CN106956171B - The numerical control grinding method of Double-conical-surface twice-enveloping enveloping worm hob side relief - Google Patents
The numerical control grinding method of Double-conical-surface twice-enveloping enveloping worm hob side relief Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
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Abstract
The present invention relates to a kind of numerical control grinding methods of Double-conical-surface twice-enveloping enveloping worm hob side relief, belong to the processing method of Double-conical-surface twice-enveloping enveloping worm hob.When being ground side relief on four-shaft linkage numerical control machine, adjust hobboing cutter corner and tool apron turntable corner, and radial distance and axial distance of the tool apron turntable center relative to hobboing cutter center are adjusted simultaneously, contact the point produced on the shape conical surface successively with each point on land line, unit normal vector of the contact point on the production shape conical surface is parallel with the unit normal vector on side relief to make bipyramid grinding wheel outer rim and hobboing cutter tooth root anchor ring tangent simultaneously, the numerical control grinding processing of Double-conical-surface twice-enveloping enveloping worm hob side relief is realized in this approach, and it can guarantee consistent from tooth top to tooth root margin width at left and right sides of each cutter tooth, and the margin width and side relief angle of the side relief of each cutter tooth are equal.
Description
Technical field
The present invention relates to a kind of method for grinding of Double-conical-surface twice-enveloping enveloping worm hob side relief, belong to Double-conical-surface
The processing method of twice-enveloping enveloping worm hob, the in particular to secondary packet of a kind of Double-conical-surface based on four-shaft linkage numerical control machine
The numerical control grinding method of network enveloping worm hob side relief.
Background technique
In enveloping worm drive field, using it is wide be that planar double-enveloping toroid worm gear and Double-conical-surface are secondary
Double enveloping worm pair, wherein the enveloping worm flank of tooth is produced by the two sides of bipyramid grinding wheel in double-cone double-enveloping toroidal worm pair
The shape conical surface is processed respectively, is all machined surface since bipyramid grinding wheel two sides produce the shape conical surface, when processing enveloping worm not corresponding flanks,
Enveloping worm or bipyramid grinding wheel need not turn around, and can reduce non-cutting time, meanwhile, in the case where bull small speed ratio, by bipyramid
The enveloping worm that grinding wheel processes can effectively avoid the problem that Gen Qie and side topping.But for the double of rolling cut worm gear
The production of conical surface twice-enveloping enveloping worm hob is sufficiently complex, and is difficult to make, because of Double-conical-surface twice-enveloping anchor ring worm gear
The worm screw helicoid having the same of land and the double-cone double-enveloping toroidal worm transmission of hobboing cutter, each of which cutter tooth two sides
Cutting edge is all different shape, and every helical angle on hobboing cutter helicoid is all different on cutting edge line, and on each cutter tooth
It needs to retain the land of one fixed width, and is ground out the side relief of certain angle.
In order to solve the processing of different types of twice-enveloping enveloping worm hob side relief, Chinese patent
(ZL93120467.4) it is directed to planar secondary enveloping ring surface worm gear hob and inner conical surface twice-enveloping enveloping worm hob, according to every
The normal direction section shape of a cutter tooth modifies grinding wheel, by screwfeed, to control blade bandwidth, but needs to modify when each cutter tooth of grinding
Different grinding wheel section shapes, and side relief angle cannot be guaranteed unanimously；Chinese patent (ZL201010104684.1) and China are special
Sharp (ZL201110206581.0) is ground side relief by the transmission ratio of workbench where changing hobboing cutter and grinding wheel, is respectively adopted
The tapered plane grinding wheel of truncated cone-shaped grinding wheel and taper pressure abrading block support, but it is consistent with side relief angle not can guarantee margin width
Property；Chinese patent (ZL201310172562.X) provides the design method of twice-enveloping enveloping worm hob side relief, finds out
The lead angle of each point in side relief start line is rotated corresponding rear corner surface angle, then presses rear corner surface by side relief start line
Forming transmission ratio obtains the helix cluster on side relief, is then milled side relief using the method for numerically-controlled machine tool Machining of Curved Surface
It cuts out and, but processing efficiency is not high；Chinese patent (ZL201410613061.5) proposes planar secondary enveloping ring surface worm gear hob
The subsequent numerical control grinding and machining method in side obtains per unit system of each point on land in each cutter tooth side relief start line first
Vector obtains unit normal vector of each point on side relief in start line, then uses according to given side relief angle
Four-axle linked lathe first passes through rotational plane grinding wheel and hobboing cutter, keeps the law vector of plane of grinding wheel and hobboing cutter side relief ground
The law vector of point is identical, then by axial position and the radial position of plane of motion grinding wheel and hobboing cutter, make flat-faced wheel outer rim with
Hobboing cutter tooth root annular face contacts, and plane of grinding wheel and hobboing cutter side relief is made to be ground point contact, it can be ground out and guarantee margin width
The side relief of the consistent and unified side relief angle of degree, but due to the difference of Forming Theory, this method is not suitable for bipyramid
The side relief grinding of face twice-enveloping enveloping worm hob.For current Double-conical-surface twice-enveloping enveloping worm hob side
Rear corner surface does not have the status of automatic grinding method, explores a kind of numerical control of Double-conical-surface twice-enveloping enveloping worm hob side relief
Method for grinding, with realize that margin width of the left and right sides of each cutter tooth from tooth top to tooth root be consistent and the margin width of each cutter tooth and
The numerical control grinding of the equal Double-conical-surface twice-enveloping enveloping worm hob side relief of side relief angle is processed, and is Double-conical-surface twice-enveloping
The extensive use of enveloping worm pair provides key technology and supports.
Summary of the invention
The invention aims to provide a kind of Double-conical-surface twice-enveloping anchor ring worm gear based on four-shaft linkage numerical control machine
The method for grinding of hobboing cutter side relief realizes that margin width of the left and right sides of single cutter tooth from tooth top to tooth root be consistent and each knife
The numerical control grinding of the equal Double-conical-surface twice-enveloping enveloping worm hob side relief of the margin width and side relief angle of tooth is processed.
Include: to reach the technical solution that the purpose of the present invention is taken
The single cutter tooth of Double-conical-surface twice-enveloping enveloping worm hob (9) is by top rear corner surface (1), top land (2), rake face
(3), flank (4), side relief (5) and land (6) are constituted, and the intersection of rake face (3) and land (6) is cutting edge line (7), root
It according to given margin width e, can be obtained land line (8), land line (8) is the intersection of side relief (5) and land (6).
P0It is any point on cutting edge line (7), with P0It is located on land line (8) with the point P on a helix, point P is arrived
P0Distance be margin width e, unit tangent vector of the P point on land line (8) be τs；Plane M crosses point P, and perpendicular to τs；Land
(6) be worm spiral face a part, unit normal vector of the P point on land (6) be ns, then ns⊥τs, and nsIn plane M；
Unit normal vector of the point P on side relief (5) is nH, nHIn plane M, if nsWith nHThe size of angle is side relief angle λ；Rolling
The axis of rotation S of knife (9)1Central point O is vertically intersected on its throat mid-plane NH1, the axis of rotation S of tool apron turntable (10)2
With S1Vertical interlaced, S2With S1Distance be x, S2Be z at a distance from throat mid-plane N, plane E crosses S1And and S2Vertically, it puts down
Face E and S2Intersection point OHd, OHdFor the centre of gyration of tool apron turntable (10), bipyramid grinding wheel (11) is mounted on tool apron turntable (10),
The rotation axis S of bipyramid grinding wheel (11)0Intersection point O, O with plane E are the center of rotation of bipyramid grinding wheel (11), OOHd⊥S0, O arrives
OHdDistance be grinding wheel away from a0, S0Angle with plane E is grinding wheel angle of inclination beta；The origin of lathe is located at OH1Point, lathe B axle and knife
The axis of rotation S of seat turntable (10)2Coaxially, the axis of rotation S of lathe C axis and hobboing cutter (9)1Coaxially, among lathe X-axis and throat
The intersection of plane N and plane E are overlapped, machine Z-axis and hobboing cutter (9) axis of rotation S1It is overlapped；Corner of the tool apron turntable (10) around B axle
ForHobboing cutter (9) is around the corner of C axisTool apron turntable (10) is x, seat of the tool apron turntable (10) along Z axis along the coordinate of X-axis
It is designated as z；If x=a, z=0 are then worked as away from for a in the center of double-cone double-enveloping toroidal worm transmission,When, it is corresponding
As any point P in the production shape conical surface (12) of bipyramid grinding wheel (11) grinding land line (8), grinding wheel is away from a0With grinding wheel angle of inclination beta
It remains unchanged, by the corner for controlling lathe C axisWith the corner of B axleAnd the X axis coordinate of tool apron turntable (10) is controlled simultaneously
X and Z axis coordinate z makes the unit normal vector n for producing the shape conical surface (12) upper point QwWith nHIn parallel, Q point and P point contact and make bipyramid sand
The outer rim for taking turns (11) and the tooth root anchor ring of hobboing cutter (9) are tangent, and bipyramid grinding wheel (11) is around rotation axis S0Rotation, by the production shape conical surface
(12) the P point being ground on land line (8), ensure that the margin width e and side relief angle λ at P point；For the land of single cutter tooth side
Each point is respectively adopted the above method and obtains on line (8)A series of respective values of x and z work out B, C, X and four axis of Z axis connection
Dynamic numerical control program, each point being successively ground on land line (8), can be ground out from tooth top to the consistent land of tooth root margin width e
(6), while the side relief (5) equal to tooth root side relief angle λ from tooth top is obtained；To the left and right two of each cutter tooth on hobboing cutter (9)
Avris rear corner surface is programmed calculating according to the above method, is successively ground the side relief grinding of the left and right sides of each cutter tooth, obtains
From tooth top to the consistent land of tooth root margin width e (6) at left and right sides of to single cutter tooth, while obtaining the margin width e of each cutter tooth
The side relief equal with side relief angle λ is realized the numerical control grinding of Double-conical-surface twice-enveloping enveloping worm hob side relief, is obtained
Double-conical-surface twice-enveloping enveloping worm hob (9).
The invention has the advantages that being ground to Double-conical-surface twice-enveloping enveloping worm hob with bipyramid facet wheel
When cutting, by adjust simultaneously the corner of hobboing cutter, the corner of tool apron turntable, tool apron turntable center relative to hobboing cutter center it is radial away from
Four-axle linked numerical control grinding is carried out from axial distance, realizes margin width one of the left and right sides of single cutter tooth from tooth top to tooth root
The numerical control grinding of the equal Double-conical-surface twice-enveloping enveloping worm hob side relief of the margin width and side relief angle of cause and each cutter tooth
Processing is cut, provides key technology support for the extensive use of double-cone double-enveloping toroidal worm pair.
Detailed description of the invention
Fig. 1 is the single knife-tooth structure schematic diagram of Double-conical-surface twice-enveloping enveloping worm hob；
Fig. 2 is the schematic diagram of arbitrary point P on the production shape conical surface grinding land line of bipyramid grinding wheel；
Fig. 3 is Double-conical-surface twice-enveloping enveloping worm hob on the four-shaft linkage numerical control machine with B, C, X and Z axis
Side relief Principle of Grinding and Cutting figure；
Fig. 4 is the land and side relief nc machining simulation effect of Double-conical-surface twice-enveloping enveloping worm hob entire row cutter tooth
Fruit figure；
Fig. 5 is the land and side relief nc machining simulation effect of the single cutter tooth of Double-conical-surface twice-enveloping enveloping worm hob
Fruit figure；
In figure: 1-top rear corner surface, 2-top lands, 3-rake faces, 4-flanks, 5-side reliefs, 6-lands,
7-cutting edge lines, 8-land lines, 9-hobboing cutters, 10-tool apron turntables, 11-bipyramid grinding wheels, 12-produce the shape conical surface.
Specific embodiment
With reference to the accompanying drawings and examples, specific embodiments of the present invention will be described in further detail.
Double-conical-surface twice-enveloping enveloping worm hob is used for the worm gear of rolling cut double-cone double-enveloping toroidal worm pair, takes double
The parameter of conical surface twice-enveloping enveloping worm are as follows: center is away from a=260mm, transmission ratio i12=8, the head number Z of right-hand worm1=5,
Reference diameter of worm d1=110mm, worm gear tooth number Z2=40, reference circle of wormwheel diameter d2=410mm, bipyramid grinding wheel profile angle
αd=20 °, outer edge radius rd=50mm and top width sa=6mm, diameter grinding wheel angle of inclination beta=30 °, grinding wheel is away from a0=164mm.
According to the principle of double-cone double-enveloping toroidal worm, the spiral shell of Double-conical-surface twice-enveloping enveloping worm hob is processed
Then radial facing opens spiral chip flute, obtain the Double-conical-surface twice-enveloping with rake face (3), flank (4) and cutting edge line (7)
The blank of enveloping worm hob.
Fig. 1 is the single knife-tooth structure schematic diagram of Double-conical-surface twice-enveloping enveloping worm hob.Double-conical-surface twice-enveloping ring
The margin width of face worm gear hob generally takes between 0.1~0.15mm, and in order to preferably observe ground effect, the present embodiment takes land
Wide e=1.0mm.It according to given margin width e, is calculated land line (8), the portion between land line (8) and cutting edge line (7)
Divide and constitutes land (6).If P0It is any point on cutting edge line (7), with P0It is located at land line (8) with the point P on a helix
On, point P to P0Distance be margin width e, unit tangent vector of the P point on land line (8) be τs；Plane M crosses point P, and perpendicular to
τs；Land (6) is a part in worm spiral face, and unit normal vector of the P point on land (6) is ns, then ns⊥τs, and nsFlat
In the M of face；Unit normal vector of the point P on side relief (5) is nH, nHIn plane M, if nsWith nHThe size of angle is behind side
Angle λ=6 °.
Fig. 3 is Double-conical-surface twice-enveloping enveloping worm hob on the four-shaft linkage numerical control machine with B, C, X and Z axis
Side relief Principle of Grinding and Cutting figure.The axis of rotation S of hobboing cutter (9)1Central point O is vertically intersected on its throat mid-plane NH1, knife
The axis of rotation S of seat turntable (10)2With S1Vertical interlaced, S2With S1Distance be x, S2With at a distance from throat mid-plane N be z,
Plane E crosses S1And and S2Vertically, plane E and S2Intersection point OHd, OHdFor the centre of gyration of tool apron turntable (10), bipyramid grinding wheel (11)
It is mounted on tool apron turntable (10), the rotation axis S of bipyramid grinding wheel (11)0Intersection point O, O with plane E are bipyramid grinding wheel (11)
Center of rotation, OOHd⊥S0, O to OHdDistance be grinding wheel away from a0=164mm, S0Angle with plane E is grinding wheel angle of inclination beta；Lathe
Origin be located at OH1Point, the axis of rotation S of lathe B axle and tool apron turntable (10)2Coaxially, the rotating shaft of lathe C axis and hobboing cutter (9)
Line S1Coaxially, lathe X-axis is overlapped with the intersection of throat mid-plane N and plane E, machine Z-axis and hobboing cutter (9) axis of rotation S1Weight
It closes；Tool apron turntable (10) is around the corner of B axleHobboing cutter (9) is around the corner of C axisCoordinate of the tool apron turntable (10) along X-axis
For x, tool apron turntable (10) is z along the coordinate of Z axis；Work as x=a, z=0,When, it is corresponding
As any point P in the production shape conical surface (12) of bipyramid grinding wheel (11) grinding land line (8), grinding wheel is away from a0=
164mm and grinding wheel angle of inclination beta=30 ° remain unchanged, by the corner for controlling lathe C axisWith the corner of lathe B axleAnd simultaneously
The X axis coordinate x and Z axis coordinate z for controlling tool apron turntable (10) make the unit normal vector n for producing the shape conical surface (12) upper point QwWith nHIt is flat
Row, Q point and P point contact, as shown in Fig. 2, and keep the outer rim of bipyramid grinding wheel (11) and the tooth root anchor ring of hobboing cutter (9) tangent, so as to
Guarantee that the production shape conical surface (12) of bipyramid grinding wheel can be ground to the point P on land line (8) close to tooth root；Bipyramid grinding wheel (11) is around certainly
Shaft axis S0Rotation is ground out the P point on land line (8) by the production shape conical surface (12), guarantees margin width e and side relief angle at P point
λ；The above method is respectively adopted to each point on the land line (8) of a cutter tooth side to obtainA series of correspondences of x and z
Value works out B, C, X and the four-axle linked numerical control program of Z axis, and each point being successively ground on land line (8) can be ground out land line
(8), it obtains from tooth top to the consistent land of tooth root margin width e (6), while obtaining the side equal to tooth root side relief angle λ from tooth top
Rear corner surface (5)；The left and right sides rear corner surface of each cutter tooth on hobboing cutter (9) is adjusted according to the above method and numerical control grinding, according to
The left and right sides of the secondary each cutter tooth of grinding, the grinding of the left and right sides land line (8) of each cutter tooth of achievable hobboing cutter (9) obtain
From tooth top to the consistent land of tooth root margin width e (6) at left and right sides of to each cutter tooth, while obtaining the margin width e of each cutter tooth
The side relief (5) equal with side relief angle λ realizes the numerical control grinding of Double-conical-surface twice-enveloping enveloping worm hob side relief,
Obtain Double-conical-surface twice-enveloping enveloping worm hob (9).
Using the process of nc machining simulation software Vericut analog simulation side relief.It is established in Vericut
Four-axle linked Virtual Machine will process the Double-conical-surface twice-enveloping enveloping worm hob hair of helicoid, rake face and rear corner surface
Base is installed on lathe C axis；Bipyramid grinding wheel is installed, grinding wheel is set away from a0=164mm, grinding wheel angle of inclination beta=30 °, in entire relief angle
In the grinding process of face, grinding wheel is away from a0Grinding wheel angle of inclination beta remains unchanged；When the Q point grinding of the production shape conical surface (12) of bipyramid grinding wheel (11)
When the arbitrary point P of land line (8), meet the unit normal vector n for producing point Q on the shape conical surface (12)wWith nHIn parallel, Q point and P point contact
And these three tangent constraint conditions of tooth root anchor ring of the outer rim of bipyramid grinding wheel (11) and hobboing cutter (9), single P point are one group correspondingLand line (8) correspondence of x and z value, the side of single cutter tooth is a series ofX and z value works out B, C, X and Z axis four
Axis linkage numerical control program, from tooth root to tooth top, each point being successively ground on land line (8) can be ground out land line (8)；It is right
The left and right sides rear corner surface of each cutter tooth is adjusted and numerical control grinding according to the above method on hobboing cutter (9), is successively ground each knife
The left and right sides of tooth, the grinding of the left and right sides land line (8) of each cutter tooth of achievable hobboing cutter (9).Double-conical-surface twice-enveloping
The nc machining simulation effect picture of enveloping worm hob entire row cutter tooth as shown in figure 4, single cutter tooth nc machining simulation effect
Figure is as shown in figure 5, realize that margin width of the left and right sides of each cutter tooth from tooth top to tooth root be consistent and the land of each cutter tooth
The numerical control grinding processing of the wide Double-conical-surface twice-enveloping enveloping worm hob side relief equal with side relief angle.
Claims (1)
1. the numerical control grinding method of Double-conical-surface twice-enveloping enveloping worm hob side relief, comprising: Double-conical-surface twice-enveloping ring
The single cutter tooth of face worm gear hob (9) is by top rear corner surface (1), top land (2), rake face (3), flank (4), side relief
(5) it is constituted with land (6), the intersection of rake face (3) and land (6) is cutting edge line (7), according to given margin width e, be can be obtained
Land line (8), land line (8) are the intersection of side relief (5) and land (6)；It is characterized in that, P0It is that cutting edge line (7) is taken up an official post
It anticipates a bit, with P0It is located on land line (8) with the point P on a helix, point P to P0Distance be margin width e, P point is in sword
It is τ with the unit tangent vector on line (8)s；Plane M crosses point P, and perpendicular to τs；Land (6) is a part in worm spiral face, P
Unit normal vector of the point on land (6) is ns, then ns⊥τs, and nsIn plane M；Unit of the point P on side relief (5)
Law vector is nH, nHIn plane M, if nsWith nHThe size of angle is side relief angle λ；The axis of rotation S of hobboing cutter (9)1With its throat
Mid-plane N is vertically intersected on central point OH1, the axis of rotation S of tool apron turntable (10)2With S1Vertical interlaced, S2With S1Distance
For x, S2Be z at a distance from throat mid-plane N, plane E crosses S1And and S2Vertically, plane E and S2Intersection point OHd, OHdFor tool apron
The centre of gyration of turntable (10), bipyramid grinding wheel (11) are mounted on tool apron turntable (10), the rotation axis S of bipyramid grinding wheel (11)0
Intersection point O, O with plane E are the center of rotation of bipyramid grinding wheel (11), OOHd⊥S0, O to OHdDistance be grinding wheel away from a0, S0With it is flat
The angle of face E is grinding wheel angle of inclination beta；The origin of lathe is located at OH1Point, the axis of rotation S of lathe B axle and tool apron turntable (10)2Together
Axis, the axis of rotation S of lathe C axis and hobboing cutter (9)1Coaxially, lathe X-axis is overlapped with the intersection of throat mid-plane N and plane E,
Machine Z-axis and hobboing cutter (9) axis of rotation S1It is overlapped；Tool apron turntable (10) is around the corner of B axleCorner of the hobboing cutter (9) around C axis
ForTool apron turntable (10) is x along the coordinate of X-axis, and tool apron turntable (10) is z along the coordinate of Z axis；If Double-conical-surface twice-enveloping ring
X=a, z=0 are then worked as away from for a in the center of surface-worm transmission,When, it is correspondingWhen the production shape conical surface of bipyramid grinding wheel (11)
(12) when any point P being ground on land line (8), grinding wheel is away from a0It is remained unchanged with grinding wheel angle of inclination beta, by controlling lathe C axis
CornerWith the corner of B axleAnd the X axis coordinate x and Z axis coordinate z of tool apron turntable (10) are controlled simultaneously, make to produce the shape conical surface
(12) the unit normal vector n of upper point QwWith nHIn parallel, Q point and P point contact and make the outer rim and hobboing cutter (9) of bipyramid grinding wheel (11)
Tooth root anchor ring it is tangent, bipyramid grinding wheel (11) is around rotation axis S0Rotation, by the P in the production shape conical surface (12) grinding land line (8)
Point ensure that margin width e and side relief angle λ at P point；Each point on the land line (8) of single cutter tooth side is respectively adopted
The method of stating obtainsA series of respective values of x and z work out B, C, X and the four-axle linked numerical control program of Z axis, are successively ground sword
It with each point on line (8), can be ground out from tooth top to the consistent land of tooth root margin width e (6), while obtain from tooth top to tooth
Root side relief angle λ equal side relief (5)；To the right and left side relief of each cutter tooth on hobboing cutter (9) according to the above method into
Row program calculation is successively ground the side relief grinding of the left and right sides of each cutter tooth, obtains at left and right sides of single cutter tooth from tooth
The consistent land of tooth root margin width e (6) is pushed up, while the side relief angle that the margin width e and side relief angle λ for obtaining each cutter tooth are equal
Face obtains Double-conical-surface twice-enveloping enveloping worm hob (9).
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| CN109176172B (en) * | 2018-10-31 | 2020-04-14 | 中车戚墅堰机车车辆工艺研究所有限公司 | Method and device for repairing and grinding hob |
| CN113175501B (en) * | 2021-05-18 | 2022-04-08 | 成都理工大学 | Plane secondary enveloping ring surface worm gear and manufacturing method thereof |
| CN113941741B (en) * | 2021-11-16 | 2022-08-05 | 天津理工大学 | Processing method of homogenization allowance curved surface of multi-head double-conical enveloping worm |
| CN114147419B (en) * | 2021-12-08 | 2022-08-19 | 天津理工大学 | Design method of side rear angle surface of torus worm gear hob |
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| CN86107189A (en) * | 1986-10-13 | 1987-05-20 | 冶金部西安冶金机械厂 | The processing method of ring surface-worm with envelop curved face |
| CN2414866Y (en) * | 2000-04-11 | 2001-01-17 | 刘晓荣 | Rotating and swinging spectial double grinding head for grinding plane second enveloping ring surface worm tooth face |
| CN101791772B (en) * | 2010-01-29 | 2011-09-21 | 浙江大学 | Numerical control relief grinding method for enveloping worm hob and machine tool for realizing same |
| CN102275016B (en) * | 2011-07-22 | 2013-03-06 | 重庆大学 | Double-side accurate grinding method and equipment for toothed surface of toroid enveloping worm |
| CN102310347A (en) * | 2011-09-05 | 2012-01-11 | 台州金剑机械制造有限公司 | Seven-axis numerical control grinding and shaping equipment for dual conical surface and double enveloping worm |
| CN104440419B (en) * | 2014-11-04 | 2016-09-21 | 中国农业大学 | The numerical control grinding and machining method of planar secondary enveloping ring surface worm gear hob side relief |
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