CN101913103B - Method for measuring angular errors of rotating table of numerical control machine - Google Patents

Method for measuring angular errors of rotating table of numerical control machine Download PDF

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CN101913103B
CN101913103B CN 201010256629 CN201010256629A CN101913103B CN 101913103 B CN101913103 B CN 101913103B CN 201010256629 CN201010256629 CN 201010256629 CN 201010256629 A CN201010256629 A CN 201010256629A CN 101913103 B CN101913103 B CN 101913103B
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rotating
numerical control
axis
control machine
standard ball
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CN101913103A (en
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李郝林
吴晓健
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上海理工大学
上海机床厂有限公司
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Abstract

The invention relates to a method for measuring the angular errors of a rotating table of a numerical control machine, which comprises the following steps of: firstly, determining the angular errors of the numerical control rotating table rotating around X axis and Y axis; using a high-precision standard ball as a measuring basis, determining the actual motion trail of the numerical control rotating table according to the special position of the measuring standard ball, and calculating the angular errors of the numerical control rotating table rotating around the X axis and the Y axis, wherein the standard ball is supported by a base bracket and fixed on the rotating table. In the invention, the standard ball and an infrared three-dimensional workpiece measuring head are used for forming a measuring system, the position of circle center and the angular errors of the numerical control rotating table are calculated by detecting the motion position of the standard ball, thereby providing a basis for compensating the annular errors of the rotating table.

Description

Method for measuring angular errors of rotating table of numerical control machine

Technical field

The present invention relates to a kind of angular errors of rotating table of numerical control machine detection method, especially a kind of for the five-axis linkage machine tools method for measuring angular errors of rotating table of numerical control machine.

Background technology

Rotating table of numerical control machine is the critical component that is applied to five-axis linkage machine tools, the positional precision of rotary table gyration is the key influence factor that determines location of workpiece benchmark, motion benchmark, therefore the angular errors of rotating table of numerical control machine detection technique is most important to the assurance of machine finish, is the key technology that high precision machine tool must solve.At present, also there is no a kind of angular errors of rotating table of numerical control machine accurate measurement method.

Summary of the invention

The present invention will provide a kind of method for measuring angular errors of rotating table of numerical control machine, the method utilizes standard ball and infrared three-dimension workpiece probe to form measuring system, detection according to the standard ball movement position, reverse goes out rotating table of numerical control machine home position and angular errors, for the compensation of the angular errors of rotary table provides foundation.

For achieving the above object, technical scheme of the present invention is: a kind of method for measuring angular errors of rotating table of numerical control machine comprises the steps:

1. the definition rotating table of numerical control machine is around the angular errors of X-axis and Z axis

δ Xi)=θ ii′????(1)

δ Zj)=θ jj′????(2)

θ in formula i, θ jBe respectively the actual measurement corner value around X-axis and Z axis rotation, θ i', θ j' be respectively the nominal corner value around the rotation of X-axis and Z axis;

2. measure and obtain rotating table of numerical control machine around the angular errors of X-axis and Z axis

With high-precision standard ball as measuring basis, standard ball is supported by base bracket, be fixed on workbench, determine the actual motion track of rotating table of numerical control machine by the locus of measurement standard ball, obtain rotating table of numerical control machine around the angular errors of X-axis and Z axis.

Concrete measuring method a: standard ball is fixed on workbench by base, control respectively the rotating table of numerical control machine transposition and drive servomotor and corner driving servomotor, make rotating table of numerical control machine do respectively the gyration of two-freedom around X-axis and Z axis, and the infrared three-dimension workpiece probe is arranged on main shaft of numerical control machine tool, in order to the centre of sphere movement locus position coordinates of measurement standard ball, and obtain the angular errors of rotating table of numerical control machine;

Rotating table of numerical control machine is measured around the Z axis angular errors:

Transposition drives servomotor rotating table of numerical control machine is fixed on apart from a certain angle position φ of horizontal plane, then controls corner driving driven by servomotor rotating table of numerical control machine and rotates around Z axis, makes it rotate respectively ψ 1, ψ 2..., ψ nAngle, and measure the spatial coordinate of spherical center (X of standard ball on rotating table of numerical control machine ψ 1, Y ψ 1, Z ψ 1), (X ψ 2, Y ψ 2, Z ψ 2) ..., (X ψ n, Y ψ n, Z ψ n), for the convenient corner that calculates rotating table of numerical control machine, pass through coordinate transformation method, calculate rotating table of numerical control machine around X-axis-φ angle, in its plan-position that rotates to φ=0 °, definition coordinate system X ' OY ', and with the spatial coordinate of spherical center (X of standard ball ψ 1, Y ψ 1, Z ψ 1), (X ψ 2, Y ψ 2, Z ψ 2) ..., (X ψ n, Y ψ n, Z ψ n) be transformed into the coordinate (X on coordinate system X ' OY ' ψ 1', Y ψ 1', Z ψ 1'), (X ψ 2', Y ψ 2', Z ψ 2') ..., (X ψ n', Y ψ n', Z ψ n'), wherein

X ψi′=X ψi???????????????????(3)

Y ψi′=Y ψicos-Z ψisinφ??????(4)

Z ψi′=Y ψisinφ+Z ψicosφ????(5)

I=1 in formula, 2 ..., n, through type (3)-Shi (5) is converted to X ' OY ' with the sphere center position coordinate of standard ball by coordinate system XOY; Standard ball centre of sphere point (X ψ i', Y ψ i', Z ψ i') and point (X ψ j', Y ψ j', Z ψ j') between around the rotational angle theta of Z axis ijTried to achieve by formula (6):

sin θ ij = Y ψj ′ - Y ψi ′ R - - - ( 6 )

R in formula be the centre of sphere apart from the distance of rotary table axis of rotation Z axis, the equation of a circle of standard ball centre of sphere track is expressed as:

(X′-X 0′) 2+(Y′-Y 0′) 2=R 2????(7)

Coordinate figure (X with three centre ofs sphere ψ i', Y ψ i'), (X ψ j', Y ψ j'), (X ψ k', Y ψ k') substitution formula (7), obtain the central coordinate of circle (X of centre of sphere track 0', Y 0') and the centre of sphere apart from the distance R of the axis of rotation of rotary table, with R substitution formula (6), try to achieve point (X ψ i', Y ψ i', Z ψ i') and point (X ψ j', Y ψ j', Z ψ j') between rotational angle theta ij, according to the nominal value θ of this angle ij' and calculate angular errors δ by formula (1) Zij); In like manner, obtain the angular errors of other position;

Rotating table of numerical control machine is around the measurement of X-axis angular errors:

When if rotating table of numerical control machine is measured angular errors around X-axis, control transposition at rotating table of numerical control machine and drive servomotor in the slewing area of X-axis, make it rotate respectively φ 1, φ 2..., φ mAngle, and measure the spatial coordinate of spherical center (X of standard ball on rotating table of numerical control machine φ 1, Y φ 1, Z φ 1), (X φ 2, Y φ 2, Z φ 2) ..., (X φ m, Y φ m, Z φ m), calculate standard ball spatial coordinate of spherical center (X φ 1, Y φ 1, Z φ 1), (X φ 2, Y φ 2, Z φ 2) ..., (X φ m, Y φ m, Z φ m) coordinate figure that is projected to the YOZ plane is: (O, Y φ 1, Z φ 1), (O, Y φ 2, Z φ 2) ..., (O, Y φ m, Z φ m); Obtain standard ball spatial coordinate of spherical center (O, Y on rotating table of numerical control machine by formula (8) φ i, Z φ i) and (O, Y φ j, Z φ j) between included angle ij

cos φ ij = b 2 + c 2 - a 2 2 bc - - - ( 8 )

Wherein, rotating table of numerical control machine swings geometrical relationship around X-axis:

a = ( Y φi - Y φj ) 2 + ( Z φi - Z φj ) 2

b = Y φi 2 + Z φi 2 - - - ( 9 )

c = Y φj 2 + Z φj 2

According to formula (8) and formula (9), by the spatial coordinate of spherical center value of standard ball on rotating table of numerical control machine, try to achieve rotating table of numerical control machine around the rotational angle φ of X-axis ij, and according to the nominal value φ of this angle ij' and calculate angular errors δ by formula (1) Xij).

The invention has the beneficial effects as follows: rotating table of numerical control machine is the critical component that is applied to five-axis linkage machine tools, the positional precision of rotary table gyration is the key influence factor that determines location of workpiece benchmark, motion benchmark, therefore the angular errors of rotating table of numerical control machine detection technique is most important to the assurance of machine finish, is the key technology that high precision machine tool must solve.The present invention utilizes standard ball and infrared three-dimension workpiece probe to form measuring system, and according to the detection of standard ball movement position, reverse goes out rotating table of numerical control machine home position and angular errors, for the angular errors compensation of rotary table provides foundation.

Description of drawings

Fig. 1 is the fundamental diagram of two-freedom rotating table of numerical control machine;

Fig. 2 is the standard ball position view;

Fig. 3 is that standard ball is measured the track schematic diagram;

Fig. 4 is standard ball initial position schematic diagram;

Fig. 5 is that rotating table of numerical control machine swings the geometrical relationship schematic diagram around X-axis.

The specific embodiment

The present invention is further illustrated below in conjunction with accompanying drawing and embodiment.

1. method for measuring angular errors of rotating table of numerical control machine

The schematic diagram of two-freedom rotating table of numerical control machine as shown in Figure 1.According to the needs of workpiece processing, rotating table of numerical control machine drives servomotor and corner driving driven by servomotor by transposition, does respectively the gyration of two-freedom around X-axis and Z axis.And the angular errors of rotating table of numerical control machine is the important indicator of rotary table system performance, is also directly determining the machining accuracy of numerical control machining center.Rotating table of numerical control machine is defined as respectively around the angular errors of X-axis and Z axis:

δ Xi)=θ ii′????(1)

δ Zj)=θ jj′????(2)

θ in formula i, θ jBe respectively the actual measurement corner value around X-axis and Z axis rotation, θ i', θ j' be respectively the nominal corner value around the rotation of X-axis and Z axis.

In order to measure the angular errors of rotating table of numerical control machine, the present invention adopts high-precision standard ball as measuring basis, standard ball is supported by base bracket, be fixed on workbench, determine the actual motion track of rotating table of numerical control machine by the locus of measurement standard ball, obtain the angular errors of rotating table of numerical control machine with the method.

Concrete measurement scheme is as follows: a standard ball is fixed on workbench, by base as shown in Figure 2.Control respectively the rotating table of numerical control machine transposition and drive servomotor and corner driving servomotor, make rotating table of numerical control machine do respectively the gyration of two-freedom around X-axis and Z axis.And the infrared three-dimension workpiece probe is arranged on main shaft of numerical control machine tool, in order to the centre of sphere movement locus position coordinates of measurement standard ball, and obtain the angular errors of rotating table of numerical control machine.Below narrate respectively rotating table of numerical control machine around the Z axis angular errors and around the measuring method of X-axis angular errors.

2. rotating table of numerical control machine is around the measuring method of Z axis angular errors

Transposition drives servomotor rotating table of numerical control machine is fixed on apart from a certain angle position φ of horizontal plane, then controls corner driving driven by servomotor rotating table of numerical control machine and rotates around Z axis, as shown in Figure 3, makes it rotate respectively ψ 1, ψ 2..., ψ nAngle, and measure the spatial coordinate of spherical center (X of standard ball on rotating table of numerical control machine ψ 1, Y ψ 1, Z ψ 1), (X ψ 2, Y ψ 2, Z ψ 2) ..., (X ψ n, Y ψ n, Z ψ n).For the convenient corner that calculates rotating table of numerical control machine, by coordinate transformation method, calculate rotating table of numerical control machine around X-axis-φ angle, in its plan-position that rotates to φ=0 °, definition coordinate system X ' OY ', and with the spatial coordinate of spherical center (X of standard ball ψ 1, Y ψ 1, Z ψ 1), (X ψ 2, Y ψ 2, Z ψ 2) ..., (X ψ n, Y ψ n, Z ψ n) be transformed into the coordinate (X on coordinate system X ' OY ' ψ 1', Y ψ 1', Z ψ 1'), (X ψ 2', Y ψ 2', Z ψ 2') ..., (X ψ n', Y ψ n', Z ψ n').Wherein

X ψi′=X ψi???????????????????(3)

Y ψi′=Y ψicosφ-Z ψisinφ????(4)

Z ψi′=Y ψisinφ+Z ψicosφ????(5)

I=1 in formula, 2 ..., n.Through type (3)-Shi (5) can be converted to X ' OY ' by coordinate system XOY with the sphere center position coordinate of standard ball.

Standard ball centre of sphere point (X ψ i', Y ψ i', Z ψ i') and point (X ψ j', Y ψ j', Z ψ j') between around the rotational angle theta of Z axis ijCan be tried to achieve by following formula:

sin θ ij = Y ψj ′ - Y ψi ′ R - - - ( 6 )

R in formula be the centre of sphere apart from the distance of rotary table axis of rotation Z axis, its value can be by three

The coordinate figure of the centre of sphere is tried to achieve.The equation of a circle of standard ball centre of sphere track can be expressed as:

(X′-X 0′) 2+(Y′-Y 0′) 2=R 2????(7)

(X in formula 0', Y 0') be the central coordinate of circle of centre of sphere track.Coordinate figure (X with three centre ofs sphere ψ i', Y ψ i'), (X ψ j', Y ψ j'), (X ψ k', Y ψ k') substitution formula (7), can obtain the central coordinate of circle (X of centre of sphere track 0', Y 0') and the centre of sphere apart from the distance R of the axis of rotation of rotary table, with R substitution formula (6), can try to achieve point (X ψ i, Y ψ i', Z ψ i') and point (X ψ j', Y ψ j', Z ψ j') between rotational angle theta ij, according to the nominal value θ of this angle ij' and calculate angular errors δ by formula (1) Zij).In like manner, can obtain the angular errors of other position.

3. rotating table of numerical control machine is around the measuring method of X-axis angular errors

When if rotating table of numerical control machine is measured angular errors around X-axis, the position A of standard ball as shown in Figure 4, rotating table of numerical control machine has certain scope around the rotation (swing) of X-axis, controls transposition and drive servomotor in its scope, makes it rotate respectively φ 1, φ 2..., φ mAngle, and measure the spatial coordinate of spherical center (X of standard ball on rotating table of numerical control machine φ 1, Y φ 1, Z φ 1), (X φ 2, Y φ 2, Z φ 2) ..., (X φ m, Y φ m, Z φ m).Around the corner of X-axis, calculate standard ball spatial coordinate of spherical center (X for the convenient rotating table of numerical control machine that calculates φ 1, Y φ 1, Z φ 1), (X φ 2, Y φ 2, Z φ 2) ..., (X φ m, Y φ m, Z φ m) coordinate figure that is projected to the YOZ plane is: (O, Y φ 1, Z φ 1), (O, Y φ 2, Z φ 2) ..., (O, Y φ m, Z φ m).

Fig. 5 illustrates rotating table of numerical control machine and swings the geometrical relationship schematic diagram around X-axis, according to the diagram geometrical relationship, can obtain standard ball spatial coordinate of spherical center (O, Y on rotating table of numerical control machine φ i, Z φ i) and (O, Y φ j, Z φ j) between included angle ijComputing formula:

cos φ ij = b 2 + c 2 - a 2 2 bc - - - ( 8 )

Wherein, rotating table of numerical control machine swings geometrical relationship around X-axis:

a = ( Y φi - Y φj ) 2 + ( Z φi - Z φj ) 2 (9)

b = Y φi 2 + Z φi 2

c = Y φj 2 + Z φj 2

According to formula (8) and formula (9), by the spatial coordinate of spherical center value of standard ball on rotating table of numerical control machine, can try to achieve rotating table of numerical control machine around the rotational angle φ of X-axis ij, and according to the nominal value φ of this angle ij' and calculate angular errors δ by formula (1) Xij).

Claims (1)

1. a method for measuring angular errors of rotating table of numerical control machine, comprise the steps:
One, the definition rotating table of numerical control machine is around the angular errors of X-axis and Z axis
δ Xi)=θ ii′????????????(1)
δ Zj)=θ jj′????????????(2)
θ in formula i, θ jBe respectively the actual measurement corner value around X-axis and Z axis rotation, θ i', θ j' be respectively the nominal corner value around the rotation of X-axis and Z axis;
Two, measure and obtain rotating table of numerical control machine around the angular errors of X-axis and Z axis
with high-precision standard ball as measuring basis, standard ball is supported by base bracket, be fixed on workbench, determine the actual motion track of rotating table of numerical control machine by the locus of measurement standard ball, obtain rotating table of numerical control machine around the angular errors of X-axis and Z axis, described measurement and obtain rotating table of numerical control machine and around the concrete measuring method of the angular errors of X-axis and Z axis be a: standard ball is fixed on workbench by base, control respectively the rotating table of numerical control machine transposition and drive servomotor and corner driving servomotor, make rotating table of numerical control machine do respectively the gyration of two-freedom around X-axis and Z axis, and the infrared three-dimension workpiece probe is arranged on main shaft of numerical control machine tool, centre of sphere movement locus position coordinates in order to the measurement standard ball, and obtain the angular errors of rotating table of numerical control machine, it is characterized in that:
Described rotating table of numerical control machine around the concrete measuring method of Z axis angular errors is:
Transposition drives servomotor rotating table of numerical control machine is fixed on apart from a certain angle position φ of horizontal plane, then controls corner driving driven by servomotor rotating table of numerical control machine and rotates around Z axis, makes it rotate respectively ψ 1, ψ 2..., ψ nAngle, and measure the spatial coordinate of spherical center (X of standard ball on rotating table of numerical control machine ψ 1, Y ψ 1, Z ψ 1), (X ψ 2, Y ψ 2, Z ψ 2) ..., (X ψ n, Y ψ n, Z ψ n), for the convenient corner that calculates rotating table of numerical control machine, pass through coordinate transformation method, calculate rotating table of numerical control machine around the corner φ of X-axis, in its plan-position that rotates to φ=0 °, definition coordinate system X ' OY ', and with the spatial coordinate of spherical center (X of standard ball ψ 1, Y ψ 1, Z ψ 1), (X ψ 2, Y ψ 2, Z ψ 2) ..., (X ψ n, Y ψ n, Z ψ n) be transformed into the coordinate (X on coordinate system X ' OY ' ψ 1', Y ψ 1', Z ψ 1'), (X ψ 2', Y ψ 2', Z ψ 2') ..., (X ψ n', Y ψ n', Z ψ n'), wherein
X ψi′=X ψi????????????(3)
Y ψi′=Y ψicosφ-Z ψisinφ?????????????????????(4)
Z ψi′=Y ψisinφ+Z ψicosφ?????????????????????(5)
I=1 in formula, 2 ..., n, through type 3-formula 5 is converted to X ' OY ' with the sphere center position coordinate of standard ball by coordinate system XOY; Standard ball centre of sphere point (X ψ i', Y ψ i', Z ψ i) and point (X ψ j', Y ψ j', Z ψ j') between around the rotational angle theta of Z axis ijTried to achieve by formula 6:
sin θ ij = Y ψj ′ - Y ψi ′ R - - - ( 6 )
R in formula be the centre of sphere apart from the distance of rotary table axis of rotation Z axis, the equation of a circle of standard ball centre of sphere track is expressed as:
(X′-X 0′) 2+(Y′-Y 0′) 2=R 2?????????????????????(7)
Coordinate figure (X with three centre ofs sphere ψ i', Y ψ i'), (X ψ j', Y ψ j'), (X ψ k', Y ψ k') substitution formula 7, obtain the central coordinate of circle (X of centre of sphere track 0', Y 0') and the centre of sphere apart from the distance R of the axis of rotation of rotary table, with R substitution formula 6, try to achieve point (X ψ i', Y ψ i', Z ψ i') and point (X ψ j', Y ψ j', Z ψ j') between rotational angle theta ij, according to the nominal value θ of this angle ij' and calculate angular errors δ by formula 1 Zij); In like manner, obtain the angular errors of other position;
Described rotating table of numerical control machine around the concrete measuring method of X-axis angular errors is:
When if rotating table of numerical control machine is measured angular errors around X-axis, control transposition at rotating table of numerical control machine and drive servomotor in the slewing area of X-axis, make it rotate respectively φ 1, φ 2..., φ mAngle, and measure the spatial coordinate of spherical center (X of standard ball on rotating table of numerical control machine φ 1, Y φ 1, Z φ 1), (X φ 2, Y φ 2, Z φ 2) ..., (X φ m, Y φ m, Z φ m), calculate standard ball spatial coordinate of spherical center (X φ 1, Y φ 1, Z φ 1), (X φ 2, Y φ 2, Z φ 2) ..., (X φ m, Y φ m, Z φ m) coordinate figure that is projected to the YOZ plane is: (O, Y φ 1, Z φ 1), (O, Y φ 2, Z φ 2) ..., (O, Y φ m, Z φ m); Obtain standard ball spatial coordinate of spherical center (O, Y on rotating table of numerical control machine by formula 8 φ i, Z φ i) and (O, Y φ j, Z φ j) between included angle ij
cos φ ij = b 2 + c 2 - a 2 2 bc - - - ( 8 )
Wherein, rotating table of numerical control machine swings geometrical relationship around X-axis:
a = ( Y φi - Y φj ) 2 + ( Z φi - Z φj ) 2
b = Y φi 2 + Z φi 2 - - - ( 9 )
According to formula 8 and formula 9, by the spatial coordinate of spherical center value of standard ball on rotating table of numerical control machine, try to achieve rotating table of numerical control machine around the rotational angle φ of X-axis ij, and according to the nominal value φ of this angle ij' and calculate angular errors δ by formula 1 Xij).
CN 201010256629 2010-08-19 2010-08-19 Method for measuring angular errors of rotating table of numerical control machine CN101913103B (en)

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