CN105134907B - A kind of big registration inside engaged gear tooth Shape Design method based on circular arc path of contact - Google Patents

A kind of big registration inside engaged gear tooth Shape Design method based on circular arc path of contact Download PDF

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CN105134907B
CN105134907B CN201510471206.7A CN201510471206A CN105134907B CN 105134907 B CN105134907 B CN 105134907B CN 201510471206 A CN201510471206 A CN 201510471206A CN 105134907 B CN105134907 B CN 105134907B
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tooth
curve
contact
gear
conjugate
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CN105134907A (en
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王延忠
李圆
吴向宇
赵鹏坤
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Beihang University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/17—Toothed wheels
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/0826—Novikov-Wildhaber profile

Abstract

The invention discloses a kind of big registration inside engaged gear tooth Shape Design method based on circular arc path of contact, the path of contact of this method design is the circular arc of one section of connection internal gear, external gear teeth tip circle intersection point and pitch circle intersection point, by theory of plane engagement, the Conjugate Equation on corresponding relation between path of contact and inside engaged gear conjugate curve is set up；Construction meets the conjugate curve of circular arc path of contact, and the conjugate curve is internal gear teeth top tooth curve and external gear teeth top tooth curve；The tooth root flank profil being conjugated with tooth top tooth curve is constructed using conjugate principle, and internally Gear Root flank profil carries out correction of the flank shape；Design the easement curve between gear teeth tooth root flank profil and root circle.The present invention has the advantages that registration is big, and registration is big more than 2 times compared with involute profile, and multiple gear teeth participate in engagement, and bearing capacity is strong, and dynamic impulsion is small, while relative slippage is low, lubricating condition is good；The problem of interference of tooth profiles will not being produced, gear parameter design is freer.

Description

A kind of big registration inside engaged gear tooth Shape Design method based on circular arc path of contact
Technical field
The invention belongs to travelling gear design field, it is related to a kind of big registration internal messing based on circular arc path of contact Form of gear tooth design method.
Background technology
Inside engaged gear transmission is gear-driven important type of belt drive, transmits power and the motion of equidirectional, and outer Meshing gear is compared, it is possible to decrease power loss caused by being slided because conjugate curve is relative, with transmission efficiency, is overlapped Degree is big, bearing capacity intensity the advantages of, be widely used in the transmission systems such as vehicle.The tooth form of inside engaged gear is mainly involute Tooth and cycloid tooth, wherein involute teeth obtain widest application with its easy to manufacture and interchangeability, form industrial mark Standard, but involute is limited by tooth form in design, is easily interfered, and minimum number of teeth is defined in the design, sometimes It must not be avoided interference with without conjugating processing, registration is also limited by the number of teeth, design pressure angle.
With the appearance and the raising to the requirement of inside engaged gear transmission performance of novel drive structure, to inside engaged gear Design proposes higher requirement：Higher bearing capacity and design freedom.The bearing capacity for improving gear passes through two aspects Realize：Improve single-tooth strength or increase simultaneously participates in the number of teeth of engagement, when using involute teeth or cycloid tooth, repaiied by the gear teeth Shape has reached the limit of inside engaged gear performance boost to improve single-tooth strength or registration, meanwhile, by existing tooth The limitation of shape, in inside engaged gear design, involute can only be avoided interference with by changing pressure angle and modification coefficient, be reduced The free degree of inside engaged gear design.Current scholar has carried out substantial amounts of research to external gear pump design, it is proposed that many new Type tooth form, but in inside engaged gear design aspect, lack corresponding research.
The content of the invention
The present invention for involute inside engaged gear design in the number of teeth, modification coefficient limitation, the problems such as registration is small there is provided A kind of big registration inside engaged gear tooth Shape Design method based on circular arc path of contact, this method is realizes that inside engaged gear is big Registration, using the circular arc of connection internal gear and external gear teeth tip circle intersection point to node as design path of contact, according to face gear The theory of engagement, establishes the Conjugate Equation on path of contact and inside engaged gear conjugate curve corresponding relation, so as to obtain The conjugate curve equation expression formula of circular arc path of contact is met, the expression formula describes the tooth top tooth of internal gear and external gear Wide curve；Then, according to conjugate principle, the tooth root tooth curve that construction is conjugated with tooth top tooth curve；To avoid at 2 points simultaneously Contact, internal Gear Root tooth curve has carried out correction of the flank shape；Finally, internal gear and external gear teeth rooted tooth exterior feature and root circle are devised Transition arc.The inside engaged gear path of contact that this method is obtained is made up of two parts, the circular arc path of contact of part design, interior Gear teeth tips tooth curve participates in the path of contact engaging with external gear teeth top tooth curve, and another part is the tooth of internal gear The wide path of contact engaged with the participation of external gear teeth root tooth curve of apical tooth, compared with involute internal messing flank profil, its registration is more Greatly, simultaneously because internal-external gear tooth top flank profil conjugation, external gear teeth rooted tooth exterior feature and internal gear teeth apical tooth exterior feature conjugation, internal gear tooth root Flank profil have passed through correction of the flank shape, will not produce gear tooth profile interference, the free degree is bigger in design.
The technical solution adopted by the present invention is：A kind of big registration inside engaged gear tooth Shape Design based on circular arc path of contact Method, it is characterised in that：This method using one section of connection internal gear, external gear teeth tip circle intersection point and pitch circle intersection point circular arc as interior The design path of contact of meshing gear, by theory of plane engagement, sets up on path of contact and inside engaged gear conjugate curve Between corresponding relation Conjugate Equation；According to Conjugate Equation, construction meets the conjugate curve of circular arc path of contact, the conjugation tooth Wide curve is internal gear teeth top tooth curve and external gear teeth top tooth curve；Utilize conjugate principle construction and tooth top tooth curve The tooth root flank profil of conjugation, and internally Gear Root flank profil carries out correction of the flank shape；Design the transition between gear teeth tooth root flank profil and root circle Curve.This method is comprised the following steps that：
Step 1: the circular arc of selection connection internal gear, external gear teeth tip circle intersection point and pitch circle intersection point is used as inside engaged gear Design path of contact, according to theory of plane engagement, set up the Conjugate Equation of inside engaged gear transmission, the equation has reacted path of contact On point and inside engaged gear conjugate curve on corresponding relation between conjugate point；
Step 2: construction meets the internal-external gear conjugation tooth top tooth curve of design circular arc path of contact.Equation of engaged line Bring Conjugate Equation into, obtain circular arc path of contact and the corresponding relation formula of conjugate curve, by coordinate transform and calculating, obtain The conjugate curve of circular arc path of contact is met, because circular arc path of contact is located between outside circle and pitch circle, only tooth top flank profil Engagement is participated in, therefore obtained conjugate curve is internal gear teeth top tooth curve and external gear teeth top tooth curve；
Step 3: the tooth root tooth curve of construction internal gear and external gear.The tooth top flank profil of known internal gear and external gear Curve and relative motion relation between them, according to conjugate principle, are constructed outer with internal gear teeth top tooth curve conjugation respectively The tooth root tooth curve of gear and the internal gear teeth rooted tooth exterior feature with external gear teeth apical tooth exterior feature conjugation；When internal gear tooth top flank profil and Tooth root flank profil is engaged with the tooth top flank profil of external gear simultaneously, will be occurred at 2 points and is contacted simultaneously, internal Gear Root flank profil is repaiied Shape, it is to avoid two-point contact in the engagement process of flank profil；
Step 4: the easement curve between design internal-external gear gear teeth tooth root and root circle.Determine that gear teeth tooth root flank profil is bent Line is tangential at end points, and construction is with root circle and tooth root tooth curve in the tangent arc transition curve of end points.
The advantage of the present invention compared with prior art is：
Proposed by the invention is a kind of tooth, is that one section of path of contact therein is connection outside circle the characteristics of prominent The circular arc of intersection point and pitch circle intersection point, has the advantages that registration is big, and registration is big more than 2 times compared with involute profile, multiple The gear teeth participate in engagement, and bearing capacity is strong, and dynamic impulsion is small, while relative slippage is low, lubricating condition is good；Due to internal gear tooth top Flank profil is conjugated with external gear teeth apical tooth exterior feature, and internal gear teeth apical tooth is wide to be conjugated with external gear teeth rooted tooth exterior feature, interior flank profil tooth root flank profil warp Correction of the flank shape is crossed, the problem of will not producing interference, gear parameter design is freer.With multi-axis linkage numerical control milling, grinding The raising of precision, solution is provided for the processing and manufacturing of tooth.
Brief description of the drawings
Fig. 1 is a kind of new big registration inside engaged gear tooth Shape Design method flow diagram of the present invention；
Fig. 2 is the design diagram of circular arc path of contact；
PP0For connection outside circle intersection point and the circular arc of pitch circle intersection point；
The path of contact schematic diagram of internal-external gear before Fig. 3 practices Buddhism or Taoism；
PP0For the wide path of contact of external gear teeth apical tooth exterior feature and internal gear teeth apical tooth, P0P' is external gear teeth rooted tooth exterior feature and internal gear Tooth top flank profil path of contact, P0P " is internal gear teeth rooted tooth exterior feature and the wide path of contact of external gear teeth apical tooth before correction of the flank shape；
Fig. 4 internal gear teeth root profile modification schematic diagrames；
Γa2Wide, the Γ for internal gear teeth apical toothf2Wide, the Γ ' for internal gear teeth rooted tooth before correction of the flank shapef2For internal gear tooth root after correction of the flank shape Flank profil；
Transition arc organigram of Fig. 5 tooth roots flank profil to root circle；
Circle O0For with tooth root flank profil ΓfJustify tangent circle, T with flank profil0、TfRespectively point of contact, t is in T0That locates is tangential；
Fig. 6 external gears and internal gear monodentate shape；
Reference implication in figure：
1,6-outside circle；4,9-transition arc curve；5,10-root circle；2-external gear teeth apical tooth is wide；3-external tooth Gear teeth rooted tooth is wide；7-internal gear teeth apical tooth is wide；8-internal gear teeth rooted tooth is wide；
Fig. 7 internal-external gears global shape and path of contact.
Embodiment
The embodiment to the inventive method elaborates below in conjunction with the accompanying drawings.
A kind of flow chart such as Fig. 1 of the big registration inside engaged gear tooth Shape Design method based on circular arc path of contact of the present invention It is shown, include circular arc the setting as inside engaged gear of (1) selection connection internal gear, external gear teeth tip circle intersection point and pitch circle intersection point Path of contact is counted, using theory of plane engagement, being total on path of contact and inside engaged gear conjugate curve corresponding relation is set up Yoke equation；(2) construction meets the internal gear teeth top tooth curve and external gear teeth top tooth curve of circular arc path of contact；(3) construct The tooth root flank profil being conjugated with tooth top tooth curve and internally Gear Root flank profil progress correction of the flank shape；(4) design gear teeth tooth root flank profil with The easement curve of root circle.This method is comprised the following steps that：
Step 1: the circular arc path of contact of design connection internal gear, external gear teeth tip circle intersection point and pitch circle intersection point, sets up conjugation Equation and on path of contact and inside engaged gear conjugate curve corresponding relation.
During gear drive, when being slided with contact point in path of contact, the track marked on gear coordinate system Exactly participate in meshed gears tooth curve.To improve the registration of inside engaged gear, connection internal gear, external gear teeth tip circle Intersection point and the circular arc of pitch circle intersection point as inside engaged gear path of contact.As shown in Fig. 2 P is internal gear and external gear teeth tip circle Intersection point, P0It is internal gear and external gear pitch circle intersection point, PP0It is the center of circle in YfTie point P and P on axle0One section of circular arc, according to several What principle, in that context it may be convenient to solve circular arc PP0Radius R.Obtained circular arc path of contact is in coordinate system SfOn equation expression formula For：
Wherein, xf, yfIt is meshing point P in rectangular coordinate system SfOn coordinate value.Because circular arc path of contact be located at internal gear and Between the outside circle and pitch circle of external gear, only tooth top flank profil participates in engagement, so the conjugation constructed by the circular arc path of contact Flank profil is the tooth top flank profil of internal gear and external gear.The path of contact is that flank profil and internal gear left side flank profil is engaged on the right side of external gear Line, it is however generally that the gear teeth of gear are symmetrical, and its path of contact is on reference axis YfSymmetrically.
Set up rectangular coordinate system S1:{O1,X1,Y1, S2:{O2,X2,Y2Be connected respectively with external gear and internal gear, coordinate It is Sf:{Of,Xf,YfIt is fixed coordinate system, and OfFor node, then OfOn gear engagement line.IfIt is respectively outer The rotational angle of gear and internal gear, gearratio isz2、z1The respectively tooth of external gear and internal gear Number, R1、R2The respectively pitch radius of external gear and internal gear.
If path of contact is in rectangular coordinate system SfOn vector expression be：
In Meshing Process of Spur Gear, contact point is slided in path of contact and along path of contact, and contact point is in rectangular coordinate system S1And S2The track of upper slip is exactly the tooth curve of external gear and internal gear.Conjugate point in path of contact is in rectangular coordinate system S1 On the vector representation of track be：
Wherein, M1fFor rectangular coordinate system SfTo S1Transformation matrix of coordinates.
Conjugate point in path of contact is in rectangular coordinate system S2On the vector representation of track be：
Wherein, M2fFor rectangular coordinate system SfTo S1Transformation matrix of coordinates.
According to face gear mesh theory, common normal of the conjugate tooth profile curve at point of contact and centre of gyration line O1O2Phase Hand over and the line is divided into two sections of O2P and O1P, the ratio of two line segments is gear ratio.Then obtain the normal vector of point P in path of contact In rectangular coordinate system SfOn vector representation be：
In rectangular coordinate system S1On point P normal vector be expressed as：
The mesh equation of the external gear obtained according to formula (7), (8) is：
Drawn from above formula：
Formula (10) integration is obtained：
The expression formula for the angular displacement for obtaining internal gear according to formula (2) is：
Circular arc Equation of engaged line formula (1) is brought into formula (11) and formula (12) is obtained：
Corresponding relation on formula (13), the point in (14) expression circular arc path of contact and conjugate curve between contact point.
Step 2: construction meets the internal gear of circular arc path of contact and the conjugation tooth top tooth curve of external gear
Wushu (13), (14) bring the expression formula that formula (3), (5) have obtained internal gear and external gear teeth top tooth curve into：
Step 3: simultaneously internally Gear Root flank profil carries out correction of the flank shape to the internal-external gear tooth root flank profil of construction and tooth top flank profil conjugation
The tooth top tooth curve of known external gear and internal gear is respectively Γa1、Γa2, it is assumed that it is wide bent with internal gear teeth apical tooth Line Γa2The external gear teeth root tooth curve of conjugation is Γf1, with external gear teeth top tooth curve Γa1The external gear teeth rooted tooth of conjugation Wide curve is Γf2, then external gear teeth root tooth curve Γf1Equation can be expressed as：
Wherein, M12For coordinate system S1To coordinate system S2Transformation matrix of coordinates,Formula (18) is engagement side Journey, according to Principles of Gear Connection, mesh equation can be expressed as：
Wherein, NfFor in fixed coordinate system SfIn unit normal vector,It is conjugate profiles relatively fast at contact point Spend, their equation expression formula is：
Wushu (19), (20) bring equation of meshing (18) into and carry out abbreviation and obtain：
Formula (21) has two solutions：
First solutionIt is identical with formula (14), demonstrate the wide tooth top tooth with external gear of internal gear teeth apical tooth Wide curve is conjugation；
Second solutionThere is provided bent with the tooth root flank profil of the external gear of internal gear teeth apical tooth exterior feature conjugation Line.Bring formula (24) into external gear teeth rooted tooth exterior feature that formula (15) obtains being conjugated with internal gear teeth apical tooth exterior feature The equation expression formula of curve is：
Internal gear teeth apical tooth is wide and path of contact of external gear teeth root tooth curve is：
Then the path of contact is that one section of radius is R-R2Circular arc, parameter θ (0<θ<θmax), then the path of contact at node with The circular arc path of contact of design is tangent.
Equally, the internal gear teeth root tooth profile curve equation expression formula with external gear teeth top tooth curve conjugation is：
External gear teeth apical tooth is wide and path of contact of internal gear teeth root tooth curve is：
Shown in Fig. 3, PP0It is the connection outside circle intersection point of design and the circular arc path of contact of pitch circle intersection point, internal gear teeth apical tooth Wide Γa2With external gear teeth apical tooth exterior feature Γa1In path of contact PP0Upper engagement, P0P' is internal gear teeth apical tooth exterior feature Γa2With external gear tooth root Flank profil Γf1Path of contact, P0P " is internal gear teeth rooted tooth exterior feature Γf2With external gear teeth apical tooth exterior feature Γa1Path of contact, work as internal gear Tooth root flank profil Γf2Γ is engaged with external gear teeth apical tooth exterior featurea1In P0When being engaged on P ", the tooth top flank profil Γ of internal geara2With external tooth The tooth top flank profil Γ of wheela1Also in path of contact PP0Upper engagement, to avoid at 2 points while engagement is, it is necessary to internal Gear Root flank profil Γf2 Carry out correction of the flank shape.
Internal gear teeth root profile modification is in Γf2On the basis of carry out correction of the flank shape, as shown in figure 4, setting T (xf2,yf2) it is internal gear Tooth root tooth curve Γf2On a bit, it arrive internal gear center O2Line and reference axis YfAngle be δ, then have relational expression：
Then for internal gear teeth root tooth curve Γf2On node P0There is δ=0, the T that sets up an office is around internal gear center O2Counterclockwise An angle is rotated to point T', T' to internal gear center O2Line and reference axis YfAngle δ ' (δ) be to be passed on δ dullness Increase continuous function, and δ ' (0)=0, then the tooth root tooth curve Γ ' formed by T'f2It is continuous and in node P0With tooth top Tooth curve Γa2It is tangent, for the sake of simplicity, δ ' (δ)=δ/2 can be taken.
Step 4: the easement curve between design internal-external gear tooth root flank profil and root circle
Determine gear teeth tooth root tooth curve in end points T0The tangential t at place, construction and root circle and tooth root tooth curve Γf The tangent arc transition curve T of end points0Tf., as shown in Figure 5.
Concrete example explanation below：
With number of teeth z1=35, z2=53 exemplified by m=4 inside engaged gear, briefly explains the embodiment of this method.Its His parameter is ha1=4mm, hf1=5mm, ha2=4mm, hf2=5mm.
Step 1: the circular arc path of contact of design is one section of connection external gear and internal gear teeth tip circle intersection point and pitch circle intersection point Circular arc, the radius for obtaining circular arc according to geometrical principle is R=84.7273mm, radian θmax=0.6932rad, its equation expression formula For：
Wherein, the span of parameter θ is 0≤θ≤0.6932.
The pitch radius of external gear and internal gear is R1=z1× m/2, R2=z2× m/2, is engaged according to circular arc is derived by Corresponding relation on point and conjugate curve on line between contact point：
Wherein, formula (31), (32) illustrate when external gear and internal gear conjugate profiles are rotated respectively from initial position Radian, by the point (x in the circular arc path of contact of designf,yf) engagement.
Step 2: the construction of internal gear and external gear teeth top tooth curve
According to formula (15) and (16), the tooth top tooth profile curve equation of internal gear and external gear is,
Wherein, θ span is 0≤θ≤0.6932.Tooth form point above is as shown in table 1.
The wide tooth form point of the external gear teeth apical tooth of table 1
The wide tooth form point of the internal gear teeth apical tooth of table 2
Step 3: the tooth root tooth curve of construction internal gear and external gear
According to formula (25), the external gear teeth root tooth profile curve equation being conjugated with internal gear teeth top tooth curve is expressed as：
Internal gear teeth apical tooth is wide and path of contact of external gear teeth root tooth curve is：
With external gear teeth top tooth curve be conjugated internal gear teeth root tooth profile curve equation expression formula be：
Wherein, θ span is 0≤θ≤0.6932.Point T (x on internal gear teeth rooted tooth exterior featuref2,yf2) arrive internal gear Center O2Line and reference axis YfAngle be δ：
Point T to internal gear center O2Apart from r0For：
When point T is around internal gear center O2An angle is rotated to point T', this time point T' and internal gear center O2Line and seat Parameter XfThe angle of formation is δ ', and δ ' is δ monotonic increase continuous function：
δ ' (δ)=5 δ2 (40)
Then internal gear teeth rooted tooth exterior feature curve is expressed as after correction of the flank shape：
Internal gear teeth rooted tooth exterior feature after practicing Buddhism or Taoism will not be engaged with external gear teeth apical tooth exterior feature.The obtained wide tooth of external gear teeth rooted tooth As shown in table 2, the tooth form point before and after internal gear teeth root profile modification is as shown in table 3 for form point.
The external gear teeth rooted tooth of table 3 exterior feature tooth form point
Tooth form point before and after the internal gear teeth root profile modification of table 4
Step 4: the easement curve between design gear teeth tooth root and root circle
The end points of external gear teeth root tooth curve is T10(0.3180, -66.4937), in end points T10Tangential direction t, outside The root circle center O of gear1(0,0), radius rf1=65mm, by geometry solving, is obtained in point T10Tangential direction is t= (0.1349,0.9909) and with being cut in point T outside external gear root circlef1One section of circular arc T10Tf1Center O10(2.0653,- 66.7315), radius r10=1.7634mm, T10With external gear center O1Line and reference axis X1 included anglemin= 1.5335rad, Tf1With external gear center O1Line and reference axis X1 included anglemaax=3.0063rad, then external gear tooth root Flank profil is to the transition arc equation expression formula of root circle：
The end points of internal gear teeth root tooth curve is T20(- 1.092, -109.7977), in end points T20Tangential direction t, The root circle center O of external gear2(0,0), radius rf2=111mm, by geometry solving, is obtained in point T20Tangential direction is t= (- 0.3896, -0.9210) and it is inscribed within point T with internal gear root circlef2One section of circular arc T20Tf2Center O20(-2.8503,- 109.0541), radius r20=1.9087mm, T20With internal gear center O2Line and reference axis X2 included anglemin=- 1.5969rad, Tf2With internal gear center O2Line and reference axis X2 included anglemaax=-0.4002rad, then internal gear teeth The wide transition arc equation expression formula to root circle of rooted tooth is：
External gear and internal gear teeth rooted tooth are wide as shown in table 5 to the point on the easement curve of root circle.
The external gear of table 5 and internal gear easement curve tooth form point
As shown in Figure 6 and Figure 7, Fig. 6 is external gear and internal gear monodentate shape to obtained external gear and internal gear teeth, is divided Be not made up of outside circle, tooth top flank profil, tooth root flank profil, transition arc curve and root circle, wherein external gear teeth apical tooth it is wide with it is interior Gear eats apical tooth exterior feature engagement, and its path of contact is the circular arc PP of design0, external gear teeth rooted tooth is wide and internal gear teeth apical tooth wheel is engaged, Path of contact is circular arc P0P ", the overall tooth form of external gear and internal gear as shown in Figure 7 and path of contact.
Non-elaborated part of the present invention belongs to techniques known.
It is described above, it is only part embodiment of the present invention, but protection scope of the present invention is not limited thereto, times What those skilled in the art the invention discloses technical scope in, the change or replacement that can be readily occurred in should all be covered Within protection scope of the present invention.

Claims (1)

1. a kind of big registration inside engaged gear tooth Shape Design method based on circular arc path of contact, it is characterised in that：This method handle One section connects the circular arc of internal gear, external gear teeth tip circle intersection point and pitch circle intersection point as the design path of contact of inside engaged gear, leads to Theory of plane engagement is crossed, the Conjugate Equation on corresponding relation between path of contact and inside engaged gear conjugate curve is set up； According to Conjugate Equation, construction meets the conjugate curve of circular arc path of contact, and the conjugate curve is that internal gear teeth apical tooth is wide Curve and external gear teeth top tooth curve；The tooth root flank profil being conjugated with tooth top tooth curve is constructed using conjugate principle, and internally Gear Root flank profil carries out correction of the flank shape；The easement curve between gear teeth tooth root flank profil and root circle is designed, this method specific steps are such as Under：
Step 1: circular arc the setting as inside engaged gear of selection connection internal gear, external gear teeth tip circle intersection point and pitch circle intersection point Path of contact is counted, the center of circle of described circular arc, according to theory of plane engagement, is built on internal gear and the line of external gear centre of pitch circle The Conjugate Equation of vertical inside engaged gear transmission, the equation has been reacted on point and inside engaged gear conjugate curve in path of contact Corresponding relation between conjugate point；
Step 2: construction meets the internal-external gear conjugation tooth top tooth curve of design circular arc path of contact, Equation of engaged line is brought into Conjugate Equation, obtains circular arc path of contact and the corresponding relation formula of conjugate curve, by coordinate transform and calculating, is met The conjugate curve of circular arc path of contact, because circular arc path of contact is located between outside circle and pitch circle, only tooth top flank profil is participated in Engagement, therefore obtained conjugate curve is internal gear teeth top tooth curve and external gear teeth top tooth curve；
Step 3: the tooth root tooth curve of construction internal gear and external gear, it is known that the tooth top tooth curve of internal gear and external gear And relative motion relation between them, according to conjugate principle, the external gear that construction is conjugated with internal gear teeth top tooth curve respectively Tooth root tooth curve and wide with the internal gear teeth rooted tooth of external gear teeth apical tooth exterior feature conjugation；When the tooth top flank profil and tooth root of internal gear Flank profil is engaged with the tooth top flank profil of external gear simultaneously, will be occurred at 2 points and is contacted simultaneously, internal Gear Root flank profil carries out correction of the flank shape, keeps away Exempt from two-point contact in the engagement process of flank profil；
Step 4: the easement curve between design internal-external gear gear teeth tooth root and root circle, determines that gear teeth tooth root tooth curve exists Tangential at end points, construction is with root circle and tooth root tooth curve in the tangent arc transition curve of end points.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1033509A2 (en) * 1999-03-02 2000-09-06 Sankyo Oilless Industry, Inc. Roller chain sprocket
CN1419064A (en) * 2002-08-28 2003-05-21 霍江明 Less teeth number large coincidence gear
WO2007013373A1 (en) * 2005-07-28 2007-02-01 Musashi Seimitsu Kogyo Kabushiki Kaisha Method of designing gear using cad system, and gear
CN102777570A (en) * 2012-08-07 2012-11-14 厦门理工学院 Mutually meshed gears and tooth outline design method thereof
CN103671825A (en) * 2013-11-30 2014-03-26 陕西秦川精密数控机床工程研究有限公司 Double-eccentricity cycloid cylindrical gear

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1033509A2 (en) * 1999-03-02 2000-09-06 Sankyo Oilless Industry, Inc. Roller chain sprocket
CN1419064A (en) * 2002-08-28 2003-05-21 霍江明 Less teeth number large coincidence gear
WO2007013373A1 (en) * 2005-07-28 2007-02-01 Musashi Seimitsu Kogyo Kabushiki Kaisha Method of designing gear using cad system, and gear
CN102777570A (en) * 2012-08-07 2012-11-14 厦门理工学院 Mutually meshed gears and tooth outline design method thereof
CN103671825A (en) * 2013-11-30 2014-03-26 陕西秦川精密数控机床工程研究有限公司 Double-eccentricity cycloid cylindrical gear

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