CN113779726B - Thermal error model creation method and solving method based on cutting force - Google Patents
Thermal error model creation method and solving method based on cutting force Download PDFInfo
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Abstract
The invention discloses a thermal error model creation method based on cutting force, which comprises the steps of firstly, because axial thermal elongation errors and radial thermal drift errors generated by a machine tool can cause the cutting depth and cutting width of a cutter to change, and therefore, the cutting force can change under the same processing conditions before and after the machine tool generates the thermal errors, measuring the cutting force before and after the machine tool generates the thermal errors under the same processing environment, establishing a mathematical model of the cutting force and the thermal errors, and obtaining the current machine tool thermal errors according to the change value of the cutting force, namely, the invention can obtain the thermal errors of the current machine tool based on the change of the cutting force, thereby creating a thermal error model.
Description
Technical Field
The invention belongs to the technical field of mechanical error analysis, and particularly relates to a thermal error model creation method and a solving method based on cutting force.
Background
With the rapid development of the industries of aerospace, mold processing and the like, the precision manufacturing requirement on complex workpieces is gradually increased, and the role of a five-axis numerical control machine tool is also more and more important. When the five-axis numerical control machine tool works, the five-axis numerical control machine tool is influenced by various complex factors inside and outside a processing system, processing errors are necessarily generated, and the errors have great influence on the precision and the surface quality of the processed parts. Numerous studies have shown that: the main error affecting the precision of the machined workpiece of the machine tool is a thermally induced error, and the ratio of the main error to the main error of the numerical control machine tool is more than 40%. Compared with the traditional three-axis machine tool, the five-axis numerical control machine tool has more axes and higher main shaft rotating speed and feeding speed, and a plurality of internal thermal factors are generated, so that the thermal error identification of the five-axis numerical control machine tool is developed, and the five-axis numerical control machine tool has important value for compensating the thermal error and improving the machining precision of the five-axis numerical control machine tool. The measurement of thermal errors of the machine spindle and feed shaft is described in detail in the ISO230-3, ISO10791-10, et al. Regarding the measurement of the thermal error of the rotating shaft (C-axis) of a five-axis numerical control machine tool, although no corresponding industry standard has been established, related scholars at home and abroad begin to try to measure the thermal error of the rotating shaft of the machine tool by using an R-test measuring device, a measuring mode of the machine tool on a machine head, a cutting test piece and the like. The main thermal errors of the machine tool comprise main shaft thermal errors and feeding driving shaft thermal errors, temperature changes of the motor and the bearing are main sources of the main shaft thermal errors, and the main shaft induced thermal errors comprise axial thermal elongation errors and radial thermal drift errors.
Although the previous studies have proposed many methods of thermal error modeling and prediction, there are also some drawbacks, mainly:
(1) A plurality of temperature sensors are needed to achieve high-precision measurement;
(2) The temperature sensitive point selection method has a plurality of defects, and can not fundamentally solve the problems of multiple collinearity and sensor coupling;
(3) The modeling method of the thermal error model is low in robustness.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a thermal error model creation method and a solving method based on cutting force, which can obtain a thermal error of a current machine tool based on a change in cutting force, thereby creating a thermal error model.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the invention firstly provides a thermal error model creation method based on cutting force, which comprises the following steps:
the cutting force F is expressed by an exponential formula:
wherein D represents a coefficient depending on the material to be processed and the cutting condition; a. b, c, d represent the indices of the respective process parameters; v c Representing the cutting speed; f (f) z Representing the feed per tooth; a, a p Represents axial depth of cut; a, a e Represents radial cutting depth;
decomposing the cutting force F into F in X, Y, Z directions of a machine tool coordinate system x 、F y 、F z Three components are respectively:
wherein D is 1 、D 2 、D 3 The three directions X, Y and Z are respectively indicated and depend on the coefficients of the processed material and the cutting condition; a1, b1, c1, d1 represent indices of the process parameters of the X-direction component force; a2, b2, c2, d2 represent the indices of the Y-direction component force process parameters; a3, b3, c3, d3 represent indices of the Z-direction component force process parameters;
radial drift and axial elongation of the machine tool spindle due to thermal errors;
the radial drift of the spindle causes the radial cutting depth of the machine tool to change, i.e. the change in radial cutting depth is a function of the radial drift of the spindle, expressed as:
Δa e ＝f(δ x ,δ y )
wherein Δa e A variation value representing a radial cutting depth; delta x 、δ y Representing radial drift of the spindle in the X, Y direction due to thermal error;
the axial elongation of the spindle causes the axial cutting depth of the machine tool to change, and the relation between the axial elongation and the axial cutting depth is as follows:
δ z ＝Δa p
wherein Δa p A variation value representing the axial cutting depth;δ z indicating the axial elongation of the spindle in the Z direction due to thermal error;
thus, the change in machine tool cutting force due to thermal error can be expressed as:
wherein DeltaF x The variation value of the cutting force in the x direction of the front and rear cutting due to the thermal error under the same processing condition is shown;
ΔF y the variation value of the cutting force in the y direction of the front and rear cutting due to the thermal error under the same processing condition is shown;
ΔF z the change value of the cutting force in the z direction of the front and rear cutting due to the thermal error under the same machining condition is shown;
so that the expression for solving the thermal error of the machine tool is as follows:
wherein V represents the rotation speed of the main shaft;
a0, A1, A2, A3, A4 represent regression coefficients of thermal errors in the X direction;
b0, B1, B2, B3, B4 represent regression coefficients of thermal errors in the Y direction;
c0, C1, C2, C3, C4 represent regression coefficients of Z-direction thermal errors;
creating a resulting thermal error model.
The invention also provides a solving method of the thermal error model created by the thermal error model creating method based on the cutting force, which is used for measuring the thermal error-cutting force data of at least 15 groups of machine tool spindles and substituting the thermal error data into the thermal error model, and solving the regression coefficient of the thermal error in the X direction, the regression coefficient of the thermal error in the Y direction and the regression coefficient of the thermal error in the Z direction in the thermal error model by utilizing a multiple regression algorithm; wherein the thermal error-cutting force data includes thermal error data and corresponding cutting force data.
Further, the measurement method of the thermal error data comprises the following steps:
two displacement sensors for detecting radial drift of the main shaft in the X direction and two displacement sensors for detecting radial drift of the main shaft in the Y direction are respectively arranged along the axial direction of the main shaft; a displacement sensor for detecting axial extension of the main shaft in the Z direction is arranged at the free end part of the main shaft; thus, it is possible to obtain:
δ z ＝z
wherein,,L x ，L y the distance between the displacement sensors closest to the main shaft fixed end in the X, Y direction is respectively set; h x ，H y The distance between the two displacement sensors in the X, Y direction respectively; x is x 1 ，x 2 Respectively measuring displacement values by two displacement sensors in the X direction; y is 1 ，y 2 Respectively measuring displacement values by two displacement sensors in the Y direction; z is a displacement value measured by a displacement sensor in the Z direction; . Alpha x ，α y Thermal tilt about the Y, X axis, respectively.
The invention has the beneficial effects that:
according to the method for creating the thermal error model based on the cutting force, firstly, the cutting depth and the cutting width of a cutter are changed due to the axial thermal elongation error and the radial thermal drift error generated by a machine tool, so that the cutting force can be changed under the same processing conditions before and after the thermal error is generated by the machine tool, the cutting force before and after the thermal error is generated by the machine tool under the same processing environment is measured, a mathematical model of the cutting force and the thermal error is built, and the current thermal error of the machine tool can be obtained according to the change value of the cutting force, namely, the thermal error of the current machine tool can be obtained based on the change of the cutting force, so that the thermal error model is created.
Drawings
In order to make the objects, technical solutions and advantageous effects of the present invention more clear, the present invention provides the following drawings for description:
FIG. 1 is a flow chart of an embodiment of a thermal error model creation method based on cutting force of the present invention;
FIG. 2 is a schematic diagram of a spindle thermal error data measurement device;
FIG. 3 is a graph of a spindle thermal error offset model;
fig. 4 is a schematic structural view of the cutting force measuring device.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to limit the invention, so that those skilled in the art may better understand the invention and practice it.
Referring to fig. 1, a flow chart of an embodiment of a thermal error model creation method based on cutting force according to the present invention is shown. The thermal error model creation method based on the cutting force in the embodiment comprises the following steps:
the cutting force F is expressed by an exponential formula:
wherein D represents a coefficient depending on the material to be processed and the cutting condition; a. b, c, d represent the indices of the respective process parameters; v c Representing the cutting speed; f (f) z Representing the feed per tooth; a, a p Represents axial depth of cut; a, a e Represents radial cutting depth;
decomposing the cutting force F into F in X, Y, Z directions of a machine tool coordinate system x 、F y 、F z Three components are respectively:
wherein D is 1 、D 2 、D 3 The three directions X, Y and Z are respectively indicated and depend on the coefficients of the processed material and the cutting condition; a1, b1, c1, d1 represent indices of the process parameters of the X-direction component force; a2, b2, c2, d2 represent the indices of the Y-direction component force process parameters; a3, b3, c3, d3 represent indices of the Z-direction component force process parameters;
radial drift and axial elongation of the machine tool spindle due to thermal errors;
the radial drift of the spindle causes the radial cutting depth of the machine tool to change, i.e. the change in radial cutting depth is a function of the radial drift of the spindle, expressed as:
Δa e ＝f(δ x ,δ y )
wherein Δa e A variation value representing a radial cutting depth; delta x 、δ y Representing radial drift of the spindle in the X, Y direction due to thermal error;
the axial elongation of the spindle causes the axial cutting depth of the machine tool to change, and the relation between the axial elongation and the axial cutting depth is as follows:
δ z ＝Δa p
wherein Δa p A variation value representing the axial cutting depth; delta z Indicating the axial elongation of the spindle in the Z direction due to thermal error;
thus, the change in machine tool cutting force due to thermal error can be expressed as:
wherein DeltaF x The variation value of the cutting force in the x direction of the front and rear cutting due to the thermal error under the same processing condition is shown;
ΔF y the variation value of the cutting force in the y direction of the front and rear cutting due to the thermal error under the same processing condition is shown;
ΔF z the change value of the cutting force in the z direction of the front and rear cutting due to the thermal error under the same machining condition is shown;
so that the expression for solving the thermal error of the machine tool is as follows:
wherein V represents the rotation speed of the main shaft;
a0, A1, A2, A3, A4 represent regression coefficients of thermal errors in the X direction;
b0, B1, B2, B3, B4 represent regression coefficients of thermal errors in the Y direction;
c0, C1, C2, C3, C4 represent regression coefficients of Z-direction thermal errors;
creating a resulting thermal error model.
The embodiment also provides a solving method of a thermal error model based on cutting force, firstly, the thermal error model is created by the thermal error model creation method based on cutting force, then thermal error-cutting force data of at least 15 groups of machine tool spindles are measured and substituted into the thermal error model, and finally, regression coefficients of thermal errors in the X direction, the Y direction and the Z direction in the thermal error model are solved by utilizing a multiple regression algorithm; wherein the thermal error-cutting force data includes thermal error data and corresponding cutting force data.
In order to better detect the thermal effect of the spindle, according to the international standard of ISO230-3, devices such as a displacement sensor are utilized to measure the thermal effect deformation according to the actual requirements of the comprehensive performance test and evaluation of the spindle product, the spindle deformation caused by the temperature rise caused by the spindle rotation is mainly detected, and the detected data are collated to obtain a spindle deformation image caused by the thermal effect. The spindle thermal error measurement device shown in fig. 2 is built according to the five-point test method in the ISO230-3 standard.
Specifically, the measurement method of the thermal error data comprises the following steps: two displacement sensors for detecting radial drift of the main shaft in the X direction and two displacement sensors for detecting radial drift of the main shaft in the Y direction are respectively arranged along the axial direction of the main shaft; a displacement sensor for detecting the axial elongation of the spindle in the Z direction is provided at the free end of the spindle.
As shown in FIG. 3, it is assumed that the test rod is not deformed during operation of the machine tool, line A 0 B 0 For initial value checking rod position, A 1 B 1 And (5) checking the position of the rod by the spindle after generating thermal errors for the spindle. A is that x ，B x For checking the position A of the spindle after thermal error 1 B 1 Projection in X direction, the same as in A y ，B y Is A 1 B 1 Projected in the Y direction. Through geometric relation analysis, an accurate expression of the five-term error can be obtained. Delta in x ，δ y Thermal drift in the direction X, Y, respectively. Alpha x ，α y Thermal tilt, delta, about Y, X axis, respectively z For Z-direction thermal elongation, x 1 ，x 2 The displacement values measured by the two displacement sensors in the X direction are respectively obtained. y is 1 ，y 2 The displacement values obtained by measurement of the two displacement sensors in the Y direction are respectively, and Z is the displacement value obtained by measurement of the displacement sensor in the Z direction. H x ，H y Distance between two displacement sensors in X, Y direction, L x ，L y The distance between the spindle fixed end and the displacement sensor nearest to the direction X, Y is respectively set. In the trapezoids formed in the figures, according to simple geometric relations, the higher order small quantities are ignored, so that the following can be obtained:
δ z ＝z
wherein x is 1 ，x 2 The displacement value measured by the displacement sensor in the X direction is approximately used for replacing the thermal drift of the principal axis average line in the X direction; y is 1 ，y 2 The displacement value measured by the displacement sensor in the Y direction is approximately used for replacing the thermal drift of the principal axis average line in the Y direction; and Z is a displacement value measured by a Z-direction sensor, and is the Z-direction thermal elongation of the main shaft obtained by direct measurement.
The measuring method of the cutting force data comprises the following steps: as shown in fig. 4, the cutting force of the tool cutting the workpiece is directly measured by the cutting force measuring device. The cutting force measuring device comprises a dynamometer, a filter connected with the dynamometer and a computer connected with the filter. When the workpiece is arranged on the dynamometer and the cutter arranged on the main shaft cutter handle cuts the workpiece, the cutting force F can be measured by the cutting force measuring device and can be decomposed into component forces F in X, Y, Z directions x 、F y 、F z 。
The above-described embodiments are merely preferred embodiments for fully explaining the present invention, and the scope of the present invention is not limited thereto. Equivalent substitutions and modifications will occur to those skilled in the art based on the present invention, and are intended to be within the scope of the present invention. The protection scope of the invention is subject to the claims.
Claims (3)
1. A thermal error model creation method based on cutting force is characterized in that:
the cutting force F is expressed by an exponential formula:
wherein D is determined by the processCoefficients of material and cutting conditions; a. b, c, d represent the indices of the respective process parameters; v c Representing the cutting speed; f (f) z Representing the feed per tooth; a, a p Represents axial depth of cut; a, a e Represents radial cutting depth;
decomposing the cutting force F into F in X, Y, Z directions of a machine tool coordinate system x 、F y 、F z Three components are respectively:
wherein D is 1 、D 2 、D 3 The three directions X, Y and Z are respectively indicated and depend on the coefficients of the processed material and the cutting condition; a1, b1, c1, d1 represent indices of the process parameters of the X-direction component force; a2, b2, c2, d2 represent the indices of the Y-direction component force process parameters; a3, b3, c3, d3 represent indices of the Z-direction component force process parameters;
radial drift and axial elongation of the machine tool spindle due to thermal errors;
the radial drift of the spindle causes the radial cutting depth of the machine tool to change, i.e. the change in radial cutting depth is a function of the radial drift of the spindle, expressed as:
Δa e ＝f(δ x ,δ y )
wherein Δa e A variation value representing a radial cutting depth; delta x 、δ y Representing radial drift of the spindle in the X, Y direction due to thermal error;
the axial elongation of the spindle causes the axial cutting depth of the machine tool to change, and the relation between the axial elongation and the axial cutting depth is as follows:
δ z ＝Δa p
wherein Δa p A variation value representing the axial cutting depth; delta z Indicating the axial elongation of the spindle in the Z direction due to thermal error;
thus, the change in machine tool cutting force due to thermal error can be expressed as:
wherein DeltaF x The variation value of the cutting force in the x direction of the front and rear cutting due to the thermal error under the same processing condition is shown;
ΔF y the variation value of the cutting force in the y direction of the front and rear cutting due to the thermal error under the same processing condition is shown;
ΔF z the change value of the cutting force in the z direction of the front and rear cutting due to the thermal error under the same machining condition is shown;
so that the expression for solving the thermal error of the machine tool is as follows:
δ x ＝A 0 ΔF x A1 ΔF y A2 ΔF z A3 V A4
δ y ＝B 0 ΔF x B1 ΔF y B2 ΔF z B3 V B4
δ z ＝C 0 ΔF x C1 ΔF y C2 ΔF z C3 V C4
wherein V represents the rotation speed of the main shaft;
a0, A1, A2, A3, A4 represent regression coefficients of thermal errors in the X direction;
b0, B1, B2, B3, B4 represent regression coefficients of thermal errors in the Y direction;
c0, C1, C2, C3, C4 represent regression coefficients of Z-direction thermal errors;
creating a resulting thermal error model.
2. A method for solving a thermal error model created by the cutting force-based thermal error model creation method according to claim 1, characterized in that: measuring thermal error-cutting force data of at least 15 groups of machine tool spindles, substituting the thermal error data into the thermal error model, and solving a regression coefficient of thermal error in the X direction, a regression coefficient of thermal error in the Y direction and a regression coefficient of thermal error in the Z direction in the thermal error model by utilizing a multiple regression algorithm; wherein the thermal error-cutting force data includes thermal error data and corresponding cutting force data.
3. The method for solving the thermal error model based on the cutting force according to claim 2, wherein: the measurement method of the thermal error data comprises the following steps:
two displacement sensors for detecting radial drift of the main shaft in the X direction and two displacement sensors for detecting radial drift of the main shaft in the Y direction are respectively arranged along the axial direction of the main shaft; a displacement sensor for detecting axial extension of the main shaft in the Z direction is arranged at the free end part of the main shaft; thus, it is possible to obtain:
δ z ＝z
wherein L is x ，L y The distance between the displacement sensors closest to the main shaft fixed end in the X, Y direction is respectively set; h x ，H y The distance between the two displacement sensors in the X, Y direction respectively; x is x 1 ，x 2 Respectively measuring displacement values by two displacement sensors in the X direction; y is 1 ，y 2 Respectively measuring displacement values by two displacement sensors in the Y direction; z is a displacement value measured by a displacement sensor in the Z direction; alpha x ，α y Thermal tilt about the Y, X axis, respectively.
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