CN114029560B - Cutter combination for machining cylindrical gear with hyperbolic circular arc toothed line and machining method - Google Patents
Cutter combination for machining cylindrical gear with hyperbolic circular arc toothed line and machining method Download PDFInfo
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- CN114029560B CN114029560B CN202111472739.9A CN202111472739A CN114029560B CN 114029560 B CN114029560 B CN 114029560B CN 202111472739 A CN202111472739 A CN 202111472739A CN 114029560 B CN114029560 B CN 114029560B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F21/00—Tools specially adapted for use in machines for manufacturing gear teeth
- B23F21/005—Tools specially adapted for use in machines for manufacturing gear teeth with plural tools on a common axis
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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
- B23F23/12—Other devices, e.g. tool holders; Checking devices for controlling workpieces in machines for manufacturing gear teeth
- B23F23/1237—Tool holders
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract
The invention discloses a cutter combination for processing a variable hyperbolic circular arc toothed line cylindrical gear and a processing method thereof, and relates to the technical field of circular arc toothed line gear processing. The gear tooth convex surface and the gear tooth concave surface can be cut at the same time, the processing efficiency is improved, the redundancy of a high-grade numerical control machine tool can be effectively reduced by adopting a special processing cutter combination, the processing cost is greatly reduced, and the processing precision is improved.
Description
Technical Field
The invention relates to the technical field of processing of circular arc toothed gears, in particular to a cutter combination for processing a cylindrical gear with a hyperbolic circular arc toothed line and a processing method.
Background
The cylindrical gear with hyperbolic arc tooth trace is a special form of circular arc tooth trace gear, its tooth trace is arc line on the plane extended along a certain generatrix of cylindrical surface, tooth thickness is narrowed from middle to two ends, except that its middle section is involute, the tooth profile of all the other sections is envelope of hyperbolic line, so that it is a new gear pair capable of meeting heavy load and high-accuracy requirements. The novel gear transmission has the advantages of good meshing performance, large superposition coefficient, large bearing capacity, high transmission efficiency, no additional axial force, long service life, high stability, low noise and the like.
However, the novel gear is used as a basic member, and the processing of a high-grade numerical control machine tool has some problems: firstly, the economical efficiency is very poor, the processing cost is very high, and the method is one of the bottlenecks for large-scale industrial application of the basic parts; secondly, the functional redundancy of the high-grade numerical control machine tool is large, and a plurality of functions are in a redundant state when the basic parts are processed; moreover, in the case of the novel gear transmission, the machining of the high-grade numerical control machine tool is a typical approximate machining, and the corresponding manufacturing is mainly carried out by interpolation, so that the principle error exists.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a cutter combination and a processing method for processing a cylindrical gear with a hyperbolic circular arc toothed line, which can cut out the convex surface and the concave surface of the tooth of the gear at the same time, improve the processing efficiency, effectively reduce the redundancy of a high-grade numerical control machine tool by adopting a special processing cutter combination, greatly reduce the processing cost and improve the processing precision.
The aim of the invention is realized by the following technical scheme: the utility model provides a processing becomes cutter combination of hyperbolic circular arc toothed spur gear, includes the blade disc, the blade disc can rotate around self axis, circumference array has a plurality of tooth's socket cutter holder group on the blade disc, tooth's socket cutter holder group includes cutter holder seat and double-edged blade, the tooth's socket has been seted up on the blade disc, cutter holder seat with the tooth's socket adaptation, double-edged blade detachable installs on the cutter holder seat, double-edged blade's external cutting edge is the positive toper, external cutting edge equals external cutting edge with the contained angle between the blade disc axis of symmetry in the double-edged blade, double-edged blade's interior cutting edge is the back taper, internal cutting edge equals internal cutting edge with the contained angle between the blade disc axis of symmetry in the double-edged blade.
Further, the cross section of the double-edge blade along the axis direction of the self-mounting hole is diamond-shaped, and the symmetry axes of the inner edge and the outer edge of the double-edge blade are parallel to the rotation axis of the cutterhead.
Further, an insert groove is formed in one side of the tool holder seat, one end of the symmetry axis of the inner and outer edges of the double-edge insert is adapted to the insert groove, and the double-edge insert is connected with the tool holder seat through an insert fixing screw.
Further, the tooth slot cutter holder group further comprises a blade side locking block, a wedge-shaped groove is arranged in the tooth slot, two sides of the blade side locking block are wedge-shaped surfaces, the blade side locking block is adapted in the wedge-shaped groove, one wedge-shaped surface of the blade side locking block abuts against the double-edge blade, and the other wedge-shaped surface of the blade side locking block abuts against the inner wall of the wedge-shaped groove.
Further, a cutter holder side locking block is arranged in the wedge-shaped groove, two sides of the cutter holder side locking block are wedge-shaped surfaces, one wedge-shaped surface of the cutter holder side locking block abuts against the cutter holder seat, and the other wedge-shaped surface of the cutter holder side locking block abuts against the inner wall of the wedge-shaped groove.
Further, two locating through holes are formed in the top of the tool holder seat in a penetrating mode, a first tool holder fixing screw and a second tool holder fixing screw are movably arranged in the two locating through holes in a penetrating mode respectively, the first tool holder fixing screw is close to the double-edge blade, the first tool holder fixing screw and the second tool holder fixing screw are connected with the cutter head in a threaded mode, a first threaded hole is formed in one end, close to the double-edge blade, of the tool holder seat, the first threaded hole is communicated with the locating through hole, a first tool holder fixing screw is matched in the first threaded hole, a second threaded hole is formed in the other end of the tool holder seat, the second threaded hole is communicated with the other locating through hole, and a second tool holder fixing screw is matched in the second threaded hole.
Further, a first locking screw is adapted to the cutter holder side locking block, the first locking screw is in threaded connection with the cutter head, a first spring is arranged at the bottom of the cutter holder side locking block, a second locking screw is adapted to the cutter blade side locking block, the second locking screw is in threaded connection with the cutter head, and a second spring is arranged at the bottom of the cutter blade side locking block.
Further, a hanging ring is arranged on the cutterhead.
A processing method for processing a cylindrical gear with a hyperbolic circular arc toothed line comprises the steps of installing a cutter disc on a main shaft of a machine tool and rotating the cutter disc around an axis M-M of the cutter disc, wherein the tooth slot cutter is provided with a cutter head which is provided with a cutter head and is provided with a cutter head which is provided with a cutter head and a cutter head which isThe clamping group is fixed on the cutter head and rotates along with the cutter head, and the tooth blank to be processed rotates around the self-axis with the rotating speed of omega 2 Meanwhile, the tooth blank to be machined performs horizontal feeding motion close to the cutter head, the speed of the horizontal feeding motion is V, so that the tooth blank to be machined and the double-edge blade form compact generating motion, in the machining process, the external cutting edge of the double-edge blade machines the tooth concave surface of the gear, the internal cutting edge machines the tooth convex surface of the gear, and the next pair of tooth surfaces are machined after the indexing of the pair of tooth surfaces is required until the machining of the whole gear is completed, and the relation between the rotating speed and the feeding speed of the tooth blank to be machined is as follows: v=ω 2 ×R 1 Wherein R is 1 Is the radius of the gear reference circle.
Further, the motion trail of the contact point of the double-edged blade and the tooth blank to be processed in the fixed coordinate system is the contact line, and the contact line equation (generating motion equation) of the double-edged blade and the tooth blank to be processed is obtained as follows:
the coordinate systems are respectively as follows: the static coordinate system of the double-edge blade (4), namely the fixed coordinate system O 1 -x 1 ，y 1 ，z 1 (coordinate basis i, j, k), static coordinate system O of tooth blank to be processed 2 -x 2 ，y 2 ，z 2 (coordinate base i) 2 ，j 2 ，k 2 ) Dynamic coordinate system O of tooth blank to be processed d -x d ，y d ，z d (coordinate base i) d ，j d ，k d )；
The indexing radius of the machined gear is R 1 The rotation angle of the dynamic coordinates of the tooth blank to be processed is phi;
the radius of the cutter head is R, theta is the corner (°) of the double-edged blade from the middle section of the tooth blank to be processed to the end face, namely the tooth profile position angle;
m is the modulus of the machined gear, alpha is the spreading angle of the double-edged blade, namely the pressure angle of the machined gear teeth, the tooth width of the machined gear is B, and u is the direction from the cutter to the reference system x along the generatrix 1 The distance of the axis and is specified at z 1 The positive half shaft is positive, and the negative half shaft is negative.
The beneficial effects of the invention are as follows:
1. the corresponding mathematical modeling and deduction are carried out by adopting the meshing principle, the cutter combination design is carried out by adopting the corresponding forming principle by adopting the corresponding spatial relation, the interpolation manufacturing error can be effectively avoided, the convex surface and the concave surface of the gear can be cut out at the same time, and the processing efficiency is improved.
2. The redundancy of the high-grade numerical control machine tool can be effectively reduced by adopting the special processing tool combination, the processing cost is greatly reduced, and the processing precision and the processing efficiency are improved.
3. The limitation of the nominal modulus of the machined gear is broken through, and the non-standard modulus can be specified for customized machining according to actual requirements.
4. The cutter holder seat does not need to be installed in a shifting mode, the position of the cutter holder group of the tooth slot is finely adjusted through the first cutter holder set screw and the second cutter holder set screw, the radial position of the cutter holder group of the tooth slot is fixed reliably and accurately, the center distance of the double-edged blade is adjusted, and the machining precision is improved.
5. The upper end and the lower end of the double-edged blade can be processed, when the double-edged blade is worn seriously, the double-edged blade can be rotated 180 degrees, and the double-edged blade can be installed and used in a repositioning way, so that the production cost can be greatly reduced.
Drawings
FIG. 1 is a schematic view of the overall structure of a cutter assembly for machining a cylindrical gear with a variable hyperbolic circular arc tooth trace according to the present invention;
FIG. 2 is a perspective view of a holder set for a tooth slot in a tool assembly for machining a cylindrical gear with a variable hyperbolic circular arc tooth trace in accordance with the present invention;
FIG. 3 is a perspective view of a tooth slot and tool holder assembly in a tool assembly for machining a cylindrical gear with a variable hyperbolic circular arc tooth trace according to the present invention;
FIG. 4 is a perspective view of a double-edged insert in a cutter assembly for machining a cylindrical gear with a variable hyperbolic circular arc tooth trace in accordance with the present invention;
FIG. 5 is a perspective view of a holder for a tool assembly for machining a cylindrical gear with a variable hyperbolic circular arc tooth trace in accordance with the present invention;
FIG. 6 is a perspective view of a cutterhead in a cutter assembly for machining a cylindrical gear with a variable hyperbolic circular arc tooth trace according to the present invention;
FIG. 7 is a perspective view of a holder side lock block in a tool assembly for machining a cylinder gear with a hyperbolic circular arc tooth trace in accordance with the present invention;
FIG. 8 is a schematic view showing the internal structure of a holder-side lock block in a tool assembly for machining a cylindrical gear with a hyperbolic circular arc tooth trace according to the present invention;
FIG. 9 is a perspective view of a blade side lock block in a cutter assembly for machining a variable hyperbolic circular arc toothed spur gear in accordance with the present invention;
FIG. 10 is a schematic view showing the internal structure of a blade-side lock block in a cutter assembly for machining a toothed spur gear with a hyperbolic circular arc in accordance with the present invention;
FIG. 11 is a schematic diagram of a rotary cutterhead double-edge blade machining variable hyperbolic circular arc toothed line cylindrical gear;
FIG. 12 is a reference frame diagram of a tool assembly and a gear to be machined;
in the figure, a 1-cutter head, a 2-tooth groove cutter holder group, a 3-cutter holder seat, a 4-double-blade, a 5-tooth groove, a 6-blade groove, a 7-blade fixing screw, an 8-blade side locking block, a 9-wedge groove, a 10-cutter holder side locking block, an 11-first cutter holder fixing screw, a 12-positioning through hole, 13-first tool holder set screw, 14-first threaded bore, 15-second threaded bore, 16-second tool holder set screw, 17-first locking screw, 18-first spring, 19-second locking screw, 20-second spring, 21-lifting ring, 22-second tool holder set screw.
Detailed Description
The technical solution of the present invention will be described in further detail with reference to the accompanying drawings, but the scope of the present invention is not limited to the following description.
As shown in fig. 1 to 10, a cutter combination for machining a cylindrical gear with a hyperbolic circular arc tooth trace comprises a cutter disc 1, wherein the cutter disc 1 can rotate around the axis of the cutter disc 1, a plurality of tooth slot cutter holder groups 2 are arranged on the circumference of the cutter disc 1, each tooth slot cutter holder group 2 comprises a cutter holder seat 3 and a double-edge blade 4, a tooth slot 5 is arranged on the cutter disc 1, the cutter holder seats 3 are matched with the tooth slots 5, the double-edge blade 4 is detachably arranged on the cutter holder seats 3, the external cutting edge of the double-edge blade 4 is in a forward conical shape, the included angle between the external cutting edge and the symmetrical axis of the internal cutting edge of the double-edge blade 4 is equal to the included angle between the external cutting edge and the axis of the cutter disc 1, the included angle between the internal cutting edge and the symmetrical axis of the double-edge blade 4 is equal to the included angle between the internal cutting edge and the axis of the cutter disc 1, the tooth slot cutter holder groups 2 are driven to rotate around the axis of the cutter disc 1, the internal cutting edge and the external cutting edge of the double-edge blade 4 are jointly used for machining a gear tooth blank, namely a convex tooth surface is machined on the gear tooth blank, and concave tooth surface is machined, and concave tooth surface machining efficiency is improved;
further, referring to fig. 4, the cross section of the double-edge blade 4 in the axial direction is diamond-shaped, and has two axes, one is a mounting hole axis, and the other is a symmetry axis of the inner and outer edges, wherein the mounting hole axis is perpendicular to the symmetry axis of the inner and outer edges, the symmetry axis of the double-edge blade 4 is parallel to the rotation axis of the cutterhead 1, the double-edge blade 4 is of a symmetrical structure, the distance from the symmetry axis of the inner and outer edges of the double-edge blade to the rotation axis of the cutterhead 1 is the radius R of the cutterhead and is also the nominal tooth line radius of the double-edge blade 4, the corresponding mathematical modeling and deducing are carried out by adopting the meshing principle, the cutter combination design is carried out by adopting the corresponding forming principle by adopting the corresponding spatial relation, the interpolation manufacturing error can be effectively avoided, and the changed hyperbolic circular arc tooth line cylindrical gear can be accurately processed; an insert groove 6 is formed in one side of the tool holder seat 3, one end of the double-edged insert 4 along the symmetry axis of the external cutting edge is adapted in the insert groove 6, the double-edged insert 4 is connected with the tool holder seat 3 through an insert fixing screw 7, namely the insert fixing screw 7 penetrates through a mounting hole of the double-edged insert 4 to be fixedly connected with the tool holder seat 3; the upper end and the lower end of the double-edged blade 4 can be processed, when the double-edged blade 4 is worn seriously, the blade fixing screw 7 is screwed off, the double-edged blade 4 is detached from the tool holder seat 3, and then the double-edged blade is rotated 180 degrees and then is positioned and installed on the tool holder seat 3 through the blade fixing screw 7 for use, so that the production cost can be greatly reduced.
Further, as shown in fig. 1 and fig. 6 to fig. 10, the tooth space holder set 2 further includes a blade side locking block 8, a wedge-shaped groove 9 is provided in the tooth space 5, both sides of the blade side locking block 8 are wedge-shaped surfaces, the blade side locking block 8 is adapted in the wedge-shaped groove 9, one wedge-shaped surface of the blade side locking block 8 abuts against the double-edged blade 4, the other wedge-shaped surface of the blade side locking block 8 abuts against the inner wall of the wedge-shaped groove 9, a holder side locking block 10 is provided in the wedge-shaped groove 9, both sides of the holder side locking block 10 are wedge-shaped surfaces, one wedge-shaped surface of the holder side locking block 10 abuts against the holder seat 3, and the other wedge-shaped surface of the holder side locking block 10 abuts against the inner wall of the wedge-shaped groove 9; the radial direction of the double-edged blade 4 is locked through the blade side locking block 8, and the radial direction of the cutter holder seat 3 is locked through the cutter holder side locking block 10, so that the mounting stability of the cutter holder group of the tooth slot is ensured; the cutter holder side locking block 10 is provided with a first locking screw 17 in a matching way, the first locking screw 17 is in threaded connection with the cutter disc 1, the bottom of the cutter holder side locking block 10 is provided with a first spring 18, the cutter blade side locking block 8 is provided with a second locking screw 19 in a matching way, the second locking screw 19 is in threaded connection with the cutter disc 1, and the bottom of the cutter blade side locking block 8 is provided with a second spring 20; the blade side locking block 8 and the cutter holder side locking block 10 are wedge-shaped blocks, the blade side locking block 8 and the cutter holder side locking block 10 are tightly pressed in the wedge-shaped groove 9, so that radial pressure is generated between the blade side locking block 8 and the cutter holder side locking block 10, the second spring 20 is in a compressed state after the blade side locking block 8 is tightly pressed, the first spring 18 is in a compressed state after the cutter holder side locking block 10 is tightly pressed due to the reaction force of the second spring 20, the cutter holder side locking block 10 is axially pressed due to the reaction force of the first spring 18, the blade side locking block 8 and the cutter holder side locking block 10 are tightly locked due to axial and radial partial pressure, the position accuracy of the cutter holder group 2 is guaranteed, the second locking screw 19 is screwed in after the blade side locking block 8 is in place after the cutter holder side locking block 10 is in place, and the cutter holder group 2 is stably installed due to the fact that the cutter holder side locking block 10 is screwed in the first locking screw 17 is screwed in.
Further, as shown in fig. 2, 3 and 5, two positioning through holes 12 are formed through the top of the tool holder seat 3, a first tool holder fixing screw 13 and a second tool holder fixing screw 22 are movably arranged in the two positioning through holes 12 in a penetrating manner, the first tool holder fixing screw 13 and the second tool holder fixing screw 22 are in threaded connection with the tool head 1, the tool holder seat 3 is mounted on the tool head 1 through the first tool holder fixing screw 13 and the second tool holder fixing screw 22, the model numbers of the first tool holder fixing screw 13 and the second tool holder fixing screw 22 are M10X30, a first threaded hole 14 is formed at one end of the tool holder seat 3 close to the double-edge blade 4, the first threaded hole 14 is communicated with the positioning through hole 12 close to the double-edge blade 4, a first tool holder set screw 11 is adapted in the first threaded hole 14, the model number of the first tool holder set screw 11 is M8X20, a second threaded hole 15 is formed at the other end of the tool holder seat 3, the second screw hole 15 is communicated with the other positioning through hole 12, the second screw hole 15 is internally provided with a second tool holder set screw 16, the model of the second tool holder set screw 16 adopts M8X8, the first tool holder set screw 11 and the second tool holder set screw 16 can perform fine adjustment on the position of the tool holder seat 3 besides the fastening function, specifically, after the first tool holder set screw 11 is connected and screwed into the tool holder seat 3, the tail end of the first tool holder set screw 11 is used for supporting the first tool holder set screw 13, after the second tool holder set screw 16 is connected and screwed into the tool holder seat 3, the tail end of the second tool holder set screw 16 is used for supporting the second tool holder set screw 22, the fastening force can cause the position for fixing the first tool holder set screw 13 and the second tool holder set screw 22 to slightly change along the radial direction, so that the fine adjustment on the position of the tool holder seat 3 is realized, therefore, the radial position of the tool holder seat is fixed reliably and accurately, the positions of the cutter holder seats 3 in the rest tooth grooves 5 are adjusted, so that the radial position error of each double-edged blade 4 on the circumference is not more than 0.005mm; a hanging ring 21 is arranged on the cutterhead 1, and the cutterhead 1 is convenient to take through the hanging ring 21; if gears with different moduli are required to be processed, only the double-edged blade 4 and the cutter holder seat 3 are required to be replaced, so that the limitation of the nominal modulus of the processed gear is broken through, and the non-standard modulus can be specified for customized processing according to actual requirements.
As shown in fig. 11 and 12, the above-mentioned cutter combination provides a processing method for processing a cylindrical gear with a hyperbolic circular arc tooth trace, wherein a cutter head 1 is arranged on a main shaft of a machine tool and rotates around an own axis M-M, a tooth slot cutter holder group 2 is fixed on the cutter head 1 and rotates along with the cutter head 1, a tooth blank to be processed rotates around the own axis, and the rotating speed is omega 2 Simultaneously, the tooth blank to be processed performs horizontal feeding motion close to the cutter disc 1, the speed of the tooth blank is V, so thatThe tooth blank to be machined and the double-edge blade 4 form compact generating motion, the outer cutting edge of the double-edge blade 4 is used for machining the tooth concave surface of the gear in the machining process, the inner cutting edge is used for machining the tooth convex surface of the gear, a pair of tooth surfaces are machined, indexing is needed, then the next pair of tooth surfaces are machined until the machining of the whole gear is completed, and the relation between the rotating speed and the feeding speed of the tooth blank to be machined is as follows: v=ω 2 ×R 1 Wherein R1 is the gear pitch circle radius.
The rated speeds of the tooth blank to be processed and the double-edged blade 4 at the meshing point are v respectively 1 、v 2 The relative speed of the tooth blank to be processed and the double-edged blade 4 at the meshing point is v 12 The space meshing principle proves that in the machining process, the following meshing conditions are satisfied between the workpiece to be machined and the double-edge blade 4:
φ＝n 1 ·v 12 ＝n 1 ·v 1 -n 1 ·v 2 ＝0
as shown in fig. 12, if the point M is an instantaneous contact point between the double-edged blade 4 and the tooth blank to be machined, it is set in the coordinate system O 1 -x 1 ,y 1 ,z 1 In point O 1 、O 2 Vector to point M, point O 1 、O 2 The vector between them is:
O 1 M＝r 1 ,O 2 M＝r 2 ,O 2 O 1 ＝ε
the relation among the three is as follows:
r 2 ＝ε+r 1
wherein:
ε＝(R 1 ψ+R)i-R 1 k
then there are:
in the gear tooth machining process, the double-edged blade 4 only rotates around the axis of the rotary cutter head 1, and can be regarded as spiral motion with zero axis displacement, and according to the characteristics of the spiral motion, the double-edged blade is provided with:
n 1 ·v 1 ＝0
further, the contact conditions during processing can be simplified as:
φ＝n 1 ·v 2 ＝e 1 ·v 2 ＝0
speed v of gear 1 The unfolding can be obtained:
w in 1 The vector v is obtained as the rotational angular velocity of the cutterhead 1 1 Vector of r dθ Parallel. The definition of the vector of the combination method is easy to know:
v 1 ⊥n 1 (e 1 )。
and k 2 = -j, and there are:
v 2 ＝w 2 k 2 ×r 2 -w 2 R 1 i＝w 2 (k 2 ×r 2 -R 1 i)
w 2 is the rotation angular velocity of the tooth blank
Simultaneously, the above formulas are as follows:
the formula is as follows:
the motion trail of the contact point of the double-edge blade 4 and the tooth blank to be processed in the fixed coordinate system is the contact line, and the contact line equation (generating motion equation) of the double-edge blade 4 and the tooth blank to be processed is obtained as follows:
the coordinate systems are respectively as follows: static coordinate system of double-edged blade 4, i.e. fixed seatStandard series O 1 -x 1 ，y 1 ，z 1 (coordinate basis i, j, k), static coordinate system O of tooth blank to be processed 2 -x 2 ，y 2 ，z 2 (coordinate base i) 2 ，j 2 ，k 2 ) Dynamic coordinate system O of tooth blank to be processed d -x d ，y d ，z d (coordinate base i) d ，j d ，k d )。
The indexing radius of the machined gear is R 1 The rotation angle of the dynamic coordinates of the tooth blank to be processed is phi;
the radius of the cutter disc 1 is R, theta is the corner (°) of the double-edge blade 4 from the middle section of the tooth blank to be processed to the end face, namely the tooth profile position angle.
m is the modulus of the machined gear, alpha is the spreading angle of the double-edged blade 4, namely the pressure angle of the machined gear teeth, and the tooth width of the machined gear is B. u is the direction of the tool along the generatrix to the reference system x 1 The distance of the axis and is specified at z 1 The positive half shaft is positive, and the negative half shaft is negative;
in actual working engineering, R, R 1 And m and alpha are determined design parameters, and theta and psi are curved surface parameters of the tooth surface of the gear tooth, so that the value ranges of the parameters theta and psi are required to be determined, wherein theta influences the position of the point on the tooth surface in the tooth width direction, and psi determines the position of the point on the tooth surface in the tooth height direction.
For the cylindrical gear with the variable hyperbolic circular arc tooth trace, as the tooth profiles of all sections are different and the curvature radiuses of any positions in the tooth height direction of the same section are also different, the corresponding workpiece rotation angles psi and theta are different in range, and the research on the workpiece rotation angles psi and theta is needed by combining the tooth profiles of all sections.
The working principle of the rotary cutterhead is easy to know, the rotating angle of the cutter from the middle section of the gear tooth to the two end faces is gradually increased, and the cutter rotation angle theta can be calculated by the following formula:
wherein b is the distance from each end section to the middle section, R e Is a tooth trace corresponding to any point on the tooth profileRadius of curvature in the direction. When b≡0 is present on the middle cross section tooth profile, θ≡0 is known from the formula. In the non-middle section tooth profile, b is not equal to 0, the curvature radius of the tooth trace direction at any point is different, and the formula shows that the range of psi and theta is to be determined.
In fact, when the radius of the cutter disc is increased in the machining process, the change of the tooth profile of each section gradually decreases, and the value range of the tooth profile psi and theta of each section gradually approaches to the parameter range of the tooth profile of the middle section. In general, when the radius of the cutterhead 1 is larger than the tooth width of the tooth, the parameter range of the whole tooth surface can be replaced by the parameter range of the middle section tooth profile.
The range of values of the section tooth profile psi in the hyperbolic circular arc toothed cylindrical gear can be expressed as:
when z is greater than or equal to (h.a+c) * ) At/(1-cos alpha)
Convex surface of the counter gear: alpha-beta-gamma 1 ≤ψ≤α-β-γ 2
Concave surface: beta-alpha + gamma 2 ≤ψ≤β-α+γ 1
When z < (h a+c) * ) At/(1-cos alpha)
Concave surface of the counter gear: beta-alpha is less than or equal to phi and less than or equal to gamma 1 +β-α
Convex surface: alpha-beta-gamma 1 ≤ψ≤α-β
Wherein:
the gear tooth jacking coefficient is h x a, and the jacking coefficient is c * Z is the number of teeth of the gear to be machined, and beta is constant (related to the number of teeth of the gear workpiece)
Under the condition of determining the pressure angle and the tooth form coefficient, the section tooth profile parameter psi in the gear teeth of the cylindrical gear with the hyperbolic circular arc tooth trace is only related to the number of teeth of the gear workpiece to be processed. This will be described by way of specific examples.
Let the machined gear tooth number z=49, the tooth width b=90 mm, the cutter radius r=500 mm, the tooth top coefficient 1, the head clearance coefficient 0.25, and the moduli m1=4 and m2=6, respectively. The value ranges of the two processed gears ψ are all as follows:
convex surface of the gear:
-0.1443≤ψ≤0.1910
concave gear:
-0.1910≤ψ≤0.1443
the cutter combination and the gear workpiece synchronously perform generating motion according to a preset gear cutting speed until the current tooth groove is processed, wherein the current tooth groove comprises a convex surface of a previous tooth and a concave surface of a next tooth, after the processing of the previous tooth groove is completed, the cutter disc 1 is separated from a processed gear, the indexing mechanism firstly returns to the initial point of indexing, and then continues to index to the angle of the next tooth groove to be processed, so that the generation of accumulated errors is avoided.
The foregoing is merely a preferred embodiment of the invention, and it is to be understood that the invention is not limited to the form disclosed herein but is not to be construed as excluding other embodiments, but is capable of numerous other combinations, modifications and environments and is capable of modifications within the scope of the inventive concept, either as taught or as a matter of routine skill or knowledge in the relevant art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (4)
1. The cutter combination for processing the hyperbolic circular-arc toothed line cylindrical gear is characterized by comprising a cutter disc (1), wherein the cutter disc (1) can rotate around the axis of the cutter disc (1), a plurality of tooth groove cutter holder groups (2) are circumferentially arranged on the cutter disc (1), each tooth groove cutter holder group (2) comprises a cutter holder seat (3) and a double-edge blade (4), tooth grooves (5) are formed in the cutter disc (1), the cutter holder seat (3) is matched with the tooth grooves (5), the double-edge blade (4) is detachably arranged on the cutter holder seat (3), the external cutting edge of the double-edge blade (4) is in a forward taper shape, the included angle between the outer cutting edge and the symmetry axis of the inner and outer edges of the double-edge blade (4) is equal to the included angle between the outer cutting edge and the axis of the cutter head (1), the inner cutting edge of the double-edge blade (4) is in an inverted cone shape, the included angle between the inner cutting edge and the symmetry axis of the inner and outer edges of the double-edge blade (4) is equal to the included angle between the inner cutting edge and the axis of the cutter head (1), the cross section of the double-edge blade (4) along the axis direction of the mounting hole of the double-edge blade is diamond-shaped, and the symmetry axis of the inner and outer edges of the double-edge blade (4) is parallel to the rotation axis of the cutter head (1);
one side of the cutter holder seat (3) is provided with an blade groove (6), one end of an inner and outer edge symmetry axis of the double-edge blade (4) is matched in the blade groove (6), the double-edge blade (4) is connected with the cutter holder seat (3) through a blade fixing screw (7), the cutter slot cutter holder group (2) further comprises a blade side locking block (8), a wedge-shaped groove (9) is arranged in the cutter slot (5), two sides of the blade side locking block (8) are wedge-shaped surfaces, the blade side locking block (8) is matched in the wedge-shaped groove (9), one wedge-shaped surface of the blade side locking block (8) is abutted against the double-edge blade (4), the other wedge-shaped surface of the blade side locking block (8) is abutted against the inner wall of the wedge-shaped groove (9), two sides of the cutter holder side locking block (10) are wedge-shaped surfaces, one wedge-shaped surface of the cutter holder side locking block (10) is abutted against the wedge-shaped surface of the cutter holder seat (9);
the cutter holder side locking block (10) is provided with a first locking screw (17) in a matching mode, the first locking screw (17) is in threaded connection with the cutter disc (1), the bottom of the cutter holder side locking block (10) is provided with a first spring (18), the cutter blade side locking block (8) is provided with a second locking screw (19) in a matching mode, the second locking screw (19) is in threaded connection with the cutter disc (1), and the bottom of the cutter blade side locking block (8) is provided with a second spring (20);
the top of cutter holder seat (3) runs through and has seted up two locating hole (12), two the activity is worn to be equipped with first cutter holder set screw (13) and second cutter holder set screw (22) in locating hole (12) respectively, first cutter holder set screw (13) are close to double-edged blade (4) set up, first cutter holder set screw (13) and second cutter holder set screw (22) all with cutter disc (1) threaded connection, first screw hole (14) have been seted up to cutter holder seat (3) one end that is close to double-edged blade (4), first screw hole (14) communicate with each other with be close to locating hole (12) of double-edged blade (4), first screw hole (14) internal adaptation has first cutter holder set screw (11), second screw hole (15) have been seted up to the other end of cutter holder seat (3), second screw hole (15) communicate with each other with another locating hole (12), second cutter holder set screw (16) are furnished with in second screw hole (15).
2. A tool assembly for machining a cylindrical gear with a variable hyperbolic circular arc tooth trace according to claim 1, wherein the cutter head (1) is provided with a hanging ring (21).
3. A method of machining a cylindrical gear with a variable hyperbolic circular arc tooth trace according to claim 1 or 2, characterized in that the cutterhead (1) is mounted on the main shaft of the machine tool and rotates around its own axis M-M, the set of cogging holders (2) is fixed to the cutterhead (1) and rotates with the cutterhead (1), the tooth blank to be machined rotates around its own axis at a rotational speed of
Meanwhile, the tooth blank to be machined is subjected to horizontal feeding motion close to the cutter head (1), the speed of the horizontal feeding motion is V, so that the tooth blank to be machined and the double-edge blade (4) form compact generating motion, in the machining process, the outer cutting edge of the double-edge blade (4) is used for machining the tooth concave surface of a gear, the inner cutting edge is used for machining the tooth convex surface of the gear, the next pair of tooth surfaces are required to be machined after indexing is performed on the machined tooth surfaces until the machining of the whole gear is completed, and the relation between the rotating speed and the feeding speed of the tooth blank to be machined is as follows: />
Which is provided withR in (B) 1 Is the radius of the gear reference circle.
4. The method for machining the cylindrical gear with the variable hyperbolic circular arc tooth trace according to claim 3, wherein the motion track of the contact point of the double-edged blade (4) and the tooth blank to be machined in a fixed coordinate system is a contact line, and the equation of the contact line of the double-edged blade (4) and the tooth blank to be machined is obtained as follows:
the coordinate systems are respectively as follows: static or fixed coordinate system of double-edged blade (4)O1-x1，y1，z1, static coordinate system of tooth blank to be processedO2-x2，y2，z2, dynamic coordinate system of tooth blank to be processedOd-xd，yd，zd；
The indexing circle radius of the processed gear isR1. The rotation angle of the dynamic coordinate of the tooth blank to be processed isψ；
The radius of the cutterhead (1) isR，θThe angle (°) from the middle section of the tooth blank to be processed to the end face of the double-edge blade (4) is the tooth profile position angle;
m in order to achieve the modulus of the gear to be processed,αfor the spreading angle of the double-edge blade (4), namely the pressure angle of the machined gear teeth, the tooth width of the machined gear isB，u For the tool in the direction of the generatrix to a reference systemx1. The distance of the axis and is defined inz1. The positive half shaft is positive, and the negative half shaft is negative.
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| CN202111472739.9A CN114029560B (en) | 2021-11-30 | 2021-11-30 | Cutter combination for machining cylindrical gear with hyperbolic circular arc toothed line and machining method |
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| CN118123138B (en) * | 2024-02-01 | 2024-09-10 | 大连理工大学 | Design method of cutting edge of gear end face tooth profile chamfering tool |
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| US3662650A (en) * | 1970-02-16 | 1972-05-16 | Bird Island Inc | Gear making |
| CN101890540A (en) * | 2010-07-16 | 2010-11-24 | 扬州大学 | Method for processing curve-tooth cylindrical gear |
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| GB659446A (en) * | 1949-03-17 | 1951-10-24 | Gleason Works | Cutters for and method of producing gears |
| SU524627A1 (en) * | 1975-01-23 | 1976-08-15 | Московский Автомобильный Завод Имени И.А.Лихачева | Cutter head |
| US6632050B2 (en) * | 2001-09-06 | 2003-10-14 | Kennametal Inc. | Face hobbing cutter |
| US20040086350A1 (en) * | 2002-10-31 | 2004-05-06 | Yaxiong Zhang | Five-simultaneously-working-axis computerized numerical controlled tooth cutting machine tool for plane enveloping toroidal worms |
| CN103252538B (en) * | 2012-02-16 | 2020-01-17 | 山特维克知识产权股份有限公司 | Face hobbing cutter system and indexable milling insert therefor |
| CN103624310B (en) * | 2012-08-28 | 2016-12-21 | 株洲钻石切削刀具股份有限公司 | A kind of cutting tool with fly-off prevention structure |
| CN107617795B (en) * | 2016-07-14 | 2019-09-17 | 方年学 | The processing method of curved tooth line gear |
| CN106438920A (en) * | 2016-08-15 | 2017-02-22 | 四川大学 | Variable-double-curve circular-arc-tooth-trace cylindrical gear |
| EP3287222A1 (en) * | 2016-08-23 | 2018-02-28 | Klingelnberg AG | Method for processing the tooth flanks of plan coupling workpieces in semi-completing method |
| CN206578343U (en) * | 2017-01-13 | 2017-10-24 | 浙江亚太机电股份有限公司 | A kind of adjustable indexable side and face milling cutter of cutter blade |
| JP7171576B2 (en) * | 2017-08-07 | 2022-11-15 | 株式会社北川鉄工所 | Chuck compensation method |
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| US3662650A (en) * | 1970-02-16 | 1972-05-16 | Bird Island Inc | Gear making |
| CN101890540A (en) * | 2010-07-16 | 2010-11-24 | 扬州大学 | Method for processing curve-tooth cylindrical gear |
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