CN110750891B - Parallel synchronous orthogonal turning and milling flutter stability lobe graph prediction method - Google Patents
Parallel synchronous orthogonal turning and milling flutter stability lobe graph prediction method Download PDFInfo
- Publication number
- CN110750891B CN110750891B CN201910969702.3A CN201910969702A CN110750891B CN 110750891 B CN110750891 B CN 110750891B CN 201910969702 A CN201910969702 A CN 201910969702A CN 110750891 B CN110750891 B CN 110750891B
- Authority
- CN
- China
- Prior art keywords
- cutting
- milling
- parallel synchronous
- synchronous orthogonal
- turn
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
Landscapes
- Engineering & Computer Science (AREA)
- Business, Economics & Management (AREA)
- Human Resources & Organizations (AREA)
- Economics (AREA)
- Strategic Management (AREA)
- Marketing (AREA)
- Physics & Mathematics (AREA)
- Entrepreneurship & Innovation (AREA)
- Development Economics (AREA)
- Operations Research (AREA)
- Quality & Reliability (AREA)
- Tourism & Hospitality (AREA)
- Game Theory and Decision Science (AREA)
- General Business, Economics & Management (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Numerical Control (AREA)
- Milling Processes (AREA)
- Automatic Control Of Machine Tools (AREA)
Abstract
The invention discloses a parallel synchronous orthogonal turn-milling flutter stability lobe graph prediction method, and belongs to the technical field of machining and manufacturing. The method comprises the following steps in sequence: analyzing a parallel synchronous orthogonal turn-milling multi-degree-of-freedom vibration model, constructing a dynamic cutting thickness model of parallel synchronous orthogonal turn-milling cutting machining, constructing a dynamic cutting force model of parallel synchronous orthogonal turn-milling cutting machining, calculating a frequency response function of a cutter-workpiece system, solving a stability limit of parallel synchronous orthogonal turn-milling cutting machining, constructing a stability lobe graph of parallel synchronous orthogonal turn-milling cutting machining and constructing the stability lobe graph of parallel synchronous orthogonal turn-milling cutting machining considering tool nose jumping. The method can accurately predict the chatter region and the stable region of the parallel synchronous orthogonal turn-milling machine, and can effectively solve the chatter problem in the parallel synchronous orthogonal turn-milling process.
Description
Technical Field
The invention belongs to the technical field of machining and manufacturing, and particularly relates to a parallel synchronous orthogonal turn-milling flutter stability lobe graph prediction method.
Background
The turning and milling technology is an advanced processing technology, is widely applied to the processing of key parts in the military and civil fields of aerospace, microminiature weapons, precise medical instruments and the like, and has the advantage of completing the processing of parts by one-time clamping. In order to improve the productivity of turn-milling processing, the simultaneous turn-milling processing of multiple milling cutters becomes a key, wherein parallel synchronous orthogonal turn-milling is a typical turn-milling processing mode of multiple milling cutters. As with other cutting processing modes, the parallel synchronous orthogonal turn-milling processing process also inevitably generates vibration, limits the cutting efficiency and the processing precision and damages a machine tool.
Aiming at the problem of machining chatter, since 1907, taylor firstly proposed the subject of machining chatter, domestic and foreign scholars have conducted extensive research on chatter phenomena, and gradually formed a method for constructing a stable lobe graph to avoid chatter in the machining process, the abscissa axis of the stable lobe graph is the spindle rotation speed, the ordinate axis is the cutting depth of a cutter, and stable region parameters in the lobe graph are selected for cutting machining, so that chatter can be effectively avoided.
At present, in the traditional construction process of a flutter stability lobe graph of a turn mill, the dynamic cutting thickness of the lobe graph depends on the vibration displacement between different cutter teeth of the same milling cutter, but the construction mechanism can not be applied to the parallel synchronous orthogonal turn mill machining process. Because the parallel synchronous orthogonal turn-milling machining is finished by the common cutting machining of the double milling cutters, the dynamic chip thickness is subjected to the combined action of the vibration displacement of the current cutter and the vibration displacement of the other cutter before a half period, the double milling cutters finish the common cutting machining through the coupling action of the cutter rest structure in the machining process, and the original turn-milling chatter prediction model is not suitable for the prediction of the parallel synchronous orthogonal turn-milling chatter.
Disclosure of Invention
In view of the above, the invention provides a parallel synchronous orthogonal turn-milling flutter stability lobe graph prediction method, which can accurately predict a parallel synchronous orthogonal turn-milling flutter region and a stability region and can effectively solve the flutter problem in the parallel synchronous orthogonal turn-milling process.
A parallel synchronous orthogonal turning milling flutter stability lobe graph prediction method comprises the following implementation steps:
the method comprises the following steps: analyzing a parallel synchronous orthogonal turning and milling multi-degree-of-freedom vibration model;
step two: constructing a dynamic cutting thickness model for parallel synchronous orthogonal turn-milling cutting;
step three: constructing a dynamic cutting force model for parallel synchronous orthogonal turn-milling cutting;
step four: calculating a frequency response function of the tool-workpiece system;
step five: solving the stability limit of parallel synchronous orthogonal turning and milling cutting;
step six: constructing a stability lobe graph of parallel synchronous orthogonal turning and milling cutting processing;
step seven: and constructing a stability lobe graph of parallel synchronous orthogonal turn-milling cutting processing considering tool nose jumping.
Further, the process of analyzing the parallel synchronous orthogonal turn-milling multi-degree-of-freedom vibration model comprises the following steps: the parallel synchronous orthogonal turn-milling processing is that two vertical milling cutters are used for orthogonally turn-milling the outer contour of a workpiece, the two vertical milling cutters are used for orthogonally turn-milling the surface of the workpiece simultaneously, the speeds of the cutters in the feeding direction are consistent, but the cutting depths of the two vertical milling cutters can be different; the cutting process is simplified into X, Y, Z three-free system with mutually perpendicular directions, the dynamic chip thickness of synchronous orthogonal turn milling is influenced by the vibration displacement of the current end mill and the vibration displacement of the other end mill before half period, so that mutual coupling effect is generated in the cutting process of the two end mills, and the dynamic cutting thickness depends on the instantaneous cutting state of the two end mills.
Further, the dynamic cutting thickness model of the parallel synchronous orthogonal turn-milling cutting process constructed in the second step is as follows: in the process of parallel synchronous orthogonal turning, milling and cutting, the end milling cutter and the workpiece generate interaction in three directions,exciting the machining system from a feed direction of the workpiece, a cutting direction of the workpiece, and a radial direction of the workpiece, respectively, the three directions being defined as a Z direction, an X direction, and a Y direction, respectively, and causing dynamic displacements Δ X, Δ Y, and Δ Z; is provided with
The instantaneous contact angle of the cutter tooth i of the end mill j is measured by clockwise rotation of an X axis in the cutting direction; gamma is a radial contact angle measured in the positive direction of the Y axis, and the coordinate transformation formula of the dynamic displacement in the radial direction is as follows:
because synchronous orthogonal parallel turn-milling is different from traditional orthogonal turn-milling machining, the dynamic chip thickness of synchronous orthogonal turn-milling is influenced by the vibration displacement of the current end mill and the vibration displacement of the other end mill before a half period; the two end mills are respectively an end mill I and an end mill II
The instantaneous cutting thickness of the end mill I,
the instantaneous cutting thickness of the end mill II;
is a unit step function for determining whether a tooth is in cut,
in order to make the angle of incidence,
to cut out the corners; the dynamic cutting thicknesses of the end mill I and the end mill II are therefore:
further, the process of constructing the dynamic cutting force model for the parallel synchronous orthogonal turn-milling cutting process in the third step is as follows: according to a cutting force prediction model established by Budak E. and Altintas Y., the tangential direction F acting on the cutter tooth i of the end mill j can be knowntjiRadial direction FrjiAnd axial cutting force FajiAnd axial depth of cut apAnd chip thickness h is proportional:
let KtcIs the tangential cutting force coefficient; krIs coefficient of radial cutting force KrcCoefficient of cutting force KtcThe ratio of (A) to (B); kaIs coefficient of axial cutting force KacCoefficient of radial cutting force KtcThe ratios of the components are all constant; and substituting the cutting thickness formula of the end mill I into a cutting force prediction model to obtain:
after the cutting force is decomposed in the direction X, Y, Z, the dynamic milling force can be obtained as follows:
the total dynamic cutting force acting on the end mill j is the sum of the cutting forces acting on all the teeth i of the tool
The formula (1) and the formula (2) are introduced into the formula (6), and the dynamic cutting force is expressed in the form of matrix coefficients as follows:
because the dynamic cutting force changes along with time and angular velocity, a cutting force formula can be expressed in a matrix form in a time domain, and a dynamic cutting force coefficient matrix is solved by Fourier series expansion:
in the formula NzThe number of teeth of the vertical milling cutter is shown;
the dynamic cutting force is thus expressed in the time domain as:
the time domain cutting force expression simplified into the orthogonal turn-milling end mill I and the end mill II is as follows:
further, the process of calculating the frequency response function of the tool-workpiece system in the fourth step is as follows: and acquiring a frequency response function of the cutter-workpiece system by adopting a hammering test method. The piezoelectric ceramic acceleration sensors are respectively arranged at the tail end of a main shaft workpiece, the tool nose part of an end milling cutter I and the tool nose part of an end milling cutter II, acceleration signals and force signals in the knocking process of a force hammer are collected and transmitted to a computer, and a frequency response transfer function G (iw) of a tool-workpiece system is obtained through analysisc)。
Further, the process of solving the stability limit of the parallel synchronous orthogonal turn-milling cutting in the step five is as follows: let the vibration vectors at the current time (T) and the previous time (T) be
Frequency response transfer function G (iw) of tool-workpiece engagementc) Using harmonic functionsObtaining the amplitude vector at the flutter frequency omegacThe frequency domain equation for the vibration function is:
thus, the regeneration dither displacement may be expressed as:
substituting the regenerative chatter displacement formula into the dynamic milling force:
let the determinant of the dynamic milling force equation be 0, the characteristic equation can be obtained as follows:
in view of transfer function G11(iwc)、G21(iwc)、G12(iwc)、G22(iwc) Is a complex number, the eigenvalue of which has a real part and an imaginary part, and the eigenvalue of the eigen equation is expressed as Λ ═ ΛR+iΛIConsidering that the minimum cut thickness is a real value, the imaginary part of the characteristic value must be less than zero; when ΛRWhen the cutting speed is more than 0, the parallel orthogonal turn-milling cutting system is in an unstable state; when ΛRWhen the frequency is less than 0, the parallel orthogonal turn-milling cutting system is in a stable state; therefore, when ΛRWhen the critical cutting thickness is 0, the critical cutting thickness a is obtained when the parallel orthogonal turn-milling cutting system is in a critical state of a stable stateplim。
Further, the process of constructing the stability lobe graph of the parallel synchronous orthogonal turn-milling cutting process in the sixth step is as follows: and calculating the cutting depth and the main shaft rotating speed corresponding to the wave crest and the wave trough of each lobe graph according to the number of the lobes of the selected stability lobe graph, and constructing the stability lobe graph by combining the critical cutting thickness and adopting a cubic curve.
Further, the process of constructing the stability lobe graph of the parallel synchronous orthogonal turning and milling cutting process considering the cutter tip runout in the seventh step is as follows: due to the eccentric problem of the installation of the end milling cutter I and the end milling cutter II, the cutter point jumps in the rotation process of the cutter, and the cutting depth of the cutter is influenced, so that the jump quantity of the cutter at different rotating speeds is measured by adopting an acceleration sensor, the jump quantity of the cutter in the cutting process is compensated into the stable lobe graph constructed in the step six one by combining a vector superposition principle, and then the stable lobe graph of the parallel synchronous orthogonal turning and milling cutting processing considering the jump of the cutter point is obtained.
Advantageous effects
1. The invention can predict the chatter vibration in the parallel synchronous orthogonal turning and milling process, and predict the chatter vibration according to different cutting processing parameters such as the rotating speed of the workpiece spindle, the rotating speed of the milling cutter spindle, the cutting depth and the like.
2. The invention considers the coupling condition of the cutting dynamic thickness between the processing of double milling cutters, namely the dynamic thickness of the parallel synchronous orthogonal turn-milling processing is the result of the combined action of the vibration displacement of the current cutter and the vibration displacement of the other cutter before half period, thereby solving the problem that the parallel synchronous orthogonal turn-milling flutter cannot be predicted by the existing turn-milling flutter stability lobe diagram.
3. The parallel synchronous orthogonal turning and milling stability lobe graph constructed by the invention considers the situation of cutter tip jumping caused by reasons such as cutter installation eccentricity and the like, and compared with the ideal stability lobe graph which does not consider the actual processing situation, the flutter region and the non-flutter region in the processing process can be more reliably predicted.
Drawings
FIG. 1 is a flow chart for constructing a parallel synchronous orthogonal turn-milling stability lobe graph;
FIG. 2 is a parallel synchronous orthogonal turn-milling model;
FIG. 3 is a parallel synchronous orthogonal turn-milling machining part dynamics model;
FIG. 4 is a schematic diagram of tool-workpiece frequency response function acquisition;
FIG. 5 is a diagram of parallel synchronous orthogonal turn-milling stability lobes;
FIG. 6 is a diagram of parallel orthogonal turn-milling stability lobes with nose runout;
wherein, 1-base, 2-spring damping simplifying device, 3-main shaft, 4-end milling cutter I, 5-workpiece, 6-end milling cutter II, 7-hammer, 8-frequency response function, 9-signal acquisition instrument, 10-computer
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
A parallel synchronous orthogonal turn-milling flutter stability lobe graph prediction method is disclosed, as shown in figure 1, a parallel synchronous orthogonal turn-milling stability lobe graph flow chart is constructed, and the method mainly comprises the following steps:
the method comprises the following steps: analyzing a parallel synchronous orthogonal turning and milling multi-degree-of-freedom vibration model;
as shown in fig. 2, the parallel synchronous orthogonal turn-milling process is to orthogonally turn-mill the outer contour of the workpiece 5 by two end mills, the end mill I4 and the end mill II6 simultaneously orthogonally turn-mill the surface of the workpiece 5, and the speeds of the tools in the feeding direction are consistent, but the cutting depths of the end mill I4 and the end mill II6 may be different. The cutting process is simplified into X, Y, Z three-free system with three mutually perpendicular directions, the dynamic chip thickness of synchronous orthogonal turn milling is influenced by the vibration displacement of the current cutter and the vibration displacement of the other end mill before half period, so that mutual coupling effect is generated in the cutting process of the two end mills, and the dynamic cutting thickness depends on the instantaneous cutting state of the two end mills.
Step two: constructing a dynamic cutting thickness model for parallel synchronous orthogonal turn-milling cutting;
as shown in fig. 3, during the parallel synchronous orthogonal turn-milling cutting, the end mill and the workpiece 5 interact in three directions, exciting the machining system from the feed direction (Z direction) of the workpiece, the cutting direction (X direction) of the workpiece 5, and the radial direction (Y direction) of the workpiece 5, respectively, and causing dynamic displacements Δ X, Δ Y, and Δ Z. Is provided with
Is the instantaneous contact angle of the cutter j and the cutter tooth i, and is measured by clockwise rotation of an X axis in the cutting direction; gamma is a radial contact angle measured in the positive direction of the Y axis, and the coordinate transformation formula of the dynamic displacement in the radial direction is as follows:
because synchronous orthogonal parallel turn-milling is different from traditional orthogonal turn-milling machining, the dynamic chip thickness of synchronous orthogonal turn-milling is influenced by the vibration displacement of the current cutter and the vibration displacement of the other cutter before a half period. Is provided with
The instantaneous cutting thickness of the end mill I,
the instantaneous cutting thickness of the end mill II;
is a unit step function for determining whether a tooth is in cut,
in order to make the angle of incidence,
to cut out the corners. The dynamic cutting thicknesses of the end mill I and the end mill II are therefore:
step three: constructing a dynamic cutting force model for parallel synchronous orthogonal turn-milling cutting;
according to a cutting force prediction model established by Budak E. and Altintas Y., the tangential direction F acting on the cutter tooth i of the end mill j can be knowntjiRadial direction FrjiAnd axial directionCutting force FajiAnd axial depth of cut apAnd chip thickness h is proportional:
setting: ktc: coefficient of tangential cutting force; kr: coefficient of radial cutting force KrcCoefficient of cutting force KtcThe ratio of (A) to (B); ka: coefficient of axial cutting force KacCoefficient of radial cutting force KtcThe ratios are all constant. And substituting the cutting thickness formula of the end mill I into a cutting force prediction model to obtain:
after the cutting force is decomposed in the direction X, Y, Z, the dynamic milling force can be obtained as follows:
the total dynamic cutting force acting on the tool j is the sum of the cutting forces acting on all the teeth i of the end mill
The formula (1) and the formula (2) are introduced into the formula (6), and the dynamic cutting force is expressed in the form of matrix coefficients as follows:
because the dynamic cutting force changes along with time and angular velocity, a cutting force formula can be expressed in a matrix form in a time domain, and a dynamic cutting force coefficient matrix is solved by Fourier series expansion:
Nz: the tool tooth count, and hence the dynamic cutting force, is expressed in the time domain as:
the time domain cutting force expression simplified into the orthogonal turn-milling end mill I and the end mill II is as follows:
step four: calculating a frequency response function of the tool-workpiece system;
as shown in fig. 4, the frequency response function of the tool-work system was obtained using a hammer test. The piezoelectric ceramic acceleration sensors are respectively arranged at the tail end of the main shaft workpiece 5, the tool nose part of the end mill I4 and the tool nose part of the end mill II6, the intelligent signal acquisition, processing and analysis system INV306DF acquires an acceleration signal and a force signal in the knocking process of the force hammer 7, the acceleration signal and the force signal are transmitted to the computer 10, and the frequency response transfer function G (iw) of the tool-workpiece system is obtained through analysisc)。
Step five: solving the stability limit of parallel synchronous orthogonal turning and milling cutting;
let the vibration vectors at the current time (T) and the previous time (T) be
Frequency response transfer function G (iw) of tool-workpiece engagementc) Obtaining amplitude vector at flutter frequency omega by using harmonic functioncThe frequency domain equation for the vibration function is:
thus, the regeneration dither displacement may be expressed as:
substituting the regenerative chatter displacement formula into the dynamic milling force:
let the determinant of the dynamic milling force equation be 0, the characteristic equation can be obtained as follows:
in view of transfer function G11(iwc)、G21(iwc)、G12(iwc)、G22(iwc) Is a complex number, the eigenvalue of which has a real part and an imaginary part, and the eigenvalue of the eigen equation is expressed as Λ ═ ΛR+iΛIConsidering that the minimum cut thickness is a real value, the imaginary part of the characteristic value must be less than zero. When ΛRWhen the cutting speed is more than 0, the parallel orthogonal turn-milling cutting system is in an unstable state; when ΛRWhen the frequency is less than 0, the parallel orthogonal turn-milling cutting system is in a stable state; therefore, when ΛRWhen the critical cutting thickness a is 0, the critical cutting thickness a can be obtained when the parallel orthogonal turn-milling cutting system is in a critical state of a steady stateplim。
Step six: and constructing a stability lobe graph of parallel synchronous orthogonal turning and milling cutting processing.
And sequentially calculating the cutting depth and the main shaft rotating speed corresponding to the wave crest and the wave trough of each lobe k according to the total number M of the lobes of the selected stability lobe graph. After the calculation of the crest and trough cutting depth of the lobe k and the main shaft rotating speed is completed, judging whether the lobe k is equal to the total lobe number M, if the current lobe k is less than M, continuously calculating the cutting depth and the main shaft rotating speed corresponding to the crest and the trough of the lobe k + 1; if the current lobe k is equal to M, calculating the cutting depth corresponding to the wave crest and the wave trough of the lobe and the rotating speed of the main shaft, and then calculating the lobe parameters; and a stability lobe graph of parallel synchronous orthogonal turn-milling cutting machining constructed by a cubic curve is shown in fig. 5.
Step seven: and constructing a stability lobe graph of parallel synchronous orthogonal turn-milling cutting processing considering tool nose jumping.
Due to the eccentric problem of the installation of the end mill I4 and the end mill II6, the tool tip jumps in the rotation process of the tool and the cutting depth of the tool is affected, so that the tool jump amount at different rotating speeds is measured by adopting an acceleration sensor, the tool jump amount in the cutting process is compensated into the stable lobe graph constructed in the six steps one by combining a vector superposition principle, and then a parallel synchronous orthogonal turning and milling cutting stability lobe graph considering tool tip jump is obtained, as shown in FIG. 6.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A parallel synchronous orthogonal turning milling flutter stability lobe graph prediction method is characterized by comprising the following implementation steps:
the method comprises the following steps: analyzing a parallel synchronous orthogonal turning and milling multi-degree-of-freedom vibration model;
step two: constructing a dynamic cutting thickness model for parallel synchronous orthogonal turn-milling cutting;
step three: constructing a dynamic cutting force model for parallel synchronous orthogonal turn-milling cutting;
step four: calculating a frequency response function of the tool-workpiece system;
step five: solving the stability limit of parallel synchronous orthogonal turning and milling cutting;
step six: constructing a stability lobe graph of parallel synchronous orthogonal turning and milling cutting processing;
step seven: constructing a stability lobe graph of parallel synchronous orthogonal turning and milling cutting processing considering tool nose jumping;
the process of analyzing the parallel synchronous orthogonal turn-milling multi-degree-of-freedom vibration model in the step one is as follows: the parallel synchronous orthogonal turn-milling processing is that two vertical milling cutters are used for orthogonally turn-milling the outer contour of a workpiece, the two vertical milling cutters are used for orthogonally turn-milling the surface of the workpiece simultaneously, the speeds of the cutters in the feeding direction are consistent, but the cutting depths of the two vertical milling cutters can be different; the cutting process is simplified into X, Y, Z three-free system with three mutually perpendicular directions, the dynamic chip thickness of synchronous orthogonal turn-milling is influenced by the vibration displacement of the current end mill and the vibration displacement of the other end mill before half period, so that mutual coupling effect is generated in the cutting process of the two end mills, and the dynamic cutting thickness depends on the instantaneous cutting state of the two end mills;
and in the second step, constructing a dynamic cutting thickness model of the parallel synchronous orthogonal turn-milling cutting process as follows: in the parallel synchronous orthogonal turning and milling cutting process, the end mill and a workpiece interact in three directions, a machining system is excited from the feeding direction of the workpiece, the cutting direction of the workpiece and the radial direction of the workpiece respectively, the three directions are defined as the Z direction, the X direction and the Y direction respectively, and dynamic displacement delta X, delta Y and delta Z are caused; is provided with
The instantaneous contact angle of the cutter tooth i of the end mill j is measured by clockwise rotation of an X axis in the cutting direction; gamma is a radial contact angle measured in the positive direction of the Y axis, and the coordinate transformation formula of the dynamic displacement in the radial direction is as follows:
because synchronous orthogonal parallel turn-milling is different from traditional orthogonal turn-milling machining, the dynamic chip thickness of synchronous orthogonal turn-milling is influenced by the vibration displacement of the current end mill and the vibration displacement of the other end mill before a half period; the two end mills are respectively an end mill I and an end mill II
The instantaneous cutting thickness of the end mill I,
the instantaneous cutting thickness of the end mill II;
is a unit step function for determining whether a tooth is in cut,
in order to make the angle of incidence,
to cut out the corners; the dynamic cutting thicknesses of the end mill I and the end mill II are therefore:
2. the method for predicting the flutter stability lobe pattern of the parallel synchronous orthogonal turn mill according to claim 1, wherein the process of constructing the dynamic cutting force model of the parallel synchronous orthogonal turn mill in the third step is as follows: according to a cutting force prediction model established by Budak E. and Altintas Y., the tangential direction F acting on the cutter tooth i of the end mill j can be knowntjiRadial direction FrjiAnd axial cutting force FajiAnd axial depth of cut apAnd chip thickness h is proportional:
let KtcIs the tangential cutting force coefficient; krIs coefficient of radial cutting force KrcCoefficient of cutting force KtcThe ratio of (A) to (B); kaIs coefficient of axial cutting force KacCoefficient of radial cutting force KtcThe ratios of the components are all constant; and substituting the cutting thickness formula of the end mill I into a cutting force prediction model to obtain:
after the cutting force is decomposed in the direction X, Y, Z, the dynamic milling force can be obtained as follows:
the total dynamic cutting force acting on the end mill j is the sum of the cutting forces acting on all the teeth i of the tool
The formula (1) and the formula (2) are introduced into the formula (6), and the dynamic cutting force is expressed in the form of matrix coefficients as follows:
because the dynamic cutting force changes along with time and angular velocity, a cutting force formula can be expressed in a matrix form in a time domain, and a dynamic cutting force coefficient matrix is solved by Fourier series expansion:
in the formula NzThe number of teeth of the vertical milling cutter is shown;
the dynamic cutting force is thus expressed in the time domain as:
the time domain cutting force expression simplified into the orthogonal turn-milling end mill I and the end mill II is as follows:
3. the method for predicting the flutter stability lobe pattern of the parallel synchronous orthogonal turning mill according to claim 2, wherein the step four of calculating the frequency response function of the tool-workpiece system comprises the following steps: acquiring a frequency response function of a cutter-workpiece system by adopting a hammering test method, respectively installing piezoelectric ceramic acceleration sensors at the tail end of a main shaft workpiece, the tool nose part of an end mill I and the tool nose part of an end mill II, acquiring an acceleration signal and a force signal in the knocking process of a force hammer, transmitting the acceleration signal and the force signal to a computer, and analyzing to obtain a frequency response transfer function G (iw) of the cutter-workpiece systemc)。
4. The method for predicting the flutter stability lobe map of the parallel synchronous orthogonal turn mill according to claim 3, wherein the process of solving the stability limit of the parallel synchronous orthogonal turn mill cutting in the fifth step is as follows: let the vibration vectors at the current time T and the previous time T be
Frequency response transfer function G (iw) of tool-workpiece engagementc) Obtaining amplitude vector at flutter frequency omega by using harmonic functioncThe frequency domain equation for the vibration function is:
thus, the regeneration dither displacement may be expressed as:
substituting the regenerative chatter displacement formula into the dynamic milling force:
let the determinant of the dynamic milling force equation be 0, the characteristic equation can be obtained as follows:
in view of transfer function G11(iwc)、G21(iwc)、G12(iwc)、G22(iwc) Is a complex number, the eigenvalue of which has a real part and an imaginary part, and the eigenvalue of the eigen equation is expressed as Λ ═ ΛR+iΛIConsidering that the minimum cut thickness is a real value, the imaginary part of the characteristic value must be less than zero; when ΛRWhen the cutting speed is more than 0, the parallel orthogonal turn-milling cutting system is in an unstable state; when ΛRWhen the frequency is less than 0, the parallel orthogonal turn-milling cutting system is in a stable state; therefore, when ΛRWhen the critical cutting thickness is 0, the critical cutting thickness a is obtained when the parallel orthogonal turn-milling cutting system is in a critical state of a stable stateplim。
5. The method for predicting the flutter stability lobe map of the parallel synchronous orthogonal turn mill according to claim 4, wherein the process of constructing the stability lobe map of the parallel synchronous orthogonal turn mill cutting in the sixth step is as follows: and calculating the cutting depth and the main shaft rotating speed corresponding to the wave crest and the wave trough of each lobe graph according to the number of the lobes of the selected stability lobe graph, and constructing the stability lobe graph by combining the critical cutting thickness and adopting a cubic curve.
6. The method for predicting the flutter stability lobe map of the parallel synchronous orthogonal turn mill according to claim 5, wherein the step seven of constructing the stability lobe map of the parallel synchronous orthogonal turn mill cutting process considering nose bounce comprises the following steps of: due to the eccentric problem of the installation of the end milling cutter I and the end milling cutter II, the cutter point jumps in the rotation process of the cutter, and the cutting depth of the cutter is influenced, so that the jump quantity of the cutter at different rotating speeds is measured by adopting an acceleration sensor, the jump quantity of the cutter in the cutting process is compensated into the stable lobe graph constructed in the step six one by combining a vector superposition principle, and then the stable lobe graph of the parallel synchronous orthogonal turning and milling cutting processing considering the jump of the cutter point is obtained.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910969702.3A CN110750891B (en) | 2019-10-12 | 2019-10-12 | Parallel synchronous orthogonal turning and milling flutter stability lobe graph prediction method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910969702.3A CN110750891B (en) | 2019-10-12 | 2019-10-12 | Parallel synchronous orthogonal turning and milling flutter stability lobe graph prediction method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110750891A CN110750891A (en) | 2020-02-04 |
| CN110750891B true CN110750891B (en) | 2021-09-21 |
Family
ID=69278204
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910969702.3A Active CN110750891B (en) | 2019-10-12 | 2019-10-12 | Parallel synchronous orthogonal turning and milling flutter stability lobe graph prediction method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110750891B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113326586B (en) * | 2021-06-20 | 2023-03-17 | 西北工业大学 | Bao Deban milling chatter prediction method |
| CN115570160A (en) * | 2022-06-22 | 2023-01-06 | 湖南工业大学 | Slender shaft turning flutter stability prediction method with follow-up tool rest |
| CN116160295B (en) * | 2023-04-26 | 2023-08-18 | 深圳市磐锋精密技术有限公司 | Intelligent cutting tracking system of numerical control machine tool |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104680000A (en) * | 2015-02-10 | 2015-06-03 | 北京理工大学 | Orthogonal polynomial-based milling stability prediction method |
| CN104778333A (en) * | 2015-04-27 | 2015-07-15 | 华中科技大学 | Three-dimensional stability modeling method for orthogonal turning-milling machining of helical endmill |
| CN107914183A (en) * | 2017-12-05 | 2018-04-17 | 上海复合材料科技有限公司 | The flutter stability Forecasting Methodology of milling carbon fiber layer plywood |
| CN208495890U (en) * | 2018-06-28 | 2019-02-15 | 若元（天津）自动化设备科技有限公司 | A kind of Numeric control milling machine |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9403252B2 (en) * | 2014-06-18 | 2016-08-02 | Sean Edward Gordon | Vise square device and method of use |
| CN106934170B (en) * | 2017-03-22 | 2019-08-09 | 大连理工大学 | Chatter stability lobes flap figure modeling method based on rose cutter and workpiece contact zone |
| CN108746795B (en) * | 2018-06-20 | 2020-02-14 | 哈尔滨理工大学 | Method for predicting flutter in numerical control milling of mold cavity |
-
2019
- 2019-10-12 CN CN201910969702.3A patent/CN110750891B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104680000A (en) * | 2015-02-10 | 2015-06-03 | 北京理工大学 | Orthogonal polynomial-based milling stability prediction method |
| CN104778333A (en) * | 2015-04-27 | 2015-07-15 | 华中科技大学 | Three-dimensional stability modeling method for orthogonal turning-milling machining of helical endmill |
| CN107914183A (en) * | 2017-12-05 | 2018-04-17 | 上海复合材料科技有限公司 | The flutter stability Forecasting Methodology of milling carbon fiber layer plywood |
| CN208495890U (en) * | 2018-06-28 | 2019-02-15 | 若元（天津）自动化设备科技有限公司 | A kind of Numeric control milling machine |
Non-Patent Citations (6)
| Title |
|---|
| Analytical Prediction of Chatter Stability in Milling—Part I_ General Formulatio;E.Budak et.al;《ASME》;19980331;第120卷;22-30 * |
| Design and chatter prediction analysis of a duplex face turning machine for manufacturing disk-like workpieces;Kun Bai et.al;《International Journal of Machine Tools and Manufacture》;20190130;第140卷;摘要、第1、2、3节 * |
| Dynamics and stability of parallel turning operations;E. Budak et.al;《CIRP Annals - Manufacturing Technology》;20111231;第60卷(第1期);第2.1节 * |
| 复杂曲面高性能侧铣加工技术与方法研究;郭强;《中国博士学位论文全文数据库工程科技Ⅰ辑（月刊）》;20130815(第8期);摘要、第5.4节 * |
| 航空发动机叶片的高速车铣加工三维颤振稳定性及表面粗糙度的研究;王晓邦;《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑（月刊）》;20170315(第03期);C031-1046 * |
| 车铣加工中心动态特性及其加工机理的仿真与实验研究;朱立达;《中国博士学位论文全文数据库工程科技Ⅰ辑（月刊）》;20100815(第08期);第5.1.1、5.2.2、5.3节 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110750891A (en) | 2020-02-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110750891B (en) | Parallel synchronous orthogonal turning and milling flutter stability lobe graph prediction method | |
| CN107914183B (en) | Chatter stability prediction method for milling carbon fiber laminated plate | |
| Song et al. | Prediction of simultaneous dynamic stability limit of time–variable parameters system in thin-walled workpiece high-speed milling processes | |
| Otto et al. | Stability of milling with non-uniform pitch and variable helix tools | |
| Budak et al. | Analytical modeling of chatter stability in turning and boring operations: a multi-dimensional approach | |
| Song et al. | Design for variable pitch end mills with high milling stability | |
| Scippa et al. | FEM based cutting velocity selection for thin walled part machining | |
| Zhenyu et al. | Influence of dynamic effects on surface roughness for face milling process | |
| CN102554326B (en) | Milling finish machining method based on dynamic rigidity of impeller blade | |
| Seguy et al. | Toolpath dependent stability lobes for the milling of thin-walled parts | |
| Tang et al. | Three-dimensional stability lobe and maximum material removal rate in end milling of thin-walled plate | |
| Iglesias et al. | Optimisation of face milling operations with structural chatter using a stability model based process planning methodology | |
| Salehi et al. | Epicycloidal versus trochoidal milling-comparison of cutting force, tool tip vibration, and machining cycle time | |
| Yan et al. | The effect of variable cutting depth and thickness on milling stability for orthogonal turn-milling | |
| CN111291479A (en) | Method for predicting milling stability of series-parallel machine tool | |
| Grossi | Accurate and fast measurement of specific cutting force coefficients changing with spindle speed | |
| Ma et al. | Tool posture dependent chatter suppression in five-axis milling of thin-walled workpiece with ball-end cutter | |
| Zhang et al. | An efficient approach for milling dynamics modeling and analysis with varying time delay and cutter runout effect | |
| Duan et al. | Cutting edge element modeling-based cutter-workpiece engagement determination and cutting force prediction in five-axis milling | |
| Jin et al. | A unified prediction model of 3D surface topography in face milling considering multi-error sources | |
| Bayly et al. | Analysis of tool oscillation and hole roundness error in a quasi-static model of reaming | |
| Qu et al. | Improved method to predict cutting force in end milling considering cutting process dynamics | |
| Munoa et al. | Optimization of hard material roughing by means of a stability model | |
| Adetoro et al. | Stability lobes prediction in thin wall machining | |
| Ma et al. | Stability recognition for high-speed milling of TC4 thin-walled parts with curved surface |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |