CN115555918A - Method for identifying comprehensive errors of rotating shaft based on single-shaft driving of ball arm instrument - Google Patents
Method for identifying comprehensive errors of rotating shaft based on single-shaft driving of ball arm instrument Download PDFInfo
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Abstract
The invention discloses a rotating shaft comprehensive error identification method based on single-shaft driving of a ball arm apparatus, which is characterized in that a rotating shaft comprehensive error identification model is established based on homogeneous coordinate transformation; on the premise of meeting the requirement of the full rank of the comprehensive error identification matrix, aiming at reducing the installation time of a workpiece ball, determining five ball rod instrument installation modes, ensuring the quick measurement of the ball rod instrument and reducing the influence of temperature change on a comprehensive error measurement result under the hot state of a machine tool; and measuring the comprehensive error of the machine tool rotating shaft under the static state of the machine tool by using the proposed ball bar instrument measuring mode, then rotating the machine tool rotating shaft at the rotating speed of 100r/min for 20 minutes, and measuring the comprehensive error of the machine tool rotating shaft under the thermal state of the machine tool by using the proposed ball bar instrument measuring mode. And substituting the measured data into the comprehensive error identification model to obtain the comprehensive error of the machine tool rotating shaft. The invention realizes the identification of the comprehensive error of the coupling of the geometric error and the thermal error and improves the error compensation precision.
Description
Technical Field
The invention belongs to the field of error measurement of numerical control machines, and relates to a method for identifying comprehensive errors of a rotating shaft based on single-shaft driving of a ball arm instrument.
Technical Field
The numerical control machine tool is affected by various errors such as geometric error, thermal error, force error, control error and the like in the operation process, so that the relative pose of the numerical control machine tool and a workpiece is changed, and a machining error is generated. The geometric error and the thermal error are the most main error sources and account for more than 80% of the machine tool error. The measurement, modeling and compensation of the error of the numerical control machine tool are effective methods for reducing the machining error.
Common measuring tools for error measurement of numerical control machines include a ball bar instrument and a laser interferometer. The ball arm instrument is simple to operate, relatively low in cost and commonly used for measuring geometric errors of a numerical control machine. In the conventional research, the influence of only a single geometric error or a thermal error is considered, and the influence of a comprehensive geometric error and a comprehensive thermal error is not considered.
Disclosure of Invention
In view of the above, the present invention provides a method for identifying a composite error of a rotating shaft based on a single-axis driving of a ball bar machine, so as to identify a composite error of coupling of a geometric error and a thermal error, thereby improving error compensation accuracy.
In order to achieve the purpose, the invention provides the following technical scheme: a method for identifying comprehensive errors of a rotating shaft based on single-shaft driving of a ball arm instrument comprises the following steps:
1) Constructing a single-shaft driven rotating shaft comprehensive error identification model: and establishing a rotating shaft comprehensive error identification model based on homogeneous coordinate transformation.
2) Determination of a ball arm instrument measurement mode: on the premise of satisfying the full rank of the comprehensive error identification matrix, the length of the ball rod instrument and the position of the initial coordinate point are changed by taking the reduction of the installation time of the workpiece ball as a target, the installation modes of the five ball rod instruments are determined, the quick measurement of the ball rod instrument is ensured, and the influence of the temperature change on the comprehensive error measurement result is reduced under the hot state of the machine tool.
3) And (3) measuring the comprehensive error of the rotating shaft: firstly, the comprehensive error of the machine tool rotating shaft under the static state of the machine tool is measured by using the proposed ball bar instrument measuring mode. And then, rotating the machine tool rotating shaft at the rotating speed of 100r/min, and measuring the comprehensive error of the machine tool rotating shaft in the hot state of the machine tool by using the proposed ball arm instrument measuring mode every 20 minutes of rotation. And substituting the measured data into the comprehensive error identification model to obtain the comprehensive error of the machine tool rotating shaft.
Further, the construction of the single-shaft driven rotating shaft comprehensive error identification model comprises the following specific contents: and establishing a comprehensive error identification model containing the geometric error and the thermal error of the rotating shaft based on homogeneous coordinate transformation.
The ball rod instrument consists of two precise small balls and a linear displacement sensor, wherein the small ball arranged on a workbench is called a workpiece ball, and the small ball arranged at the end of a spindle is called a cutter ball. Let the spherical coordinate of the workpiece be P [ x ] 0 ,y 0 ,z 0 ,1] T The coordinates of the cutter ball are Q [0, h,1 ]] T And when the rotating angle is C, obtaining a workpiece ball spatial error matrix delta r:
Δr=[Δx,Δy,Δz,0] T =T(T e -I)P
where Δ x, Δ y, Δ z are error components on the x-axis, y-axis and z-axis, respectively, T is an ideal coordinate transformation matrix, and T is a value of e Is a coordinate transformation error matrix.
Obtaining an error component of the comprehensive error on the rotating shaft:
in the formula, delta x (C, T) is the moving comprehensive error of the C axis along the X axis coordinate axis direction, delta y (C, T) is the moving comprehensive error of the C axis along the Y axis coordinate axis direction, delta z (C, T) is the moving comprehensive error of the C axis along the coordinate axis direction of the Z axis, epsilon x (C, T) is the angle integral error of the C axis around the X axis, epsilon y (C, T) is the angle integral error of the C axis around the Y axis, epsilon z And (C, T) is the angle comprehensive error of the C axis around the Z axis.
Separating six error elements e = [ delta ] x (C,T),δ y (C,T),δ z (C,T),ε x (C,T),ε y (C,T),ε z (C,T)]In which epsilon z Is reduced in the calculation, so that ε cannot be calculated z To obtain Δ r:
L 0 (= Δ rcos β), β is the angle between the error vector and the theoretical position of the club instrument, and when β tends to infinity, L is 0 ≈ΔL。
In the formula, L 0 The projection length of deltar on the theoretical position of the cue instrument is shown, and deltaL is the change of the cue instrument length.
Obtaining the relation between the length transformation quantity delta L of the ball arm instrument and the errors of the rotating shaft:
in the formula, a is a unit direction of a theoretical position of the cue stick instrument, and L represents an initial length of the cue stick instrument.
The relationship between the change of the club length of the club and the comprehensive error is obtained as follows:
establishing a comprehensive error identification model:
when the full rank of the delta T matrix is satisfied, e can be solved r =[δ x (C,T),δ y (C,T),δ z (C,T),ε x (C,T),ε y (C,T)]。
Further, the club instrument measurement mode is determined, and the specific content is as follows: in order to meet the identification of the comprehensive error of the rotating shaft of the numerical control machine tool, a ball arm instrument measurement mode needs to meet two conditions, namely, a comprehensive error identification matrix ensures a full rank so as to ensure that a comprehensive error identification model has a solution; the different measurement modes are replaced quickly, the measurement is convenient, the installation times of the center seat are minimum, and the influence of the temperature change in the measurement process of the ball bar instrument on the error is reduced under the hot state of the machine tool; and constructing five ball arm instrument measurement modes suitable for the model according to the two points. The installation time of the workpiece ball is reduced by simply changing the length of the ball rod instrument and the position of the initial coordinate point. The specific installation method is as follows:
satisfy the full rank of comprehensive error identification matrix under this installation mode, work piece ball simple to operate need not frequent dismouting, reduces measurement and installation time, guarantees comprehensive error and measures the accuracy, obtains delta T this moment:
compared with the prior art, the invention has the beneficial effects that:
(1) And establishing a comprehensive error identification model for coupling the geometric error and the thermal error. The comprehensive error identification method is provided on the basis of the traditional static six-degree-of-freedom uniaxial geometric error measurement and dynamic single-degree-of-freedom thermal error measurement of the numerical control machine tool, so that the comprehensive error identification of coupling of the geometric error and the thermal error is realized, and the error compensation precision is improved.
(2) A method for quickly measuring the comprehensive error of a rotating shaft of a numerical control machine tool is provided. The convenient center seat installation mode is adopted, the center seat is only installed once, the measurement is quick, frequent disassembly and assembly are not needed, the measurement of comprehensive errors is convenient, and the influence of temperature change in the measurement process of the ball rod instrument on the errors in the hot state of the machine tool is reduced.
Drawings
FIG. 1 is a flow chart of a method for identifying a comprehensive error of a rotating shaft based on a single-shaft drive of a ball arm apparatus;
FIG. 2 is a schematic diagram of a single-axis driven rotation axis comprehensive error identification model construction;
fig. 3 and 4 are schematic diagrams of five measurement modes of the cue stick instrument. The symbols in the drawings mean: 1-a first measurement mode, 2-a second measurement mode, 3-a third measurement mode, 4-a fourth measurement mode, 5-a fifth measurement mode.
Detailed Description
The present invention will be described in further detail with reference to the attached drawings and detailed description so that those skilled in the art can better understand the present invention and can implement the present invention, but the present invention is not limited by the illustrated examples.
As shown in fig. 1, the method for identifying the comprehensive error of the rotating shaft based on the single-axis driving of the ball bar machine provided by the invention comprises the following steps:
1) Constructing a single-shaft driven rotating shaft comprehensive error identification model: and establishing a comprehensive error identification model containing the geometric error and the thermal error of the rotating shaft based on homogeneous coordinate transformation. The process of constructing the comprehensive error identification model is shown in fig. 2, the ball rod instrument consists of two precise small balls and a linear displacement sensor, the small ball arranged on a workbench is called a workpiece ball when the ball rod instrument is used, and the small ball arranged at the main shaft end is called a cutter ball. Let the spherical coordinate of the workpiece be P [ x ] 0 ,y 0 ,z 0 ,1] T The coordinates of the cutter ball are Q [0, h,1 ]] T And when the rotating angle is C, obtaining a workpiece ball spatial error matrix delta r:
Δr=[Δx,Δy,Δz,0] T =T(T e -I)P
where Δ x, Δ y, Δ z are error components on the x-axis, y-axis and z-axis, respectively, T is an ideal coordinate transformation matrix, and T is a value of e Is a coordinate transformation error matrix.
Obtaining an error component of the comprehensive error on the rotating shaft:
in the formula, delta x (C, T) is the moving comprehensive error of the C axis along the X axis coordinate axis direction, delta y (C, T) is the moving comprehensive error of the C axis along the Y axis coordinate axis direction, delta z (C, T) is the moving comprehensive error of the C axis along the coordinate axis direction of the Z axis, epsilon x (C, T) is the angle integral error of the C axis around the X axis, epsilon y (C, T) is the angle integral error of the C axis around the Y axis, epsilon z And (C, T) is the angle comprehensive error of the C axis around the Z axis.
Separating six error elements e = [ delta ] x (C,T),δ y (C,T),δ z (C,T),ε x (C,T),ε y (C,T),ε z (C,T)]In which epsilon z Is reduced in the calculation, so that ε cannot be calculated z Obtaining delta r:
L 0 = Delta rcos beta, beta is the angle between the error vector and the theoretical position of the cue instrument, and when beta is approaching infinity, L is 0 ≈ΔL。
In the formula, L 0 The projected length of deltar on the theoretical position of the cue instrument is shown, and deltaL is the change of the cue instrument length.
Obtaining the relation between the length transformation quantity delta L of the ball arm instrument and the errors of the rotating shaft:
in the formula, a is a unit direction of a theoretical position of the cue stick instrument, and L represents an initial length of the cue stick instrument.
The relationship between the change of the club length of the club and the comprehensive error is obtained as follows:
establishing a comprehensive error identification model:
when the full rank of the delta T matrix is satisfied, e can be solved r =[δ x (C,T),δ y (C,T),δ z (C,T),ε x (C,T),ε y (C,T)]。
2) Determination of a ball arm instrument measurement mode: in order to meet the identification of the comprehensive error of the rotating shaft of the numerical control machine tool, a ball arm instrument measurement mode needs to meet two conditions, namely, a comprehensive error identification matrix ensures a full rank so as to ensure that a comprehensive error identification model has a solution; the different measurement modes are replaced quickly, the measurement is convenient, the installation times of the center seat are minimum, and the influence of the temperature change in the measurement process of the ball bar instrument on the error is reduced under the hot state of the machine tool; and constructing five ball arm instrument measurement modes suitable for the model according to the two points. The installation time of the workpiece ball is reduced by simply changing the length of the ball arm apparatus and the position of the initial coordinate point. As shown in fig. 3 and 4, the specific mounting method is as follows:
satisfy the full rank of comprehensive error identification matrix under this installation mode, work piece ball simple to operate need not frequent dismouting, reduces measurement and installation time, guarantees comprehensive error and measures the accuracy, obtains delta T this moment:
3) And (3) measuring the comprehensive error of the rotating shaft: firstly, the comprehensive error of the machine tool rotating shaft under the static state of the machine tool is measured by using the proposed ball bar instrument measuring mode. And then, rotating the machine tool rotating shaft at the rotating speed of 100r/min, and measuring the comprehensive error of the machine tool rotating shaft in the hot state of the machine tool by using the proposed ball arm instrument measuring mode every 20 minutes of rotation. And substituting the measured data into the comprehensive error identification model to obtain the comprehensive error of the machine tool rotating shaft.
Claims (4)
1. A method for identifying comprehensive errors of a rotating shaft based on single-shaft driving of a ball arm instrument is characterized by comprising the following steps: the method comprises the following steps:
1) Constructing a single-shaft driven rotating shaft comprehensive error identification model: establishing a rotating shaft comprehensive error identification model based on homogeneous coordinate transformation;
2) Determination of a ball arm instrument measurement mode: on the premise of satisfying the full rank of the comprehensive error identification matrix, the length of a ball rod instrument and the position of an initial coordinate point are changed by taking the reduction of the installation time of a workpiece ball as a target, five ball rod instrument installation modes are determined, the quick measurement of the ball rod instrument is ensured, and the influence of temperature change on the comprehensive error measurement result is reduced under the hot state of a machine tool;
3) And (3) measuring the comprehensive error of the rotating shaft: firstly, measuring the comprehensive error of a machine tool rotating shaft under the static state of the machine tool by using the proposed ball bar instrument measuring mode; then, the machine tool rotating shaft rotates at the rotating speed of 100r/min, and the comprehensive error of the machine tool rotating shaft in the hot state of the machine tool is measured by using the ball arm instrument measuring mode every 20 minutes; and substituting the measured data into the comprehensive error identification model to obtain the comprehensive error of the machine tool rotating shaft.
2. The single-axis driven rotational axis synthetic error identification model construction according to claim 1, wherein: establishing a comprehensive error identification model containing a geometric error and a thermal error of a rotating shaft based on homogeneous coordinate transformation;
the ball rod instrument consists of two precise small balls and a linear displacement sensor, wherein the small balls arranged on the workbench are called workpiece balls, and the small balls arranged at the end of the main shaft are called tool balls; let the spherical coordinate of the workpiece be P [ x ] 0 ,y 0 ,z 0 ,1] T The coordinates of the cutter ball are Q [0, h,1 ]] T When the rotation angle is C, a workpiece ball space error matrix delta r = [ delta x, delta y, delta z,0 ] is obtained] T :
Δr=[Δx,Δy,Δz,0] T =T(T e -I)P
In the formula: Δ x, Δ y, Δ z are error components on the x-axis, y-axis and z-axis, respectively, T is an ideal coordinate transformation matrix, T e A coordinate transformation error matrix;
obtaining an error component of the comprehensive error on the rotating shaft:
in the formula, delta x (C, T) is the moving comprehensive error of the C axis along the X axis coordinate axis direction, delta y (C, T) is the moving comprehensive error of the C axis along the Y axis coordinate axis direction, delta z (C, T) is the moving comprehensive error of the C axis along the coordinate axis direction of the Z axis, epsilon x (C, T) is the angle integral error of the C axis around the X axis, epsilon y (C, T) is the angle integral error of the C axis around the Y axis, epsilon z (C, T) is the angle comprehensive error of the C axis around the Z axis;
separating six error elements e = [ delta ] x (C,T),δ y (C,T),δ z (C,T),ε x (C,T),ε y (C,T),ε z (C,T)]In which epsilon z Is reduced in the calculation, so that epsilon cannot be calculated z Obtaining delta r:
L 0 = Δ rcos β, β is the angle between the error vector and the theoretical position of the cue stick, L when β goes to infinity 0 ≈ΔL;
Wherein L is 0 The projection length of delta r on the theoretical position of the cue instrument is shown, and delta L is the change of the cue length of the cue instrument;
obtaining the relation between the length transformation quantity delta L of the ball arm instrument and the errors of the rotating shaft:
wherein a is the unit direction of the theoretical position of the cue instrument, and L represents the initial length of the cue instrument;
the relationship between the change of the club length of the club and the comprehensive error is obtained as follows:
establishing a comprehensive error identification model:
when the full rank of the delta T matrix is satisfied, e can be solved r =[δ x (C,T),δ y (C,T),δ z (C,T),ε x (C,T),ε y (C,T)]。
3. The cue meter measurement mode determination of claim 1: the method is characterized in that: in order to meet the identification of the comprehensive error of the rotating shaft of the numerical control machine tool, a ball arm instrument measurement mode needs to meet two conditions, namely, a comprehensive error identification matrix ensures a full rank so as to ensure that a comprehensive error identification model has a solution; the different measurement modes are replaced quickly, the measurement is convenient, the installation times of the center seat are minimum, and the influence of the temperature change in the measurement process of the ball bar instrument on the error is reduced under the hot state of the machine tool; according to the two points, five ball arm instrument measurement modes suitable for the model are constructed; the installation time of the workpiece ball is reduced by simply changing the length of the ball rod instrument and the position of the initial coordinate point;
the specific installation method is as follows:
Satisfy comprehensive error and discern the full rank of matrix under this installation mode, work piece ball simple to operate need not frequent dismouting, reduces measurement and installation time, guarantees the accuracy of comprehensive error measurement, obtains delta T this moment:
4. the rotating shaft composite error measurement of claim 1, wherein: firstly, measuring the comprehensive error of a machine tool rotating shaft under the static state of the machine tool by using the proposed ball bar instrument measuring mode; then, the machine tool rotating shaft rotates at the rotating speed of 100r/min, and the comprehensive error of the machine tool rotating shaft in the hot state of the machine tool is measured by using the ball arm instrument measuring mode every 20 minutes; and substituting the measured data into the comprehensive error identification model to obtain the comprehensive error of the machine tool rotating shaft.
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