CN109047947A - A kind of numerically controlled tooth grinding machine bed machined parameters modification method considering space geometry error - Google Patents
A kind of numerically controlled tooth grinding machine bed machined parameters modification method considering space geometry error Download PDFInfo
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- CN109047947A CN109047947A CN201811037785.4A CN201811037785A CN109047947A CN 109047947 A CN109047947 A CN 109047947A CN 201811037785 A CN201811037785 A CN 201811037785A CN 109047947 A CN109047947 A CN 109047947A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F9/00—Making gears having teeth curved in their longitudinal direction
- B23F9/02—Making gears having teeth curved in their longitudinal direction by grinding
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F23/00—Accessories or equipment combined with or arranged in, or specially designed to form part of, gear-cutting machines
- B23F23/10—Arrangements for compensating irregularities in drives or indexing mechanisms
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
- B23Q23/00—Arrangements for compensating for irregularities or wear, e.g. of ways, of setting mechanisms
Abstract
The invention discloses a kind of numerically controlled tooth grinding machine bed machined parameters modification methods for considering space geometry error, are related to field of machining and machinebuilding technology, comprising the following steps: S1, determine tooth surface geometry design parameter to be processed and initial roll flute machined parameters；S2, precise measurement lathe SGEs and compensation；S3, default flank of tooth ease-off；S4, total anti-tune amount is solved using numerical algorithm；S5, it determines the anti-tune amount for considering SGEs and considers the accurate machined parameters of SGEs.The present invention program proposes corresponding driving parameter processing scheme, provides basic theories and method for shape Collaborative Manufacturing driving parameter decision, and the product size after the machined parameters processing that scheme determines through the invention is accurate.
Description
Technical field
The present invention relates to field of machining and machinebuilding technology, and in particular to a kind of consideration space geometry error (Spatial
Geometric errors, SGEs) numerically controlled tooth grinding machine bed machined parameters modification method.
Background technique
In the machined parameters anti-tune system of high-precision spiral bevel gear, it is especially desirable to consider the soft of driving parameter design
Property, that is, the compatibility and consistency of Theoretical Design and actual processing are considered, by default flank of tooth ease-off as design
Tolerance realizes design driving parameter process integrated with the shape collaboration of manufacture.And the design of scheme of the tolerances in design, have quite
A part is for making up inevitable foozle factor in practical manufacture.And in the error of practical spiral bevel gear manufacture
In tracing to the source, foozle is to cause one of the principal element of the theoretical flank of tooth Yu practical surface deviation.The attainable flank of tooth of lathe institute
The factors such as machining accuracy and cutter, lathe, fixture, cutting force, workpiece size, operating procedure and processing environment are related.Have
Result of study shows that the geometric error of lathe and thermal deformation errors account for the 45%-65% of total foozle amount, for accurate or
For person's ultra-precision machine tool, this ratio is higher.Wherein, geometric error does not change with ambient temperature, while being also lathe
Most basic error source.
In the numerical control processing of spiral bevel gear, the cutting process that entire gear is completed in usually five main shaft linkages,
In include three shafts in translation and two rotary shafts；And another live spindle, that is, cutter spindle is that itself rotation keeps relatively quiet
Only state, and it is not involved in entire linkage manufacturing process.According to omnipotent motion concept (Universal motion concept,
UMC design concept), general machined parameters be suitable for no matter mechanical lathe or the multi-shaft interlocked lathe of digital control type either
Therefore milling or grinding with spiral bevel gear five-shaft numerical control grinding machine bed, are ground to carry out the processing of its SGEs driving parameter
Study carefully, the data of acquisition have practicability and versatility.
Summary of the invention
The technical problems to be solved by the present invention are: providing a kind of numerically controlled tooth grinding machine bed processing for considering space geometry error
Parameter correction method, present invention is particularly suitable for spiral bevel gear five-shaft numerical control grinding machine beds.
In order to solve the above-mentioned technical problem, a kind of the technical solution adopted by the present invention are as follows: number for considering space geometry error
Control grinding machine bed machined parameters modification method, comprising the following steps:
S1, tooth surface geometry design parameter to be processed and initial roll flute machined parameters are determined；
S2, precise measurement lathe SGEs and compensation, wherein the SGEs includes by knife position, wheel position, rollingization and denaturation coefficient
Caused error, the knife position are relative position of the grinding wheel cutterhead relative to lathe center, including angular knife position and radial；
The wheel position is position of the wheel blank relative to lathe center, including workhead offset, horizontal wheels position, bed, tooth root wheel blank established angle；
Than the transmission ratio to produce shape wheel and wheel blank, the denaturation coefficient is the change rate for rolling ratio for the rolling；
S3, default flank of tooth ease-off；
S4, total anti-tune amount is solved using numerical algorithm；
S5, it determines the anti-tune amount for considering SGEs and considers the accurate machined parameters of SGEs, the anti-tune amount and machined parameters
Between meet following relationship (1):
ΔxInstead=x*-x0=Δ xInstead M+ΔxInstead C (1)
In formula (1), Δ xInsteadFor anti-tune amount, x0For initial roll flute machined parameters, x* is the accurate machined parameters for considering SGEs,
ΔxInstead MFor the anti-tune amount for carrying out numerical value calculating, Δ xInstead CFor the anti-tune amount for practical precise measurement and compensation.
Further, the accurate machined parameters meet following formula (2):
[p* CMM-p((u,θ,φ[i]),x)]·n((u,θ,φ[i]), x)=h[i] (2)
In formula, p*CMM is true tooth point, p ((μ, θ, φi), x) it is Theoretical Design flank of tooth point, n expression is sent to vector；μ
The Gaussian parameter of tool geometry is respectively indicated with θ；φ indicates most basic machine tool motion parameter；I is then expressed as required
Tooth surface error order, x be required solution accurate machined parameters.Being defined by UMC machined parameters can obtain, order and tooth
Surface error order is consistent, it can uses φ[i]It is expressed as higher-order forms.
Further, in the step S2, the precise measurement of the lathe SGEs is digital control by Simens 840D
(Numerical Control, NC) systematic survey obtains.
Further, in the step S2, the compensating operation includes the lathe SGEs information obtained according to precise measurement,
NC compensation is carried out using the penalty function in the Simens 840D NC system.
Further, the NC compensation is the following steps are included: S21, system generate after compensating file, by the compensation file
It is changed to processing routine；S22, the processing routine is submitted by operation panel (Operation pannel, OP) unit and is run.
Further, the numerically controlled tooth grinding machine bed machined parameters modification method for considering space geometry error further includes opening
The step of S4 is repeated several times before the step of beginning S5.
Preferably, the numerically controlled tooth grinding machine bed is 5-shaft linkage numerical control grinding machine bed.
The beneficial effects of the present invention are: in the driving parameter planning of shape Collaborative Manufacturing System proposed by the present invention,
Other than installation error, lathe space geometry error is also used as one of the noise factor during entire driving parameter.Therefore, make
For link important during entire Collaborative Manufacturing, the present invention program proposes the driving parameter processing of its given noise factor
With optimization method.According to the processing characteristics of spiral bevel gear numerically-controlled machine tool, the present invention program participates in the machine tool chief axis of working motion
SGEs mainly includes translation shaft SGEs and rotary shaft SGEs two major classes；Meanwhile for this two major classes lathe SGEs, correspondence is proposed
Driving parameter processing scheme, provide basic theories and method for shape Collaborative Manufacturing driving parameter decision, through the invention side
Product size after the machined parameters processing that case determines is accurate.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of the Cutter coordinate system of five-axle linkage spiral bevel gear numerically controlled tooth grinding machine bed；
Fig. 2 is the SGEs model structure schematic diagram of translation shaft；
Fig. 3 is the SGEs model structure schematic diagram of rotary shaft；
Fig. 4 is to consider that the Machine-settings that SGEs influences demodulate correction model；
Fig. 5 is that the machined parameters for the basic flank of tooth for considering that SGEs influences demodulate correction model；
Fig. 6 is the structural schematic diagram that the laser doppler interferometer MCV2002 of turntable is driven with motor；
Fig. 7 is that list Dogleg walks and its trust domain policy schematic diagram；
Fig. 8 is the graph of relation of position and position error that the MCV2002 of lathe SGE Dz (z) is measured；
Fig. 9 is that SGE Dz (z) carry out the compensated precise measurements of NC；
Figure 10 is default flank of tooth ease-off pattern topological diagram；
Figure 11 is default flank of tooth ease-off distribution map；
Figure 12 is to consider that the machined parameters of SGEs demodulate the residual error ease-off result schematic diagram solved；
Figure 13 is that only considered Δ xMAnti-tune after the remnants ease-off flank of tooth pattern topological diagram；
Figure 14 is that only considered Δ xMAnti-tune after the remnants ease-off flank of tooth ease-off distribution map.
Label declaration:
1, rotary shaft to be measured；2, motor drives turntable；3, double light beam laser head；4, adjustable fixer；5, laser
Beam.
Specific embodiment
To explain the technical content, the achieved purpose and the effect of the present invention in detail, below in conjunction with embodiment and cooperate attached
Figure is explained.
The foundation of roll flute machined parameters and Cutter coordinate system: the basic structure model of 5-shaft linkage numerical control gear grinding machines and its add
Work coordinate system is as shown in Figure 1.Wherein, participating in Gear Processing includes three translation shafts, that is, cutter spindle horizontal movement axis x, cutterhead master
Axis vertical movement y-axis and saddle shifting axle z and two rotary shafts i.e. work cage chair rotary shaft A, wheel blank main shaft rotary motion axis B,
Cutter spindle C, since cutter spindle C axis is opposing stationary, then any tooth in its three-dimensional geometric space can be completed in five-axle linkage
The accurate processing of shape.In process, origin of the virtual lathe center as Machine-settings is still set, then the master
Want machined parameters that can conclude are as follows: i) knife position, relative position of the grinding wheel cutterhead relative to lathe center, such as angular knife position q, radial direction
Knife position Sr；Ii position, position of the wheel blank relative to lathe center, such as workhead offset E) are taken turnsM, horizontal wheels position XD, bed XB, tooth root wheel
Base established angle γmDeng；Iii) rolling is when denaturalized coefficient, and the former produces the transmission ratio of shape wheel and wheel blank, and the latter indicates rolling ratio
Change rate.In Cutter coordinate system shown in Fig. 1, lathe center is { O1；x1,y1,z1, grinding wheel cutter head center is { Ow；xw,yw,
zw, coordinate system { OA；xA,yA,zAAnd { OB；xB,yB,zBRespectively indicate the movement of A axis and B axle.
In machine tool motion relationship, it usually needs define range of motion pair to realize the relative motion of cutter and workpiece.?
Ideally, each kinematic pair of lathe should only have 1 freedom degree: translation shaft is translation freedoms；Rotary shaft is to rotate certainly
By spending.But in fact, each kinematic pair is in actual processing process due to the presence for manufacturing the factors such as installation error and numerical control error
In often exist 6 freedom degrees.Numerically controlled tooth grinding machine bed shown in FIG. 1 includes 3 freedom of motion and 2 rotary freedoms.
Translation shaft SGEs model is as shown in Fig. 2, when machine tool guideway translates along the x-axis direction, since straightness error is difficult to survey
Amount and definition, the linear fit and its residual error for generalling use error curve combine to describe its reference direction.Along reference direction, machine
The deviation of bed guide rail amount of movement is known as x-axis linear displacement error.Deviation point between guide rail actual motion direction and reference direction
The direction y and the direction z are solved, x-axis vertical line degree error is defined as) and horizontal linear degree error.By guide rail reference direction to x-y
Plane and z-x plane projection and x-axis form low-angle, are respectively defined as the beat angle error and pitching angle error of x-axis.Define x
Axis is tilt angle error along itself rotation angular deviation.In addition, the angular error between the reference direction of x, y, z axis is defined as
The error of perpendicularity between the linear main shaft of lathe.Since there are 6 errors for each shifting axle, in addition the verticality between three axis is missed
Difference, three translation shafts co-exist in 21 SGEs.
Revolute SGEs model is as shown in figure 3, Fig. 3 gives the SGEs model of rotary shaft.Under theoretical case, rotary shaft B
Degree is overlapped with coordinate system y.Defining the angle of practical rotation axis and theoretical rotation axis in x-y plane and y-z plane is B axle
Beat angle error and pitching angle error；Rotary shaft relative theory position offset is respectively horizontal linear degree error, vertical line
Spend error；It is angular errors around rotation angle of rotating shaft error；Offset deviation amount along rotary shaft is installation error.Due to every
Axis is there are 6 to error, then A and B axle one co-exist in 12 SGEs.Therefore, entire grinding machine bed one co-exists in 33 SGEs.
The determination of functional relation between SGEs and machined parameters, the relationship including machined parameters Yu translation shaft SGEs are false
If cutterhead grinding wheel moves along the x-axis distance x1When, grinding wheel movement can be described with homogeneous transform matrix:
T is translation transformation matrix in formula (3), and R is rotational transformation matrix, is represented by as shown in following formula (4) and (5):
T=X+ δx+θx×X (5)
X=(x in formula1 0 0)TIt is guide rail along the amount of exercise of x-axis, δx=(Dx(x)Dy(x)Dz(x))TIt is guide rail along reference
In x, y, z direction when direction is mobile, there is θx=(0Syx Sxz)。
In lathe parameter determination process, knife position is mainly realized by the transformation campaign of machine tool chief axis x-axis and y-axis
, then corresponding amount of movement is
Formula (6) are substituted into (5), associative transformation matrix (3) obtains formula (7)
Mc=MxMy (7)
In formula, MxIndicate the transformation matrix along x-axis, MyIndicate the transformation matrix along y-axis, cutterhead grinding wheel center is under coordinate
For rco=(0 0 0)T, substitute into formula (7), grinding wheel center can be obtained relative to the expression formula at lathe center respectively such as formula (8) and (9)
It is shown:
(rcom1)=MxMy(rco 1)T (8)
rcom=rsxi+rsyj+rszk (9)
Above two formula shows respectively actual radial and angular knife position
Functional relation such as formula (12) by the derivation of last transform matrix, between roll flute machined parameters and translation shaft SGEs
It is shown:
S′r=[((Dx(y)-tan(Syx)Srsinαc+sinAz(x)Srsinαc+Srcosαc+Dx(x))2
+sin(Ay(x))tan(Szy)Srsinαc+(sin(Az(x)tan(Syx)Srsinαc)
+sin(Ax(x)(tan(Szy)Srsinαc)+Dy(y)+Srsinαc+Dy(x))2]1/2 (12)
Q ' is parsed as shown in formula (13):
Q '=arctan { [sinAz(x)(tan(Syx)Srsinαc)+Dy(y)+Srsinαc+Dy(x)
+sinAx(x)(tan(Szy)Srsinαc)]/[Dx(y)-tan(Syx)Srsinαc+Dx(x)
+sinAz(x)(Srsinαc)+Srsinαc+sinAy(x)(tan(Szy)Srsinαc]} (13)
The relationship of machined parameters and vertical axis SGEs, it is assumed that when machine tool component turns over angle γ around rotary shaftmWhen, exist with
Down conversion matrix is shown to describe machine coordinates transformation such as following formula (14):
In formula, R is rotational transformation matrix, and H is translation transformation matrix, and there are following relationships:
R=R1R2 (15)
H=(Dx(B)Dy(B)Dz(B))T (18)
In machine tooling motion process, the movement of the wheel position of lathe is by guide rail along the moving of z-axis, rotary shaft B axle
Rotation, the installation of A axis and rotation then have following fundamental relation come what is realized: the amount of movement along z-axis is XB, the rotation angle of B axle is
γm, the vertical installation position of B axle is EM, the axially mounted position of A axis is XD.The above machined parameters are substituted into formula (19), then may be used
Obtain about gear blank move transformation matrix be
Q1=MzTBTA (19)
In formula, MzIndicate the transformation matrix of coordinates being translatable along z-axis；TBAnd TARespectively indicate the coordinate transform along B axle and A axis
Matrix.
It is assumed that gear blank main shaft is overlapped with A axis direction, the major axes orientation under gear blank coordinate system is expressed as r1=(000)T, then
The vector can be expressed as in lathe coordinate system
(r1m1)=Q1(r1 1) (20)
r1m=r1mxi+r1myj+r1mzk (21)
Practical tooth root wheel blank established angle, which can be acquired, by formula (21) is
γ′m=arctan (r1mz/r1mx) (22)
It is derived by relation above, it can be deduced that following formula:
γ′m=arctan { [(- sinAz(z)cos(γm+AB(B))+sin(γm+AB(B))-cos(γm+AB(B)))
sinAy(A)+(-sinAy(z)cos(γm+AB(B))+Dz(B)sin(γm+AB(B)))
(Dx(A)+XD)+XB+Dz(z)+(sinAy(z)sin(γm+AB(B))+cos(γm+AB(B)))
Dz(A)-EMsinAx(z)]/[(cos(γm+AB(B))+sinAy(z)sin(γm+AB(B))+
sin(γm+AB(B))sinAy(A)+(cos(γm+AB(B))+sin(γm+AB(B))
sinAy(z))(Dx(A)+XD)-sin(γm+AB(B))-Dx(B)-EmsinAy(A)
-sinAy(z)Dz(B)-Dx(z)]} (23)
Vector of the gear blank center under its coordinate is r1o=(000)T, have the vector can under machine coordinates according to formula (20)
It indicates are as follows:
(r1om1)=Q1(r1o 1) (24)
r1om=r1omxi+r1omyj+r1omzk (25)
Workhead offset EMIndicate vertical offset of the gear blank center relative to lathe center, then actual workhead offset are as follows:
E′M=r1omy (26)
Through coordinate transform, have:
E′M=((- sinAz(z)-sinAz(B))cos(γm+AB(B)+(sinAx(B)+Dy(z)+
Dy(A)+EM+Dy(B)+sinAx(z))sin(γm+AB(B)))(Dx(A)+XD) (27)
Practical axial wheel position then indicates are as follows:
Similarly, it can obtain
X′D=[(cos (γm+AB(B))+sinAy(z)sin(γm+AB(B))(Dx(A)+XD)-sin(γm+
AB(B))cos(γm+AB(B))Dz(A)+Dx(B)+sinAz(z)EM+Dx(z)]/cosγ′m (29)
Practical bed is then expressed as
X′B=rlomz-X′Dsinγ′ (30)
Similarly, it can obtain
X′B=((- sinAz(z)-sinAz(B))×cos(γ+AB(B))+(sinAx(B)+Dy(B)+Dy(z)
+sinAx(z))×sinγm+AB(B)))(Dx(A)+XD)+EM-X′Dsinγ′m (31)
Consider the five-shaft numerical control grinding machine bed machined parameters driving processing of SGEs:
Precise measurement and compensation: fully considering the flexibility of actual design and manufacture, introduces omnipotent kinematic parameter as design
Variable measures the goal-selling flank of tooth by the CMM flank of tooth, theorizes and design the least square that the flank of tooth is constantly approached to the target flank of tooth
Objective function constructs the advanced tooth surface error topological optimization based on Machine-settings and controls basic model (such as Fig. 4 institute
Show, top-surface camber is the target flank of tooth in Fig. 4, and it is between the two the ease-off of the flank of tooth), parameterisable that lower surface camber, which is the basic flank of tooth,
For
(2)
[p* CMM-p((u,θ,φ[i]),x)]·n((u,θ,φ[i]), x)=h[i]
What above formula was actually expressed is the infinitesimal numerical optimization routines of tooth surface error, and objective function is with lathe
Machined parameters are two optimization problem of minimum of design variable.In formula, p*CMM is true tooth point, p ((μ, θ, φi), x) it is reason
By design flank of tooth point, i is then expressed as the order of required tooth surface error, and x is the accurate machined parameters of required solution.By
The definition of UMC machined parameters can obtain, and order is consistent with tooth surface error order, it can uses φ[i]It is expressed as higher-order forms.
Machined parameters according to Fig.4, demodulate method, due to there is function pass between Machine-settings and lathe SGEs
System, then Machine-settings demodulate the SGEs progress driving parameter processing that method can be used in enantiomorphism Collaborative Manufacturing.In addition,
The SGEs of five-shaft numerical control grinding machine bed can carry out precise measurement and compensation, then can demodulate numerical solution in machined parameters
Measurement and compensation that a part of numerical value carries out SGEs are reserved in anti-tune amount.In then considering that the machined parameters of SGEs influence demodulate,
Entirely the allocation processing of anti-tune amount is
ΔxInstead=x*-x0=Δ xInstead M+ΔxInstead C (1)
In formula (1), Δ xInsteadFor anti-tune amount, x0For initial roll flute machined parameters, x* is the accurate machined parameters for considering SGEs,
ΔxInstead MFor the anti-tune amount for carrying out numerical value calculating, Δ xInstead CFor the anti-tune amount for practical precise measurement and compensation.
And in the present invention, using the LDDM laser measurement of the laser doppler interferometer of ISO 230-2 (1997) standard
System MCV2002 is used for the SGEs precise measurement of translation shaft.In addition, being equipped with motor driving turntable 2 (RT-100)
MCV2002 is used to measure two live spindles, as shown in Figure 5.Turntable RT-100 is an additional component, equipped with small-sized
Driving motor can make Double sided mirror rotate a certain angle automatically.In order to obtain accurate measured value, the rotation center of Double sided mirror,
Motor drive turntable 2 and test device (including for emitting laser beams 5 double light beam laser head 3, the double light beam laser head
It is mounted on adjustable fixer 4, the adjustable height of the adjustable fixer 4 and angle) it must be consistent as far as possible.
By accurately finely tuning, motor driving turntable 2 and rotary shaft to be measured 1 must all return zero-bit.Then, position to be measured is adjusted just
Precise measurement can be achieved.
After precise measurement, SGEs compensation is carried out using the Software error compensation method with NC code.The SGEs value of precise measurement
It can be compensated in lathe NC system.In numerical control processing, system meeting automatic identification is compensated about the NC code of anti-tune amount
The influence of SGEs in driver's process.This NC penalty method, it is versatile, it is easily operated, it is suitable for open numerical control
System.
In the present invention program, for that can have some random errors, thermal deformation errors etc., all one in practical SGEs measurement
One ignores.In addition, the setting of measurement data, needs to meet user's permissible accuracy range.And in fact, SGEs measurement it is accurate
Property it is main related to the design feature of lathe itself.In the present invention program, the measurement accuracy of translation shaft is preset as 0.0001mm,
And the measurement accuracy of rotary shaft is preset as 0.001deg.It is handled by the driving parameter as shown in formula (31), numerical value calculates and NC
Compensation, which can be completed at the same time, considers that the machined parameters of true SGEs demodulate process.
Process is demodulated according to accurate machined parameters, can determine target teeth face once given ease-off precision, is established
The non-linear least square objective function that roll flute machined parameters demodulate carries out the accurate solution of accurate parameters and its anti-tune amount.This
Invention proposes the trust region method of the step containing single Dogleg.The trust region method one of basic solution procedure and the step containing double Dogleg
It causes, the i.e. d of single Dogleg step has only been selected in trusting domain policyK DLComplete nonlinear iteration process, as shown in Figure 6.Its
In, it is most important that the intersection point of circle is single where determining single path Dogleg and Trust Region Radius by solving coefficient lambda
Dogleg iteration point MK+1.Since Dogleg algorithm is a mature algorithm, in the machined parameters of consideration SGEs of the invention
The application demodulated in amendment repeats no more.
The embodiment of the present invention one are as follows: a kind of numerically controlled tooth grinding machine bed machined parameters modification method for considering space geometry error,
Tooth surface geometry design parameter and initial roll flute machined parameters are determined first, as shown in table 1 below:
1 steamboat tooth surface geometry parameter of table and initial grinding machine bed machined parameters
Then, the SGEs measurement and compensation for carrying out five-axle linkage grinding machine bed, using equipped with Siemens 840D NC system
The domestic five-shaft numerical control gear grinding machines of systemSGEs measuring device.Dz(z) accurate results, as shown in figure 8,
As can be seen from Figure 8 the measurement result follows international standard ISO-230-2 (1997).In the measurements, Mf indicates positive direction
Average value, Mb indicate the average value of negative direction；And the result that Mf and Mb rotate ± 2 seconds every time is also measured.It can by Fig. 8
Know, has recorded seven kinds respectively as a result, other curves all keep gradually passing other than reversion result is approximately parallel to horizontal line substantially
The trend of increasing, maximum value can achieve 0.011092mm in the position range of 300-400.
The measurement result of 24 kinds of SGEs of MCV2002/+RT100 measurement is as shown in table 2, and the 9 kinds of SGEs in addition not provided are
0.For these accurate measured values, that is, it can be utilized for NC compensation.According to ISO 230-2 (1997) standard, the application utilizes 9
Kind error evaluation project carries out SGE assessment.
The SGEs result of 2 MCV2002/+RT100 of table measurement
Table 3 and table 4 are respectively to give the D of digital control (Numerical Control, NC) compensation front and backz(z) survey
Value assessment, including system deviation, repetitive positioning accuracy and positioning accuracy, it is also contemplated that different Test Cycles is pros
To, opposite direction and three kinds two-way.
SGE item D before 3 NC of table compensationz(z) error assessment
The compensated SGE D of 4 NC of tablez(z) error assessment
In evaluation table, symbol ↑ expression numerical value is from positive direction close to measured value, and symbol ↓ expression numerical value is from negative direction
Close to measured value., it is apparent that NC compensation front and back, positioning accuracy have apparent variation from table.In IMENS
In 840D NC system, the SINUMERIK 840D system that lathe provides has powerful error compensation function, is equipped with various mistakes
Difference setting penalty function.In NC compensation of the invention, mainly comprise the steps that i) system generates compensation file, format
It is changed to processing routine；Ii program) is submitted by OP unit and is run.For example, the partial code that the NC of z-axis is compensated are as follows:
$ AA_ENC_COMP [1,0, AX3]=- 0.000061
$ AA_ENC_COMP [1,1, AX3]=- 0.000712
$ AA_ENC_COMP [1,2, AX3]=- 0.001857
…………
$ AA_ENC_COMP [1,18, AX3]=- 0.009261
$ AA_ENC_COMP [1,19, AX3]=- 0.009147
$ AA_ENC_COMP [1,20, AX3]=- 0.009607
$ AA_ENC_COMP_STEP [1, AX3]=20
$ AA_ENC_COMP_MIN [1, AX3]=50
$ AA_ENC_COMP_MAX [1, AX3]=450
$ AA_ENC_COMP_IS_MODULO [1, AX3]=0
SGE Dz(z) compensated accurate results are as shown in Figure 9.As shown in Figure 9, within the scope of 50~250mm
Repetitive positioning accuracy error is its main source, and unidirectional positioning accuracy is higher.Measurement result before comparing compensation, can reflect
NC measurement is a kind of driving parameter processing method of impact factor in good spiral bevel gear shape Collaborative Manufacturing with compensation.
After the precise measurement and compensation of lathe SGEs, consider that the roll flute machined parameters that SGEs influences demodulate progress.Firstly,
Preset flank of tooth ease-off pattern topological diagram and distribution map difference are as shown in Figure 10 and Figure 11, and wherein RMSE is 6.0897 μm,
The larger value is mainly distributed on tooth top and tooth root region, and smaller value is then concentrated on close to small end regions.Letter with list Dogleg step
Rely the iteration quality of domain algorithm as shown in table 5.
Iteration quality of the table 5 with single Dogleg Trust Region Algorithm walked
As can be seen from Table 5, it is only necessary to which 10 step iteration can reach convergence.In trusting domain policy, walked by determining
The numerical result of long coefficient lambda can preferably guarantee the convergence rate of the iterative calculation of entire Trust Region Algorithm.Based on default
Ease-off requirement, Figure 12 give consider SGEs machined parameters demodulate solve residual error ease-off result.?
After 2nd iteration, RMSE is just reduced to 3.0314 μm；After the 7th iteration, RMSE is reduced to 0.4267 μm, and large error is mainly divided
Cloth is in flank of tooth borderline region；At the 9th iteration, there is apparent reduction, RMSE is 0.0246 μm, and being distributed becomes to homogenize,
And the larger value appears in intermediate region；And at the 10th i.e. convergence position, RMSE is 0.001617 μm, and maximum value is
0.00246 μm, minimum value is -0.00228 μm, and maximum value is mainly appeared on close to tooth top region.
It is demodulated using SGEs roll flute machined parameters the considerations of the Trust Region Algorithm and L-M algorithm walked with list Dogleg and calculates knot
Fruit is as shown in table 6, and L-M is current one of the common Nonlinear Least-Square Algorithm for solving machined parameters and demodulating problem, the calculation
Method can effectively solve the problem that parameter coupling caused by strong nonlinear problem and Jacobian matrix morbid state phenomenon, obtain more
Stable numerical solution.
Table 6 demodulates result ratio with SGEs roll flute machined parameters the considerations of L-M algorithm with the Trust Region Algorithm that single Dogleg is walked
Compared with
It can be seen that two methods effect approximation, machined parameters S from the data result in table 6rAnd XBIt can be preferentially used for reality
During the anti-tune of border processing.
After numerical solution entirely considers the anti-tune amount that the roll flute machined parameters of SGEs demodulate, scheme is proposed according to the present invention
Driving parameter processing method carries out the optimization distribution of anti-tune amount.Wherein, a part of anti-tune amount Δ xInstead CPass through in above-mentioned example
SGEs precise measurement and NC compensate to be handled, and another part anti-tune amount Δ xInstead MIt can then be solved by formula (29),
The results are shown in Table 7 for it.Only consider Δ xInstead MRoll flute machined parameters demodulate after remnants ease-off flank of tooth pattern and its distribution map
As shown in Figure 13 and Figure 14.Wherein, RMSE be 0.0016293 μm, maximum value be 0.00262847 μm, minimum value be-
0.001911μm；Compared with the data result of Figure 12, remaining ease-off has reduction, and is distributed more uniform, variation tendency
It is not apparent.
The accurate roll flute machined parameters anti-tune amount of the consideration of table 7 SGEs
The above description is only an embodiment of the present invention, is not intended to limit the scope of the invention, all to utilize this hair
Equivalents made by bright specification and accompanying drawing content are applied directly or indirectly in relevant technical field, similarly include
In scope of patent protection of the invention.
Claims (7)
1. a kind of numerically controlled tooth grinding machine bed machined parameters modification method for considering space geometry error, it is characterised in that: including following
Step:
S1, tooth surface geometry design parameter to be processed and initial roll flute machined parameters are determined；
S2, precise measurement lathe SGEs and compensation, wherein the SGEs includes being caused by knife position, wheel position, rollingization and denaturation coefficient
Error, the knife position is relative position of the grinding wheel cutterhead relative to lathe center, including angular knife position and radial；It is described
Wheel position is position of the wheel blank relative to lathe center, including workhead offset, horizontal wheels position, bed, tooth root wheel blank established angle；It is described
Than the transmission ratio to produce shape wheel and wheel blank, the denaturation coefficient is the change rate for rolling ratio for rolling；
S3, default flank of tooth ease-off；
S4, total anti-tune amount is solved using numerical algorithm；
S5, it determines the anti-tune amount for considering SGEs and considers the accurate machined parameters of SGEs, between the anti-tune amount and machined parameters
Meet following relationship (1):
ΔxInstead=x*-x0=Δ xInstead M+ΔxInstead C (1)
In formula (1), Δ xInsteadFor anti-tune amount, x0For initial roll flute machined parameters, x*For the accurate machined parameters for considering SGEs, Δ xInstead M
For the anti-tune amount for carrying out numerical value calculating, Δ xInstead CFor the anti-tune amount for practical precise measurement and compensation.
2. the numerically controlled tooth grinding machine bed machined parameters modification method according to claim 1 for considering space geometry error, special
Sign is: the accurate machined parameters meet following formula (2):
[p* CMM-p((u,θ,φ[i]),x)]·n((u,θ,φ[i]), x)=h[i] (2)
In formula, p*CMM is true tooth point, p ((μ, θ, φi), x) it is Theoretical Design flank of tooth point, n expression is sent to vector；μ and θ points
Not Biao Shi tool geometry Gaussian parameter；φ indicates most basic machine tool motion parameter；I is then expressed as the required flank of tooth
The order of error, x are the accurate machined parameters of required solution.
3. the numerically controlled tooth grinding machine bed machined parameters modification method according to claim 1 for considering space geometry error, special
Sign is: in the step S2, the precise measurement of the lathe SGEs is obtained by Simens 840D NC systematic survey.
4. the numerically controlled tooth grinding machine bed machined parameters modification method according to claim 3 for considering space geometry error, special
Sign is: in the step S2, the compensating operation includes the lathe SGEs information obtained according to precise measurement, using described
Penalty function in Simens 840D NC system carries out NC compensation.
5. the numerically controlled tooth grinding machine bed machined parameters modification method according to claim 4 for considering space geometry error, special
Sign is: the compensation file is changed to processing journey the following steps are included: after S21, system generation compensation file by the NC compensation
Sequence；S22, the processing routine is submitted by OP unit and is run.
6. the numerically controlled tooth grinding machine bed machined parameters modification method according to claim 1 for considering space geometry error, special
Sign is: the numerically controlled tooth grinding machine bed machined parameters modification method for considering space geometry error further includes the steps that starting S5
The step of S4 is repeated several times before.
7. the numerically controlled tooth grinding machine bed machined parameters modification method according to claim 1 for considering space geometry error, special
Sign is: the numerically controlled tooth grinding machine bed is 5-shaft linkage numerical control grinding machine bed.
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