# Accurate hyperboloid gear and the unity that helix bevel gear designs are algorithmic

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Summary purpose allows hyperboloid gear and method of calculation of geometry of helix bevel gear to achieve to make unified.

The method analysed the characteristic of method of calculation of geometry of these two kinds of bevel gear, define two to slant buy horn coefficient.

In the meantime, undertook two kinds of bevel gear calculate an analysis.

The result gave out to agree with calculative of geometry of these two kinds of bevel gear unites basic formula and iteration method.

The application that conclusion integrates the methodological standardization to bevel gear, seriation and CAD technology this kind has certain sense.

Keyword gear; Allow hyperboloid gear wheel; Helix bevel gear; Liang Guiming(School Of Mechanical Engineering And Automation of 　 of 　 of Jiang Xizhuo of 　 of 　 of Wan Xiaofeng of 　 of 　 of TH19Unified Methods For The Design Of HypoidGears And Spiral Bevel GearsWan Xiaoli of date of gear design classification, beijing Institute Of Technology, to Unify The Design Methods Of Hypoid Gears And Spiral Bevel Gears of 　 of Aim of 　 of Beijing 　 100081)Abstract.

Methods 　 The Geometric Calculation Of These Two Kinds Of Bevel Gears Was Analyzed And Two Coefficents Of Offset Angle Were Defined.

Many Instances Of These Two Bevel Gears Were Checked.

Results 　 Some Basic Equations And The Methods Of Evaluation Were Given, which Can Be Used Not Only To Hypoid Gears But Also To Spiral Bevel Gears.

Conclusion 　 The Unified Method Is Helpful To The Standardization And Seriation Of Bevel Gears And To CAD Technique.

Positive drive of accurate hyperboloid of 　 of Gear; Hypoid Gear; Spiral Bevel Gear; Gear Design of Key Words 　 is the common form in bevel gear drive, helix bevel gear is a kind of its special situation.

Slant when what allow hyperboloid gear wheel when buy is apart from E12=0, make drive of helix bevel gear.

On appearance and treatment method, accurate hyperboloid gear and helix bevel gear do not have substaintial distinction, difference of angrily calculation method is not big also [1, 2] .

In be designed actually, their geometrical calculation method is not same however.

Should slant when buy is apart from E12 approach Yu Ling, the error increases the geometrical computation formula of active accurate hyperboloid gear, even invalidation.

Because the geometry of design of this helix bevel gear is calculated,cannot use formula of computation of geometry of accurate hyperboloid gear and computational method.

Must part to these two kinds of bevel gear in CAD software development undertake handling.

The author puts forward a kind to agree with the method of unified geometry calculation of accurate hyperboloid gear and design of helix bevel gear, its characteristic is to should slant buy is apart from when E12 is bigger, it and accurate hyperboloid gear are active computation agrees as a result; Should slant buy is apart from E12 to be zero hour, get parameter of correct geometry of helix bevel gear; When E12 is lesser, computational error is very small.

Because this is in development of software of bevel gear CAD, can include these two kinds of bevel gear straight bevel gear to unite processing even.

The parameter of 1 graduation awl is the biggest distinction in gear of basic and formulary accurate hyperboloid and computation of geometry of helix bevel gear depends on the affirmatory method of graduation awl parameter.

The analysis is active computation of geometry of accurate hyperboloid gear is formulary and knowable, should slant when buy is apart from E12 approach Yu Ling, of gear slant buy horn η , ε , ε ′ also approach Yu Ling, bring about formulary computation error to increase consequently even invalidation.

The author is analysing the discovery in the process, although E12 hasten is bordering on zero hour, of gear slant buy horn η , ε , ε ′ also approach Yu Ling, but they are belonged to with rank infinitesimal.

Namely the limit and existence.

The E1 in your type and E2 are slant buy horn coefficient.

The basis slants buy horn coefficient, can give out graduation awl parameter is basic and formulary the K in be type is enlarge coefficient; This group of basic formula agree with not only above accurate hyperboloid gear, also agree with helix bevel gear, won't because of E12=0 invalidation.

Of parameter of 2 graduation awl seeking the basic formula that gives out above solution is a group nonlinear equation group, having 5 parameter among them is affirmatory before geometry is calculated.

Wait for those who ask to decide gear first to slant according to transmission and intensity buy is apart from E12, ° of =90 of σ of axial angle of cut - Σ , tine teeth of a cogwheel counts Z1 and Z2, mt2 of modulus of gear midpoint end panel, pinion midpoint helix angle β 1.

Criterion above the foregone parameter in basic formula is I12=z2/z1, r2=mt2z2/2, reach E12, σ , β 1.

As a result of group of equation of linear of basic and formulary dispute, use iterative method to seek solution here.

Namely primary election K and E1 value, press face measure has iteration: ξ of ≤ of ｜ of the K*-k that be like ｜ (the some particle) that decides by computational precision, can have the iteration below; Change K initial value otherwise new iteration.

The Rc in type is bit body radius.

Be like ξ of ＞ of ｜ K0-kc ｜ , change E1 initial value new iteration, till ξ of ≤ of ｜ K0-kc ｜ till.

Iteration ends, got all graduation awl parameter.

Tilt according to coefficient of facewidth, tooth depth, modification coeffication and tine root next type, the method that presses accurate hyperboloid gear has other the computation of parameter of all geometry dimension.

3 calculate exemple author to use the unified formula above and algorithm to aim hyperboloid gear and helix bevel gear respectively two kinds of circumstances undertook much consideration is analysed.

Watch 1 it is to slant the helix bevel gear that buy is apart from E12=0 calculates exemple result; Watch 2 it is to slant the accurate hyperboloid gear that buy is apart from E12=30mm calculates exemple result.

Many computational analysis makes clear as a result: When E12=0, the graduation awl parameter that methodological place decides above and result of computation of geometry of active helix bevel gear are consistent; When E12 ≠ 0 when, above method and result of computation of geometry of gear of active accurate hyperboloid are consistent; Become especially E12 special hour, this methodological earnings result is more accurate.

Accordingly, usable above the method calculates the geometry of these two kinds of bevel gear methodological gather into one comes along.

Express pinion of gear of parameter of parameter of 1 helix bevel gear to age several Z2722 law to modulus Mn/mm5.

Mt/mm6 of modulus of 6124 end panel.

85156.

8515 helix angle β / (° ) 35.

R/mm92 of radius of 000035 reference circle.

495375.

3665 awl are apart from A/mm119.

3125119.

δ of 3125 minutes of cone angle / (° ) 50.

826339.

1737 slant buy is apart from Σ of E12/mm0 axis angle of cut / (° ) Rc/mm152 of radius of 90 bit body.

K1 of 4 enlarge coefficient.

000000 slant E1/mm-10 of buy horn coefficient.

005294274 slant E2/mm-10 of buy horn coefficient.

006497509 slant ′ of buy horn ε / (° ) 0 watches law of Z377 of number of teeth of a cogwheel of denticulation of gear of parameter of parameter of gear of 2 accurate hyperboloid to modulus Mn/mm4.

Mt/mm5 of modulus of 7767 end panel.

77487.

4313 helix angle β / (° ) 34.

R/mm106 of radius of 190850 reference circle.

834126.

0096 awl are apart from A/mm109.

0763123.

δ of 9444 minutes of cone angle / (° ) 77.

425112.

1135 slant buy is apart from Σ of E12/mm30 axis angle of cut / (° ) Rc/mm114 of radius of 90 bit body.

K1 of 3 enlarge coefficient.

286849 slant E1/mm-10 of buy horn coefficient.

001977110 slant E2/mm-10 of buy horn coefficient.

008878960 slant ′ of buy horn ε / (° ) 15.

The issue in 80924 unified designs is active the standard parameter of accurate hyperboloid gear and helix bevel gear, wait to be defined like coefficient of modulus, tooth depth, modification coeffication in main aspects.

Gear of this alignment hyperboloid can bring about midpoint of facewidth of deviate of academic working pitch point and differ with helix bevel gear.

Because this suggests to define standard parameter,be in facewidth midpoint, also can agree with intensity calculation method so  .

In addition, the helix angle in parameter of standard of gear of active accurate hyperboloid is pinion helix angle, and the modulus in standard parameter is modulus of gear end panel.

Proposal standard parameter takes gear helix angle and way to modulus, such more reasonable.

5 conclusion calculate exemple and actual application to make clear in great quantities, the geometrical computation means that the author offers is feasible.

The author had developed CAD application software according to this principle, use in actual design.

Make allow hyperboloid gear and helix bevel gear so even the unity of the geometrical calculation method in design of straight bevel gear had a basis.

The result also announced to allow the substaintial connection with hyperboloid gear and helix theoretic bevel gear on certain level.

Also have certain sense to the standardization of bevel gear, seriation and CAD technology.