CN108303251B - Rigidity modeling and indirect detection method in electric spindle rotation state - Google Patents
Rigidity modeling and indirect detection method in electric spindle rotation state Download PDFInfo
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- CN108303251B CN108303251B CN201810355005.4A CN201810355005A CN108303251B CN 108303251 B CN108303251 B CN 108303251B CN 201810355005 A CN201810355005 A CN 201810355005A CN 108303251 B CN108303251 B CN 108303251B
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Abstract
The invention discloses a rigidity modeling and indirect detection method of an electric spindle in a rotating state, and mainly aims to solve the problem that the rigidity of the electric spindle in the rotating state is difficult to directly detect. The method adopts a small deflection differential equation and Hooke's law to respectively establish deformation equations of a joint surface of a rotating shaft, a bearing, a customized tool holder and a main shaft tool holder; and obtaining a rigidity model of the electric spindle system consisting of the rotating shaft, the bearing, the spindle and tool shank combining surface, the customized tool shank and the like by using a superposition principle. Based on a detection system consisting of a loading device and a main shaft rotation error analyzer, rigidity values of a rotating shaft, a main shaft cutter handle joint surface and a customized cutter handle in a static state of the electric main shaft are identified, then bearing rigidity values in a rotating state of the electric main shaft are identified, and finally the real rigidity of the electric main shaft is calculated based on a rigidity model of the electric main shaft. The method can accurately detect the rigidity of the electric spindle and can be used for testing the performance of the electric spindle.
Description
Technical Field
The invention relates to the field of electric spindle performance detection, in particular to a rigidity modeling and indirect detection method of an electric spindle in a rotating state.
Background
The rapid development of the electric spindle technology enables the high-speed numerical control machining technology to be widely applied. The electric spindle integrates the spindle of the numerical control machine tool with the spindle motor, so that the spindle part of the numerical control machine tool is independent from a transmission system and an integral structure of the machine tool, and the electric spindle has the advantages of compact structure, light weight, small inertia, high rotating speed, high precision, low noise, quick response and the like. At present, the electric spindle is required to have not only high-speed operation with precision but also high rigidity. The motion precision and rigidity of the electric spindle directly influence the machining precision of the numerical control machine tool and the surface quality of a workpiece. Too low a stiffness of the electric spindle in rotation usually results in chatter, excessive blade tilt and unwanted back-cutting. Therefore, in order to ensure an optimal machining process and reliable operation, it is necessary to detect the rigidity of the electric spindle and evaluate its performance in a rotating state.
The stiffness of the motorized spindle can be divided into static stiffness and stiffness under rotational conditions. Since the force cannot be applied to the tip of the electric spindle and the amount of deformation in the direction of the applied force cannot be detected at the same time when the electric spindle is rotated at high speed, the rigidity of the electric spindle is generally detected in a stationary state. However, when the numerical control machine tool is processed, the electric spindle is in a rotating state, so that the rigidity of the electric spindle in the rotating state is detected, and the rigidity of the electric spindle can be more accurately evaluated. In addition, the electric spindle generates centrifugal force and gyroscopic moment when rotating, so that the positions and gaps among internal elements of the electric spindle are changed, and the rigidity of the electric spindle is changed. Therefore, the rigidity of the electric spindle in a rotating state needs to be detected.
The invention provides a rigidity modeling and indirect detection method under a rotating state of an electric spindle, aiming at the problem that the rigidity of the electric spindle cannot be directly detected under the rotating state, firstly, a rigidity model of an electric spindle system is established through a deformation equation and a superposition principle, parameters in the rigidity model of the electric spindle system are identified under the static state and the rotating state of the electric spindle respectively, and finally, rigidity values of the electric spindle under different rotating speeds are obtained through model conversion. The method can be applied to the performance test of the electric spindle, and can accurately detect the rigidity of the electric spindle.
Disclosure of Invention
The invention aims to provide a rigidity modeling and indirect detection method under the rotation state of an electric spindle, which is mainly used for solving the problem that the rotation rigidity of the electric spindle is difficult to directly detect.
The technical scheme of the invention is as follows:
a rigidity modeling and indirect detection method under the rotation state of a main shaft is disclosed, wherein the electric main shaft comprises a front bearing, a rear bearing and a rotating shaft; the electric spindle, the customized tool holder, the spindle tool holder joint surface and the standard ball target jointly form an electric spindle system, and the rigidity modeling and detecting method is characterized by comprising the following steps:
1) simplifying a rotating shaft and a customized tool holder in an electric spindle system into two connected simple supporting beams, and establishing a deformation equation of the rotating shaft and the customized tool holder based on a small deflection differential equation:
wherein, w1(z) is the deformation of the simply supported beam formed by the rotating shaft and the customized tool holder, F is the external force applied on the customized tool holder, z is the length between the point on the simply supported beam formed by the rotating shaft and the customized tool holder and the rear bearing, and l1Is the length of the front bearing from the rear bearing,/2Is the length of the foremost end of the electric spindle from the front bearing3Is to customize the length, k, of the shank1、k2Respectively representing the stiffness of the spindle, the customized shank, C1,C2,C3,C4,D1,D2,D3And D4Is a constant, determined by the internal structure of the spindle system;
2) based on Hooke's law, the deformation equation of the front bearing and the rear bearing in the electric spindle system is established:
wherein, w2(z) represents the amount of deformation occurring in the front bearing and the rear bearing, k3、k4Respectively representing the rigidity of the rear bearing and the front bearing;
3) based on Hooke's law, a deformation equation of the joint surface of the spindle and the tool shank is established:
wherein, w3(z) represents the amount of deformation, k, produced at the joint surface of the spindle and the shank5The rigidity of the joint surface of the main shaft cutter handle is shown;
4) based on a superposition principle, adding the deformation of the rotating shaft and the customized tool handle in the step 1), the deformation of the front bearing and the rear bearing in the step 2) and the deformation of the main shaft tool handle joint surface in the step 3) to establish a deformation equation of the electric main shaft system:
wherein w (z) represents the deformation of the electric spindle system, B1(z),B2(z),B3(z),B4(z) and B5(z) constants of the joint surfaces of the rotating shaft, the customized tool holder, the front bearing, the rear bearing and the main shaft tool holder at a z point are respectively;
5) dividing the external force applied to the customized tool handle by the deformation of the electric spindle system to obtain a rigidity model of the electric spindle system:
wherein Kd(z) represents a stiffness value of the electric spindle system at point z;
6) based on a superposition principle, adding the deformation of the rotating shaft and the customized tool handle in the step 1) and the deformation of the front bearing and the rear bearing in the step 2) to obtain the deformation of the electric spindle, and dividing the external force applied to the front end of the electric spindle by the deformation of the electric spindle to obtain a rigidity model of the electric spindle:
wherein KspindleRepresenting a stiffness value of the electric spindle;
7) applying force to the customized tool handle in a static state of the electric spindle, and acquiring displacement of the electric spindle system under different force action conditions through a displacement sensor; based on a linear least square method, establishing a linear equation of force and displacement, wherein the slope of the linear equation is the rigidity value of the electric spindle system at the detection position of the displacement sensor, and the calculation formula of the rigidity value of the electric spindle system at the detection position of the displacement sensor is as follows:
wherein, wi(z) is when the force applied to the custom tool shank (4) is FiDisplacement of the time z point; n represents the number of detections,
to representThe average value of the applied forces is detected n times,
represents the average of the displacements detected n times;
8) changing the detection position of a displacement sensor, and repeating the step 7) m times to obtain rigidity values of m different positions in the electric spindle system, wherein m is a positive integer greater than or equal to 5;
9) based on the generalized inverse, fitting the rigidity values of the m positions on the electric spindle system obtained in the step 8) with the rigidity value of the electric spindle system obtained by calculation in the step 5), and calculating to obtain the rigidity values of the joint surface of the rotating shaft, the customized tool holder and the main shaft tool holder and the rigidity values of the front bearing and the rear bearing in a static state, namely:
wherein z is6,z7,z8Representing measuring points at different positions on the electric spindle system;
10) applying force to the customized tool handle in the rotation state of the electric spindle, and collecting a rotary motion curve of a standard ball target by adopting a spindle rotary error analyzer; based on a least square circle algorithm, obtaining the circle center position of a least square circle of a rotary motion curve of a standard spherical target under different forces; obtaining the displacement of the circle center position of the least square circle under different forces based on the pythagorean theorem; based on a linear least square method, establishing a linear equation of the displacement of the circle center positions of different forces and least squares circles, wherein the slope of the linear equation is the stiffness value of the electric spindle system in a rotating state, and the stiffness value calculation formula of the electric spindle in the rotating state is as follows:
wherein d isj(z) is the force applied to the custom tool shank is FjThe displacement of the circle center position of the least square circle of the revolution motion curve of the z point; n denotes inspectionThe number of times of measurement is counted,
which represents the average of the forces applied in n detections,
an average value representing the displacement amount at the center position of the least square circle detected n times;
11) fitting the rigidity value of the electric main shaft system obtained in the step 10) in a rotating state with the rigidity value of the electric main shaft system obtained by calculation in the step 5), and calculating the rigidity values of the front bearing and the rear bearing at different rotating speeds, wherein the calculation formula is as follows:
wherein z is4And z5Respectively representing two different positions on a standard ball target;
12) based on the electric spindle rigidity model in the step 6), substituting the rotating shaft rigidity value, the front bearing rigidity value and the rear bearing rigidity value identified in the step 9) and the step 11) into the electric spindle rigidity model to obtain a final electric spindle rigidity value:
the rigidity modeling and indirect detection method under the electric spindle rotation state is characterized in that the least square circle algorithm adopts a least square circle approximation algorithm to calculate the circle center of a least square circle, and the calculation formula is as follows:
wherein x0And y0Abscissa and ordinate representing the centre of a least square circleLabel, A1、A2、A3、A4And A5Represents intermediate variables, respectively:
wherein xiAnd yiIndicating the signals detected by the two displacement sensors, and n indicates the number of detections.
The rigidity modeling and indirect detection method under the rotation state of the electric spindle is characterized in that the standard ball target adopts a double standard ball, a precise pin gauge or a standard rod.
The invention has the following advantages and prominent technical effects:
the invention provides a rigidity modeling and indirect detection method of an electric spindle in a rotating state, aiming at the problem that the rigidity of the electric spindle cannot be detected, firstly, a rigidity model of an electric spindle system is established through a small deflection differential equation, Hooke's law and a superposition principle, parameters in the rigidity model of the electric spindle system are identified respectively in a static state and a rotating state of the electric spindle, and finally, rigidity values of the electric spindle at different rotating speeds are obtained through model conversion. The method can be applied to the performance test of the electric spindle, and can accurately detect the rigidity of the electric spindle.
Drawings
Fig. 1 is a flowchart of a stiffness modeling and indirect detection method in a rotational state of an electric spindle according to the present invention.
Figure 2 is a diagram of an electric spindle system and performance detection system.
FIG. 3 is a stiffness model schematic of a spindle and a custom tool shank.
FIG. 4 is a schematic diagram of a stiffness model of the front and rear bearings.
FIG. 5 is a schematic diagram of a stiffness model of the bonding surface of the spindle and tool shank.
Fig. 6 is a spherical center rotation curve of a standard ball at the front end of the motorized spindle.
Fig. 7 is a schematic diagram of the least square circle with the loading force in the rotation state of the electric spindle.
FIG. 8 is a graph of stiffness performance of a domestic electric spindle obtained by using the present invention.
In the figure: 1-a rear bearing; 2-a rotating shaft; 3-a front bearing; 4, customizing a tool shank; 5-double standard ball; 6-a displacement sensor; 7-the center of the least square circle; 8-maximum inscribed circle; 9-least squares circle; 10-minimum circumscribed circle.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific embodiments:
fig. 1 is a flowchart of a stiffness modeling and indirect detection method in a rotational state of an electric spindle according to the present invention, and fig. 2 is a diagram of an electric spindle system and a performance detection system, and the stiffness modeling and identification method according to the present invention is applied to the embodiment of the electric spindle system of fig. 2, so as to describe in detail the flow of the stiffness modeling and identification method of the electric spindle. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
Since the electric spindle cannot apply force and detect displacement at the front end of the electric spindle when rotating at a high speed, an electric spindle system and a rigidity detection device as shown in fig. 2 are designed. The customized tool handle 4 is arranged at the front end of the electric spindle, the bearing is arranged above the customized tool handle 4, and the load is applied to the spindle in a rotating state by applying force to the bearing. Meanwhile, the double-standard ball 5 is arranged at the front end of the customized tool handle 4, and the movement turning curve of the electric spindle is detected through the double-standard ball 5. As can be seen from fig. 2, the electric spindle system includes a rotating shaft 2, a customized tool holder 4, a spindle tool holder joint surface, a double-standard ball 5, a front bearing 1, a rear bearing 3, and the like, so that stress and deformation of each part are separately analyzed, and a superposition principle is applied to obtain a deformation and rigidity model of the electric spindle system.
1) Deformation analysis of the spindle 2 and the customized tool shank 4
Fig. 3 is a schematic diagram of a stiffness model of the rotating shaft 2 and the customized tool holder 4, the rotating shaft 2 and the customized tool holder 4 are simplified into two connected simple beams, and the stiffness model can be obtained according to a small deflection differential equation:
wherein, theta1The corner of a point on a simple support beam consisting of the rotating shaft 2 and the customized tool holder 4 is shown, and z shows the distance between the point on the simple support beam and the rear bearing 1; w is a1And M is simply supported beam deflection and bending moment on the simply supported beam cross-section respectively; i is the inertia moment of the simple support beam section to the neutral axis; e is the elastic modulus of the material; and C and D are integral constants determined by the constraint conditions of the corner and the deflection of the simply supported beam.
Carrying out stress analysis on the main shaft to obtain a bending moment equation:
where F is the external force applied to the custom tool shank 4, l1Is the length of the front bearing 3 from the rear bearing 1, l2Is the distance l from the foremost end of the electric spindle to the front bearing 33Is to customize the length of the shank 4.
Substituting equation (3) into equation (2) to obtain the deformation equation of the simply supported beam consisting of the rotating shaft 2 and the customized tool holder 4, namely
Wherein k is1、k2Respectively showing the rigidity, C, of the rotating shaft 2 and the customized tool holder 41,C2,C3,C4,D1,D2,D3And D4Is an intermediate variable constant, and the specific relation is as follows:
D1＝0 (9)
2) front bearing 3 and rear bearing 1 deformation analysis
Fig. 4 is a schematic diagram of a stiffness model of the front bearing 3 and the rear bearing 1, and when the stiffness of the front bearing 3 and the rear bearing 1 is analyzed, the joint surfaces of the rotating shaft 2, the customized tool holder 4 and the main shaft tool holder are considered as rigid bodies. Therefore, when the customized tool holder 4 is subjected to radial force load, the electric spindle is inclined, the stress of the electric spindle is analyzed, and a force balance equation is obtained:
wherein
And
respectively, showing the electric spindle system in z0Point, z1Point sum z3The force to which the point is subjected, hence in z0Point sum z1The point deformation amounts are respectively:
wherein
And
respectively, showing the electric spindle system in z0Point sum z1Amount of deformation of dots, k3And k4The stiffness of the rear bearing 1 and the front bearing 3 are expressed separately, so the deformation equations of the front bearing 3 and the rear bearing 1 can be obtained:
3) deformation analysis of main shaft and tool shank joint surface
Fig. 5 is a stiffness model schematic diagram of a joint surface of the spindle and the tool holder, and it is assumed that the rotating shaft 2 and the customized tool holder 4 are connected by a spring, and therefore, the deformation at the joint surface of the spindle and the tool holder is as follows:
wherein
And
respectively, when the customized tool handle 4 is applied with a load force F, the rotating shaft 2 and the customized tool handle 4 are at the joint z2Amount of deformation of dots, k5The equivalent rigidity of the joint surface of the main shaft cutter handle;
therefore, the deformation equation of the joint surface of the main shaft and the tool holder is as follows:
4) electric spindle system and spindle stiffness model
And (3) superposing the equation (4), the equation (16) and the equation (18) through a superposition principle to obtain a total deformation equation of the electric spindle system
Wherein B is1(z),B2(z),B3(z),B4(z) and B5(z) are constants respectively relating to the positions of the detection points.
Dividing the external force by the deformation to obtain a rigidity model of the electric spindle system, wherein the expression is
The actual stiffness of the electric spindle is at the front end z of the electric spindle2Point applied load force
And is divided by z2And (4) displacement of the point, wherein the obtained value is the rigidity value of the electric spindle. The rigidity model of the electric spindle is similar to the rigidity model analysis of the electric spindle system, and only the external load force F is translated to z2The points are combined with the superposition principle to obtain the calculation main shaftStiffness models, i.e.
5) Rigidity parameter identification in static state of electric spindle
Firstly, identifying the rigidity of a rotating shaft 2, the rigidity of a customized tool holder 4 and the rigidity of a joint surface of a tool holder of the main shaft when the electric main shaft is in a static state, and then identifying the rigidity of a front bearing 3 and the rigidity of a rear bearing 1 when the electric main shaft is in a high-speed rotating state. And finally, calculating the rigidity of the main shaft by combining the identification parameter results of the first two steps to obtain the rigidity of the electric main shaft at different rotating speeds.
By mounting displacement sensors 6 at a plurality of points on the electric spindle, z, which is the point where an external load acts, is detected3When in point measurement, the displacement of each measuring point is fitted by adopting a least square method to obtain a linear equation of two elements, the slope of the equation is the equivalent stiffness of the measuring point, and the equivalent stiffness calculation equation is
Wherein wiWhen z is3Point loading force of FiThe displacement value of the z point.
Because certain measurement errors exist in the experiment, when parameters in the rigidity model of the spindle system are identified, more than measurement points for solving variable values are detected to construct an over-determined equation set, and the least square solution of the equation is solved by adopting the generalized inverse of the matrix, so that the errors in the experiment are reduced, and finally the rigidity values of the rotating shaft 2, the customized tool holder 4 and the joint surface of the spindle tool holder and the rigidity values of the front bearing 3 and the rear bearing 1 in the static state of the spindle, namely the rigidity values of the front bearing 3 and the rear bearing 1, are obtained
Wherein z is6,z7,z8Representing the measurement points at different positions on the electric spindle system.
6) Stiffness parameter identification in electric spindle rotation state
When the electric spindle rotates at a high speed, due to the existence of centrifugal force, the deformation of the electric spindle system comprises the deformation caused by external force and the deformation caused by centrifugal force, so that the value obtained by directly dividing the external force by the radial displacement of the electric spindle cannot be used as the rigidity value of the electric spindle system in the rotating state, and the rigidity of the spindle is slightly low. Due to the isotropic nature of the centrifugal force, the offset of the center of rotation of the electric spindle can be used as the radial displacement of the electric spindle. Therefore, the double-standard ball 5 is arranged at the front end of the motorized spindle, the radial gyration curve of the motorized spindle is detected by arranging the displacement sensor 6 in the horizontal direction and the vertical direction of the double-standard ball 5, and the circle center 7 of the least square circle of the gyration track of the spindle is calculated by the least square circle algorithm. And obtaining the relative offset of the main shaft rotation center under different loading forces according to the coordinates of the circle center 7 of the least square circle under different loading forces. And finally, combining a least square method and an electric spindle rigidity model to obtain the rigidity of the electric spindle at different rotation speeds.
Fig. 6 is a spherical center rotation curve of a standard ball at the front end of the motorized spindle. The solid line in the figure is a sphere center rotation curve of a standard sphere at the front end of the electric spindle, three dotted concentric circles are respectively a maximum inscribed circle 8, a least square circle 9 and a minimum circumscribed circle 10 from inside to outside, wherein the calculation formula of the least square circle 9 is as follows:
by solving for x0、y0And rlmsSo that
And minimum. Wherein xiAnd yiRespectively representing displacement signals, x, detected by two mutually perpendicular displacement sensors 60、y0Respectively representing the abscissa and the ordinate, r, of the centre 7 of the least-squares circlelmsRepresenting the least squares circle radius. Because the least square circle 9 has no analytic solution, the circle center 7 of the least square circle is solved by adopting an approximate algorithm, and the calculation formula is
Wherein the content of the first and second substances,
fig. 7 is a schematic diagram of the least square circle 9 along with the loading force in the rotation state of the motorized spindle. The electric spindle is rotated, the external force of the electric spindle is gradually increased, and a radial motion curve diagram of the electric spindle under different loading forces is drawn. And calculating to obtain the circle center 7 positions of the least square circles under different loading forces by the least square circle algorithm, and calculating to obtain the circle center offset under different radial forces based on the pythagorean theorem by taking the circle center 7 of the least square circle without the loading force as a starting point. And finally fitting a linear relation curve between the loading force and the circle center displacement based on a linear least square method, wherein the slope of the linear relation curve is the equivalent stiffness at the position, and the calculation equation of the stiffness is as follows:
wherein d isj(z) is represented by z3Point loading force of FjThe displacement of the circle center 7 of the least square circle of the z point is as follows:
wherein x0And y0The circle center 7 coordinate of the z point representing no loading force.
Combining the rigidity characteristic values of the combining surfaces of the rotating shaft 2, the customized tool holder 4 and the main shaft tool holder which are identified in the static state, the rigidity model of the electric main shaft system is simplified as follows:
the rigidity of the front bearing 3 and the rigidity of the rear bearing 1 of the electric spindle under different rotating speeds can be obtained by matrix inversion, and the calculation formula is
Wherein z is4And z5The distance of the two ball centers of the double standard balls 5 from the center of the rear bearing 1 is shown separately.
And finally, substituting the identified rigidity value of the rotating shaft 2, the rigidity value of the front bearing 3 and the rigidity value of the rear bearing 1 into the rigidity model of the electric spindle to obtain the rigidity value of the electric spindle, wherein the calculation formula is as follows:
fig. 8 is a stiffness graph obtained by identifying the stiffness of a domestic electric spindle after the method is adopted, wherein the abscissa in the graph represents the variation range of the rotating speed of the electric spindle, and the ordinate represents the stiffness value of the electric spindle. The detection result shows that the static rigidity value of the electric spindle is 72N/micron, the rigidity value in the rotating state is about 50N/micron, and when the electric spindle rotates, the rigidity of the electric spindle rises firstly and then falls along with the rise of the rotating speed. The rigidity modeling and indirect detection method under the electric spindle rotation state provided by the invention can be applied to the performance detection and monitoring of the electric spindle, and can also be used for making a cutting process in future real cutting and researching the motion state and performance degradation in reliability research.
Claims (3)
1. A rigidity modeling and indirect detection method under the rotation state of an electric spindle comprises a front bearing (3), a rear bearing (1) and a rotating shaft (2); the electric spindle, the customized tool holder (4), the spindle tool holder joint surface and the standard ball target jointly form an electric spindle system, and the rigidity modeling and detecting method is characterized by comprising the following steps:
1) simplifying a rotating shaft (2) and a customized tool handle (4) in an electric spindle system into two connected simple supporting beams, and establishing deformation equations of the rotating shaft (2) and the customized tool handle (4) based on a small deflection differential equation:
wherein, w1(z) is the deformation of the simple support beam formed by the rotating shaft (2) and the customized tool holder (4), F is the external force applied on the customized tool holder (4), z is the length between a point on the simple support beam formed by the rotating shaft (2) and the customized tool holder (4) and the rear bearing (1), and l is the length between the point on the simple support beam and the rear bearing (1)1Is the length of the front bearing (3) from the rear bearing (1) |2Is the length of the foremost end of the electric main shaft from the front bearing (3) |3Is to customize the length, k, of the tool shank (4)1、k2Respectively showing the rigidity of the rotating shaft (2) and the customized tool holder (4), C1，C2，C3，C4，D1，D2，D3And D4Is a constant, determined by the internal structure of the spindle system;
2) based on Hooke's law, a deformation equation of a front bearing (3) and a rear bearing (1) in the electric spindle system is established:
wherein, w2(z) represents the amount of deformation, k, occurring in the front bearing (3) and the rear bearing (1)3、k4Respectively showing the rigidity of the rear bearing (1) and the front bearing (3);
3) based on Hooke's law, a deformation equation of the joint surface of the spindle and the tool shank is established:
wherein, w3(z) represents the amount of deformation, k, produced at the joint surface of the spindle and the shank5The rigidity of the joint surface of the main shaft cutter handle is shown;
4) based on a superposition principle, adding the deformation of the rotating shaft (2) and the customized tool handle (4) in the step 1), the deformation of the front bearing (3) and the rear bearing (1) in the step 2), and the deformation of the joint surface of the main shaft tool handle in the step 3) to establish a deformation equation of the electric main shaft system:
wherein w (z) represents the deformation of the electric spindle system, B1(z)，B2(z)，B3(z)，B4(z) and B5(z) constants of the rotating shaft (2), the customized tool holder (4), the front bearing (3), the rear bearing (1) and the main shaft tool holder joint surface at a z point are respectively;
5) dividing the external force applied to the customized tool handle (4) by the deformation of the electric spindle system to obtain a rigidity model of the electric spindle system:
wherein Kd(z) represents a stiffness value of the electric spindle system at point z;
6) based on a superposition principle, adding the deformation of the rotating shaft (2) and the customized tool handle (4) in the step 1) and the deformation of the front bearing (3) and the rear bearing (1) in the step 2) to obtain the deformation of the electric spindle, and dividing the external force applied to the front end of the electric spindle by the deformation of the electric spindle to obtain a rigidity model of the electric spindle:
wherein KspindelRepresenting a stiffness value of the electric spindle;
7) in the static state of the electric spindle, force is applied to the customized tool handle (4), and displacement of the electric spindle system under different force action conditions is acquired through a displacement sensor (6); based on a linear least square method, establishing a linear equation of force and displacement, wherein the slope of the linear equation is the rigidity value of the electric spindle system at the detection position of the displacement sensor (6), and the calculation formula of the rigidity value of the electric spindle system at the detection position of the displacement sensor (6) is as follows:
wherein, wi(z) is when the force applied to the custom tool shank (4) is FiDisplacement of the time z point; n represents the number of detections,
which represents the average of the forces applied in n detections,
represents the average of the displacements detected n times;
8) changing the detection position of a displacement sensor (6), and repeating the step 7) m times to obtain rigidity values of m different positions in the electric spindle system, wherein m is a positive integer greater than or equal to 5;
9) based on the generalized inverse, fitting the rigidity values of m positions on the electric spindle system obtained in the step 8) with the rigidity value of the electric spindle system obtained by calculation in the step 5), and calculating to obtain the rigidity values of the joint surface of the rotating shaft (2), the customized tool holder (4) and the main shaft tool holder and the rigidity values of the front bearing (3) and the rear bearing (1) in a static state, namely:
wherein z is6，z7，z8Representing measuring points at different positions on the electric spindle system;
10) applying force to the customized tool handle (4) in the rotation state of the electric spindle, and collecting a rotary motion curve of a standard ball target by adopting a spindle rotary error analyzer; based on a least square circle algorithm, obtaining the circle center (7) position of a least square circle of a rotary motion curve of a standard spherical target under different forces; obtaining the displacement of the circle center (7) of the least square circle under different forces based on the pythagorean theorem; based on a linear least square method, establishing a linear equation of the displacement of the circle center (7) positions of different forces and least squares circles, wherein the slope of the linear equation is the stiffness value of the electric spindle system in a rotating state, and the stiffness value calculation formula of the electric spindle in the rotating state is as follows:
wherein d isj(z) is the force applied to the custom tool shank is FjThe displacement of the circle center (7) position of the least square circle of the revolution motion curve of the z point; n represents the number of detections,
which represents the average of the forces applied in n detections,
an average value representing the displacement amount at the center (7) of the least square circle detected n times;
11) fitting the rigidity value of the electric main shaft system obtained in the step 10) in a rotating state with the rigidity value of the electric main shaft system obtained by calculation in the step 5), and calculating the rigidity values of the front bearing (3) and the rear bearing (1) at different rotating speeds, wherein the calculation formula is as follows:
wherein z is4And z5Respectively representing two different positions on a standard ball target;
12) based on the electric spindle rigidity model in the step 6), substituting the rigidity value of the rotating shaft (2), the rigidity value of the front bearing (3) and the rigidity value of the rear bearing (1) identified in the steps 9) and 11) into the electric spindle rigidity model to obtain a final electric spindle rigidity value:
2. the stiffness modeling and indirect detection method in the rotational state of the motorized spindle according to claim 1, characterized in that the least square circle algorithm uses a least square circle approximation algorithm to calculate the center (7) of the least square circle, and the calculation formula is:
wherein x0And y0Denotes the abscissa and ordinate of the center (7) of the least-squares circle, A1、A2、A3、A4And A5Represents intermediate variables, respectively:
wherein xiAnd yiIndicating the signals detected by the two displacement sensors, and n indicates the number of detections.
3. The rigidity modeling and indirect detection method under the rotation state of the motorized spindle of claim 1, characterized in that the standard ball target adopts a double standard ball (5), a precision pin gauge or a standard rod.
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