CN103791869B - A kind of measuring method of plane-generated double enveloping anchor ring hobboing cutter - Google Patents
A kind of measuring method of plane-generated double enveloping anchor ring hobboing cutter Download PDFInfo
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Abstract
The present invention relates to a kind of measuring method of plane-generated double enveloping anchor ring hobboing cutter, belong to Precision Inspection and instrument, mechanical transmissioning technology and metal cutting tool field. The tooth surface equation of the method based on the gear space theory of engagement and corresponding worm screw, and according to the definition of the every error of hobboing cutter, set up the Mathematical Modeling of the every error of hobboing cutter, and it is carried out to coordinate transform, be broken down into the motion of three axles of measuring machine, utilize method of value solving, obtain the numerical solution of three coordinates. Computer carries out sample path planning according to coordinate figure, coordinate figure is inputted to digital control system and is come the motion of control survey machine three axles, data collection system synchronizing gathers three axle raster values and gauge head data, the data that gather are carried out to data processing, thereby realize the high-acruracy survey of cutting edge helix error, cutting edge profile error and chip pocket circular pitch error to plane-generated double enveloping anchor ring hobboing cutter.
Description
Technical field
The present invention relates to a kind of measuring method of plane-generated double enveloping anchor ring hobboing cutter, belong to Precision Inspection and instrument, mechanical transmissioning technology and metal cutting tool field.
Background technology
Planar double-enveloping toroid worm gear is to produce under the background of high speed, heavy duty, efficient future development in mechanical industry, is the basic part in machine driving. This worm gear pair has that multiple tooth engagement, instantaneous doublet contact, radius of curvature are large, contact wire and the feature such as relative sliding velocity angle is large, makes that its bearing capacity is large, transmission efficiency is high, easy self-lubricate, long service life.
Along with scientific and technical development, the precision of enveloping worm drive system has been proposed to more and more higher requirement, and utilize the plane-generated double enveloping anchor ring hobboing cutter of generating machining worm wheel, because it is complex-shaped, lack again detection means, its quality control is the technical barrier during planar double-enveloping toroid worm gear is produced always, and this worm-drive performance that has also affected this advantages of planar double-enveloping worm represents the expansion with practical application.
So far the research of plane-generated double enveloping anchor ring hobboing cutter is mainly concentrated on to digitization modeling aspect: as the helicoid equation of right cone face twice-enveloping enveloping worm worm gear hob, cutting edge equation, lead angle and side edge relief angle computing formula etc.
The accurate measurement of plane-generated double enveloping anchor ring hobboing cutter becomes the research blank in this field. For promoting the quality of planar double-enveloping worm transmission, accelerate applying of enveloping worm drive, be badly in need of solving the measurement problem of twice-enveloping anchor ring hobboing cutter.
Summary of the invention
In order to realize the measurement of plane-generated double enveloping anchor ring hobboing cutter, the invention provides a kind of special-purpose hob cutter measuring machine, can carry out high-acruracy survey to cutting edge helix error, cutting edge profile error and the chip pocket circular pitch error of plane-generated double enveloping anchor ring hobboing cutter.
The scheme that technical solution problem of the present invention adopts is with reference to national standard (GB/T6084-2001) gear hob general technical specifications. The method that plane-generated double enveloping anchor ring hob measurement adopts comprises the steps:
1, set up the Mathematical Modeling of the every error of hobboing cutter
I) set up the Mathematical Model of Teeth of the corresponding worm screw of plane-generated double enveloping anchor ring hobboing cutter according to space meshing principle, as shown in formula (1):
Wherein S1(O1-x1,y1,z1) and S2(O2-x2,y2,z2) be respectively the kinetic coordinate system being connected with planar double-enveloping worm and worm gear,The angle that worm screw turns over from original position wraparound rotating shaft,It is the angle that worm gear turns over from original position wraparound rotating shaft, set up the circular cone of an axis and worm gear dead in line, and female plane and this circular cone tangent, u is female Plane-point to the distance of female plane and circular cone tangent line, t is the coordinate figure on this some place axle vertical with u in female plane, i12Be the gearratio of worm and wheel, a is the centre-to-centre spacing of worm and wheel, rbBe the main base radius of worm gear, β is female plane camber angle of worm gear, and on two bag hob measurement machines, a newly-built kinetic coordinate system S (O-X, Y, Z), makes S (O-X, Y, Z) and S1(O1-x1,y1,z1) overlap, therefore above-mentioned formula can be expressed as f (X, Y, Z)=0 in the measurement coordinate system of lathe;
Ii) on the basis of the corresponding worm tooth-surface Mathematical Modeling of plane-generated double enveloping anchor ring hobboing cutter, according to the definition of hobboing cutter cutting edge helix error, cutting edge profile error and chip pocket circular pitch error, set up the Mathematical Modeling of three errors:
The Mathematical Modeling of cutting edge helix error is as shown in formula (2):
Wherein R is reference circle of wormwheel radius;
The plane-generated double enveloping anchor ring hobboing cutter rake face of studying is Archimedes' helicoid, and the bus of Archimedes' helicoid is vertical with hobboing cutter axis of rotation Z, and the Mathematical Modeling of plane-generated double enveloping anchor ring hobboing cutter rake face is as shown in formula (3):
Wherein r is that on hobboing cutter rake face, any point is to the normal distance of gyroaxis Z, and θ is the angle that the hobboing cutter amount of testing oneself original position turns over around Z axis, and p is helix parameter, p=pz/2π，pzFor the helical pitch of plane-generated double enveloping anchor ring hobboing cutter, it is a constant. Formula (3) is also the required Mathematical Modeling of the plane-generated double enveloping anchor ring hobboing cutter chip pocket measurement of pitch error.
Formula (1) (3) simultaneous is obtained to the Mathematical Modeling of plane-generated double enveloping anchor ring hobboing cutter cutting edge profile error:
Iii) Mathematical Modeling of three errors is carried out to coordinate transform, coordinate system is converted into the rotation around hobboing cutter gyroaxis, along cutter shaft to movement and along these three directions of hobboing cutter movement radially;
Iv) utilize iterative method to obtain the numerical solution of the rear each coordinate of conversion, and it is stand-by to compile array.
2, utilize plane-generated double enveloping anchor ring hob measurement machine to determine hobboing cutter larynx plan-position
I) tested hobboing cutter is arranged on hob measurement machine, utilizes gauge head to determine the transverse plane position of hobboing cutter, hobboing cutter is processed taking this end face as benchmark, according to transverse plane position, drafts hobboing cutter larynx plane initial position Zh0, mobile gauge head is from larynx plane initial position Zh0Round, hobboing cutter is carried out to the error measure of cutting edge helix, obtain helix error fh1_0；
Ii) after measurement finishes, gauge head is retracted to larynx plane initial position Zh0, gauge head is from larynx plane initial position Zh0(or-5～-10 μ m), and this position is decided to be to hobboing cutter larynx plane initial position Z to move axially 5～10 μ mh1, gauge head carries out the error measure of cutting edge helix for one week around hobboing cutter again, obtains fh1_1；
Iii) repeating step ii) 10 times, make the hobboing cutter larynx plane initial position Z at every turn choosingh1～Zh10Be evenly distributed on initial larynx plan-position Zh0The left and right sides, thereby obtain hobboing cutter larynx plane initial position Zh1～Zh1011 groups of corresponding cutting edge helix error measure data, with minimum cutting edge helix error min{fh1_0,fh1_1,…,fh1_11Corresponding larynx plane initial position is as definite larynx plan-position Z of hobboing cutter to be measuredhi。
3, controlling hob measurement machine measures plane-generated double enveloping anchor ring hobboing cutter cutting edge helix error, cutting edge profile error and chip pocket circular pitch error
1. the method for measuring cutting edge helix error is as follows:
I) set up the Mathematical Modeling of plane-generated double enveloping anchor ring hobboing cutter cutting edge helix according to step 1, the row-coordinate of going forward side by side conversion, coordinate system is converted into the rotation around hobboing cutter gyroaxis, along cutter shaft to movement and along these three directions of hobboing cutter movement radially, and solve respectively the numerical solution of each coordinate, result is input to digital control system motion control card, in order to the motion of control survey machine three axles;
Ii) i) as basis, hobboing cutter cutting edge helix error is carried out to scanning survey, synchronously obtain grating reading and the gauge head data of three axles;
Iii) carry out error compensation by the measurement data that data collecting system is obtained, utilize cutting edge recognition technology, solve the helix error at the each cutting edge point of hobboing cutter place by intensive sampling point method, and rendering error curve, the error measure of cutting edge helix finally completed.
2. the method for measuring cutting edge profile error is as follows:
I) set up the Mathematical Modeling of plane-generated double enveloping anchor ring hob profile error according to step 1, the row-coordinate of going forward side by side conversion, coordinate system is converted into the rotation around hobboing cutter gyroaxis, along cutter shaft to movement and along these three directions of hobboing cutter movement radially, and solve respectively the numerical solution of each coordinate, result is input to digital control system motion control card, in order to the motion of control survey machine three axles;
Ii) taking i) as basis, gauge head obtains near grating reading and the gauge head data at certain cutting edge point place tooth tooth root to be measured along hobboing cutter cutting edge spiral trajectory, each axle stop motion afterwards, the Y-axis 10-20 μ m that setovers in the other direction, hobboing cutter is inverted to initial measurement angle value simultaneously, Z-direction declines highly corresponding according to cutting edge theory of tooth form formula, gauge head is contact Tooth again;
Iii) repeating step ii), synchronously get three axle grating readings and the gauge head data at a series of cutting edge point of hobboing cutter tooth to be measured place;
Iv) carry out error compensation by the measurement data that data collecting system is obtained, solve cutting edge profile error, and rendering error curve, the measurement of cutting edge profile error finally completed.
3. the method for measuring chip pocket circular pitch error is as follows:
I) set up plane-generated double enveloping anchor ring hobboing cutter rake face Mathematical Modeling according to step 1, the row-coordinate of going forward side by side conversion, coordinate system is converted into the rotation around hobboing cutter gyroaxis, along cutter shaft to movement and along these three directions of hobboing cutter movement radially, and solve respectively the numerical solution of each coordinate, result is input to digital control system motion control card, in order to the motion of control survey machine three axles;
Ii) according to step 2, control gauge head and move near definite larynx plane reference circle position, contact rake face point, obtain the three axle grating readings at this some place;
Iii) computer obtains in i) according to step I data and blas, set up the rake face at this place and the theoretical model of each rake face, and hobboing cutter rake face to be measured is Archimedes' helicoid, and chip pocket number is 6;
Iv) gauge head exits chip pocket, controls Z axis and rotates 60 °, and gauge head enters next teeth groove again near reference circle position, controls gauge head and contacts the point on next rake face, obtains the three axle grating reading gauge head data at this some place;
V) repeating step iv), until hobboing cutter rotates a circle. Carry out error compensation by the measurement data that data collecting system is obtained, solve the chip pocket circular pitch error of hobboing cutter, and rendering error curve, the measurement of chip pocket circular pitch error finally completed.
The present invention has realized the high-acruracy survey of cutting edge helix error, cutting edge profile error and the chip pocket circular pitch error of plane-generated double enveloping anchor ring hobboing cutter, fill up the specialty blank of domestic plane-generated double enveloping anchor ring hob measurement, by analysis to measure result, can improve targetedly hobboing cutter process technology, thereby improve the machining accuracy of plane-generated double enveloping anchor ring hobboing cutter and corresponding worm gear, optimizing product quality.
Brief description of the drawings
Fig. 1 tooth surface equation coordinate system
Fig. 2 hobboing cutter helix schematic diagram
Fig. 3 gauge head and hobboing cutter relative motion relation schematic diagram
The cutaway view of Fig. 4 cutter tooth and gauge head
The partial enlarged drawing of Fig. 5 cutaway view
Fig. 6 cutting edge profile of tooth schematic diagram
Fig. 7 rake face forms schematic diagram
Fig. 8 cutting edge profile error measuring process sketch
Fig. 9 chip pocket measurement of pitch error process sketch
Figure 10 measurement procedure figure
Crouch/vertical hob measurement machine structural representation of Figure 11
Detailed description of the invention
The measurement of cutting edge helix error, cutting edge profile error and these three error projects of chip pocket circular pitch error below in conjunction with accompanying drawing to plane-generated double enveloping anchor ring hobboing cutter is further described:
1, the measurement of cutting edge helix error
1) set up the Mathematical Modeling of plane-generated double enveloping anchor ring hobboing cutter helix error
I) be basis with the coordinate in Fig. 1, set up the Mathematical Model of Teeth of the corresponding worm screw of plane-generated double enveloping anchor ring hobboing cutter according to space meshing principle, as shown in formula (1):
Wherein S1(O1-x1,y1,z1) and S2(O2-x2,y2,z2) be respectively the kinetic coordinate system being connected with planar double-enveloping worm and worm gear,The angle that worm screw turns over from original position wraparound rotating shaft,It is the angle that worm gear turns over from original position wraparound rotating shaft, set up the circular cone of an axis and worm gear dead in line, and female plane and this circular cone tangent, u is female Plane-point to the distance of female plane and circular cone tangent line, t is the coordinate figure on this some place axle vertical with u in female plane, i12Be the gearratio of worm and wheel, a is the centre-to-centre spacing of worm and wheel, rbBe the main base radius of worm gear, β is female plane camber angle of worm gear, and on two bag hob measurement machines, a newly-built kinetic coordinate system S (O-X, Y, Z), makes S (O-X, Y, Z) and S1(O1-x1,y1,z1) overlap, therefore above-mentioned formula can be expressed as f (X, Y, Z)=0 in the measurement coordinate system of lathe;
Ii) on the basis of the Mathematical Model of Teeth of the corresponding worm screw of hobboing cutter, according to the definition of hobboing cutter helix---the hobboing cutter flank of tooth and the intersection around the surface of revolution of hobboing cutter axis are hobboing cutter helixes, and Fig. 2 is the schematic diagram of hobboing cutter helix definition. If the reference circle of wormwheel radius coordinating with worm screw is R, the circular arc that is R at XOZ plane inside radius rotates around Z axis, and its equation of curled curved surface is as shown in formula (2):
By equation (1) (2) simultaneous, obtain hobboing cutter cutting edge helix equation:
Iii) set up contacting of X, Y and θ: sin θ=X/Y, by hobboing cutter cutting edge helix math equation through coordinate transform, coordinate system is converted into the rotation θ around hobboing cutter gyroaxis, along cutter shaft to mobile Z and along these three directions of hobboing cutter mobile X radially;
Iv) utilize the method for iteration to obtain the numerical solution of rear three coordinates of conversion (X, Z, θ), compiled array:
2) utilize hob measurement machine to determine the position of hobboing cutter larynx plane
I) tested hobboing cutter is arranged on hob measurement machine, hob measurement machine as shown in figure 11, utilizes gauge head to determine the transverse plane position of hobboing cutter, and hobboing cutter is processed taking this end face as benchmark, according to transverse plane position, drafts hobboing cutter larynx plane initial position Zh0, mobile gauge head is from larynx plane initial position Zh0Round, hobboing cutter is carried out to the error measure of cutting edge helix, obtain helix error fh1_0；
Ii) after measurement finishes, gauge head is retracted to larynx plane initial position Zh0, gauge head is from larynx plane initial position Zh0(or-5～-10 μ m), and this position is decided to be to hobboing cutter larynx plane initial position Z to move axially 5～10 μ mh1, gauge head carries out the error measure of cutting edge helix for one week around hobboing cutter again, obtains fh1_1；
Iii) repeating step ii) 10 times, make the hobboing cutter larynx plane initial position Z at every turn choosingh1～Zh10Be evenly distributed on initial larynx plan-position Zh0The left and right sides, thereby obtain hobboing cutter larynx plane initial position Zh1～Zh1011 groups of corresponding cutting edge helix error measure data, with minimum cutting edge helix error min{fh1_0,fh1_1,…,fh1_11Corresponding larynx plane initial position is as definite larynx plan-position Z of hobboing cutter to be measuredhi。
3) controlling hob measurement machine measures hobboing cutter cutting edge helix error
I) be input to digital control system motion control card according to the coordinate array obtaining in step 1, the motion of control survey machine X, Z and C gyroaxis, as shown in figure 11;
Ii) i) as basis, plane-generated double enveloping anchor ring hobboing cutter cutting edge helix error is carried out to scanning survey, synchronously obtain three axle grating readings and the gauge head data of X, Z and C gyroaxis;
Iii) carry out error compensation by the measurement data that data collecting system is obtained, utilize cutting edge recognition technology, use intensive sampling method solves the helix error at hobboing cutter cutting edge point place, and rendering error curve, finally completes the error measure of cutting edge helix.
4) cutting edge recognition technology and intensive sampling point method are determined helix error
While carrying out cutting edge identifying, the relative motion relation of gauge head and hobboing cutter as shown in Figure 3. Gauge head adopts back taper gauge head, and its cone baseplane is parallel with Z axis. When after gauge head contact roller cutter tooth face, measuring head base still moves along Z axis by set speed, and hobboing cutter is by set rotating speed revolution simultaneously, and the cutaway view of cutter tooth and gauge head as shown in Figure 4. Because measuring head base exists kinematic error, therefore measuring head base is a curve T with respect to the actual motion track of hobboing cutter, and theory movement track is L, and the movement locus at gauge head center is S. For clearer explanation problem, amplify as shown in Figure 5 local this figure. In Fig. 5, G is first sampling point, by this point corresponding each grating initial value be made as 0, so for arbitrary sampled point, its helix error be just this grating reading along Z axis and gauge head reading with, deduct theory movement distance, i.e. EF length. When gauge head completes after scanning, computer is obtained the helix error of each sampled point successively, and the cutting edge corresponding points A that point corresponding to helix max value of error will be looked for is exactly reflected as AB line segment the longest in Fig. 5. The i.e. helix error of cutting edge point for this reason of AB value.
5) measure error correction
In measuring process, on helix the normal vector at each point place along hobboing cutter radially the projection Δ Y of Y-direction change, and hob measurement machine gauge head is motionless along Y-direction in measuring process, the variation of Y-direction projection causes gyroaxis to introduce measure error Δ Z to Z direction. Utilize the lead angle γ at each point place to calculate the margin of error that Z direction is introduced, Δ Z=Δ Ytan γ, realizes the correction to measure error.
2, the measurement of cutting edge profile error
1) set up the Mathematical Modeling of cutting edge profile error
On the basis of Mathematical Model of Teeth, according to the definition of hobboing cutter cutting edge profile of tooth---the rake face of plane-generated double enveloping anchor ring hobboing cutter and the front cutting edge that the left and right flank of tooth intersection of hobboing cutter basic worm is plane-generated double enveloping anchor ring hobboing cutter, as shown in Figure 6. According to the process principle of studied model hobboing cutter, rake face is Archimedes' helicoid, and bus is vertical with axis Z, and the formation principle of rake face as shown in Figure 7. The Mathematical Modeling of rake face is as shown in formula (4):
Wherein r is that on hobboing cutter rake face, any point is to the normal distance of gyroaxis Z, and θ is the angle that the hobboing cutter amount of testing oneself original position turns over around Z axis, and p is helix parameter, p=pz/2π，pzFor the helical pitch of plane-generated double enveloping anchor ring hobboing cutter, it is a constant. (1) (4) simultaneous is obtained to the Mathematical Modeling of cutting edge profile error, that is:
2) controlling hob measurement machine measures hobboing cutter cutting edge profile error
I) according to step 1) Mathematical Modeling of cutting edge profile of tooth set up, it is carried out to coordinate transform, be translated into the three-axis moving of hob measurement machine, and solve the numerical solution of three coordinates, and be entered into digital control system motion control card, control survey machine three-axis moving;
Ii) taking i) as basis, according to step 4 in helix error measurement method) described cutting edge recognition technology, gauge head obtains near grating reading and the gauge head data at certain cutting edge point place tooth tooth root to be measured along spiral trajectory, each axle stop motion afterwards, the Y-axis 10-20 μ m that setovers in the other direction, hobboing cutter is inverted to original angle value simultaneously, and Z-direction is according to the cutting edge theory of tooth form formula corresponding height that declines, gauge head is contact Tooth again, as shown in Figure 8;
Iii) repeating step ii), thus synchronously get three axle grating readings and the gauge head data at a series of cutting edge point of tooth to be measured place;
Iv) carry out error compensation by the measurement data that data collecting system is obtained, then solve cutting edge profile error, and rendering error curve, finally complete cutting edge profile error and measure.
3) measure error correction is with reference to the modification method of helix error, i.e. step 5).
2, the measurement of chip pocket circular pitch error
1) according to the definition of chip pocket circular pitch error, on plane-generated double enveloping anchor ring hobboing cutter reference circle anchor ring, the chip pocket circular pitch error that the mutual position error between the upper cutter tooth rake face of same head is hobboing cutter. The rake face of the hobboing cutter model of studying is Archimedes' helicoid, and chip pocket number is 6, and namely angle is 60 degree each other. The Mathematical Modeling of the each rake face of model, the rake face equation with in cutting edge profile error:
Wherein r is that on hobboing cutter rake face, any point is to the normal distance of gyroaxis, and θ is the angle that hobboing cutter turns over around Z axis, and p is helix parameter, p=pz/2π，pzFor the helical pitch of plane-generated double enveloping anchor ring hobboing cutter, it is a constant. θ gets respectively 60 °, 120 °, 180 °, 240 ° and 300 ° and 360 °, obtains six corresponding rake face equations.
2) controlling hob measurement machine measures hobboing cutter chip pocket circular pitch error
I) according to step 1) set up rake face Mathematical Modeling, it is carried out to coordinate transform, coordinate system is converted into the rotation θ around hobboing cutter gyroaxis, along cutter shaft to mobile Z and along these three directions of hobboing cutter mobile X radially;
Ii) taking i) as basis, control gauge head and move near fixed larynx plane reference circle position, contact certain point on rake face, obtain the grating reading at this some place, the acquisition methods of larynx plane is with the step 3 in helix measurement);
Iii) computer is set up the rake face at this place and the theoretical model of each rake face according to blas and formula (4), and hobboing cutter rake face to be measured is Archimedes' helicoid, and chip pocket number is 6;
Iv) gauge head exits chip pocket, controls Z axis and rotates 60 °, and gauge head enters next teeth groove again near reference circle position, and touches certain point on next rake face, obtains the three axle grating reading gauge head data at this some place, as shown in Figure 9;
V) repeating step iv), until hobboing cutter rotates a circle. Carry out error compensation by the measurement data that data collecting system is obtained, solve chip pocket circular pitch error, and rendering error curve, the chip pocket measurement of pitch error finally completed.
3) measure error correction is with reference to helix error correcting method, i.e. step 5).
For the detailed measurements flow process of plane-generated double enveloping anchor ring hobboing cutter cutting edge helix error, cutting edge profile error and chip pocket circular pitch error as shown in figure 10.
Claims (7)
1. a measuring method for plane-generated double enveloping anchor ring hobboing cutter, is characterized in that: according to space meshing principle,Set up the Mathematical Model of Teeth of the corresponding worm screw of plane-generated double enveloping anchor ring hobboing cutter, with hobboing cutter cutting edge helix mistakeDifference, cutting edge profile error and chip pocket circular pitch error are defined as constraint, obtain the Mathematical Modeling of error term; WillThe Mathematical Modeling of three described errors is carried out coordinate transform, and coordinate system direction is converted into around hobboing cutter gyroaxisRotate, along cutter shaft to movement and along these three directions of hobboing cutter movement radially, utilize iterative method obtain through sitNumerical solution after mark conversion, and it is stand-by that numerical solution is compiled to array; Utilize hob measurement machine to determine the larynx of hobboing cutterPlan-position; With the mathematical modulo of hobboing cutter cutting edge helix error, cutting edge profile error and chip pocket circular pitch errorType is basis, and the measurement data that data collecting system is obtained is carried out error compensation, utilizes cutting edge recognition technology,Use intensive sampling method to solve cutting edge helix error, the cutting edge profile error of plane-generated double enveloping anchor ring hobboing cutterWith chip pocket circular pitch error, and rendering error curve, the measurement of plane-generated double enveloping anchor ring hobboing cutter finally completed.
2. the measuring method of plane-generated double enveloping anchor ring hobboing cutter according to claim 1, is characterized in that: measureMethod adopts a kind of horizontal or vertical hob measurement machine realization; Tested hobboing cutter be supported in rotationally two top itBetween, hobboing cutter is driven by machine driving reducing gear by stepper motor, and gauge head adopts cone baseplane shape two dimension gauge head,Can record directions X and Z deflection error value; The round grating taking measurement of an angle is synchronizeed and is rotated with tested hobboing cutter, long lightGrid and gauge head form a bulk measurement length by connecting piece, long grating be arranged on tested cutter shaft to prolonging radiallyStretch on line, and can move along this extension line, grating and gauge head are bearing in respectively on static pressure air-float guide rail, by anotherIndividual stepper motor drives by machine driving reducing gear, moves as step-by-step movement; Two stepper motors are by computerHandle and coordinate to rotate, computer carries out sample path planning according to coordinate figure, and coordinate figure is inputted to digital control systemThe motion of the each axle of control survey machine, data collection system synchronizing gathers each axle raster values and gauge head data, to gatheringData carry out data processing, thereby realize cutting edge helix error to plane-generated double enveloping anchor ring hobboing cutter,The high-acruracy survey of cutting edge profile error and chip pocket circular pitch error.
3. the measuring method of plane-generated double enveloping anchor ring hobboing cutter according to claim 1, is characterized in that:
Set up the Mathematical Model of Teeth of the corresponding worm screw of plane-generated double enveloping anchor ring hobboing cutter according to space meshing principle, asShown in formula (1):
Wherein S1(O1-x1,y1,z1) and S2(O2-x2,y2,z2) be respectively with planar double-enveloping worm andThe kinetic coordinate system that worm gear is connected,The angle that worm screw turns over from original position wraparound rotating shaft,Worm gear fromThe angle that original position wraparound rotating shaft turns over, sets up the circular cone of an axis and worm gear dead in line, and female planeTangent with this circular cone, u is the distance of female Plane-point to female plane and circular cone tangent line, and t is this point in female planeLocate the coordinate figure on the axle vertical with u, i12Be the gearratio of worm and wheel, a is the center of worm and wheelDistance, rbBe the main base radius of worm gear, β is female plane camber angle of worm gear, on hob measurement machine newly-built oneKinetic coordinate system S (O-X, Y, Z), makes S (O-X, Y, Z) and S1(O1-x1,y1,z1) overlap, therefore above-mentioned formulaIn the measurement coordinate system of lathe, can be expressed as f (X, Y, Z)=0;
The Mathematical Modeling of cutting edge helix error is as shown in formula (2):
Wherein R is reference circle of wormwheel radius;
The plane-generated double enveloping anchor ring hobboing cutter rake face of studying is Archimedes' helicoid, Archimedes' helicoidBus vertical with hobboing cutter axis of rotation Z, the Mathematical Modeling of plane-generated double enveloping anchor ring hobboing cutter rake face is as public affairsShown in formula (3):
Wherein r is that on hobboing cutter rake face, any point is to the normal distance of gyroaxis Z, and θ is the hobboing cutter amount of testing oneself start bitPut the angle turning over around Z axis, p is helix parameter, p=pz/2π，pzFor plane-generated double enveloping anchor ring rollsThe helical pitch of cutter is a constant; Formula (3) is also plane-generated double enveloping anchor ring hobboing cutter chip pocket circular pitch errorMeasure required Mathematical Modeling;
Formula (1) (3) simultaneous is obtained to the mathematics of plane-generated double enveloping anchor ring hobboing cutter cutting edge profile errorModel:
4. the measuring method of plane-generated double enveloping anchor ring hobboing cutter according to claim 1, is characterized in that cutting edgeRecognition technology and intensive sampling point method are determined the cutting edge helix error of plane-generated double enveloping anchor ring hobboing cutter, stepAs follows:
I) in cutting edge identifying, gauge head adopts back taper gauge head, and its cone baseplane is parallel with gyroaxis Z axis; WhenAfter gauge head contact roller cutter tooth face, measuring head base still moves along Z axis by set speed, and hobboing cutter turns by set simultaneouslySpeed revolution; Ii) corresponding first sampling point each grating initial value is made as to 0, obtains the helix mistake of arbitrary sampled pointPoor, this grating reading along Z axis and gauge head reading with, deduct theory movement distance;
Iii) when gauge head completes after scanning, computer is obtained the helix error of each sampled point, the spiral shell of each sampled point successivelyCutting edge corresponding points that point corresponding to spin line max value of error will be identified exactly, the i.e. cutting edge point for this reason of respective valueHelix error.
5. the measuring method of plane-generated double enveloping anchor ring hobboing cutter according to claim 1, is characterized in that planeTwice-enveloping anchor ring hobboing cutter cutting edge profile error is measured, and step is as follows:
I), according to described cutting edge recognition technology, gauge head obtains near certain cutting edge point place tooth tooth root to be measured along spiral trajectoryGrating reading and gauge head data;
Ii) each axle stop motion, hobboing cutter is the Y-axis 10-20 μ m that setovers in the other direction radially, and hobboing cutter is inverted to original angle simultaneouslyDegree value, Z-direction declines highly corresponding according to cutting edge theory of tooth form formula, and gauge head is contact Tooth again;
Iii) repeating step ii), thus grating reading and the gauge head data at a series of cutting edge point of tooth to be measured place synchronously obtained,The measurement data that data collecting system is obtained is carried out error compensation, solves cutting edge profile error, and drawsError curve, finally completes cutting edge profile error and measures.
6. the measuring method of plane-generated double enveloping anchor ring hobboing cutter according to claim 1, is characterized in that, measuresError correction: in measuring process, on helix, the normal vector at each point place is along the radially projection of Y-direction of hobboing cutterΔ Y changes, and hob measurement machine gauge head is motionless along Y-direction in measuring process, and Y-direction is thrownThe variation of shadow causes gyroaxis to introduce measure error Δ Z to Z direction; Utilize the lead angle γ at each point place to calculate ZThe margin of error that direction is introduced, Δ Z=Δ Ytan γ, realizes the correction to measure error.
7. the measuring method of plane-generated double enveloping anchor ring hobboing cutter according to claim 1, is characterized in that planeThe measuring method of twice-enveloping anchor ring hobboing cutter is all suitable in vertical hob measurement machine and horizontal hob measurement machine.
Priority Applications (1)
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| CN105867298B (en) * | 2016-05-25 | 2018-04-06 | 重庆大学 | Spiral camber transforms into the point vector twice-enveloping method that tool profile is determined in processing |
| CN106679589A (en) * | 2017-03-07 | 2017-05-17 | 华侨大学 | High-speed high-precision non-contact type coordinate measuring machine and measuring method thereof |
| CN107876902B (en) * | 2017-11-24 | 2019-04-05 | 上海合纵重工机械有限公司 | A kind of processing method for matching enveloping worm |
| CN113124800B (en) * | 2021-04-20 | 2022-03-01 | 重庆大学 | Archimedes spiral surface worm wheel rolling shaving processing precision detection method |
| CN113103080B (en) * | 2021-04-21 | 2022-04-05 | 重庆大学 | Archimedes worm gear hob design method, cutter grinding correction method and worm gear master machine configuration method |
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| CN102269568B (en) * | 2011-07-15 | 2012-10-31 | 重庆工具厂有限责任公司 | Method for measuring accuracy of large helix angle worm hob |
| CN103093054B (en) * | 2013-01-29 | 2016-02-24 | 福州大学 | Double enveloping hourglass worm gearing worm gear hob flank profil modeling method |
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