CN107368032B - Large-lead screw turning process system integrates frequency response function equation construction method - Google Patents
Large-lead screw turning process system integrates frequency response function equation construction method Download PDFInfo
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Abstract
The present invention relates to a kind of comprehensive frequency response function equation construction method of large-lead screw turning process system, steps are as follows: Step 1: building cutter-Machine Tool Feeding System subsystem frequency response function model；Step 2: building workpiece-machine tool chief axis subsystem frequency response function model；Step 3: by cutter-Machine Tool Feeding System subsystem frequency response function and workpiece-linear superposition of the machine tool chief axis subsystem frequency response function on corresponding direction, the comprehensive frequency response function equation of building large-lead screw turning process system.The present invention is in view of the comprehensive influence to system of processing kinetic characteristics of lathe, cutter and workpiece three, it is proposed " broad sense dynamics space " concept, expand the space scale of dynamics research, method for building up based on the comprehensive frequency response function equation of broad sense dynamics space large-lead screw turning system, the vibration characteristics that cutting system can be characterized more accurately, reflects the dynamic behavior of entire process system.
Description
Technical field
The present invention relates to cutting system comprehensive frequency response function construction method, especially a kind of large-lead screw turning process systems
Synthesis of uniting frequency response function equation construction method, belongs to screw rod turning technical field.
Background technique
Main parts size of the large-lead screw as large pressing machine, in nuclear power, aerospace and large ship key zero
It plays a key effect in the manufacture and forging and stamping of component.Large-lead screw has long, the radial cutting-in of screw thread process size greatly and feeding
The big processing characteristic of speed, using the slow-speed of revolution, the processing method of layered cutting in turning process.Due to row long in process
The high feeding turning of journey, multi-direction intersection, vibration characteristics is complicated and changeable, influences very on large-lead screw machining accuracy and roughness
Greatly, while the service life of tooling system is affected.
Currently, to the research vibrated in cutting process mostly with lathe, cutter, workpiece, main shaft-knife handle-cutter, cutter-work
Part or lathe-workpiece are research object, establish corresponding vibration equation and kinetic model, but these models do not consider machine
The comprehensive influence to system of processing kinetic characteristics of bed, cutter and workpiece three, can not reflect the dynamics of entire process system
Behavior.
It can not reflect the dynamics of entire system of processing in view of high feeding cutting technology and current existing establishing equation method
The status of behavior.Therefore the scale of development of research object provides foundation and meets comprehensive frequency in practical height feeding Tutrning Process
Functional equation construction method is rung, processing stability more accurately can be predicted by established model, is added to optimize cutting
Work parameter and prediction simultaneously inhibit mismachining tolerance, and then reach the machining accuracy purpose for improving workpiece, are that complex parts high-precision is created
At providing fundamental basis and technical guarantee, just there is very important researching value.
Summary of the invention
The present invention is to solve technical problem present in well-known technique and provide a kind of large-lead screw turning process system
Comprehensive frequency response function equation construction method, the construction method is comprehensive for research object with three kinds of lathe, cutter and workpiece persons, by this
The frequency response function equation of construction method building can characterize the vibration characteristics of process system more accurately, can more accurately predict
Processing stability so as to optimize Cutting Parameters and prediction and inhibit mismachining tolerance, and then can reach and improve adding for workpiece
Work precision purpose is also complex parts high-precision wound at providing fundamental basis and technical guarantee.
The technical scheme adopted by the present invention to solve the technical problems existing in the known art is that
Large-lead screw turning process system integrates frequency response function equation construction method, which is characterized in that including walking as follows
It is rapid:
Step 1: building cutter-Machine Tool Feeding System subsystem frequency response function model；
Step 2: building workpiece-machine tool chief axis subsystem frequency response function model；
Step 3: passing through cutter-Machine Tool Feeding System subsystem frequency response function and workpiece-machine tool chief axis subsystem frequency response letter
Linear superposition of the number on corresponding direction, the comprehensive frequency response function equation of building large-lead screw turning process system.
It is further: component cutter-Machine Tool Feeding System subsystem frequency response function model step are as follows:
Firstly, cutter-Machine Tool Feeding System subsystem is reduced to screw rod, nut, guide rail, workbench, knife rest-part knife
Tool and cutter overhanging part；Law theory is coupled based on response, is I, II and III 3 by cutter-Machine Tool Feeding System system subdivision
A minor structure I is screw rod, II be nut-workbench-knife rest-part cutter, III be cutter overhanging part, and consider following four
A faying face is to the influence of cutter-Machine Tool Feeding System subsystem point of a knife point frequency response function: bearing-screw rod, screw rod-nut, work
Make platform-guide rail and knife rest-cutter.
Then, coupling calculating is carried out to minor structure I, II and III frequency response function；It is isometrical that minor structure I is reduced to homogeneous elasticity
Girder construction, while rigid support will be reduced to the structure that lathe feed screw is played a supporting role；I and II minor structure is rigidly coupled
At assembly, 1 position is defined as at the left side edge of minor structure I, nut junction is defined as 2 in right side and minor structure II
It sets, while the left side junction of nut is defined as 2 ' positions, 3 positions being defined as at nut right side edge in minor structure II；It is filling
Apply load at ligand 1 position, consider translation and rotation two-degree-of-freedom system, the power applied at minor structure endpoint is qi=(fi,
mi)T(i=1,2,2 '), obtaining corresponding position dynamic respond is formula (1)；Simultaneously according to the equilibrium relation (2) and consistency condition of power
(3), it acquires shown in frequency response function of the assembly at 1 such as formula (4)；Similarly acquire the frequency response function such as formula (5) at 3；Antithetical phrase knot
Structure I-II and III is coupled, and the junction of nut is defined as 3 ' positions in the left side of II intermediate slide of minor structure and minor structure II,
The right side of II intermediate slide of minor structure and the junction of minor structure III are defined as 4 positions, while III cutter of minor structure is in conjunction with knife rest
Place is defined as 4 ' positions, 5 positions being defined as at cutter right side edge.The frequency response function in 5 and 3 ' positions is similarly obtained, such as formula
(6)。
q2+q2′=0
q1=Q1 (2)
S2+H2+W2=S2′ (3)
RS11=R11+R12(R22′-R’22′-R″ii+R22)-1R21 (4)
RS33=R33+R32′(R22′-R’22′-R″22′+R22)-1R2′3 (5)
In formula, RijIt is the frequency response function matrix of corresponding position when i is identical as j for frequency response function matrix, when the two not phase
For across a frequency response function matrix whens equal；Si=(Xi,θi)TFor the dynamic respond at minor structure coordinate points i, Wi=(Ui,θi)TFor silk
The dynamic respond of bar, Hi=(Pi,θi)TFor dynamic respond at faying face, wherein Xi、UiAnd PiFor dynamic respond, θiFor rotation displacement
Response；Q1Assume that the load applied at the point 1 of assembly I-II.
Subsequently, on the basis of the minor structure Coupling frequency response acquired, the influence of translation displacements at faying face is considered, such as formula
(7) shown in, by III cutter junction of II knife rest of minor structure and minor structure, cutter bound fraction is set as a, and knife rest bound fraction is b；
By II nut junction of I screw rod of minor structure and minor structure, screw rod bound fraction is set as c, and nut bound fraction is d；It obtains any
Position considers the frequency response function that faying face influences, such as formula (8)；Derive frequency response function, formula (9)；Sound at point of a knife point
It answers, formula (10)；Based on frequency response function matrix symmetry feature, three-dimensional frequency response receptance function at point of a knife point after being coupled is public
Formula (11),
RSxx=Rxx-Rax[Rbb+Raa-R′ab+R2′2′]-1Rxa (8)
In formula, RijFor frequency response matrix；Rij、R′ijWith R "ijFormula such as formula (9)-(11)；Wherein hij、nijAnd lij、
pijApply dynamic respond of the unit force at the position i in the position j for minor structure I and applies specific torque at the position i in the position j
Rotational response, formula (12)；DiFor faying face response, formula (14)；U is existing screw rod length travel response, formula (15)；
Response formula at frequency response function and point of a knife is further obtained, such as formula (16)-(17)；Based on matrix symmetric feature, finally
Cutter-lathe subsystem point of a knife point three-dimensional frequency response function is acquired, such as formula (18),
In formula, I is the moment of inertia；E is elasticity modulus；For frequency parameter；η be damping because
Son；L is the length of beam；FiFormula such as (13).
F1=sin λ l+cosh λ l
F3=sin λ lcosh λ l
F5=sinh λ lcos λ l-sin λ lcosh λ l
F6=sinh λ lcos λ l+sin λ lcosh λ l
F7=sin λ l+sinh λ l
F8=sin λ l-sinh λ l
F10=cos λ l-cosh λ l (13)
In formula, DiFor screw rod length travel response；kij(i, j=1,2,3,4,5,6) is the element in stiffness matrix；F(Fx
=-∫SpxdS、Fy=-∫SpyDS and Fz=-∫SpzdS)、M(Mx=-∫SpzydS+∫SpyzdS、My=-∫SpxzdS+∫SpzXdS and Mz
=-∫SpyxdS+∫SpxYdS), S and P be respectively power, torque, faying face area and combine surface pressure.
In formula, U is screw rod length travel response；ku1For fore bearing x to longitudinal rigidity；E is screw rod
Elasticity modulus；ωuFor screw rod vibration frequency.
RSxx=Rxx-Rax[Rdd-R′ab-R″ab+R2′2′]-1Rxa (16)
In formula: Gxt、GytAnd GztIt is workpiece-frequency response function of the feed system subsystem on the direction x, y and z respectively；Wherein
hij、nij、lijAnd pijApply dynamic respond of the unit force at the position i in the position j for minor structure I, application specific torque at point j
Apply the rotational response at point i caused by unit force at dynamic respond, point j at caused point i and applies unit force in the position j
Rotational response of the square at the position i；DiFor faying face response；U is feed system length travel response；Footnote x is indicated in the x-direction
On any position, footnote y indicate in the y-direction on any position, footnote z indicate in the z-direction on any position.
It is further: building workpiece-machine tool chief axis subsystem frequency response function model step are as follows:
Firstly, workpiece-machine tool chief axis subsystem is reduced to three main shaft, chuck and workpiece parts；It is coupled based on response
Workpiece-machine tool chief axis system subdivision is main shaft, three minor structures of chuck-workpiece and workpiece, respectively minor structure by law theory
I ', minor structure II ' and minor structure III ', and consider following two faying face to part-machine-tool spindle system workpiece any position frequency response
The influence of function: main shaft-chuck and chuck-workpiece；
It is successively coupled by the minor structure of division, constructs workpiece-machine tool chief axis subsystem kinetic model, by responding coupling
The legal frequency response function for obtaining each minor structure endpoint；By establishing the model of vibration of the faying face of machine chuck and work end, tie
State hammering experiment is molded, main shaft-chuck Complexed Prostate Specific Antigen is identified；
Workpiece-machine tool chief axis subsystem different location point frequency response function after finally being coupled using IRCSA method, is based on
Matrix symmetric feature, same to cutter-Machine Tool Feeding System subsystem point of a knife point frequency response method for solving, finally acquires any position of workpiece
Coupling three-way frequency response function is set, such as formula (19).
In formula: Gxw、GywAnd GzwIt is workpiece-frequency response function of the machine tool chief axis subsystem on the direction x, y and z respectively；Wherein
h′ij、n′ij、l′ijWith p 'ijApply dynamic respond of the unit force at the position i in the position j for minor structure I ', application unit at point j
Apply the rotational response at point i caused by unit force at dynamic respond, point j at point i caused by torque and applies in the position j single
Rotational response of the position torque at the position i, calculation formula are identical as formula (12)；D′iFor workpiece faying face response, calculation formula with
(14) identical；U ' is main shaft length travel response；By III ' workpiece junction of II ' chuck of minor structure and minor structure, chuck engaging portion
It is divided into a ', workpiece interface is divided into b '；By II ' chuck junction of I ' main shaft of minor structure and minor structure, main shaft engaging portion is set up separately
For c ', chuck bound fraction is d '；Footnote x indicates any position in the x-direction, and footnote y indicates any position in the y-direction
It sets, footnote z indicates any position in the z-direction.
It is further: the method for the comprehensive frequency response function equation of building large-lead screw turning process system are as follows:
Large-lead screw turnery processing system includes the cutter-Machine Tool Feeding System subsystem and the workpiece-machine
Bed main shaft subsystem, cutter-Machine Tool Feeding System subsystem are shown in frequency response function such as formula (20)-(21) in the direction x, z；Work
Part-machine tool chief axis subsystem is shown in frequency response function such as formula (22)-(23) in the corresponding direction x, z.Wherein, Gxxt、GzztFor knife
Frequency response function of the tool-Machine Tool Feeding System subsystem in the direction x, z；Gxxw、GzzwIt is workpiece-machine tool chief axis subsystem in x, the side z
To frequency response function；Rxxt、RzztFor cutter-Machine Tool Feeding System subsystem the frequency response function in the direction x, z real part；Rxxw、
RzzwFor workpiece-machine tool chief axis subsystem the frequency response function in the direction x, z real part；Ixxt、IzztFor cutter-Machine Tool Feeding System
Imaginary part of the subsystem in the frequency response function in the direction x, z；Ixxw、IzzwFrequency response letter for workpiece-machine tool chief axis subsystem in the direction x, z
Several imaginary parts；Sxxt、SzztVibration displacement for cutter-Machine Tool Feeding System subsystem in the direction x, z；Sxxw、SzzwFor workpiece-machine
Vibration displacement of the bed main shaft subsystem in the direction x, z；Fxxt、FzztIt is cut for cutter-Machine Tool Feeding System subsystem the direction x, z
Cut power；Fxxw、FzzwCutting force for workpiece-machine tool chief axis subsystem in the direction x, z；
During height feeding turning large-lead screw part, formed turning tool and the value of big screw pitch external thread piece relative displacement are equal to
The sum of lathe tool displacement and the displacement of big screw pitch external thread piece, wherein relative transfer function is respectively such as on the direction x, z for lathe tool and screw rod
Shown in formula (24) and (25), meanwhile, in frequency domain, x, z are to shown in frequency response function such as formula (26), (27).Wherein, Gxx、GzzFor knife
Opposite frequency response function of the tool-Machine Tool Feeding System subsystem with workpiece-machine tool chief axis subsystem in the direction x, z；Sxx、SzzFor knife
The Relative Vibration of tool-Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem in the direction x, z is displaced；Fxx、FzzFor knife
Opposite cutting force of the tool-Machine Tool Feeding System subsystem with workpiece-machine tool chief axis subsystem in the direction x, z；
Gxx=Gxxt+Gxxt (26)
Gzz=Gzzt+Gzzw (27)
Respectively by cutter-Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem under respective coordinate system
Axially it is considered as rigidity, establishes 0-xyz coordinate system, for x to be radial, positive direction is outside；Y is axially that positive direction is to the right；The direction z is
It is radial, and be upwards positive direction；Height feeding turning process system x is to comprehensive frequency response function by cutter-Machine Tool Feeding System subsystem
The x of system is to decision, formula (28)；Y is to comprehensive frequency response from workpiece-machine tool chief axis subsystem y to decision, formula (29)；Process system z to
It is codetermined by cutter-Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem, shown in formula (30)；Obtain high feeding
Shown in the comprehensive frequency response function such as formula (31) of turning process system.
Gx(iw)=[Gxt(iwt)] (28)
Gy(iw)=[Gyw(iww)] (29)
[G (iw)]=[Gxt(iw) Gyw(iw) Gz(iw)] (31)
Beneficial effects of the present invention
1, dynamics research space is disclosed, has been also limited in cutting system in the range of each subsystem, space is studied
Belong to narrow sense space, while not yet considering the comprehensive influence to system of processing kinetic characteristics of lathe, cutter and workpiece three, nothing
Method reflects the dynamic behavior of entire process system；The present invention is comprehensive to system of processing in view of lathe, cutter and workpiece three
The influence of kinetic characteristics proposes " broad sense dynamics space " concept, expands the space scale of dynamics research, is based on broad sense
The method for building up of the comprehensive frequency response function equation of dynamics space large-lead screw turning system, can characterize cutting more accurately
The vibration characteristics of system reflects the dynamic behavior of entire process system.
2, it is relatively more for the prediction of knife end dynamic characteristic and research that frequency response function research is disclosed, and
Very high precision is reached.But the part of thin-walled parts processing is concentrated mainly on to the analysis of work end dynamic characteristic, and very
The rare influence lathe to the synthesis frequency response of system is taken into account.And it studies high feeding turnery processing stability and must be taken into consideration extensively
Process system kinetic characteristics under adopted dynamics space, especially system of processing integrate Frequency Response, only accurately prediction
System integrates frequency response, could establish more accurate Machine Tool Dynamics model to be applied to high feeding turning large-lead screw processing and cut
It cuts in the optimization of parameter.The present invention provides foundation and meets comprehensive frequency response function method in practical height feeding Tutrning Process, energy
It is enough more accurately to predict processing stability by establishing comprehensive frequency response function, to optimize Cutting Parameters and prediction simultaneously
Inhibit mismachining tolerance, and then reaches the machining accuracy purpose for improving workpiece.
Detailed description of the invention
Fig. 1 is based on the comprehensive frequency response function construction method flow chart of broad sense dynamics space large-lead screw turning system；
Fig. 2 is cutter-Machine Tool Feeding System subsystem structure division and faying face position view；
Faying face of the faying face 1 between workbench and guide rail；Faying face of the faying face 2 between knife rest and cutter；Knot
Faying face of the conjunction face 3 between bearing and screw rod；Faying face of the faying face 4 between screw rod and nut；
Fig. 3 is workpiece-machine tool chief axis subsystem structure division and faying face position view；
Faying face of the faying face 1 between main shaft and chuck；Faying face of the faying face 2 between chuck and workpiece；
Fig. 4 is power hammer hammering experiment test system；
Fig. 5 high feeds turnery processing system schematic.
Specific embodiment
In order to further understand the content, features and effects of the present invention, the following examples are hereby given, and cooperate attached drawing
Detailed description are as follows:
Referring to Figure 1-5, the present invention is based on the comprehensive frequency response functions of the large-lead screw turning system in broad sense dynamics space
Construction method, specifically includes the following steps:
Step 1: building cutter-Machine Tool Feeding System subsystem frequency response function model
Firstly, cutter-Machine Tool Feeding System subsystem is carried out to be reduced to screw rod, nut, guide rail, workbench, knife rest-portion
Divide cutter and cutter overhanging part；Law theory is coupled based on response, is I (silk by cutter-Machine Tool Feeding System system subdivision
Bar), II (nut-workbench-knife rest-part cutter) and the minor structure of III (cutter overhanging part) three, and consider following four
Faying face is to the influence of cutter-Machine Tool Feeding System subsystem point of a knife point frequency response function: bearing-screw rod, screw rod-nut, work
Platform-guide rail and knife rest-cutter.Wherein cutter minor structure divides and faying face position such as attached drawing 2 shows.
Then, coupling calculating is carried out to minor structure I, II and III frequency response function；It is isometrical that minor structure I is reduced to homogeneous elasticity
Girder construction, while rigid support will be reduced to the structure that lathe feed screw is played a supporting role；I and II minor structure is rigidly coupled
At assembly, 1 position is defined as at the left side edge of minor structure I, nut junction is defined as 2 in right side and minor structure II
It sets, while the left side junction of nut is defined as 2 ' positions, 3 positions being defined as at nut right side edge in minor structure II；It is filling
Apply load at ligand 1 position, consider translation and rotation two-degree-of-freedom system, the power applied at minor structure endpoint is qi=(fi,
mi)T(i=1,2,2 '), obtaining corresponding position dynamic respond is formula (1)；Simultaneously according to the equilibrium relation (2) and consistency condition of power
(3), it acquires shown in frequency response function of the assembly at 1 such as formula (4)；Similarly acquire the frequency response function such as formula (5) at 3；Antithetical phrase knot
Structure I-II and III is coupled, and the junction of nut is defined as 3 ' positions in the left side of II intermediate slide of minor structure and minor structure II,
The right side of II intermediate slide of minor structure and the junction of minor structure III are defined as 4 positions, while III cutter of minor structure is in conjunction with knife rest
Place is defined as 4 ' positions, 5 positions being defined as at cutter right side edge.The frequency response function in 5 and 3 ' positions is similarly obtained, such as formula
(6)。
S1=R11q1+R12q2
S2=R21q1+R22q2
S2′=R2′2′q2′
S3=R32′q2′
H2=R '22′q2′
Wi=R "iiqi (1)
q2+q2′=0
q1=Q1 (2)
S2+H2+W2=S2′ (3)
RS11=R11+R12(R22′-R’22′-R″ii+R22)-1R21 (4)
RS33=R33+R32′(R22′-R’22′-R″22′+R22)-1R2′3 (5)
In formula, RijIt is the frequency response function matrix of corresponding position when i is identical as j for frequency response function matrix, when the two not phase
For across a frequency response function matrix whens equal；Si=(Xi,θi)TFor the dynamic respond at minor structure coordinate points i, Wi=(Ui,θi)TFor silk
The dynamic respond of bar, Hi=(Pi,θi)TFor dynamic respond at faying face, wherein Xi、UiAnd PiFor dynamic respond, θiFor rotation displacement
Response；Q1Assume that the load applied at the point 1 of assembly I-II.
Subsequently, on the basis of the minor structure Coupling frequency response acquired, the influence of translation displacements at faying face is considered, such as formula
(7) shown in, by III cutter junction of II knife rest of minor structure and minor structure, cutter bound fraction is set as a, and knife rest bound fraction is b；
By II nut junction of I screw rod of minor structure and minor structure, screw rod bound fraction is set as c, and nut bound fraction is d；It obtains any
Position considers the frequency response function that faying face influences, such as formula (8)；Derive frequency response function, formula (9)；Sound at point of a knife point
It answers, formula (10)；Based on frequency response function matrix symmetry feature, three-dimensional frequency response receptance function at point of a knife point after being coupled is public
Formula (11),
RSxx=Rxx-Rax[Rbb+Raa-R′ab+R2′2′]-1Rxa (8)
In formula, RijFor frequency response matrix；Rij、R′ijWith R "ijFormula such as formula (9)-(11)；Wherein hij、nijAnd lij、
pijApply dynamic respond of the unit force at the position i in the position j for minor structure I and applies specific torque at the position i in the position j
Rotational response, formula (12)；DiFor faying face response, formula (14)；U is existing screw rod length travel response, formula (15)；
Response formula at frequency response function and point of a knife is further obtained, such as formula (16)-(17)；Based on matrix symmetric feature, finally
Cutter-lathe subsystem point of a knife point three-dimensional frequency response function is acquired, such as formula (18).
In formula, I is the moment of inertia；E is elasticity modulus；For frequency parameter；η be damping because
Son；L is the length of beam；FiFormula such as (13).
F1=sin λ l+cosh λ l
F3=sin λ lcosh λ l
F5=sinh λ lcos λ l-sin λ lcosh λ l
F6=sinh λ lcos λ l+sin λ lcosh λ l
F7=sin λ l+sinh λ l
F8=sin λ l-sinh λ l
F10=cos λ l-cosh λ l (13)
In formula, DiFor screw rod length travel response；kij(i, j=1,2,3,4,5,6) is the element in stiffness matrix；F(Fx
=-∫SpxdS、Fy=-∫SpyDS and Fz=-∫SpzdS)、M(Mx=-∫SpzydS+∫SpyzdS、My=-∫SpxzdS+∫SpzXdS and Mz
=-∫SpyxdS+∫SpxYdS), S and P be respectively power, torque, faying face area and combine surface pressure.
In formula, U is screw rod length travel response；ku1For fore bearing x to longitudinal rigidity；E is screw rod
Elasticity modulus；ωuFor screw rod vibration frequency.
RSxx=Rxx-Rax[Rdd-R′ab-R″ab+R2′2′]-1Rxa (16)
In formula: Gxt、GytAnd GztIt is workpiece-frequency response function of the feed system subsystem on the direction x, y and z respectively；Wherein
hij、nij、lijAnd pijApply dynamic respond of the unit force at the position i in the position j for minor structure I, application specific torque at point j
Apply the rotational response at point i caused by unit force at dynamic respond, point j at caused point i and applies unit force in the position j
Rotational response of the square at the position i；DiFor faying face response；U is feed system length travel response；Footnote x is indicated in the x-direction
On any position, footnote y indicate in the y-direction on any position, footnote z indicate in the z-direction on any position.
Step 2: building workpiece-machine tool chief axis subsystem frequency response function model
Firstly, workpiece-machine tool chief axis subsystem is reduced to three main shaft, chuck and workpiece parts；It is coupled based on response
Workpiece-machine tool chief axis system subdivision is main shaft, three minor structures of chuck-workpiece and workpiece, respectively minor structure by law theory
I ', minor structure II ' and minor structure III ', and consider following two faying face to part-machine-tool spindle system workpiece any position frequency response
The influence of function: main shaft-chuck and chuck-workpiece, wherein workpiece-machine tool chief axis subsystem structure divide and faying face position such as
Shown in attached drawing 3.
It is successively coupled by the minor structure of division, constructs workpiece-lathe subsystem kinetic model, by responding coupled method
Obtain the frequency response function of each minor structure endpoint；By establishing the model of vibration of the faying face of machine chuck and work end, in conjunction with mould
State hammering experiment, identifies main shaft-chuck Complexed Prostate Specific Antigen；
Workpiece-machine tool chief axis subsystem different location point frequency response function after finally being coupled using IRCSA method.It is based on
Matrix symmetric feature, same to cutter-lathe subsystem point of a knife point frequency response method for solving finally acquire workpiece any position coupling three
To frequency response function, such as formula (19).
In formula: Gxw、GywAnd GzwIt is workpiece-frequency response function of the machine tool chief axis subsystem on the direction x, y and z respectively；Wherein
h′ij、n′ij、l′ijWith p 'ijApply dynamic respond of the unit force at the position i in the position j for minor structure I ', application unit at point j
Apply the rotational response at point i caused by unit force at dynamic respond, point j at point i caused by torque and applies in the position j single
Rotational response of the position torque at the position i, calculation formula are identical as formula (12)；D′iFor workpiece faying face response, calculation formula with
(14) identical；U ' is main shaft length travel response；By III ' workpiece junction of II ' chuck of minor structure and minor structure, chuck engaging portion
It is divided into a ', workpiece interface is divided into b '；By II ' chuck junction of I ' main shaft of minor structure and minor structure, main shaft engaging portion is set up separately
For c ', chuck bound fraction is d '；Footnote x indicates any position in the x-direction, and footnote y indicates any position in the y-direction
It sets, footnote z indicates any position in the z-direction.
Above-mentioned hammering experimental modal parameter obtains and boundary condition resolving embodiment is as follows:
For measuring the big screw pitch external thread piece modal parameter experiment of turning on CA6140 center lathe.Preparing experiment is set
Have: DHDAS_5922 transient signal tests test macro, PCB (353A02 type) piezoelectric acceleration transducer, desktop computer (packet
Include data collection system) and sensitivity be 3.41 5KN power hammer into shape.Power hammer hammering experiment test system is as shown in Figure 4.Respectively to machine
Bed main shaft, Machine Tool Feeding System, cutter (difference overhangs) and workpiece (different location) carry out mode hammering experiment, acquire phase respectively
Intrinsic frequency, Mode Shape, modal damping, modal mass and the modal stiffness answered.
Step 3: the high comprehensive frequency response function construction method of feeding turning system
During height feeds turning large-lead screw, cutting force is applied respectively as equal in magnitude, contrary load
It is added in above steep-pitch thread part and formed turning tool.Under force, Relative Vibration occurs for steep-pitch thread part and lathe tool.Greatly
Pitch screw turnery processing system includes cutter-Machine Tool Feeding System subsystem (lathe, feed system, knife rest, cutter) and work
Part-machine tool chief axis subsystem (lathe, chuck, workpiece) two parts.Height feeding turnery processing system schematic is as shown in Figure 5.Knife
Tool-Machine Tool Feeding System subsystem is shown in frequency response function such as formula (20)-(21) in the direction x, z；Workpiece-machine tool chief axis subsystem
System is shown in frequency response function such as formula (22)-(23) in the corresponding direction x, z.Wherein, Gxxt、GzztFor cutter-Machine Tool Feeding System
Frequency response function of the system in the direction x, z；Gxxw、GzzwFrequency response function for workpiece-machine tool chief axis subsystem in the direction x, z；Rxxt、
RzztFor cutter-Machine Tool Feeding System subsystem the frequency response function in the direction x, z real part；Rxxw、RzzwFor workpiece-machine tool chief axis
Real part of the subsystem in the frequency response function in the direction x, z；Ixxt、IzztFrequency for cutter-Machine Tool Feeding System subsystem in the direction x, z
Ring the imaginary part of function；Ixxw、IzzwFor workpiece-machine tool chief axis subsystem the frequency response function in the direction x, z imaginary part；Sxxt、SzztFor
Vibration displacement of the cutter-Machine Tool Feeding System subsystem in the direction x, z；Sxxw、SzzwIt is workpiece-machine tool chief axis subsystem in x, z
The vibration displacement in direction；Fxxt、FzztCutting force for cutter-Machine Tool Feeding System subsystem in the direction x, z；Fxxw、FzzwFor work
Cutting force of the part-machine tool chief axis subsystem in the direction x, z.
During height feeding turning large-lead screw part, formed turning tool and the value of big screw pitch external thread piece relative displacement are equal to
The sum of lathe tool displacement and the displacement of big screw pitch external thread piece.Wherein, relative transfer function is respectively such as on the direction x, z for lathe tool and screw rod
Shown in formula (24) and (25).Meanwhile x, z are shown to frequency response function such as formula (26), (27) in frequency domain.To obtain big screw pitch spiral shell
The synthesis frequency response function of bar turning process system is cutter-Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem frequency
Function is rung in the linear superposition of respective direction.Wherein, Gxx、GzzFor cutter-Machine Tool Feeding System subsystem and workpiece-lathe master
Opposite frequency response function of the sub-system in the direction x, z；Sxx、SzzFor cutter-Machine Tool Feeding System subsystem and workpiece-lathe master
Relative Vibration of the sub-system in the direction x, z is displaced；Fxx、FzzFor cutter-Machine Tool Feeding System subsystem and workpiece-lathe master
Opposite cutting force of the sub-system in the direction x, z.
Gxx=Gxxt+Gxxt (26)
Gzz=Gzzt+Gzzw (27)
Height feeding turning process System describe is that revolving part carries out large-lead screw under formed turning tool effect on lathe
The process of processing, the dynamic characteristic of process system embody a concentrated reflection of at the contact point of cutter and workpiece, large-lead screw turning work
The synthesis frequency response of process system be coupling after point of a knife point frequency response function and coupling after workpiece different location point frequency response function in counterparty
Upward linear superposition.Since large-lead screw is by chuck and top both ends clamping, so workpiece-in process
Machine tool chief axis subsystem is obviously greater than in axial rigidity in radial rigidity；Similarly, passed through due to cutter by spring knife handle
Jackscrew is fixed on knife rest, and cutter-Machine Tool Feeding System subsystem axial direction rigidity is significantly better than radial rigidity.In consideration of it,
By cutter-Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem, the axial direction under respective coordinate system is considered as respectively
Rigidity.0-xyz coordinate system is established, for x to be radial, positive direction is outside；Y is axially that positive direction is to the right；The direction z is radial, and to
Upper is positive direction.So high feeding turning process system x is to comprehensive frequency response function by cutter-Machine Tool Feeding System subsystem x
To decision, formula (28)；Y is to comprehensive frequency response from workpiece-machine tool chief axis subsystem y to decision, formula (29)；Process system z is to by knife
Tool-Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem codetermine, shown in formula (30)；Obtain high feeding turning
Shown in the comprehensive frequency response function such as formula (31) of process system.
Gx(iw)=[Gxt(iwt)] (28)
Gy(iw)=[Gyw(iww)] (29)
[G (iw)]=[Gxt(iw) Gyw(iw) Gz(iw)] (31)
Claims (2)
1. large-lead screw turning process system integrates frequency response function equation construction method, which comprises the steps of:
Step 1: building cutter-Machine Tool Feeding System subsystem frequency response function model；
Step 2: building workpiece-machine tool chief axis subsystem frequency response function model；
Step 3: being existed by cutter-Machine Tool Feeding System subsystem frequency response function and workpiece-machine tool chief axis subsystem frequency response function
Linear superposition on corresponding direction, the comprehensive frequency response function equation of building large-lead screw turning process system；
Construct cutter-Machine Tool Feeding System subsystem frequency response function model step are as follows:
Firstly, by cutter-Machine Tool Feeding System subsystem be reduced to screw rod, nut, guide rail, workbench, knife rest-part cutter and
Cutter overhanging part；Law theory is coupled based on response, is I, II and III 3 sons by cutter-Machine Tool Feeding System system subdivision
Structure I is screw rod, II be nut-workbench-knife rest-part cutter, III be cutter overhanging part, and consider following four knot
It closes and faces cutter-Machine Tool Feeding System subsystem point of a knife point frequency response function influence: bearing-screw rod, screw rod-nut, workbench-
Guide rail and knife rest-cutter；
Then, coupling calculating is carried out to minor structure I, II and III frequency response function；Minor structure I is reduced to the isometrical beam knot of homogeneous elasticity
Structure, while rigid support will be reduced to the structure that lathe feed screw is played a supporting role；I and II minor structure is rigidly coupled into dress
Ligand is defined as 1 position at the left side edge of minor structure I, and nut junction is defined as 2 positions in right side and minor structure II, together
When minor structure II in the left side junction of nut be defined as 2 ' positions, 3 positions being defined as at nut right side edge；In assembly 1
Apply load at position, consider translation and rotation two-degree-of-freedom system, the power applied at minor structure endpoint is qi=(fi, mi)T,
Wherein i=1,2,2 ', obtaining corresponding position dynamic respond is formula (1)；Simultaneously according to the equilibrium relation (2) and consistency condition of power
(3), it acquires shown in frequency response function of the assembly at 1 such as formula (4)；Similarly acquire the frequency response function such as formula (5) at 3；Antithetical phrase knot
Structure I-II and III is coupled, and the junction of nut is defined as 3 ' positions in the left side of II intermediate slide of minor structure and minor structure II,
The right side of II intermediate slide of minor structure and the junction of minor structure III are defined as 4 positions, while III cutter of minor structure is in conjunction with knife rest
Place is defined as 4 ' positions, 5 positions being defined as at cutter right side edge, the frequency response function in 5 and 3 ' positions is similarly obtained, such as formula
(6)；
q2+q2′=0
q1=Q1 (2)
S2+H2+W2=S2′ (3)
RS11=R11+R12(R22′-R'22′-R"ii+R22)-1R21 (4)
RS33=R33+R32′(R22′-R'22′-R"22′+R22)-1R2′3 (5)
In formula, RijIt is the frequency response function matrix of corresponding position when i is identical as j, when the two is unequal for frequency response function matrix
For across a frequency response function matrix；Si=(Xi,θi)TFor the dynamic respond at minor structure coordinate points i, Wi=(Ui,θi)TFor screw rod
Dynamic respond, Hi=(Pi,θi)TFor dynamic respond at faying face, wherein Xi、UiAnd PiFor dynamic respond, θiIt is rung for rotation displacement
It answers；Q1Assume that the load applied at the point 1 of assembly I-II；
Subsequently, on the basis of the minor structure Coupling frequency response acquired, the influence of translation displacements at faying face is considered, such as formula (7)
Shown, by III cutter junction of II knife rest of minor structure and minor structure, cutter bound fraction is set as a, and knife rest bound fraction is b；It will
II nut junction of I screw rod of minor structure and minor structure, screw rod bound fraction are set as c, and nut bound fraction is d；Obtain any position
The frequency response function for considering that faying face influences is set, such as formula (8)；Derive frequency response function, formula (9)；Response at point of a knife point,
Formula (10)；Based on frequency response function matrix symmetry feature, three-dimensional frequency response receptance function, formula at point of a knife point after being coupled
(11)；
RSxx=Rxx-Rax[Rbb+Raa-R′ab+R2′2′]-1Rxa (8)
In formula, RijFor frequency response matrix；Rij、R′ijWith R "ijFormula such as formula (9)-(11)；Wherein hij、nij、lijAnd pijFor
Minor structure I applies dynamic respond of the unit force at the position i in the position j, the position at point j at point i caused by application specific torque
It moves and responds, applies the rotational response at point i caused by unit force at point j and turn at the position i in the position j application specific torque
Angular response, formula (12)；DiFor faying face response, formula (14)；U is existing screw rod length travel response, formula (15)；Into one
Step obtains response formula at frequency response function and point of a knife, such as formula (16)-(17)；Based on matrix symmetric feature, finally acquire
Cutter-lathe subsystem point of a knife point three-dimensional frequency response function, such as formula (18)；
In formula, I is the moment of inertia；E is elasticity modulus；For frequency parameter；η is damping factor；L is
The length of beam；FiFormula such as (13)；
F1=sin λ l+cosh λ l
F3=sin λ lcosh λ l
F5=sinh λ lcos λ l-sin λ lcosh λ l
F6=sinh λ lcos λ l+sin λ lcosh λ l
F7=sin λ l+sinh λ l
F8=sin λ l-sinh λ l
F10=cos λ l-cosh λ l (13)
In formula, DiFor screw rod length travel response；kijFor the element in stiffness matrix, wherein i, j=1,2,3,4,5,6；F,M,
S and P be respectively power, torque, faying face area and combine surface pressure, wherein Fx=-∫SpxdS、Fy=-∫SpyDS and Fz=-∫SpzdS；Mx=-∫SpzydS+∫SpyzdS、My=-∫SpxzdS+∫SpzXdS and Mz=-∫SpyxdS+∫SpxydS；
In formula, U is screw rod length travel response；ku1For fore bearing x to longitudinal rigidity；E is screw rod elasticity
Modulus；ωuFor screw rod vibration frequency；
RSxx=Rxx-Rax[Rdd-R′ab-R″ab+R2′2′]-1Rxa (16)
In formula: Gxt、GytAnd GztIt is workpiece-frequency response function of the feed system subsystem on the direction x, y and z respectively；Wherein hij、
nij、lijAnd pijApply in the position j that dynamic respond of the unit force at the position i, application specific torque causes at point j for minor structure I
Point i at dynamic respond, apply the rotational response at point i caused by unit force at point j and exist in the position j application specific torque
Rotational response at the position i；DiFor faying face response；U is feed system length travel response；Footnote x is indicated in the x-direction
Any position, footnote y indicate any position in the y-direction, and footnote z indicates any position in the z-direction；
Construct workpiece-machine tool chief axis subsystem frequency response function model step are as follows:
Firstly, workpiece-machine tool chief axis subsystem is reduced to three main shaft, chuck and workpiece parts；Legal principle is coupled based on response
By, by workpiece-machine tool chief axis system subdivision be three main shaft, chuck-workpiece and workpiece minor structures, respectively minor structure I ',
Minor structure II ' and minor structure III ', and consider following two faying face to part-machine-tool spindle system workpiece any position frequency response letter
Several influence: main shaft-chuck and chuck-workpiece；
It is successively coupled by the minor structure of division, constructs workpiece-machine tool chief axis subsystem kinetic model, by responding coupled method
Obtain the frequency response function of each minor structure endpoint；By establishing the model of vibration of the faying face of machine chuck and work end, in conjunction with mould
State hammering experiment, identifies main shaft-chuck Complexed Prostate Specific Antigen；
Workpiece-machine tool chief axis subsystem different location point frequency response function after finally being coupled using IRCSA method is based on matrix
Symmetry feature, same to cutter-Machine Tool Feeding System subsystem point of a knife point frequency response method for solving, finally acquires workpiece any position coupling
Three-dimensional frequency response function is closed, such as formula (19)；
In formula: Gxw、GywAnd GzwIt is workpiece-frequency response function of the machine tool chief axis subsystem on the direction x, y and z respectively；Wherein h 'ij、
n′ij、l′ijWith p 'ijApply dynamic respond of the unit force at the position i in the position j for minor structure I ', application specific torque at point j
Apply the rotational response at point i caused by unit force at dynamic respond, point j at caused point i and applies unit force in the position j
Rotational response of the square at the position i, calculation formula are identical as formula (12)；D′iFor the response of workpiece faying face, calculation formula and (14)
It is identical；U ' is main shaft length travel response；By III ' workpiece junction of II ' chuck of minor structure and minor structure, chuck engaging portion is set up separately
For a ', workpiece interface is divided into b '；By II ' chuck junction of I ' main shaft of minor structure and minor structure, main shaft bound fraction is set as c ',
Chuck bound fraction is d '；Footnote x indicates any position in the x-direction, and footnote y indicates any position in the y-direction, foot
Mark any position in z expression in the z-direction.
2. the comprehensive frequency response function equation construction method of large-lead screw turning process system according to claim 1, special
Sign is: the method for the comprehensive frequency response function equation of building large-lead screw turning process system are as follows:
Large-lead screw turnery processing system includes the cutter-Machine Tool Feeding System subsystem and the workpiece-lathe master
Sub-system, cutter-Machine Tool Feeding System subsystem are shown in frequency response function such as formula (20)-(21) in the direction x, z；Workpiece-machine
Bed main shaft subsystem is shown in frequency response function such as formula (22)-(23) in the corresponding direction x, z, wherein Gxxt、GzztFor cutter-lathe
Frequency response function of the feed system subsystem in the direction x, z；Gxxw、GzzwFrequency response for workpiece-machine tool chief axis subsystem in the direction x, z
Function；Rxxt、RzztFor cutter-Machine Tool Feeding System subsystem the frequency response function in the direction x, z real part；Rxxw、RzzwFor workpiece-
Real part of the machine tool chief axis subsystem in the frequency response function in the direction x, z；Ixxt、IzztIt is cutter-Machine Tool Feeding System subsystem in x, z
The imaginary part of the frequency response function in direction；Ixxw、IzzwFor workpiece-machine tool chief axis subsystem the frequency response function in the direction x, z imaginary part；
Sxxt、SzztVibration displacement for cutter-Machine Tool Feeding System subsystem in the direction x, z；Sxxw、SzzwFor workpiece-machine tool chief axis
Vibration displacement of the system in the direction x, z；Fxxt、FzztCutting force for cutter-Machine Tool Feeding System subsystem in the direction x, z；
Fxxw、FzzwCutting force for workpiece-machine tool chief axis subsystem in the direction x, z；
During height feeding turning large-lead screw part, the value of formed turning tool and big screw pitch external thread piece relative displacement is equal to lathe tool
The sum of displacement and the displacement of big screw pitch external thread piece, wherein lathe tool and screw rod on the direction x, z relative transfer function respectively such as formula
(24) and shown in (25), meanwhile, in frequency domain, x, z are to shown in frequency response function such as formula (26), (27), wherein Gxx、GzzFor cutter-
Opposite frequency response function of the Machine Tool Feeding System subsystem with workpiece-machine tool chief axis subsystem in the direction x, z；Sxx、SzzFor cutter-
The Relative Vibration of Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem in the direction x, z is displaced；Fxx、FzzFor cutter-
Opposite cutting force of the Machine Tool Feeding System subsystem with workpiece-machine tool chief axis subsystem in the direction x, z；
Gxx=Gxxt+Gxxt (26)
Gzz=Gzzt+Gzzw (27)
The axial direction under respective coordinate system by cutter-Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem respectively
It is considered as rigidity, establishes 0-xyz coordinate system, for x to be radial, positive direction is outside；Y is axially that positive direction is to the right；The direction z is radial direction,
It and is upwards positive direction；Height feeding turning process system x is to comprehensive frequency response function by cutter-Machine Tool Feeding System subsystem x
To decision, formula (28)；Y is to comprehensive frequency response from workpiece-machine tool chief axis subsystem y to decision, formula (29)；Process system z is to by knife
Tool-Machine Tool Feeding System subsystem and workpiece-machine tool chief axis subsystem codetermine, shown in formula (30)；Obtain high feeding turning
Shown in the comprehensive frequency response function such as formula (31) of process system；
Gx(iw)=[Gxt(iwt)] (28)
Gy(iw)=[Gyw(iww)] (29)
[G (iw)]=[Gxt(iw) Gyw(iw) Gz(iw)] (31) 。
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