CN1201119A - Curve-bevel-teeth gear pair - Google Patents

Abstract

The present invention discloses a conical gear pair with curved teeth. It is designed and manufactured by adopting the principle of variable pitch cone radius and radial-tangential modification, and is characterized by that under the condition of that the crossed axis angle sigma is not changed, the normal pitch cone radius R is changed into R=R0+delta R, the central distance a0v of correspondent big-end equivalent gear is changed into av=a0v+delta a, at this moment, the equivalent gear is changed into gear with variable central distance. When delta a is greater than 0, its central distance becomes long, said gear becomes gear with long central distance, and when the delta a is less than 0, its central distance becomes short, said gear becomes gear with short central distance. Said invented conical gear pair possesses the advantages of high strength, long sevice life, small volume, low noise and simple production process, etc.

Description

A kind of spiral bevel gear pair

The present invention relates to the transmission that a kind of mechanical transmission fields is used, be particularly useful for transmitting the bent tooth awl tooth commentaries on classics pair that two-phase is returned rotating shaft load.

At present countries in the world come processing industry to be shaped on nearly ten kinds with the spiral bevel gear profile of tooth with rack cutter and generating method, pass through only 4～5 kinds of the profile of tooth systems of competing and surviving and occupying the international market, and Here it is:

1, the Gleason profile of tooth system of U.S.'s Jackie Gleason factory;

2, the Oerlikon profile of tooth system of Switzerland Ao Likang factory;

3, the Klingelnerg profile of tooth system of German crin Bei Ge factory;

4, former Soviet Union З н и м с profile of tooth system;

5, the Captov profile of tooth system of Russian Saratov factory.

Also have some countries and architect,, some parameter is had change slightly, but still belong to similar with reference on the basis of above-mentioned profile of tooth system.

But above-mentioned these profile of tooth systems have adopted standard cone apart from R without any exception.Spiral bevel gear, that is:

R ₀＝0.5d ₂/sind′ ₂……(1)

D in the formula ₂-bevel gear wheel standard pitch circle (equaling pitch circle) diameter

D ' ₂-bevel gear wheel pitch circle awl (partly) angle

Standard cone has reference center distance a apart from the virtual gear pair of spiral bevel gear pair _Ov, standard pitch circle (that is pitch circle is because this moments two, the circle overlapped) radius of establishing virtual gear is r _V1With r _V2, then have:

a _ov＝r _v1+r _v2??……(2)

Adopt the virtual gear pair of reference center distance, its advantage is that the crossed axis angle ∑ does not change (consulting Fig. 1), and adopts zero transmission in the displacement design.If the modification coefficient of small gear and gearwheel is X ₁With X ₂, then itself and be:

X _∑＝X ₁+X ₂＝0??……(3)

Adopt the shortcoming of the virtual gear pair of reference center distance to be: the transmission meshing performance is restricted, and for example: comprehensive strength is lower, volume big (the routine Gleason system regulation number of teeth and Z ₁+ Z ₂〉=40～50), noise higher (limited by contact ratio, for example during β＞30 °, some contact ratio ε _r＜3), gear ratio can not be excessive, U≤10 etc.These shortcomings have only secondary could the elimination of the change of employing centre distance virtual gear.But become the change (consulting Fig. 2) that centre distance virtual gear pair can cause crossed axis angle.Therefore classify the forbidden zone as, not popular with users, Here it is, and the reason that becomes centre distance virtual gear pair is not adopted in present countries in the world.

The objective of the invention is to design high strength, long lifetime, volume is little, noise is low, and a kind of spiral bevel gear pair that just can make with existing cutting equipment.

Purpose of the present invention is reached by following technological scheme:

A kind of spiral bevel gear pair adopts to become pitch cone radius and radial shift and tangent modification principle design and manufacturing, it is characterized in that under crossed axis angle ∑ permanence condition standard knot circular cone pitch cone radius R ₀Change into R, R=R ₀+ Δ R, corresponding large end face virtual gear centre distance a _OvBecome a _v, a _v=a _Ov+ Δ a

In the formula, R ₀=0.5d ₂/ sind ' ₂

a _ov＝r _v1+r _v2＝mZ _vm

Δa＝(tgd′ ₁+tgd′ ₂)·ΔR≠0

This moment, virtual gear became in the change apart from gear, when

Δ a＞0 o'clock, centre distance is elongated, becomes long centre distance gear

Δ a＜0 o'clock, centre distance shortens, and becomes short central apart from gear.

Purpose of the present invention can also further be realized by following technical measures:

Aforesaid change pitch cone radius spiral bevel gear pair, the pitch circle awl separates with calibration circular cone (being the cutting circular cone) two awls, and two awl sizes are different after separating, and virtual gear pitch cone radius r ' and the proportional K of its pitch cone radius r: $K=\frac{r_{v1}^{\′}}{r_{v1}}=\frac{r_{v2}^{\′}}{r_{v2}}=\frac{a_v}{a_{\mathrm{ov}}}\≠1$

Aforesaid gear pair, addendum h is by the overlap arc X of small gear and gearwheel ₁With X ₂Determine:

ha _1，2＝(ha ^*+X _1，2)·m

Work as X _1,2＞0, ha _1,2＞full-height tooth is risen ha ^*During m, be long addendum.

Work as X _1,2＜0, ha _1,2＜full-height tooth is risen ha ^*During m, be short addendum, four kinds of combining forms of three classes correspondingly arranged this moment:

1) long--long addendum, X ₁＞X ₂＞0, positive drive design X ₁+ X ₂〉=0,

2) long--short addendum, X ₁＞0＞X ₂, positive drive design X ₁+ X ₂＞0,

3) long--short addendum, X ₁＞0＞X ₂, negative transmission design X ₁+ X ₂＜0,

4) short--short addendum, X ₂＜X ₁＜0, negative transmission design X ₁+ X ₂＜0.

Aforesaid gear pair, the pitch circle pressure angle α ' that becomes centre distance end face virtual gear is unequal with pressure angle of graduated circle α, and the difference of its involute function is:

Δinvα＝invα′-invα＝X _btgα/Zvm≠0

Aforesaid gear pair, its system tooth technology is to machine on the spiral bevel gear lathe of existing processing criterion pitch cone radius with straight blade rack shape cutter and generating method.

Advantage of the present invention is: because under retainer shaft angle of cut ∑ permanence condition, adopt and become pitch cone radius to constitute change centre distance virtual gear pair, novel bevel gear pair by the manufacturing of four modification coefficient optimal design has high strength, and the long lifetime, volume is little, noise is low, big speed ratio and do not increase obviously advantage such as construction equipment investment.

Figure of description:

Fig. 1 standard cone is apart from bevel gear and the secondary schematic representation of end face virtual gear thereof.

Fig. 2 standard cone causes the schematic representation that the crossed axis angle ∑ changes apart from bevel gear after becoming centre distance.

Fig. 3 becomes the pitch cone radius bevel gear and end face is worked as quantitative change centre distance gear pair, and centre distance strengthens figure.

Fig. 4 becomes the pitch cone radius bevel gear and end face is worked as quantitative change centre distance gear pair, and centre distance is dwindled figure.

Fig. 5 radial shift Closed Graph.

Fig. 6 tangent modification Closed Graph.

Below in conjunction with Figure of description embodiment of the present invention are further described:

As can be seen, under the constant condition of crossed axis angle, change pitch cone radius from Fig. 3 and Fig. 4, the pitch cone radius that makes spiral bevel gear is by reference value R ₀Change into R, establishing the change amount is Δ R, then has

R=R ₀+ Δ R ... (4) in the formula, R ₀=0.5d ₂/ sind ' ₂

d ₂-bevel gear wheel standard pitch circle (standard R ₀Standard pitch circle equals pitch circle) diameter

D ' ₂The corresponding large end face virtual gear of-bevel gear wheel pitch circle awl half-angle sub-center is apart from a by standard _OvChange into a _v, change into Δ a, then have

a _v=a _Ov+ Δ a ... (5) in the formula, a _Ov=r _V1+ r _V2=mZ _Vm

Δa＝(tgδ′+tgδ′ ₂)·ΔR≠0

M-large end face virtual gear transverse module, or represent with diametral pitch P=25.4/m

Z _VmThe average number of teeth of-virtual gear, i.e. Z _Vm=0.5 (Z _V1+ Z _V2),

r _V1, r _V2-be little virtual gear, big virtual gear reference radius.

Z _V1, Z _V2-be little virtual gear, the big virtual gear number of teeth,

δ ' ₁, δ ' ₂-be little virtual gear, big virtual gear pitch circle awl half-angle,

At this moment, virtual gear has changed over and has become the centre distance gear.When

Δ a＞0 o'clock, centre distance elongated (extending out) becomes long centre distance gear, as shown in Figure 3.

Δ a＜0 o'clock, centre distance shorten (in contract), become short central apart from gear, as shown in Figure 4.

In Fig. 3,

Be standardization equivalent Gear center distance, when along pitch cone radius OP.Outwards (away from vertex of a cone O) prolongs one section symbol

After, the centre distance of the expansion virtual gear pair of formation is

, cross the big end working pitch point of standardization equivalent gear P ₀Outwards make two rotational axis OO ₀₁With OO ₀₂Parallel lines, with enlarge after the centre distance line Intersect at Q respectively ₁, and Q ₂Point then has:

Δa＝Q ₁Q ₂＝(tgδ′ ₁+tgδ′ ₂)·ΔR＞0……(6)

Connect OQ ₁With OQ ₂, ∠ O is then arranged ₁OQ ₁=small gear calibration cone angle δ ₁＜δ ' ₁, ∠ O ₂OQ ₂=gearwheel calibration cone angle δ ₂＜δ ' ₂

In like manner, for gear pair as shown in Figure 4, must dwindle the virtual gear pair of centre distance, its centre distance change amount (reduction volume) is; $\mathrm{\&Delta;a}=\stackrel{\&OverBar;}{Q_1{Q}_2}=({\mathrm{tg}{\mathrm{\&delta;}}^{\&prime;}}_1+{\mathrm{tg}{\mathrm{\&delta;}}^{\&prime;}}_2)\&CenterDot;R<0\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\left(7\right)$

For the Equidep (see figure 3), cross Q ₁, Q ₂Do and OP ₀Parallel lines, hand over axis in O ' ₁, O ' ₂, ∠ Q then ₁O ' ₁O ₁With ∠ Q ₂O ' ₂O ₂Be small gear and gearwheel pitch cone (partly) angle δ ₁, δ ₂, and δ ₁=δ ' ₁, δ ₂=δ ' ₂

After the pitch cone radius of spiral bevel gear changes (extend out or in contract), formed change centre distance gear pair, the pitch cone of this moment separates with pitch cone, it is different to separate back two awl sizes, constitute the sizes of two cover bevel gears, this feature-pitch cone that just is different from the virtual gear of the permanent center distance that constant pitch cone radius constitutes overlaps with pitch cone.If the virtual gear radius of two cover different sizes is pitch cone radius r _v' and the pitch cone radius r _v, their ratio is K, then has $K=\frac{r_{v1}^{\&prime;}}{r_{v1}}=\frac{r_{v2}^{\&prime;}}{r_{v2}}=\frac{R}{R-\mathrm{\&Delta;R}}=\frac{a_v}{a_{\mathrm{ov}}}\&NotEqual;1\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\left(8\right)$

By a _v=a _Ov+ Δ a then has

Δ a=(K-1) a _Ov(9) establish the overlap arc that becomes centre distance virtual gear pair and be X ₁With X ₂, itself and X _∑=X ₁+ X ₂, the centre distance change amount of virtual gear pair $Y=\frac{\mathrm{\&Delta;a}}{m}=X_{\mathrm{\&Sigma;}}-\mathrm{\&delta;}\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\left(10\right)$

In the formula, δ-addendum coefficient of alteration, tool value＜X _∑/ 10, be used for the corrected tooth overall height, make the pairing virtual gear do theoretic no sideshake engagement.

Work as X _∑＞0 o'clock, Δ a＞0 (long centre distance virtual gear) claimed the positive drive design,

Work as X _∑＜0 o'clock, Δ a＜0 (short central is apart from virtual gear) claimed negative transmission design.

From as can be seen, work as X here _∑=0 o'clock, Δ a=0 (permanent center is apart from virtual gear), Δ R=0 were called zero transmission design, and the industrial spiral bevel gear system in all countries in the world all adopts this zero transmission design.Therefore, various countries are existing in this sense uses profile of tooth system, can be regarded as a kind of special case of the present invention (boundary conditions).

In addition by overlap arc X ₁With X ₂, determined the addendum ha of virtual gear _1,2, promptly

ha _1，2＝(ha ^*+X _1，2)·m……(11)

Addendum coefficient ha ^*The acquisition of can from design handbook, tabling look-up.

Work as X _1,2＞0 o'clock, ha _1,2＞ha ^*M (full-height tooth is risen) is called long addendum

Work as X _1,2＜0 o'clock, ha _1,2＜ha ^*M is called short addendum

Four kinds of combining forms of three classes are correspondingly arranged:

Length-long addendum	Length-weak point addendum		Weak point-weak point tooth is high in advance
				X 1＞X 2＞0?X 1＞0＞X 2	X 2＜X 1＜0
????I	????II	???III	???IV
				Positive drive X 1+X 2＞0		Negative transmission X 1+X 2＜0

Overlap arc X ₁, X ₂Selection, should guarantee that at first profile of tooth is intact, can mesh this primary condition continuously, it can use X ₁With X ₂Represent (consulting Fig. 5) for the border of the Closed Graph of right angled coordinates, comprise among the figure: 1, zero transmission design (X _∑=X ₁+ X ₂=0) boundary line OG, it and X-axis are at 45, and G is the coordinate position of Jackie Gleason (Gleason) tooth system.For example: (X is designed for positive drive in the upper right of OG line ₁+ X ₂＞0) zone, the left bottom of OG is negative transmission (X ₁+ X ₂＜0) zone, two zones can be crossed G and make two and coordinate axes X ₁, X ₂Parallel straight line is divided.

2, owing to a little less than small gear than gearwheel is, choose X ₁＞X ₂, promptly cross initial point and do 45 ° and represent with skew lines AOH.

3, guarantee to mesh continuously, choose ε along gear-profile _α〉=1, be the boundary promptly with curve B C.

4, cooperate the gear teeth when tooth top and tooth root engagement, not have interference phenomenon, promptly cross addendum coefficient point F (X ₁=-X ₂=ha ^*) and L (X ₁=-ha ^*=-X ₂) two cross curve LM of some work, LI and FJ, FC.

5, guarantee that tooth top does not come to a point Sa 〉=0, i.e. DE curve.

6, guarantee that tooth root does not have undercut, i.e. X ₁〉=X _1min, X ₂〉=X _2minArticle two, straight line.

Above-mentioned curve forms two radial shift allowable districts allowable, and two districts are divided into four little districts allowable, i.e. 1 (ABCD on Fig. 5 by coordinate axes again ₁A ₁) district, II (A ₁D ₁BEG) district, III (O ₂GKK ₁) district and IV (HO ₂K ₁J) district.The positive drive design is distinguished with I, II, negative transmission design district III, IV.

Among the figure: ε _α-be the contact ratio curve

U-for waiting sliding ratio curve

Y-be iso-intensity curve

Slip ratio curves such as η-be

Sa-addendum boundary

X _1,2min-overlap arc minimum value boundary line

δ ₂-node area bidentate is to the meshing zone.

On the basis that overlap arc is selected for use, can adopt tangential (along the tangent line of transverse tooth thickness) displacement.Its modification coefficient (Xt ₁And X _T2) selection, should guarantee at first that tooth top does not come to a point, tooth root is only thin, on the not too big basis of whole depth change, can be in order to X _T1, X _T2For representing the boundary line of the Closed Graph (see figure 6) of right angled coordinates.It comprises:

1, tooth top does not come to a point: the thick S of tooth top _A1,2〉=0.3m is curve A B and CD.

2, the whole depth change is little :-0.5≤X _T2≤ 0.5, i.e. straight line BC and AD.

Among the figure: σ-outside pitch line length coefficient of alteration curve.

X _T1And X _T2---be respectively the tangent modification coefficient of equivalent small gear and gearwheel.

X _{The t ∑}=X _T1+ X _T2Be tangential coefficient sum

After adopting change pitch cone radius spiral bevel gear pair, with four modification coefficient X ₁X ₂And X _T1, X _T2Be variable, under Fig. 5 and D boundary conditions shown in Figure 6 (i.e. the boundary line of two cover Closed Graph), need by design, can mesh quality (curve) to transmission and be optimized design, to obtain high strength, long lifetime, volume is little, noise is low spiral bevel gear transmission.For example:

1, improves pitting corrosion resistant performance: make node area be in biconjugate tooth engaging position, promptly

δ ₂ ^*=0.15～0.25, little C point on Fig. 5 for example ... (12)

2, improve antiwear property: sliding ratio coefficient U ₁With U ₂Balance, promptly

U ₁≈ U ₂B point on Fig. 5 for example ... (13)

3, improve anti-folded tooth ability: form factor Y ₁With Y ₂Minimum and close, promptly

Y ₁≈ CY ₂E point on Fig. 6 for example ... (14)

4, improve antiscuffing capacity: the slip ratio coefficient is minimum and close, promptly

η ₁≈ η ₂Fig. 5 a point for example ... (15)

5, improve contact ratio, make stable drive, promptly

Profile contact ratio ε _a〉=1.6, total contact ratio ε ₁〉=2～3 d points on Fig. 5 for example ... (16)

6, the whole depth that maintains the standard, promptly

Outside pitch line length coefficient of alteration σ=0, for example e point on Fig. 6 ... (17)

7, improve the comprehensive strength of the gear teeth: promptly adopt the comprehensive selection of above-mentioned relative curve,

E point on a, b, d point and Fig. 6 on Fig. 5 for example.

8, obtain minimum teeth number and: make overlap arc

X ₁+ X ₂〉=X _1min+ X _2min＞0 (see figure 5) ... (18)

9, obtain maximum gear ratio: U＞10 ... (19)

In addition, become two cover displacement (overlap arc and X in the centre distance virtual gear pair _∑With tangent modification coefficient and X _{The t ∑}) comprehensive, further make to become pitch cone radius spiral bevel gear pair and have best comprehensive engagement quality, this is that present standard cone is apart from the inaccessiable advantage of bevel gear pair.For example:

1, high comprehensive strength (high anti-spot corrosion, anti-broken teeth, anti-bonding, antiwear property) and long lifetime, the present invention can obtain routine b point by the various intersection point in formula (11)～(19) in the II district on figure.

2, low noise steady transmission can be obtained routine e point by formula (15) in the IV district on Fig. 5.

3, small volume can be obtained by formula (18) in the I district on Fig. 5.

4, big retarding ratio can obtain in I, the II district on Fig. 5.

Modification coefficient after comprehensive can be decomposed into the comprehensive overlap arc X along the tooth depth direction _bWith comprehensive tangent modification coefficient X along the transverse tooth thickness direction _s

X _b＝X _∑+0.5X _t∑/tgα≠0……(20)

X _s＝2X _∑tgα+X _t∑≠0……(21)

Because the change of the secondary pitch cone radius of spiral bevel gear also changes corresponding large end face virtual gear centre distance thereupon.Therefore, become centre distance virtual gear pair and have pitch circle and standard pitch circle two cover pressure angles (being α ' and α), the difference of its involute function is

Δinvα＝invα′-invα＝X _htgα/Zvm≠0……(22)

In the formula, α '-pitch circle awl pressure angle

α-pressure angle of graduated circle

The average tooth number Z vm=(Z of Zvm-virtual gear _V1+ Z _V2)

Gear pair of the present invention, its system tooth technology is with straight blade rack shape cutter and generating method, machines on existing processing criterion pitch cone radius spiral bevel gear working machine tool.[by formula (1)～(22) create] do not need to do in addition very easily popularization of frock and equipment investment, event.

The present invention is not limited to embodiment, and its protection domain is defined by the claims.

Claims (6)

1, a kind of spiral bevel gear pair adopts to become pitch cone radius and radial shift and tangent modification principle design and manufacturing, it is characterized in that under crossed axis angle ∑ permanence condition standard knot circular cone pitch cone radius R ₀Change into R, R=R ₀+ Δ R, corresponding large end face virtual gear centre distance a _0vBecome a _v, a _v=a _0vIn+Δ a the formula: R ₀=0.5d ₂/ sin δ ' ₂

a _0v＝r _v1+r _v2＝mZ _vm

Δ a=(tg δ ' ₁+ tg δ ' ₂) Δ R ≠ 0 this moment, virtual gear becomes the centre distance gear, when

Δ a＞0 o'clock, centre distance is elongated, becomes long centre distance gear

Δ a＜0 o'clock, centre distance shortens, and becomes short central apart from gear

2, gear pair according to claim 1 is characterized in that the pitch circle awl separates with calibration circular cone (being the generating rolling circle awl) two awls, and two awl sizes are different after separating, and virtual gear pitch cone radius r ' and the proportional K of its pitch cone radius r: $K=\frac{r_{v1}^{\&prime;}}{r_{v1}}=\frac{r_{v2}^{\&prime;}}{r_{v2}}=\frac{a_v}{a_{ov}}\&NotEqual;1$

3, gear pair according to claim 1 is characterized in that the overlap arc X of addendum ha by small gear and gearwheel ₁With X ₂Determine;

ha _1，2＝(ha ^*+X _1，2)·m

Work as X _1,2＞0, ha _1,2＞full-height tooth is risen ha ^*During m, be called long addendum

Work as X _1,2＞0, ha _1,2＜full-height tooth is risen ha ^*During m, be called short addendum, four kinds of combining forms of three classes correspondingly arranged this moment:

1) length-long addendum, X ₁＞X ₂＞0, positive drive design X ₁+ X ₂＞0,

2) length-weak point addendum, X ₁＞0＞X ₂, positive drive design X ₁+ X ₂＞0,

3) length-weak point addendum, X ₁＞0＞X ₂, negative transmission design X ₁+ X ₂＜0,

4) weak point-weak point addendum, X ₂＜X ₁＜0, negative transmission design X ₁+ X ₂＜0.

4, according to claim 1,2 or 3 described gear pairs, the pitch circle pressure angle α ' that it is characterized in that becoming centre distance end face virtual gear is unequal with pressure angle of graduated circle α, its involute function difference is: Δ inv α=inv α '-inv α=Xhtg α/Zvm ≠ 0 is when Δ a＞0, Δ inv α＞0, i.e. α '＞α; When Δ a＜0, Δ inv α＜0, i.e. α '＜α.

5, according to claim 1,2 or 3 described gear pairs, it is characterized in that making tooth technology is to machine on the spiral bevel gear lathe of existing processing criterion pitch cone radius with straight blade rack shape cutter and generating method.

6, gear pair according to claim 4 is characterized in that making tooth technology and machines on the spiral bevel gear lathe of existing processing criterion pitch cone radius with straight blade rack shape cutter and generating method.

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