CN110008784B - Milling force identification method and system based on conjugate gradient least square algorithm - Google Patents
Milling force identification method and system based on conjugate gradient least square algorithm Download PDFInfo
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Abstract
The invention discloses a milling force identification method and an identification system based on a conjugate gradient least square algorithm, wherein the method comprises the following steps: establishing a coordinate system, wherein the feeding direction is the X direction, and the Y direction is vertical to the feeding direction; carrying out multiple hammering experiments on the milling cutter along the X direction and the Y direction at certain angles uniformly along the circumferential direction to obtain transfer functions of the milling cutter at different angular positions; averaging the transfer functions to obtain an average transfer function; measuring a force signal related to the action of the milling force and an acceleration signal related to the acceleration in the milling process; and processing the average transfer function and the filtered acceleration signal by adopting a conjugate gradient least square iterative algorithm, comparing the milling force obtained by identification with the milling force obtained by measurement, and estimating the milling force identification error. The method can accurately identify the milling force in the milling process in real time, and can be used for milling process state monitoring, fault diagnosis, flutter identification and as a basis for milling parameter selection optimization.
Description
Technical Field
The invention belongs to the field of milling processing, and particularly relates to a milling force identification method and system based on a conjugate gradient least square algorithm.
Background
The current numerical control machining is developing towards high speed, high machining efficiency can be realized under a high-speed machining environment, the cutting temperature is kept low, the service life of the milling cutter is prolonged, and meanwhile, thin-wall parts can be machined possibly. However, during the high-speed machining process of the machine tool, the cutting force is always an important reference for monitoring the operating environment of the machine tool and the cutting process. The traditional cutting force prediction is based on a cutting force prediction model, and the cutting force prediction is carried out by measuring various cutting force coefficients, but the method is more complex and has more assumptions, and is only suitable for the cutting process under certain specific conditions.
In the conventional cutting force prediction, no research has been found on reversely obtaining the cutting force by the cutting process acceleration signal. During the actual cutting process, the acceleration signal can be easily measured by an acceleration sensor, and the cost is negligibly lower compared with the dynamometer for measuring the cutting force. Furthermore, the load cell has limitations in bandwidth and workpiece shape that are not suitable for practical production processes.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
The invention provides a milling force identification method based on a conjugate gradient least square algorithm, aiming at the problems in the prior art.
The purpose of the invention is realized by the following technical scheme.
In one aspect of the invention, a milling force identification method based on a conjugate gradient least square algorithm comprises the following steps:
in the first step: firstly, establishing a coordinate system, wherein the feeding direction is the X direction, and the Y direction is vertical to the feeding direction; carrying out multiple hammering experiments on the milling cutter along the X direction and the Y direction at certain angles uniformly along the circumferential direction to obtain transfer functions of the milling cutter at different angular positions;
in the second step: averaging the transfer functions to obtain an average transfer function;
in the third step: measuring a force signal related to the action of the milling force and an acceleration signal related to the acceleration in the milling process;
in the fourth step: filtering the measured acceleration signal by adopting a band-pass filter, wherein the amplitude of the band-pass filter in a passband is kept flat and 1, and the cut-off frequency is 250-1200 Hz;
in the fifth step: processing the average transfer function and the filtered acceleration signal by adopting a conjugate gradient least square iterative algorithm, and identifying to obtain the milling force in the milling process;
in the sixth step: and comparing the milling force obtained by identification with the force action signal of the milling force obtained by measurement, and estimating the identification error of the milling force.
In the method, in the first step, acceleration sensors are respectively installed in the X direction and the Y direction of a main shaft box of a milling machine, a hammer is used for knocking in the X direction and the Y direction uniformly at intervals of a certain angle along the circumferential direction at the free end of a tool nose, and multiple hammering experiments are carried out; and acquiring and calculating signals measured by a hammering experiment through a data acquisition unit to obtain transfer functions in the X direction and the Y direction.
In the method, in the third step, the cutting speed is 5000rpm, the cutting depth is 3mm, the cutting width is 2mm, and the feed per tooth is 0.1 mm/tooth during the milling process.
In the method, in a fourth step, the acceleration signal is band-pass filtered using a butterworth band-pass filter.
In the method, in a fourth step, the band-pass filter is kept flat and 1 in amplitude in the pass band.
In the method, in the first step, a milling cutter is subjected to a hammering experiment of 300-8000 times in the X and Y directions at intervals of 30 degrees uniformly along the circumferential direction.
According to another aspect of the invention, an identification system for implementing the method comprises a milling part, a data collector, a band-pass filter and a calculation part, wherein the milling part comprises a milling machine spindle box and a force hammer for knocking the tool nose of a milling cutter, the milling cutter is arranged on the spindle, a first acceleration sensor and a second acceleration sensor which are respectively used for measuring in the X direction and the Y direction are arranged at the milling machine spindle box, and the calculation part connected with the data collector and the band-pass filter comprises a first calculation unit for calculating an average transfer function, a second calculation unit based on a conjugate gradient least square iterative algorithm and a comparison unit.
In the identification system, the first acceleration sensor and/or the second acceleration sensor is a resistive or capacitive acceleration sensor.
In the identification system, the calculation part is a general processor, a digital signal processor, an Application Specific Integrated Circuit (ASIC) or a Field Programmable Gate Array (FPGA).
In the identification system, the computing portion includes a memory including one or more of a read only memory ROM, a random access memory RAM, a flash memory, or an electrically erasable programmable read only memory EEPROM.
The above description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly apparent, and to make the implementation of the content of the description possible for those skilled in the art, and to make the above and other objects, features and advantages of the present invention more obvious, the following description is given by way of example of the specific embodiments of the present invention.
Drawings
Various other advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a schematic diagram of the steps of a milling force identification method based on a conjugate gradient least squares algorithm according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a milling force identification method based on a conjugate gradient least squares algorithm according to an embodiment of the present invention;
3(a) -3 (d) are schematic diagrams of the measured transfer functions and the average transfer function of the milling force identification method based on the conjugate gradient least square algorithm according to one embodiment of the invention;
FIG. 4 is a schematic frequency domain diagram of a milling force signal of a milling force identification method based on a conjugate gradient least square algorithm according to an embodiment of the invention;
5(a) -5 (b) are frequency domain diagrams of idle and under-ablation acceleration signals of a milling force identification method based on a conjugate gradient least squares algorithm according to an embodiment of the present invention;
6(a) -6 (b) are schematic diagrams of amplitude-frequency characteristics and phase-frequency characteristics of a Butterworth band-pass filter based on a conjugate gradient least squares algorithm according to one embodiment of the present invention;
7(a) -7 (b) are schematic diagrams comparing milling forces in the X direction of the milling force identification method based on the conjugate gradient least square algorithm according to one embodiment of the present invention;
8(a) -8 (b) are schematic diagrams comparing milling forces in Y direction of the milling force identification method based on the conjugate gradient least square algorithm according to an embodiment of the present invention;
fig. 9 is a schematic structural diagram of an identification system implementing the method according to an embodiment of the present invention.
The invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, fig. 1 is a schematic diagram of the steps of the milling force identification method based on the conjugate gradient least square algorithm, and as shown in fig. 1, the milling force identification method based on the conjugate gradient least square algorithm includes the following steps:
in the first step S1: establishing a coordinate system, wherein the feeding direction is the X direction, and the Y direction is vertical to the feeding direction; carrying out multiple hammering experiments on the milling cutter along the X direction and the Y direction at certain angles uniformly along the circumferential direction to obtain transfer functions of the milling cutter at different angular positions;
in the second step S2: averaging the transfer functions to obtain an average transfer function;
in the third step S3: measuring a force signal related to the action of the milling force and an acceleration signal related to the acceleration in the milling process;
in the fourth step S4: filtering the measured acceleration signal by adopting a band-pass filter;
in the fifth step S5: processing the average transfer function and the filtered acceleration signal by adopting a conjugate gradient least square iterative algorithm, and identifying to obtain the milling force in the milling process;
in the sixth step S6: and comparing the milling force obtained by identification with the force of the milling force obtained by measurement, and estimating the identification error of the milling force.
The milling force identification method based on the conjugate gradient least square algorithm has the advantages of no need of inversion, no need of definite regularization parameters, high convergence speed, high iteration efficiency and the like.
To further illustrate the method of the present invention, fig. 2 is a flowchart of a milling force identification method based on conjugate gradient least squares algorithm according to an embodiment of the present invention, and in the first step S1: firstly, establishing a coordinate system, wherein the feeding direction is the X direction and is perpendicular to the Y direction of the feeding direction; and carrying out multiple hammering experiments on the milling cutter uniformly at intervals of a certain angle along the circumferential direction along the X and Y directions to obtain the transfer functions of the milling cutter at different angular positions.
In the second step S2: the measured transfer functions are averaged to minimize occasional errors in the measurement and errors due to tool asymmetry.
In the third step S3: the milling force and acceleration during milling are measured.
In the fourth step S4: the measured acceleration signal is filtered using a butterworth bandpass filter.
In the fifth step S5: and processing the average transfer function and the filtered acceleration signal by adopting a conjugate gradient least square iterative algorithm, and identifying to obtain the milling force in the milling process.
In the sixth step S6: and comparing the milling force obtained by identification with the actually measured milling force, and estimating the identification error of the milling force.
In one embodiment, FIGS. 3(a) -3 (d) are schematic diagrams of the measured transfer functions and the average transfer function of the milling force identification method based on the conjugate gradient least squares algorithm according to one embodiment of the present invention, wherein FIG. 3(a) shows a schematic diagram of the transfer function in the x-x direction and the average transfer function, FIG. 3(b) shows a schematic of the transfer function in the y-x direction and the average transfer function, FIG. 3(c) shows a schematic of the transfer function in the x-y direction and the average transfer function, figure 3(d) shows a schematic of the transfer function in the y-y direction and the average transfer function, carrying out multiple hammering experiments on the milling cutter along the X direction and the Y direction uniformly at intervals of 30 degrees along the circumferential direction to obtain the transfer functions of the milling cutter at different angular positions, wherein the cutter parameters are as follows: 3 teeth, high speed steel, 10mm diameter, 55mm overhang length, 45 ° helix angle, the results are shown in fig. 3(a) -fig. 3(d) as thin solid lines. The measured results are shown in fig. 3(a) -3 (d) as thin solid lines, and the measured transfer functions are averaged to minimize accidental errors in measurement and errors due to tool asymmetry, and the averaged transfer functions are shown in fig. 3(a) -3 (d) as thick solid lines.
The invention relates to a milling force identification method based on a conjugate gradient least square algorithmIn a preferred embodiment, in the third step S3: measuring milling force and acceleration in the milling process, wherein the cutting parameters are as follows: the rotating speed is 5000rpm, the back milling is carried out, the cutting depth is 3mm, the cutting width is 2mm, and the feeding amount per tooth is 0.1mm per tooth. The workpiece material parameters are as follows: 6061 aluminum alloy, elastic modulus 68.9Gpa, density 2690kg/m3Poisson's ratio of 0.33.
Fig. 4 is a schematic frequency domain diagram of a milling force signal of a milling force identification method based on a conjugate gradient least square algorithm, wherein the rotation speed is 5000rpm, the 3-tooth end mill, as shown in fig. 4, has a main frequency band range of an actual milling force between 250Hz and 1200 Hz.
Fig. 5(a) -5 (b) are schematic frequency domain diagrams of idle and cut acceleration signals of a milling force identification method based on a conjugate gradient least square algorithm according to an embodiment of the present invention, and a butterworth band-pass filter is used to filter the measured acceleration signals, where fig. 5(a) shows the schematic frequency domain diagram of the idle acceleration signals, fig. 5(b) shows the schematic frequency domain diagram of the cut acceleration signals, and as can be seen from fig. 5(a) -5 (b), the frequency of the idle acceleration signals is mainly concentrated below 250Hz, which belongs to noise signals, and needs to be filtered, and the acceleration signals during cutting contain components above 1200Hz, which are caused by too high sampling frequency and system nonlinearity, and also need to be filtered.
Fig. 6(a) -6 (b) are schematic diagrams of amplitude-frequency characteristics and phase-frequency characteristics of a butterworth band-pass filter based on a conjugate gradient least square algorithm according to an embodiment of the present invention, where fig. 6(a) shows the amplitude-frequency characteristics, fig. 6(b) shows the phase-frequency characteristics, and the amplitude of the butterworth band-pass filter in a pass band is kept flat and 1, which is important to improve the milling force identification accuracy.
Processing the average transfer function and the filtered acceleration signal by adopting a conjugate gradient least square iterative algorithm, identifying and obtaining the milling force in the milling process, fig. 7(a) -7 (b) are schematic diagrams showing the X-direction milling force comparison of the milling force identification method based on the conjugate gradient least square algorithm according to one embodiment of the present invention, wherein, fig. 7(a) is a general diagram, fig. 7(b) is a partial enlarged view, fig. 8(a) -8 (b) are schematic diagrams comparing milling forces in Y direction of the milling force identification method based on the conjugate gradient least square algorithm according to an embodiment of the present invention, wherein, fig. 8(a) is an overall diagram, and fig. 8(b) is a partially enlarged diagram, and it can be seen from these two diagrams that the method of the present invention can effectively identify the milling force from the acceleration signal of the milling process, and can achieve sufficient accuracy.
In a preferred embodiment of the method for identifying the milling force based on the conjugate gradient least square algorithm, in a first step S1, acceleration sensors are respectively installed in the X and Y directions of a spindle box of a milling machine, a free end of a cutter tip of the milling machine is uniformly knocked in the X and Y directions by a force hammer at a certain angle along the circumferential direction, and multiple hammering experiments are performed; and acquiring and calculating signals measured by a hammering experiment through a data acquisition unit to obtain transfer functions in the X direction and the Y direction.
In the preferred embodiment of the milling force identification method based on the conjugate gradient least square algorithm, the cutting speed is 5000rpm, the cutting depth is 3mm, the cutting width is 2mm, and the feed per tooth is 0.1 mm/tooth in the milling process.
In a preferred embodiment of the milling force identification method based on the conjugate gradient least square algorithm, a butterworth band-pass filter is adopted to perform band-pass filtering on the acceleration signal.
In a preferred embodiment of the milling force identification method based on the conjugate gradient least square algorithm, the milling cutter is subjected to 300-.
In a preferred embodiment of the milling force identification method based on the conjugate gradient least square algorithm of the present invention, the cut-off frequencies of the band-pass filters may be 250Hz and 1200Hz, respectively.
In a preferred embodiment of the method for identifying a milling force based on a conjugate gradient least squares algorithm according to the present invention, the butterworth band-pass filter remains flat and 1 in amplitude within the passband.
In the preferred embodiment of the milling force identification method based on the conjugate gradient least square algorithm, the milling cutter is a high-speed steel three-tooth milling cutter, the diameter of the milling cutter is 10mm, the overhang length of the milling cutter is 50mm, the milling cutter is a milling cutter commonly used for cutting aluminum alloy workpieces, and the workpieces are made of 6061 aluminum alloy.
Fig. 9 is a schematic structural diagram of an identification system for implementing the method according to an embodiment of the present invention, the identification system for implementing the method includes a milling part 1, a data collector 2, a band pass filter 3 and a calculation part 4, the milling part 1 includes a milling machine headstock and a force hammer 7 for knocking a tool nose of a milling cutter, the milling cutter is arranged on the headstock, the milling machine headstock is provided with a first acceleration sensor 5 and a second acceleration sensor 6 for measuring X and Y directions respectively, the calculation part 4 connecting the data collector 2 and the band pass filter 3 includes a first calculation unit 8 for calculating an average transfer function, a second calculation unit 9 based on a conjugate gradient least square iterative algorithm and a comparison unit 10.
In a preferred embodiment of the identification system according to the invention, the first acceleration sensor 5 and/or the second acceleration sensor 6 are resistive or capacitive acceleration sensors.
In a preferred embodiment of the identification system according to the invention, the calculation part 4 is a general processor, a digital signal processor, an application specific integrated circuit ASIC or a field programmable gate array FPGA.
In a preferred embodiment of the identification system according to the invention, the calculation portion 4 comprises a memory comprising one or more read only memories ROM, random access memories RAM, flash memories or electrically erasable programmable read only memories EEPROM.
The identification system can accurately identify the milling force in the milling process in real time, and can be used for milling process state monitoring, fault diagnosis, flutter identification and as a basis for milling parameter selection and optimization.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.
Claims (8)
1. A milling force identification method based on a conjugate gradient least square algorithm comprises the following steps:
in the first step (S1): establishing a coordinate system, wherein the feeding direction is the X direction, and the Y direction is vertical to the feeding direction; carrying out multiple hammering experiments on the milling cutter along the X direction and the Y direction at certain angles uniformly along the circumferential direction to obtain transfer functions of the milling cutter at different angular positions;
in the second step (S2): averaging the transfer functions to obtain an average transfer function;
in the third step (S3): measuring a force signal related to the action of the milling force and an acceleration signal related to the acceleration in the milling process;
in the fourth step (S4): filtering the measured acceleration signal by adopting a band-pass filter, wherein the amplitude of the band-pass filter in a passband is kept flat and 1, and the cut-off frequency is 250-1200 Hz;
in the fifth step (S5): processing the average transfer function and the filtered acceleration signal based on a conjugate gradient least square algorithm, and identifying to obtain the milling force in the milling process;
in the sixth step (S6): and comparing the milling force obtained by identification with the force of the milling force obtained by measurement, and estimating the identification error of the milling force.
2. The method according to claim 1, wherein in the first step (S1), acceleration sensors are respectively installed in X and Y directions at a milling machine headstock, and a hammer is uniformly struck with a force in the X and Y directions at regular intervals in a circumferential direction at a free end of a milling cutter nose to perform a plurality of hammering experiments; and acquiring and calculating signals measured by a hammering experiment through a data acquisition unit to obtain transfer functions in the X direction and the Y direction.
3. The method according to claim 1, characterized in that in a fourth step (S4), the acceleration signal is band-pass filtered using a butterworth band-pass filter.
4. The method as claimed in claim 1, wherein in the first step (S1), 300-8000 hammering tests are performed on the milling cutter in the X and Y directions evenly every 30 ° in the circumferential direction.
5. An identification system for implementing the method according to any one of claims 1-4, said identification system comprising a milling part (1), a data collector (2), a band-pass filter (3) and a calculation part (4), characterized in that the milling part (1) comprises a milling machine headstock on which the milling machine is arranged with a first acceleration sensor (5) and a second acceleration sensor (6) for measuring the X and Y directions, respectively, and a force hammer (7) for striking the tip of the milling machine, said calculation part (4) connecting said data collector (2) and band-pass filter (3) comprising a first calculation unit (8) for calculating the mean transfer function, a second calculation unit (9) based on the conjugate gradient least squares algorithm and a comparison unit (10).
6. The identification system of claim 5, wherein: the first acceleration sensor (5) and/or the second acceleration sensor (6) are/is a resistive or capacitive acceleration sensor.
7. The identification system of claim 5, wherein: the computing part (4) is a general processor, a digital signal processor, an Application Specific Integrated Circuit (ASIC) or a Field Programmable Gate Array (FPGA).
8. The identification system of claim 5, wherein: the computing section (4) comprises a memory comprising one or more of a read only memory ROM, a random access memory RAM, a flash memory or an electrically erasable programmable read only memory EEPROM.
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