CN1084440A - Processing method of point-contact enveloping ring surface worm wheel pair - Google Patents
Processing method of point-contact enveloping ring surface worm wheel pair Download PDFInfo
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- CN1084440A CN1084440A CN 92111916 CN92111916A CN1084440A CN 1084440 A CN1084440 A CN 1084440A CN 92111916 CN92111916 CN 92111916 CN 92111916 A CN92111916 A CN 92111916A CN 1084440 A CN1084440 A CN 1084440A
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- worm gear
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Abstract
The present invention is a kind of processing method of point-contact enveloping ring surface worm wheel pair.This method can obtain insensitive some Contact Transmission of foozle, worm gear tool precision height, and the cutting edge number is many, worm gear stock-removing efficiency height, flank of tooth kish is few, and the seating time that forms normal contact is short.Principal character is that worm screw and hobboing cutter are used plane and the cutter grinding of the revolving body conical surface respectively, and female plane and female coupling tap face are tangent along specific bus.The installation parameter β on female plane
0, R
0Need satisfy specific mathematical expression.Change the semiapex angle γ of conical surface instrument, can process the different some Contact Transmission of contact condition, to be suitable for different machine tool accuracy and technical merits.
Description
The present invention relates to a kind of processing method of point-contact enveloping ring surface worm wheel pair.
The contacting state of tooth surface and the kinematic accuracy of line contact enveloping ring surface worm wheel pair are very sensitive to foozle.When having foozle, contacting state of tooth surface contacts (being actually a kind of scraping of the flank of tooth in edge) by the bias that the line contact becomes at flank of tooth edge, make worm gear produce kinematic error simultaneously, and the kinematic error curve is discontinuous, causes the shock and vibration in the worm gear operation process.In the production process of actual worm gear, foozle is inevitably, thus the line that comes into operation contact enveloping ring surface worm wheel pair at first all or light or important place the bias contact of flank of tooth edge takes place.Only the running (running-in) in a period of time could realize the line contact afterwards.When the flank of tooth contacts serious bias, usually cause the flank of tooth failure damage in the running.In order to reduce the sensitiveness of line contact ring surface worm wheel pair to foozle, people compare with the line Contact Transmission according to a Contact Transmission, to the insensitive principle of foozle, have proposed new type of belt drive, i.e. point-contact enveloping ring surface worm wheel pair.The bias contact of flank of tooth edge still can not take place in this new type worm wheel pair when having foozle, reduced the possibility of flank of tooth failure damage in the runing condensation procedure.This point-contact enveloping ring surface wheel set after running after a while, can realize the line contact between the flank of tooth.
1979 and Japanese scholar in 1981 herd the research report " research of some contact ring surface-worm transmission (the 1st newspaper and the 2nd newspaper) " of the people such as filling and delivering (can collection of thesis the 45th volume rolling up No. 417 for No. 400 and the 47th referring to Japanese mechanics), what touch upon is exactly two kinds of forms of the novel transmission of this class, and this also is the prior art of publishing settled the present the most approaching with the present invention.The worm screw of these two kinds of worm gears is by a flat tool generate, and the cutter of cutting worm gear becomes by a straight line tooth shape, different just these straight line swords concrete set-up mode and the position is set.Worm gear is formed by above-mentioned worm gear Tool in Cutting.The worm gear of these two kinds of forms all can be implemented in the some contact in the flank of tooth profile, when having foozle, still can keep in touch the relatively stable of a position, has reached the purpose that proposes this type of belt drive.But because the worm gear cutter of these two kinds of worm gears is all formed by a line (rather than face), can not meet the grinding of generating principle, cutter can only be made fabricated, installs by artificial.The result: the one, the worm gear tool precision is low, and the 2nd, the cutting edge number of cutter is few, and makes trouble.Worm gear precision by the cutting of above-mentioned worm gear cutter is low, and the tooth surface kish is many, need the running-in through the long period could realize normal engaged, and the stock-removing efficiency of worm gear is also very low.
The objective of the invention is to overcome above-mentioned the deficiencies in the prior art, a kind of processing method of point-contact enveloping ring surface worm wheel pair is provided, the worm gear Tool in Cutting sword number that is obtained by this method is many, the precision height, cut worm gear flank of tooth kish few, it is short to reach the required seating time of normal contact, cuts the efficient height of worm gear simultaneously.
In order to achieve the above object, the present invention has done improvement to the processing method of initial point contact enveloping ring surface worm wheel pair, and the worm gear cutter that former cause straight line tooth shape is become makes the hobboing cutter by single-revolution body cone generate into, uses this hobboing cutter machining worm wheel again; For guaranteeing to realize that with the worm screw of reason plane generate point contacts by the worm gear of hobboing cutter cutting, make two curved surfaces (plane is a kind of of curved surface) tangent installing of plane and conical surface instrument, and make the installation parameter of the flat tool of generate worm screw satisfy specific mathematic(al) representation along specific bus.
Concrete processing method of the present invention is as follows with the principle accompanying drawings that the formation point contacts:
Fig. 1 is a schematic diagram of using the face grinding wheel machining worm on gear-hobbing machine.
Fig. 2 is a schematic diagram of processing hobboing cutter on gear-hobbing machine with revolving body conical surface emery wheel.
Fig. 3 is that the position of the tool plan and the instrument revolving body conical surface concerns schematic diagram.
Fig. 4 is for forming the principle schematic of some contact.
Fig. 5 is the contact condition figure of the worm gear that obtained by processing method of the present invention.
Set up three rectangular coordinate system Oe-e
1e
2n，O
o-X
oY
oZ
o，O
s-X
sY
sZ
s。O
e-e
1e
2N is fixed on the flat tool; Oo-X
oY
oZ
oBe fixed on the rotary table; Os-X
sY
sZ
sBe fixed on the conical surface instrument.
1. the processing of worm screw: worm screw can be processed at gear-hobbing machine. As shown in Figure 1, the worm screw workpiece is placed on the gear hobbing machine knife frame, and around workpiece rotating shaft [1] with angular velocity omega1Rotate, the bistrique that face grinding wheel [2] is housed is placed on the gear hobbing machine worktable, and with workbench rotating shaft [3] with angular velocity omegaoRotate. ω1/ω
o=i is the gearratio of worm gear, ω1Value and processing plane enveloping worm wheel identical when secondary, A is the centre-to-centre spacing of worm gear. Adjust bistrique, make emery wheel plane [2] become β with workbench rotating shaft [3]oAngle, and with the horizontal plane that contains worm screw rotating shaft [1] in take the workbench rotating shaft as the center of circle, RoFor the circle of radius tangent. The adjustment method is installed thus just can processes worm tooth-surface.
2. the processing of worm gear hob: worm gear hob is available gear-hobbing machine processing also. As shown in Figure 2, the hobboing cutter workpiece is contained on the gear hobbing machine knife frame, and around knife rest rotating shaft [4] with angular velocity omega1Rotate, the bistrique that conical surface emery wheel [5] is housed be placed on the gear hobbing machine worktable and with workbench rotating shaft [3] with angular velocity omegaoRotate. Adjust conical surface emery wheel, take the workbench rotating shaft as the center of circle, arrive distance R between the extended line of this bus with this center of circle in the extended line that makes bus parallel with horizontal plane on the revolving body conical surface and the horizontal planebFor the circle of radius tangent, and make revolving body conical surface emery wheel [5] around this horizontal bus clockwise or inhour turn over the β angle.
3. the processing of worm gear: hobboing cutter is contained on the gear-hobbing machine knife rest, and the worm gear workpiece is placed on the workbench, can process the worm gear flank of tooth by the cutting process of common anchor ring worm gear.
The bistrique of used band plane and revolving body conical surface emery wheel in the processing of above-mentioned worm screw and hobboing cutter is structurally identical with the used bistrique of processing plane and toroid enveloping worm with cone generatrix respectively.For guaranteeing the contact of worm and worm wheel origination point, the parameter beta of grinding worm and worm gear hob
o, R
oWith β, R
bBetween must satisfy specific mathematic(al) representation so that the revolving body conical surface instrument [5] of the tool plan of generate worm screw [2] and generate worm gear hob is tangent along the cone element that with the angle parameter is u, as shown in Figure 3.
The principle of the worm gear origination point contact that processing method of the present invention obtains as shown in Figure 4.When with flat tool [2] generate worm tooth-surface [6], plane [2] and worm tooth-surface [6] are along L
1The contact of generation line.When with the basic flank of tooth of conical surface instrument [5] generate hobboing cutter [7], the conical surface instrument [5] and the basic flank of tooth of hobboing cutter [7] are along L
2The contact of generation line.According to generating principle, the worm gear flank of tooth [8] of hobboing cutter [7] cutting can with the conical surface [5] along L
2The contact of realization line.Because plane [2] is tangent along bus T with the conical surface [5], then L
1With L
2On T, intersect at Q, when worm tooth-surface [6] and the worm gear flank of tooth [8] mating engagement, contact at intersection point Q place origination point.
The relevant machined parameters of the present invention determines by following described method: during the processing hobboing cutter, the half cone drift angle γ of revolving body conical surface emery wheel [5] (see figure 2) has determined that near the applying degree contact point and worm gear are to the sensitivity of error between the worm and gear flank of tooth, γ is big more, the applying degree is good more, but susceptibility is high more, and vice versa.The span of γ is 45 °～89 °, is preferably 60 °～85 °.The bottom surface diameter d of conical surface emery wheel is decided according to the size of worm gear centre-to-centre spacing.The installation parameter β and the R of the revolving body conical surface emery wheel during processing hobboing cutter
bDistribute according to line contact toroid enveloping worm with cone generatrix Tooth Surface contact wire, choose by tentative calculation.Tool plan is directly related with the distribution of contact point on the flank of tooth with the tangent position of the instrument conical surface, this tangent determining positions is seen Fig. 3 in angle parameter u(), choosing of u can be by tentative calculation, sees that the middle part whether distribution of contact point on the worm gear flank of tooth is positioned at this flank of tooth decides.For guaranteeing to realize some contact, the adjustment parameter beta during face grinding wheel generate worm tooth-surface
oAnd R
o(see figure 1) must satisfy specific mathematic(al) representation.This mathematic(al) representation can be pushed away by following method:
As shown in Figure 3, the method for plane [2] vows to be exactly that the method for the conical surface [5] on tangent bus vows that the conical surface [5] is at coordinate system O
s-X
sY
sZ
sIn can be expressed as:
The method of the conical surface [5] is vowed and can be expressed as:
Formula (2) is transformed to coordinate system O
o-X
oY
oZ
oMiddle (see figure 2) gets:
n
xo＝sinγcosγcosu-sinγcosγ （3）
n
yo＝-cos
2γcosucosβ-cosγsinβsinu-sin
2γcosβ
n
xo＝cos
2γcosusinβ-cosγcosβsinu+sin
2γsinβ
Workbench rotating shaft [3] (is Z
oAxle) direction vector is:
Plane [2] is to the mounted angle β of workbench rotating shaft [3]
oFor:
Parameters R
oCan determine as follows: as shown in Figure 1, R
oBe exactly plane [2] and the Z of generate worm screw
oThe intersection L on=0 plane is to the rotary table center O
oThe distance of (0,0,0) point.According to Fig. 3, plane [2] can be expressed as:
(6) in the formula, ζ and ξ are the parameter of plane [2].
(6) formula is converted into coordinate system O
s-X
sY
sZ
sIn:
x
ps＝-ξsinu+ξsinγcosu （7）
y
ps＝ξcosu+ξsinγsinu
z
ps＝ξcosγ
(7) formula is converted into coordinate system O
o-X
oY
oZ
oIn:
x
po＝x
pssinγ+z
pscosγ+h （8）
y
po＝-x
pscosγcosβ-y
pssinβ+z
pssinγcosβ-R
b
z
po＝x
pscosγsinβ-y
pscosβ-z
pssinγsinβ
With (7) formula substitution (8) formula, plane [2] can be expressed as:
x
po＝C
x1ζ+C
x2ξ+C
x3
y
po＝C
y1ζ+C
y2ξ+C
y3（9）
z
po＝C
z1ζ+C
z2ξ+C
z3
(9) in the formula:
C
x1＝-sinusinγ
C
x2＝-sin
2γcosu+cos
2γ
C
x3＝h
C
y1＝sinucosγcosβ-cosusinβ
C
y2＝-sinγcosγcosucosβ-sinγsinusinβ+cosγsinγcosβ
C
y3＝-R
b
C
z1＝-sinucosγsinβ-cosucosβ
C
z2＝sinγcosucosγsinβ-sinγsinucosβ-cosγsinγsinβ
C
z3＝0
Make Z in (9) formula
Po=0, can get the equation of intersection L:
x
po＝K
xξ+K
xc（10）
y
po＝K
yξ+K
yc
(10) in the formula:
K
x＝C
x2-C
x1C
z2/C
z1
K
y＝C
y2-C
y1C
z2/C
z1
K
xc＝C
x3-C
x1C
z3/C
z1
K
yc＝C
y3-C
y1C
z3/C
z1
Intersection L is to the workbench center O
oThe distance of (0,0,0) point:
Above-mentioned about in various:
β
o-face grinding wheel is for the inclination angle of rotary table rotating shaft;
R
oPlane of-generate worm screw [2] and Z
oThe intersection L on=0 plane is to the rotary table center O
oThe distance of (0,0,0) point.
The unit vector of-rotary table rotor shaft direction;
The half cone drift angle of γ-revolving body conical surface emery wheel;
The angle parameter of the u-decision revolving body conical surface and tangent position, plane;
The established angle that β-revolving body conical surface turns over around self the bus parallel with horizontal plane;
R
bBus extended line in conical surface emery wheel [5] horizontal plane of-generate worm gear hob is to the rotary table center O
oDistance (promptly forming radius of circle).
The summit O of the conical surface emery wheel of h-generate worm gear hob
sTo the distance of above-mentioned formation circle with the points of tangency of the extended line of the interior bus of horizontal plane.
Press β
oAnd R
oAdjust face grinding wheel [2], the worm screw that then processes just can realize that point contacts with worm gear.
The worm gear cutting tool of the point-contact enveloping ring surface worm wheel pair that the present invention provides can be by the generating principle Precise Grinding, cutter can be made solid hob, simple for production, the cutting edge number is many, the precision height, the stock-removing efficiency height of worm gear, cut worm gear flank of tooth kish few, it is short to reach required seating time of normal contact.In addition,, just can change the curvature difference between the tool plan and the instrument conical surface, thereby adjust the contact condition between the worm and gear flank of tooth because the worm and worm wheel hobboing cutter respectively by plane and conical surface generate, changes the half cone drift angle of the conical surface.When γ approached 90 °, the conical surface and plane were very approaching, and the contact condition of the planar double-enveloping worm that the contact condition between the worm and gear flank of tooth contacts with line is very approaching, and vice versa.This shows that the processing method that the present invention proposes can process the different some contact ring surface worm wheel pair of contacting state of tooth surface, to adapt to different machining tool precision and technical merit by changing the half cone drift angle γ of conical surface emery wheel.
Specific embodiments of the invention are described as follows:
Given the centre-to-centre spacing A=100mm of hourglass worm pair, gearratio i=41/1.
A. at first determine the machined parameters R of worm gear hob according to the mesh analysis of conical surface twice-enveloping hourglass worm pair
b=30mm, β=12.5 °, d=150mm, γ=70 °, h=2.81mm.And according to Fig. 2 and aforementioned method with conical surface emery wheel generate worm gear hob, press above-mentioned parameter and select emery wheel, adjust gear-hobbing machine and bistrique, process worm gear hob.
B. parameters u=3.2 ° of decision plane and the tangent position of the conical surface are determined in the distribution of finding the solution contact point of gear surface according to the mesh analysis of this processing method gained point gearing transmission, the quality that distributes according to contact point.Again by above-mentioned about the installation parameter β of known parameters by the tool plan when trying to achieve machining worm of method shown in this explanation by formula (5) and formula (11)
o=11.4 °, R
o=29.5mm.And press Fig. 1 and aforementioned method adjustment gear-hobbing machine and bistrique with face grinding wheel generate worm screw, grind worm screw.
C. on gear-hobbing machine, press the method rolling cut worm gear of common rolling cut anchor ring worm gear.
Process the worm gear that obtains as stated above, can realize the some contact of the flank of tooth.The contacting state of tooth surface of present embodiment as shown in Figure 5.Two solid lines on the worm gear flank of tooth among the figure are two contact point trace line (track that the contact point motion is passed by) of contact simultaneously, and the direction of arrow is the direction of motion of contact point.Each instantaneous two point that exists on every pair of engaging tooth of the worm gear that processing method of the present invention as seen from the figure obtains contacts.Dotted line encloses the flank of tooth gap of part less than 5 * 10 among the figure
-4Radian (promptly this part more arbitrarily, when worm gear turns over less than 5 * 10 with respect to worm screw
-4During the additional rotation angle of radian, this Dian Chu gap disappears, and comes in contact).When after running (running-in) after a while, the contact zone on the flank of tooth will be similar to part that dotted line encloses.
Claims (1)
1, a kind of processing method of point-contact enveloping ring surface worm wheel pair, step comprise the procedure of processing of existing some contact ring surface worm wheel pair:
(1) with flat tool generate worm screw;
(2) make the worm gear cutting tool;
(3) with worm gear cutting tool cutting worm gear;
(4) determine the installation site and the parameter of worm gear machining tool.
Feature of the present invention is:
(2.1) during the grinding worm gear hob, the hobboing cutter workpiece is contained on the gear-hobbing machine knife rest, around hobboing cutter rotating shaft [4] with angular velocity omega
1Rotate.
(2.2) during the grinding worm gear hob, it is 45 °～89 ° that half cone drift angle γ will be housed, and the bistrique that is preferably 60 °～85 ° revolving body conical surface emery wheel [5] is placed on the gear hobbing machine worktable, and with workbench rotating shaft [3] with angular velocity omega
0Rotate.
(2.3) before the grinding worm gear hob, adjust revolving body conical surface emery wheel [5], make in the extended line of bus parallel on the revolving body conical surface and this horizontal plane with rotary table center 0 with horizontal plane
oBeing the center of circle, is radius R with this center of circle to the distance between the extended line of this bus
bCircle tangent, and make this take turns [5] around this horizontal bus clockwise or inhour turn over the β angle.
When (4.1) the revolving body conical surface instrument of flat tool of generate worm screw and generate worm gear hob was installed, flat tool should be that the cone element of u is tangent along angle parameter with conical surface instrument, and the installation parameter β when making face grinding wheel generate worm tooth-surface
0, R
0Satisfy following mathematic(al) representation:
In formula (1) formula:
In (3) formula:
(5)n
x0=sinγcosγcosu-sinγcosγ
n
yo=-cos
2γcosucosβ-cosγsinβsinu-sin
2γcosβ
n
zo=cos
2γcosusinβ-cosγcosβsinu+sin
2γsinβ
In (2) formula:
K
x=C
x2-C
x1C
z2/C
z1
K
y=C
y2-C
y1C
z2/C
z1
(6)K
xc=C
x3-C
x1C
z3/C
z1
K
yc=C
y3-C
y1C
z3/C
z1
In (6) formula:
C
x1=-sinusinγ
C
x2=-sin
2γcosu+cos
2γ
C
x3=h
C
y1=sinucosγcosβ
C
y2=-sinγcosγcosucosβ-sinγsinγsinusinβ+cosγsinγcosβ
C
y3=-R
b
C
z1=-sinucosγsinβ-cosucosβ
C
z2=sinγcosucosγsinβ-sinγsinucosβ-cosγsinγsinβ
C
z3=0
Above-mentioned about in various:
β
o-face grinding wheel is for the inclination angle of rotary table rotating shaft;
R
oPlane of-generate worm screw [2] and Z
O=the intersection L on plane to the rotary table center O
oThe distance of (0,0,0) point.
The half cone drift angle of γ-revolving body conical surface emery wheel;
The angle parameter of the u-decision revolving body conical surface and tangent position, plane;
The established angle that β-revolving body conical surface turns over around self the bus parallel with horizontal plane;
R
bBus extended line in conical surface emery wheel [5] horizontal plane of-generate worm gear hob is to the rotary table center O
oDistance (promptly forming radius of circle).
The summit O of the conical surface emery wheel of h-generate worm gear hob
sTo the distance of above-mentioned formation circle with the points of tangency of the extended line of the interior bus of horizontal plane
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 92111916 CN1084440A (en) | 1992-09-23 | 1992-09-23 | Processing method of point-contact enveloping ring surface worm wheel pair |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 92111916 CN1084440A (en) | 1992-09-23 | 1992-09-23 | Processing method of point-contact enveloping ring surface worm wheel pair |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN1084440A true CN1084440A (en) | 1994-03-30 |
Family
ID=4945616
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN 92111916 Pending CN1084440A (en) | 1992-09-23 | 1992-09-23 | Processing method of point-contact enveloping ring surface worm wheel pair |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN1084440A (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1057720C (en) * | 1998-01-15 | 2000-10-25 | 重庆大学 | Processing tech. of worm gears and abrasive wheel for working worm |
| CN102091980A (en) * | 2010-12-05 | 2011-06-15 | 天津大学 | Method for processing rotating member with convex function-shaped profile outline through creep feed end face grinding |
| CN104385084A (en) * | 2014-10-15 | 2015-03-04 | 天津大学 | Five-axis grinding method for variably-formed base circle planar envelope convex surface workpiece |
| CN112024999A (en) * | 2020-09-07 | 2020-12-04 | 中国农业大学 | Method for generating point contact ring surface worm gear pair by involute spiral double-generating surface |
-
1992
- 1992-09-23 CN CN 92111916 patent/CN1084440A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1057720C (en) * | 1998-01-15 | 2000-10-25 | 重庆大学 | Processing tech. of worm gears and abrasive wheel for working worm |
| CN102091980A (en) * | 2010-12-05 | 2011-06-15 | 天津大学 | Method for processing rotating member with convex function-shaped profile outline through creep feed end face grinding |
| CN102091980B (en) * | 2010-12-05 | 2012-11-07 | 天津大学 | Method for processing rotating member with convex function-shaped profile outline through creep feed end face grinding |
| CN104385084A (en) * | 2014-10-15 | 2015-03-04 | 天津大学 | Five-axis grinding method for variably-formed base circle planar envelope convex surface workpiece |
| CN112024999A (en) * | 2020-09-07 | 2020-12-04 | 中国农业大学 | Method for generating point contact ring surface worm gear pair by involute spiral double-generating surface |
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