rotary shaft is 0 °
It marks mechanical coordinate and calculates rotation center, also i.e. by intersecting point coordinate and the target mechanical coordinate obtained when the angle of rotary shaft is 0 °
Difference be determined as rotation center.
Wherein, if obtaining n (n > 3) a initial mechanical coordinate altogether, any three points share n (n-1) (n-2)/6 kind of combination,
Every kind of combination can find out an intersection point, and in order to keep calculated result more acurrate, the calculated result that every kind is combined can be averaged,
The average value being calculated is determined as to final intersecting point coordinate, and is 0 ° by final intersecting point coordinate and the angle when rotary shaft
When the target mechanical coordinate that obtains make the difference, obtain rotation center.
(2) normal vector of plane (plane that the first computing unit is fitted) is labeled as by third computing unitIt calculates
Target mechanical coordinate QjProjection coordinate Q ' in the planej, calculating willThe spin matrix R of Z axis forward direction is rotated to be, and rotation
Matrix R is applied to projection coordinate Q 'jOn, obtain postrotational coordinate Q "j, each Q "jZ coordinate be the same, be denoted as
z0;Third computing unit is also used to utilize least square method by Q "jIt is fitted to circle, equation of a circle is (x-a)2+(y-b)2=R2, will
(a, b, z0) be determined as initial center of circle O, and calculate Z axis rotate in the forward direction forSpin matrix R ', spin matrix R ' is applied to
On initial center of circle O, by the coordinate of postrotational center of circle O ' and the target mechanical coordinate that is obtained when the angle of rotary shaft is 0 °
Difference is determined as rotation center.Wherein, z0Indicate Q "jCoordinate on Z axis.
(3) third computing unit uses least square method by target mechanical coordinate QjIt is fitted to the second spherical surface, the second spherical surface
Equation is (x-d)2+(y-e)2+(z-c)2=R2, (d, e, c) is determined as initial centre of sphere S, and calculate initial centre of sphere S in plane
Subpoint S ' in (plane that the first computing unit is fitted), by S ' and the target obtained when the angle of rotary shaft is 0 °
The difference of mechanical coordinate is determined as rotation center.
Wherein, j is the subscript for indicating sequence number, if there is m target mechanical coordinate, gives each target mechanical coordinate one
Sequence number, so j=1,2 ..., m.
It should be noted that illustrating only the calibration process of a rotary shaft in the present embodiment, other rotary shafts are also made
It is demarcated in the same way, but other rotary shafts that do not demarcate currently need to be gone to 0.
Embodiment 2
The scaling method of the lathe of the present embodiment is realized using the calibration system of embodiment 1, as shown in figure 8, scaling method
The following steps are included:
Standard ball component is fixed on the worktable by step 101, and probe assembly is fixed on yaw.
Step 102, control rotary shaft rotate at least three angles, and are calculated each by standard ball component and probe assembly
The target mechanical coordinate of lathe identification point under angle.
Wherein, an angle at least three angles is 0 °.
Specifically, as shown in figure 9, step 102 specifically includes:
It step 102-1, is 0 ° by the angular adjustment of rotary shaft.
Step 102-2, driving yaw does relative motion relative to standard ball, so that probe ball is from least three directions close to mark
Quasi- ball with standard ball until contact, and the coordinate of lathe identification point when probe ball and standard ball are contacted is determined as initial mechanical and sits
Mark.
Step 102-3, target mechanical coordinate is calculated according at least three initial mechanical coordinates.
If the quantity for obtaining initial mechanical coordinate in step 102-2 is three, it is also necessary to obtain the radius R of probe ballqAnd mark
The radius R of quasi- ballb, the formula of target machine tool coordinate (X, Y, Z) is calculated in step 102-3, as follows:
(X-x1)2+(Y-y1)2+(Z-z1)2=(Rb+Rq)2;
(X-x2)2+(Y-y2)2+(Z-z2)2=(Rb+Rq)2;
(X-x3)2+(Y-y3)2+(Z-z3)2=(Rb+Rq)2;
Wherein, x1, x2 and x3 are respectively coordinate of three initial mechanical coordinates in x-axis, and y1, y2 and y3 are respectively three
The coordinate of initial mechanical coordinate on the y axis, z1, z2 and z3 are respectively coordinate of three initial mechanical coordinates in z-axis;RbIt indicates
The radius of standard ball;RqIndicate the radius of probe ball.
If the quantity of the initial mechanical coordinate obtained in step 102-2 is four, target machine tool is calculated in step 102-3 and is sat
The formula of (X, Y, Z) is marked, as follows:
(X-x1)2+(Y-y1)2+(Z-z1)2=α;
(X-x2)2+(Y-y2)2+(Z-z2)2=α;
(X-x3)2+(Y-y3)2+(Z-z3)2=α;
(X-x4)2+(Y-y4)2+(Z-z4)2=α;
Wherein, x1, x2, x3 and x4 are respectively coordinate of four initial mechanical coordinates in x-axis, y1, y2, y3 and y4 difference
For the coordinate of four initial mechanical coordinates on the y axis, z1, z2, z3 and z4 are respectively seat of four initial mechanical coordinates in z-axis
Mark;α indicates unknown constant.
If the quantity of the initial mechanical coordinate obtained in step 102-3 is greater than four, least square is used in step 102-3
The sphere centre coordinate of first spherical surface at the first spherical surface, is determined as target mechanical coordinate (X, Y, Z) by initial mechanical coordinate fitting by method,
It is specific:
Assuming that n group initial mechanical coordinate is expressed as (Xi, Yi, Zi), i=1,2 ..., n.Simultaneously based on least square method
According to n group initial mechanical coordinate fitting spherical surface, it is assumed that the radius of the ball is R, and R is a unknown constant, is enabled:
A=-2X;
B=-2Y;
C=-2Z;
D=X2+Y2+Z2-R2;
According to the principle of least square method, available following equation group:
(n∑Xi2-∑Xi∑Xi)A+(n∑Xi Yi-∑Xi∑Yi)B+(n∑Xi Zi-∑Xi∑Zi)C+N∑Xi3+N
∑XiYi2+N∑XiZi2-∑(Xi2+Yi2+Zi2) ∑ Xi=0;
(n∑XiYi-∑Xi∑Yi)A+(n∑Yi2-∑Yi∑Yi)B+(n∑Yi Zi-∑Yi∑Zi)C+N∑Xi2Yi+N
∑Yi3+N∑YiZi2-∑(Xi2+Yi2+Zi2) ∑ Yi=0;
(n∑XiZi-∑Xi∑Zi)A+(n∑YiZi-∑Yi∑Zi)B+(n∑Zi2-∑Zi∑Zi)C+N∑Xi2Zi+N
∑Yi2Zi+N∑Zi3-∑(Xi2+Yi2+Zi2) ∑ Xi=0;
It is thus possible to solve A, B, C, and then obtaining target mechanical coordinate is (X, Y, Z).
Step 102-4, judge whether the quantity of target mechanical coordinate is equal to n, n >=3.When being judged as YES, step is executed
103, step 102-5 is executed when being judged as NO.
Step 102-5, the angle of rotary shaft, and return step 102-2 are adjusted.
The side of step 103, the rotation center that rotary shaft is demarcated according at least three target mechanical coordinates and/or rotary shaft
To.
In the present embodiment, in step 103, the step of demarcating the direction of rotary shaft, is specifically included:
Based on least square method and according at least three target machinery coordinate fitting initial planes, by the initial plane
Normal direction is determined as the direction of the rotary shaft.
The possible implementation of three kinds of calibration rotation center presented below:
The first
Step 103-1a, three coordinate Q are arbitrarily chosen from least three target mechanical coordinatesm、QpAnd Qq。
Step 103-2a, line segment Q is calculatedmQpMiddle vertical plane M1, line segment QpQqMiddle vertical plane M2 and M1 and M2 intersection
L。
Step 103-3a, the intersecting point coordinate for calculating intersection L and plane, by intersecting point coordinate and when the angle of rotary shaft is 0 °
The difference of the target mechanical coordinate of acquisition is determined as rotation center.
In the present embodiment, if obtaining n (n > 3) a initial mechanical coordinate altogether, any three points share n (n-1) (n-2)/6
Kind combination, every kind of combination can find out an intersection point, in order to keep calculated result more acurrate, can seek the calculated result that every kind is combined
The average value being calculated is determined as final intersecting point coordinate by average value, and by final intersecting point coordinate and when rotary shaft
The target mechanical coordinate that angle obtains when being 0 ° makes the difference, and obtains rotation center.
Second
Step 103-1b, the normal vector of plane is labeled as
Step 103-2b, target mechanical coordinate Q is calculatedjProjection coordinate Q ' in the planej;
Step 103-3b, calculating willThe spin matrix R of Z axis forward direction is rotated to be, and spin matrix R is applied to projection and is sat
Mark Q 'jOn, obtain postrotational coordinate Q "j;
Step 103-4b, using least square method by Q "jIt is fitted to circle, equation of a circle is (x-a)2+(y-b)2=R2, will (a,
B, z0) it is determined as initial rotation center O;
z0Indicate Q "jCoordinate on Z axis;
Step 103-5b, calculate Z axis rotate in the forward direction forSpin matrix R ', spin matrix R ' is applied to initial center of circle O
On, obtain the coordinate of postrotational center of circle O ';
Step 103-6b, the coordinate of postrotational center of circle O ' and the target obtained when the angle of rotary shaft is 0 ° is mechanical
The difference of coordinate is determined as rotation center.
The third
Step 103-1c, using least square method by target mechanical coordinate QjIt is fitted to the second spherical surface, the second spherical equation
For (x-d)2+(y-e)2+(z-c)2=R2, (d, e, c) is determined as initial centre of sphere S;
Step 103-2c, the subpoint S ' of initial centre of sphere S in the plane is calculated;
Step 103-3c, by the coordinate of subpoint S ' with when the angle of rotary shaft is 0 ° the target mechanical coordinate that obtains it is true
It is set to rotation center.
Although specific embodiments of the present invention have been described above, it will be appreciated by those of skill in the art that this is only
For example, protection scope of the present invention is to be defined by the appended claims.Those skilled in the art without departing substantially from
Under the premise of the principle and substance of the present invention, many changes and modifications may be made, but these change and
Modification each falls within protection scope of the present invention.
Claims (14)
1. a kind of scaling method of lathe yaw, the lathe includes workbench and yaw;The yaw includes rotary shaft, special
Sign is that the scaling method includes:
S1, standard ball component is fixed on the workbench, probe assembly is fixed on the yaw;
S2, control rotary shaft rotates at least three angles, and passes through the standard ball component and each angle of probe assembly calculating
Spend the target mechanical coordinate of lower lathe identification point;
Wherein, an angle at least three angle is 0 °;
S3, according at least three target mechanical coordinates demarcate the rotation center of the rotary shaft and/or the direction of rotary shaft.
2. scaling method as described in claim 1, which is characterized in that step S3In, the step of demarcating the direction of rotary shaft, is specific
Include:
Based on least square method and according at least three targets machinery coordinate fitting plane, the normal direction of the plane is determined
For the direction of the rotary shaft.
3. scaling method as claimed in claim 2, which is characterized in that the probe assembly includes: probe ball;The standard ball group
Part includes standard ball;
Step S2In, the target machine of lathe identification point under each angle is calculated by the standard ball component and the probe assembly
The step of tool coordinate, specifically includes:
S21, the driving yaw do relative motion relative to the standard ball so that the probe ball is close from least three directions
The standard ball with the standard ball until contact, and the seat of the lathe identification point when probe ball and the standard ball are contacted
Mark is determined as initial mechanical coordinate;
S22, according at least three initial mechanical coordinates calculate the target mechanical coordinate.
4. scaling method as claimed in claim 3, which is characterized in that if the quantity of the initial mechanical coordinate is three, step
Rapid S22The middle formula for calculating the target mechanical coordinate (X, Y, Z), as follows:
(X-x1)2+(Y-y1)2+(Z-z1)2=(Rb+Rq)2;
(X-x2)2+(Y-y2)2+(Z-z2)2=(Rb+Rq)2;
(X-x3)2+(Y-y3)2+(Z-z3)2=(Rb+Rq)2;
Wherein, x1, x2 and x3 are respectively coordinate of three initial mechanical coordinates in x-axis, and y1, y2 and y3 are respectively three initial
The coordinate of mechanical coordinate on the y axis, z1, z2 and z3 are respectively coordinate of three initial mechanical coordinates in z-axis;RbExpression standard
The radius of ball;RqIndicate the radius of probe ball.
5. scaling method as claimed in claim 3, which is characterized in that if the quantity of the initial mechanical coordinate is four, step
Rapid S22The middle formula for calculating the target mechanical coordinate (X, Y, Z), as follows:
(X-x1)2+(Y-y1)2+(Z-z1)2=α;
(X-x2)2+(Y-y2)2+(Z-z2)2=α;
(X-x3)2+(Y-y3)2+(Z-z3)2=α;
(X-x4)2+(Y-y4)2+(Z-z4)2=α;
Wherein, x1, x2, x3 and x4 are respectively coordinate of four initial mechanical coordinates in x-axis, and y1, y2, y3 and y4 are respectively four
The coordinate of a initial mechanical coordinate on the y axis, z1, z2, z3 and z4 are respectively coordinate of four initial mechanical coordinates in z-axis;α
Indicate unknown constant.
6. scaling method as claimed in claim 3, which is characterized in that if the quantity of the initial mechanical coordinate is greater than four,
Step S22The step of middle calculating target mechanical coordinate (X, Y, Z), specifically includes:
It is using least square method by the initial mechanical coordinate fitting at the first spherical surface, the sphere centre coordinate of first spherical surface is true
It is set to target mechanical coordinate (X, Y, Z).
7. scaling method as claimed in claim 6, which is characterized in that step S3In, demarcate rotation center the step of specifically wrap
It includes:
S3-1a, three coordinate Q are arbitrarily chosen from at least three targets mechanical coordinatem、QpAnd Qq;
S3-2a, calculate line segment QmQpMiddle vertical plane M1, line segment QpQqMiddle vertical plane M2 and M1 and M2 intersection L;
S3-3a, calculate the intersecting point coordinate of the intersection L and the plane, according to the intersecting point coordinate and when the angle of rotary shaft is
The target mechanical coordinate obtained at 0 ° calculates the rotation center;
Or, S3-1b, the normal vector of the plane is labeled as
S3-2b, calculate target mechanical coordinate QjProjection coordinate Q ' on the planej;
S3-3b, willThe spin matrix R of Z axis forward direction is rotated to be, and spin matrix R is applied to projection coordinate Q 'jOn, it is rotated
Point coordinate Q " afterwardsj;
S3-4b, using least square method by Q "jIt is fitted to circle, equation of a circle is (x-a)2+(y-b)2=R2, by (a, b, z0) be determined as
Initial center of circle O;
z0Indicate Q "jCoordinate on Z axis;
S3-5b, calculate Z axis rotate in the forward direction forSpin matrix R ', spin matrix R ' is applied on initial center of circle O, is revolved
The coordinate of center of circle O ' after turning;
S3-6b, calculated according to the coordinate of postrotational center of circle O ' and the target mechanical coordinate obtained when the angle of rotary shaft is 0 °
The rotation center;
Or, S3-1c, using least square method by target mechanical coordinate QjIt is fitted to the second spherical surface, the equation of the second spherical surface is (x-d
)2+(y-e)2+(z-c)2=R2, (d, e, c) is determined as initial centre of sphere S;
S3-2c, calculate the subpoint S ' of initial centre of sphere S on the plane;
S3-2c, the target mechanical coordinate that obtains when being 0 ° of the coordinate according to subpoint S ' and the angle when rotary shaft calculate the rotation
Turn center;
J is the integer greater than 0.
8. a kind of calibration system of lathe yaw, lathe includes workbench and yaw;The yaw includes rotary shaft, and feature exists
In the calibration system includes: standard ball component, probe assembly, control module and computing module;
The standard ball component is fixed on the workbench;
The probe assembly is fixed on the yaw;
The control module rotates at least three angles for controlling the rotary shaft;
Wherein, an angle at least three angle is 0 °;
The computing module is used to calculate lathe identification point under each angle by the standard ball component and the probe assembly
Target mechanical coordinate, and demarcate according at least three target mechanical coordinates the rotation center and/or rotary shaft of the rotary shaft
Direction.
9. calibration system as claimed in claim 8, which is characterized in that the computing module specifically includes the first computing unit;
First computing unit is used for based on least square method and according at least three targets machinery coordinate fitting plane,
And the normal direction of the plane is determined as to the direction of the rotary shaft.
10. calibration system as claimed in claim 9, which is characterized in that the probe assembly includes: probe ball;The standard ball
Component includes standard ball;
The control module includes: driving unit;
The computing module further include: the second computing unit;
The driving unit is for driving the yaw to do relative motion relative to the standard ball, so that the probe ball is from least
Until contact with the standard ball, and second computing unit is called close to the standard ball in three directions;
The coordinate that second computing unit is used for lathe identification point when contacting the probe ball with the standard ball is determined as
Initial mechanical coordinate, and the target mechanical coordinate is calculated according at least three initial mechanical coordinates.
11. calibration system as claimed in claim 10, which is characterized in that if the quantity of the initial mechanical coordinate is three,
Second computing unit calculates target mechanical coordinate (X, Y, Z) by following formula:
(X-x1)2+(Y-y1)2+(Z-z1)2=(Rb+Rq)2;
(X-x2)2+(Y-y2)2+(Z-z2)2=(Rb+Rq)2;
(X-x3)2+(Y-y3)2+(Z-z3)2=(Rb+Rq)2;
Wherein, x1, x2 and x3 are respectively coordinate of three initial mechanical coordinates in x-axis, and y1, y2 and y3 are respectively three initial
The coordinate of mechanical coordinate on the y axis, z1, z2 and z3 are respectively coordinate of three initial mechanical coordinates in z-axis;RbExpression standard
The radius of ball;RqIndicate the radius of probe ball.
12. calibration system as claimed in claim 10, which is characterized in that if the quantity of the initial mechanical coordinate is four,
Second computing unit calculates target mechanical coordinate (X, Y, Z) by following formula:
(X-x1)2+(Y-y1)2+(Z-z1)2=α;
(X-x2)2+(Y-y2)2+(Z-z2)2=α;
(X-x3)2+(Y-y3)2+(Z-z3)2=α;
(X-x4)2+(Y-y4)2+(Z-z4)2=α;
Wherein, x1, x2, x3 and x4 are respectively coordinate of four initial mechanical coordinates in x-axis, and y1, y2, y3 and y4 are respectively four
The coordinate of a initial mechanical coordinate on the y axis, z1, z2, z3 and z4 are respectively coordinate of four initial mechanical coordinates in z-axis;α
Indicate unknown constant.
13. calibration system as claimed in claim 10, which is characterized in that if the quantity of the initial mechanical coordinate is greater than four
A, second computing unit is specifically used for the initial mechanical coordinate fitting using least square method into the first spherical surface, will
The sphere centre coordinate of first spherical surface is determined as target mechanical coordinate (X, Y, Z).
14. calibration system as claimed in claim 13, which is characterized in that the computing module further include: third computing unit;
The third computing unit from least three target mechanical coordinates for arbitrarily choosing three coordinate Qm、QpAnd Qq, calculate
Line segment QmQpMiddle vertical plane M1, line segment QpQqMiddle vertical plane M2 and M1 and M2 intersection L, calculate the intersection L and described flat
The intersecting point coordinate in face, and institute is calculated according to the intersecting point coordinate and the target mechanical coordinate obtained when the angle of rotary shaft is 0 °
State rotation center;
Or, the third computing unit is for the normal vector of the plane to be labeled asCalculate target mechanical coordinate QjDescribed
Projection coordinate Q ' in planej, willThe spin matrix R of Z axis forward direction is rotated to be, and spin matrix R is applied to projection coordinate
Q′jOn, obtain postrotational coordinate Q "j;The third computing unit is also used to utilize least square method by Q "jCircle is fitted to,
Equation of a circle is (x-a)2+(y-b)2=R2, by (a, b, z0) be determined as initial center of circle O, and calculate Z axis rotate in the forward direction forRotation
Matrix R ' is applied to spin matrix R ' on initial center of circle O, obtains the coordinate of postrotational center of circle O ', and according to postrotational
The coordinate of center of circle O ' and the target mechanical coordinate obtained when the angle of rotary shaft is 0 ° calculate the rotation center;Wherein, z0
Indicate Q "jCoordinate on Z axis;
Or, the third computing unit is used to use least square method by target mechanical coordinate QjIt is fitted to the second spherical surface, the second ball
Face equation is (x-d)2+(y-e)2+(z-c)2=R2, (d, e, c) is determined as initial centre of sphere S, and calculate initial centre of sphere S in institute
State the subpoint S ' in plane;The third computing unit is also used to the coordinate according to subpoint S ' and the angle when rotary shaft is
The target mechanical coordinate obtained at 0 ° calculates the rotation center;
J is the integer greater than 0.
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