CN109751386A - A kind of design and calculation method of anti-Involutes Gears Transmission engagement - Google Patents
A kind of design and calculation method of anti-Involutes Gears Transmission engagement Download PDFInfo
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Abstract
The invention discloses a kind of design and calculation method of anti-Involutes Gears Transmission engagement, the design and calculation method establishes the functional relation of anti-involute the following steps are included: model on the basis of rolling circle；And derive related mesh equation；Confirm the value of anti-Profile Shift Coefficient of Involute Gear；Calculate anti-involute transmission parameter；The transmission parameter of calculation and check；Examine Gear Processing quality.The path of action of anti-involute profile is designed on involute gear, the bearing capacity of main working face can be improved, due to considering flexible deformation in design, and strength of gear deformation is corrected using elastic deformation amount, also meet the requirement of Elasticity conjugate tooth curve simultaneously, the error that gear manufacture can also suitably be relaxed reduces the difficulty that gear manufacture meets required precision.
Description
Technical field
The present invention relates to gear manufacture field, in particular to a kind of design calculating side of anti-Involutes Gears Transmission engagement
Method.
Background technique
Involute gear is the evagination flank profil of two sections of symmetrical involute compositions, and flank profil is convexo-convex contact in transmission process,
According to hertz (H.Hertz) sphere-contact stress theory, convexo-convex contact is flexible deformation, and stress concentrates on contact point, and covariant
Shape region is distributed from big to small, and the contact stress of contact point is big, is mostly made in big power, high-power transmission with pitting corrosion
Gear failure, therefore gear life is short, reliability is low, and transmission mechanism maintenance cost is big.Gear drive have it is space crossed with it is flat
Two kinds of face form, involute cylindrical gear are usually plane transmission, and space transmission seldom uses.
Summary of the invention
The technical problem to be solved in the present invention is to provide it is a kind of can make the transmission of anti-involute gear correct engagement it is anti-gradually
The design and calculation method of involute gear transmission engagement.
Technical scheme is as follows:
A kind of design and calculation method of anti-Involutes Gears Transmission engagement, the design and calculation method the following steps are included:
1): being modeled on the basis of rolling circle, establish the functional relation of anti-involute, and engaged by involute profile
It is driven open top container ship equation, derives anti-involute profile engaged transmission open top container ship equation；
2): according to the condition of anti-involute profile, confirming the calculating value of anti-Profile Shift Coefficient of Involute Gear.
3): calculating boundary radius of circle or diameter；
4): choosing fully teeth height and radius of addendum, it is high to calculate involute teeth；
5): engaged transmission Interference Check；
6): the calculating of related slide coefficient is checked；
7): the inspection of Gear Processing quality.
Further, in the step 1), on the rolling circle, the right angle of any point of contact P (x, y) geometric locus
Coordinate function expression formula changes polar coordinates functional equation into, obtains
invαk=tan αk-αk
In formula, αkFor pressure angle, βkFor helical angle, here it is infolute functions, and the curve in basic circle is from basic circle
Initial point starts to the curve of hobboing cutter point of a knife highest cutting point to be also involute, because in basic circle with involute outside basic circle about rise
Initial point is symmetrical, because of referred to herein as anti-involute.
Further, in the step 1), based on involute profile engaged transmission open top container ship equation, that is, involute
Gear open top container ship equation, equation are
Or
In conjunction with αt、αwt、αnThere is following relationship with spiral angle of graduated circle β:
Since the tooth curve of major-minor engaged transmission smoothly transits connection, modification coefficient be it is identical, it is only total to become
Potential coefficient is different, therefore open top container ship equation is also involute gear open top container ship equation, and equation is
x∑snIt is the total normal direction modification coefficient of auxiliary engaged transmission, because of xn2For negative value, it is clear that αwtn> αwt, this is instead gradually to open
Line flank profil engaged transmission open top container ship equation.
The utility model has the advantages that designing the path of action of anti-involute profile on involute gear, holding for main working face can be improved
Loading capability is corrected strength of gear deformation due to considering flexible deformation in design, and using elastic deformation amount, together
When also meet the requirement of Elasticity conjugate tooth curve, can also suitably relax the error of gear manufacture, reduce gear manufacture satisfaction
The difficulty of required precision.
Detailed description of the invention
Fig. 1 is root portion easement curve forming process.
Fig. 2 is involute profile starting point schematic diagram in basic circle.
Fig. 3 engages figure with involute profile at the top of gear wheel for pinion gear root.
Fig. 4 is to engage figure with gear wheel root involute with anti-involute at the top of pinion gear.
Fig. 5 is enlarged drawing at the D in Fig. 4.
Fig. 6 is that anti-involute circular tooth thickness calculates schematic diagram.
Fig. 7 is that root tangent condition schematic diagram does not occur for gear.
Fig. 8 is gear root involute starting point schematic diagram.
Fig. 9 engages contact point schematic diagram with gear wheel tip circle for pinion gear root.
Figure 10 is gear wheel root process schematic diagram.
Figure 11 is the registration schematic diagram of the inside and outside flank profil engagement of basic circle.
Figure 12 is the sliding schematic diagram in engagement process.
Figure 13 is enlarged drawing at the E of Figure 12.
Figure 14 is common normal spanning measure tooth number schematic diagram.
Figure 15 is pinion gear hobboing cutter normal profile figure.
Figure 16 is gear wheel hobboing cutter normal profile figure.
Figure 17 is the hobboing cutter normal profile figure of transmission ratio i=1.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings.
As shown in Fig. 1 to Fig. 7, design method of the invention the following steps are included:
One, there are anti-involute engaged transmissions for modeling analysis gear.
1): being modeled on the basis of rolling circle, through geometrical analysis, obtain the functional relation of anti-involute；
According to known, when hobboing cutter or slotting tool when the machining outside basic circle, the generation line of involute is formed along basic circle
, when hobboing cutter or slotting tool extend in basic circle, then direction change occurs in basic circle starting point, cutting for basic circle is made with starting point
Line, connection starting point and the basic circle center of circle and extends, and can prove that line of centres and tangent line are orthogonal, composition flat squares
Coordinate system, if tangent line is x line, line of centres is y line, and coordinate origin is starting point O, can prove in basic circle involute be with
The outer involute of basic circle is symmetrical about starting point, forms basic circle and anti-basic circle, and line and anti-generation line occurs, completely corresponding
Mirror curve, that is, positive and negative involute is respectively two about origin symmetry in two, four-quadrant in plane right-angle coordinate
Mirror curve.
Specific geometrical analysis and modeling derive as follows:
As shown in Figure 1, hobboing cutter is really a rack gear, it is cut gear and is rotated with angular velocity omega, the tooth on hobboing cutter is with straight
Linear velocity vk is moved forward, and hobboing cutter point of a knife (top) center of arc moves along straight line always, vk=ωbs, it is equivalent to gear
Make pure rolling with hobboing cutter, tool arc central point and a circle are that tangent, round radius is equal to root radius r alwaysfWith
Hobboing cutter corner radius ρfSum, i.e. rbs=rf+ρf, because point of a knife is a circular arc, the cutting point of hobboing cutter is in tool arc
On, cutting point is different, then the radius of this circle is that meeting is changed.It crosses hobboing cutter tool arc center and makees cutter tooth on hobboing cutter and cut
The vertical line of chamfered edge and sideline intersect at P (x, y) point, while P (x, y) point is also intersected at circular arc, this is hobboing cutter cutter tooth cutting edge
Highest point, hobboing cutter point of a knife is always mobile to gear centre is left when because of spur roller gear, but P (x, y) point always with rolling circle
Interior flank profil is in contact, this is also the point of contact of actual cut of the hobboing cutter in basic circle inner curve, and basic circle inner curve is exactly hobboing cutter cutter tooth side
The envelope curve at line highest point of contact, therefore, the angle of hobboing cutter tool arc point of contact tangent line are equal to hobboing cutter transverse-profile angle αt, most
The high tangent radius of circle of cutting point reduces ρf sinαt, this is the tangent radius of circle for the flank profil that actual cut comes out, and uses rsTable
Show,
rs=rf+ρf(1-sinαt) (1-1)
Because hobboing cutter point of a knife is one section of circular arc, so involute also has starting point in basic circle, and since hobboing cutter cutter tooth has centainly
Thickness, therefore root circle should be made of to involute starting point two sections of curves, the highest cutting point on hobboing cutter cutter tooth side is two
The separation of section curve.
It establishes using gear center of circle O as the rectangular coordinate system of origin, P (x, y) is any point of contact, straight line O2Q=rf+ρf, △
POO2With △ OO2Q is right angled triangle.Then have
It is obtained according to relation above
R in formulask=rf+ρf(1-sinαk), it is the tangent radius of circle of any point of contact P (x, y), rskWith pressure angle αkVariation
And change.To the helixangleβ of helical gear point of contact P (x, y)k
Formula (1-2) substitution above formula is converted into the functional expression of pressure angle α k
The rectangular co-ordinate function of any point of contact P (x, y)
X=O2Psinαk cosβk
Y=O2Pcosαk
Because of O2P with it is related, substitute into relational expression above, be converted into αkFunctional expression
According to trigonometric function relationship:
(sinαk)2+(cosαk)2=1
Therefore the initial segment any point coordinate P (x, y) meets
In the initial segmentIt is a constant constant, therefore, this is an elliptical rectangular co-ordinate function, and long axis isShort axle isThe easement curve for proving root portions is still elliptic curve.It is now to prove with hobboing cutter knife
Sharp highest cutting point is that the curve of starting point on separation to basic circle is involute.
According to formula (1-2), cutting point P (x, y) is become into pressure angle αkRectangular co-ordinate functional expression:
X=rsktanαkcosβk
Y=rskcosβk
Here it is the rectangular co-ordinate function expressions of any point of contact P (x, y) geometric locus, also indicate that cusp position and pressure
Power angle is closely related.It changes rectangular co-ordinate function expression into polar coordinates functional equation, obtains
invαk=tan αk-αk
Here it is infolute functions, according to researching and analysing above, demonstrated from mathematical model curve in basic circle from
Starting point starts to the curve of hobboing cutter point of a knife highest cutting point to be also involute on basic circle, because gradually opening in basic circle with outside basic circle
Line is about starting point symmetry, because of referred to herein as anti-involute.
About the starting point of easement curve in basic circle and involute, mathematical formulae also can be expressed as.
As shown in Fig. 2, P point is involute starting point in basic circle, αdIt is starting point pressure angle, P point stretches straight line and basic circle
It is circumscribed to intersect at N point,
According to the available following relational expression of diagram:
PN=PJN-PPJ
PJN=rssinαt
It obtains:
In formula, αtIt is hob profile angle, haIt * is addendum coefficient, xnIt is the modification coefficient of gear, rsIt is tangent circle half
Diameter.
If the above coordinate system is changed outside using basic circle that involute starting point is origin, with the tangent line of starting point and basic circle
In the plane right-angle coordinate established with starting point and basic circle circle center line connecting, two involutes are about origin symmetry.
2): by main engaged transmission open top container ship equation, deriving auxiliary engaged transmission open top container ship equation；
As shown in figure 3, main engaged transmission is gear wheel top and pinion gear root flank profil engaged transmission, if rbFor canine tooth
Base radius is taken turns, if raFor gear wheel tip circle radius, if P point is node, if one section of nodel line of pinion gear pitch circle is 1-1, canine tooth
One section of nodel line of wheel pitch circle is set as 2-2, and corresponding point B is taken on nodel line 2-22, B2To the camber line B of P point2P, B2P is public
Normal, C2Curve is also the envelope curve of hobboing cutter or slotting tool.Hobboing cutter or slotting tool flank profil C1Curve is involute, according to " flank profil is nibbled
The characteristic of conjunction philosophy " and involute, can prove the flank profil C for being cut gear2It is also involute, accordingly, no sideshake is nibbled
Closing equation is also involute gear open top container ship equation, and equation is
Or
In formula, z1It is the pinion gear number of teeth, z2It is canine tooth tooth number, αwtIt is the end face angle of engagement, αtIt is reference circle end force
Angle, αnIt is reference circle normal pressure angle, x∑nIt is the total normal direction modification coefficient of main engaged transmission, xn1It is pinion gear normal direction displacement system
Number, xn2It is gear wheel normal direction modification coefficient.αt、αwt、αnThere is following relationship with spiral angle of graduated circle β:
In formula a be the actual installation center of two gears away from, a ' be two gears theoretical center away from.
Derive auxiliary engaged transmission open top container ship equation:
As shown in Figure 4 and Figure 5, if J2It is gear wheel basic circle, J2' be the anti-involute profile in gear wheel root anti-basic circle,
If A point is meshing point, αt1It is transverse pressure angle of the pinion gear in A point, αt2It is transverse pressure angle of the gear wheel in A point, αwtnIt is
A point gearing angle, that is, the angle of size gearing power and horizontal line (X-axis).Because gear wheel root is anti-involute,
It is identical as internal gear transmission, thus transverse tooth thickness changing rule be also it is opposite, it is major-minor engaged transmission tooth curve be to smoothly transit
Connection, modification coefficient be it is identical, only net slip coefficient is different, therefore open top container ship equation is also involute gear
Open top container ship equation, equation are
x∑snIt is the total normal direction modification coefficient of auxiliary engaged transmission, because of xn2It is negative value, it is clear that αwtn> αwt, calculated result and make
The case where figure be it is completely the same, also illustrate Double Involute Gear engaged transmission when gear-profile each point Impact direction be
Inconsistent.
In gear, there are under conditions of anti-involute, need to calculate corresponding parametric, wherein
1, including anti-involute profile circular tooth thickness calculates；
As shown in Figure 6, if O is the gear wheel center of circle, O ' is the anti-basic circle center of circle, if A is any point on involute profile,
A ' be and on A symmetrically anti-involute profile a bit, riIt is the radius of any point A, rkIt is the radius of symmetric points A ', θiIt is to appoint
The exhibition angle of one point A, θkIt is the exhibition angle of symmetric points A '.It can prove two triangle △ AOO ' ≌ △ A ' OO ', θk=θi.Because
OA=ri, OA '=rk, OO '=2rb, in AOO ' triangle, had according to corner relationship
Had according to the property of involute
According to involute property, angle of the involute starting point at basic circle
According to involute property
θk=θi=inv αk=inv αi
Simultaneous solution obtains equation
Because of θ i very little, θ i=inv αk≈ 0, can approximation obtain
Have
rb-rk=ri-rb
Or
rk=2rb-ri
ri=2rb-rk
It is obtained according to infolute function formula
This is a property about anti-involute: involute and any symmetric points of anti-involute and gear centre point
Angle is divided equally by the line of starting point and gear centre, in other words, on involute and anti-involute in any symmetric points and gear
Heart point line is equal with the angle of starting point and gear centre line.It is any in gear wheel basic circle according to circular tooth thickness calculation formula
The place point A ' circular tooth thickness calculation formula is
Therefore, as long as determining A ' point, i.e. rkNumerical value, so that it may acquire circular tooth thickness herein.
2, including bottom clearance and height of teeth top shorten coefficient calculating；
Guarantee a pair of of gear correct engagement, there are certain interval between gear root and top, this gap is known as tooth top
Gap, abbreviation bottom clearance.Profile modified gear according to the requirement for guaranteeing open top container ship select installation center away from, then it is impossible to ensure that bottom clearance,
Installation center is selected away from then it is impossible to ensure that open top container ship, therefore, profile modified gear will guarantee according to the requirement of guarantee bottom clearance
Bottom clearance then shortens tooth top with open top container ship, claims height of teeth top to shorten coefficient with the ratio of modulus, uses δyIt indicates, calculates public
Formula
Y in formulanIt is center separation, calculation formula
Formula (1-6), (1-14) are substituted into formula (1-13), obtain δyCalculation formula
The limiting case of a pair of of involute gear engaged transmission is exactly meshingangleαwt>=0, it is obtained according to formula (1-15)
This is also to obtain the condition of anti-involute profile.Gear hobbing, gear shaping can also be determined according to the relationship of tooth height and basic circle
Machining obtains the condition of anti-involute profile.I.e. root circle must be less than basic circle.
r-2hf< rb
According to involute gear calculation formula
hf=(ha *-δy+c*)mn
Relevant calculation formula is substituted into obtain
Therefore height of teeth top, which shortens the range of coefficient, is
This is the range that anti-involute gear teeth height shortens and the condition that anti-involute profile is formed, and be can be used for really
Surely design the parameter of anti-involute gear, at the same be also check anti-involute gear tooth height it is whether reasonable.
3, including the involute gear conditional that root is not cut；
As shown in fig. 7, anti-involute gear is also big negative addendum modification involute gear, thus, it is ensured that root is not cut, engagement
Transmission is not interfered, then canine tooth tooth number and modification coefficient and helical angle will meet certain relationship, or select numerical value appropriate.
According to profile modified gear principle, profile modified gear is that hobboing cutter by normal place moves radially xnmnThe gear come out apart from institute's cutting.
Wherein xnIt is normal direction modification coefficient, mnIt is normal module.
The cusp position N of plane and the point of intersection of basic circle where taking corresponding reference circle tooth tip1, root does not cut the item of interference
Part is
N1Q > ha-xnmn
Or
xnmn> ha-N1Q
H in formulaaIt is reference addendum, αtIt is gear face pressure angle of graduated circle, r is gear compound graduation circular diameter, respectively
It is calculated by following formula
ha=(ha *-δy)mn
N1Q=P N1sinαt
PN1=rsin αt
The above calculating formula is substituted into the conditional that root does not occur and cuts interference, the check of modification coefficient is obtained according to mathematical operation
Formula
Or the number of teeth is checked according to modification coefficient, helical angle, pressure angle
Or helical angle is checked according to modification coefficient, the number of teeth, pressure angle
Formula (1-17), (1-18), (1-19) be check modification coefficient, the number of teeth, helical angle three meet mutually condition,
Wherein, ha* is addendum coefficient, δyCoefficient, m are shortened for tooth topnFor modulus.
3): finally, by the above-mentioned formation condition that anti-involute profile is calculated, it is also necessary to confirm anti-involute gear
The calculating value of modification coefficient, verification step are as follows:
Anti- involute formation condition is that the smallest circle of work flank profil should be less than base radius, does not consider that bottom clearance has
r-(ha *-xn)mn< rb
In formula, r is reference radius, rbIt is base radius, substitutes into relevant calculation formula and obtain
According to the condition i.e. formula that value range condition i.e. formula (1-17) and the anti-involute of formation that root is cut does not occur
(1-20) obtains gear wheel modification coefficient xnRange of choice
Choosing modification coefficient xnWhen, do not consider that tooth top shortens the influence of coefficient, therefore modification coefficient xnValue range
It is
Two sections of flank profils of Double Involute Gear are uniformly distributed, and the flank profil that works then has using basic circle as line of symmetry
R is reference radius, rbIt is base radius, substitutes into calculation formula and obtain
Formula (1-22) is exactly the value range for the condition and modification coefficient for obtaining anti-involute profile, meets formula (1-
It 23) is the best modification coefficient for designing anti-involute gear.
Anti- involute profile engaged transmission is similar to the internal tooth of involute profile engaged transmission, but anti-involute profile is nibbled
The engaged transmission that transmission is different from involute profile is closed, therefore, involute profile internal tooth engaged transmission is nibbled with anti-involute profile
Closing transmission has following identical point and difference:
Identical point
Anti- involute profile is interior flank profil engagement, identical as internal gear tooth engagement.
Difference.
The flank profil of internal gear is distributed along inner periphery, and anti-involute profile is distributed along excircle；Internal gear transmission
The direction of motion it is identical, the anti-involute profile direction of motion is opposite；Anti- Involutes Gears Transmission is that main and auxiliary engaged transmission coexists,
I.e. convexo-convex flank profil coexists with convex-concave profile contact, and internal gear transmission only has convex-concave profile contact.
Again based on the aforementioned process for deriving and calculating, it can be seen that the center of circle of intermeshing two gears is relatively fixed
Constant, i.e. center is away from constant, when pinion gear is with ω1Angular speed rotation when, drive gear wheel with ω2Angular speed rotation, from
In the diagram of Fig. 1 to Fig. 4, J1It is the basic circle of pinion gear, J2It is the basic circle of gear wheel, when contact flank profil of the pinion gear with gear wheel
When being outside the basic circle of gear wheel, the flank profil of large and small gear is necessary to cross node, so transmission ratio and angular velocity of rotation are constant not
Become, the angle of engagement is consistent with the Impact direction of two gear teeth faces here it is the engaged transmission of involute profile, i.e., main engagement passes
It is dynamic.
When the contact point of pinion gear and gear wheel is in the basic circle of gear wheel, this section is auxiliary engaged transmission, if the angle of engagement
For αwtn, the pressure angle of pinion gear is αt1, the pressure angle of gear wheel is αt2, αt1And αwtnAnd αt2Triangle has following relationship:
αt1> αwtn> αt2
This relationship explanation, when the contact point of pinion gear and gear wheel is in the basic circle of gear wheel, the flank profil of gear wheel
It is anti-involute, is the interior generated profile opposite with involute, the normal of contact point and anti-basic circle are tangent, pinion gear flank profil
The normal of contact point and pinion gear basic circle are tangent, and the flank profil of pinion gear and gear wheel does not have common normal, but along the auxiliary angle of engagement
αwtnForce action is formed on the flank of tooth of two gears；But the size at three angles be it is unequal, contact point has one to cut always
To component, sliding is generated, is equivalent to grinding, test discovery leads to one section of operation of excessive loads transmission when anti-involute profile
Be after time, at the top of gear wheel root and pinion gear it is smooth, as grinding, exactly because there is a tangential component
The result of interaction.This sliding phenomenon in Involutes Gears Transmission there is also, when using conjugate involute profile when,
Pressure angle is unequal, α when using normal shift with the angle of engagementwt> αt, when using negative addendum modification, αwt< αt, that is, conjugate gradually
The flank profil that bursts at the seams engaged transmission is not pure rolling, and there is also slidings, are usually evaluated with slide coefficient, it is desirable that slide coefficient is not
Obtaining is more than a certain numerical value.As a same reason, as long as the Relative sliding ratio for controlling anti-involute profile is no more than a certain numerical value
It is allowed, and because this section of flank profil is auxiliary engaged transmission, motion profile is controlled by main engaged transmission, only assisted
Supporting role.
According to the above analysis, involute and anti-involute profile can be completely used for engaged transmission, but this is that have item
Part, it needs to find optimal use range, guarantees slide coefficient in condition tolerance band, to design calculating double involute
Gear.
When gear wheel is identical as the pinion gear number of teeth, transmission ratio is 1, i.e. input speed is identical as output revolving speed, here it is
Not speed change engaged transmission, if still using anti-involute profile engaged transmission, according to xn1=xn2, then αwtn=αt, this is
Do not allow, according to anti-involute formation condition (1-21) or (1-22) and open top container ship equation (1-4) and (1-5),
It can be proved that if xn1=xn2, then it is impossible to meet anti-involute conditions；Therefore, when the pinion gear number of teeth and canine tooth tooth number phase
It concurrently there are relational expression xn1=x∑n-xn2, this is the special circumstances of Double Involute Gear transmission.Ordinary circumstance, when transmission ratio very
Hour, it can be in this way.
In addition, according to the feature of basic circle inner curve, anti-involute and the starting point symmetry that involute is about involute
, therefore the boundary circle of double involute is exactly basic circle.For the gear of a pair of transmission that is meshed, basic circle is also pitch circle, and correspondence is small
The pitch circle of gear i.e. the boundary circle of pinion gear, therefore have
rJ2=rb2 (1–24)
rJ1=a-rb2 (1–25)
In formula, rb2It is gear wheel base radius, rJ2It is gear wheel boundary radius of circle, a is gear pair operating center distance, rJ1
It is pinion gear boundary radius of circle.
Two, the correlativity formula for having obtained the anti-involute of gear, using the high value of fully teeth height and involute teeth, with
Confirm addendum coefficient and tip clearance coefficient and chamfering coefficient, the specific steps are as follows:
1., calculate addendum coefficient, tip clearance coefficient and chamfering coefficient, if the addendum coefficient ha* of Double Involute Gear,
Tip clearance coefficient c* can use involute gear standard, and general addendum coefficient ha* take 1, tip clearance coefficient c* to take 0.25, it is double gradually
Involute gear takes the long tooth greater than 1 using ha*, and double involute flank profil generally requires tooth top to remove wedge angle burr, i.e. tooth top will fall
Wedge angle burr chamfering c is usually removed at anglea× 45 °, wherein caIt is calculated as follows
ca=ca *mn (2–1)
In formula, ca* removes wedge angle burr chamfering coefficient, and abbreviation tooth top chamfering coefficient takes ca*=0.05~0.1, modulus is got over
Greatly, value is smaller, guarantees chamfering between 0.1~0.5；
2., need to carry out the calculating of the normal module and normal pressure angle, since involute gear has an indexing
Circle, normal module and normal pressure angle and helical angle are calculated with reference circle, full name be reference circle normal module with point
Circle normal pressure angle and spiral angle of graduated circle are spent, so reference circle is the parameter for designing convenience of calculation and needing and setting up.Pressure angle
Also known as profile angle, the number of teeth z of gear, reference diameter d, normal module mn, there is following relationship between helixangleβ:
Reference circle normal pressure angle αnWith the relationship of reference circle transverse pressure angle,
Base circle diameter (BCD) db, reference diameter d, reference circle transverse pressure angle αtRelationship
db=dcos αt
Gear face modulus mtWith normal module mnRelationship
3., the involute teeth is high, calculating of fully teeth height and radius of addendum, the mainly high calculating of involute teeth
With selection, the calculating of the wokring depth of tooth and pinion gear tip circle radius and the calculating of other parameters, specifically,
(1), for the flank profil of Double Involute Gear respectively outside basic circle and in basic circle, the tooth that can be calculated outside basic circle is high, if
The a height of hb of tooth outside basic circle, calculation formula are
hb=ra–rb
According to involute gear calculating fraction-ness circle radius r, radius of addendum ra, base radius rbFormula
ra=r+ (ha *+xn–δy)mn
Above formula is substituted into obtain
This is that the tooth for the basic circle outer portion flank profil calculated according to involute gear is high, and Double Involute Gear can be just
Often engaged transmission, will also check the parameters such as interference, slide coefficient, so the involute teeth height of Double Involute Gear is less than hb,
That is the high h of involute teethJSelection range
hJ≤hb
Formula (2-2) is the high calculation formula of involute teeth, and above formula is the numberical range chosen；
(2), the calculating of fully teeth height and the radius of addendum of gear wheel；
Firstly, the calculating of the wokring depth of tooth and pinion gear tip circle radius, calculates, gear pair according to the design of involute gear
The wokring depth of tooth (do not include tooth top gap and root gap) calculation formula
hw=(2ha *-δy)mn
In Double Involute Gear engaged transmission, the wokring depth of tooth of pinion gear is less than or is equal to according to involute gear meter
The wokring depth of tooth calculated, i.e.,
hw1≤(2ha *-δy)mn (2–3)
According to gear pair installation requirement, the root radius r of pinion gearf1Meet condition
rf1≤a–ra2=a-rb2–hb
In formula
The root radius r of pinion gearf1Meet condition
If pinion head radius of circle is ra1, then pinion head radius of circle
ra1=rf1+hw1
Tooth top gap is c*mn, the actual radius of addendum of pinion gear will be plus tooth top gap, substitution formula (2-2) and (2-3)
It obtains
Formula (2-3) is the determining pinion gear wokring depth of tooth, and formula (2-4) is the range for choosing pinion gear tip circle radius
4., the calculating of the radius of addendum of the fully teeth height and gear wheel, the fully teeth height is one more than the wokring depth of tooth
Gap, i.e. fully teeth height calculation formula
h1=hw1+c*mn (2–5)
The radius of addendum and fully teeth height calculation formula of gear wheel are obtained as a same reason
ra2=a-rf1+h1 (2–6)
h2=h1+cf *mn (2–7)
C* is tooth tip clearance coefficient in formula, chooses c*=0.25, c according to involute gear standardfIt * is between gear wheel root
Gap coefficient generally chooses 0.05~0.1.
Three, it after relevant parameter has been calculated, is checked, includes:
(1), the engaged transmission of the outer involute profile of the gear wheel basic circle is checked, the specific steps are,
Gear wheel involute profile engaged transmission is checked, and really the tooth top of gear wheel engages biography with the root of pinion gear
It is dynamic to check.Gear wheel tooth top must be engaged with the involute of pinion gear root, and easement curve is avoided to interfere, because gear wheel is
Double involute flank profil, while should can also check pinion gear by the basic circle of gear wheel.
(1), pinion gear root involute processes starting point pressure angle αd
As shown in figure 8, setting B point is involute starting point.Involute processing starting point pressure angle is set as αd, have with ShiShimonoseki
It is formula
PN1=r sin αt
rb=rcos αt
R is pinion gear reference radius, α in formulatIt is end face pressure angle of graduated circle, H is small tooth, and the practical tooth in wheel root is high
H=(h* a–xn1)mn
Therefore
(2), gear wheel tooth top starting point of meshing pressure angle αc
As shown in figure 9, setting B point is the pinion gear root flank profil starting point of meshing and gear wheel tip circle job initiation point, αcIt is
Flank profil work starting point of meshing pressure angle, N1N2For tangent line, there is following formula
BN1=N1N2–N2B
N1N2=(rb1+rb2)tanαwt
N2B=rb2tanαat2
In formula, rb1It is pinion gear base radius, rb2It is gear wheel base radius, αwtIt is the angle of engagement, according to formula (1-4)
It calculates, αat2It is the tooth top transverse pressure angle of gear wheel, calculation formula is
Therefore have
tanαc=tan αwt–i(tanαat2–tanαwt)
According to the condition that easement curve interference does not occur, have
tanαc≥tanαd
I.e. gear wheel outside circle is in the check formula that easement curve interference does not occur for pinion gear root
Similarly, available pinion gear teeth tip circle is in the calculation formulas that easement curve interference does not occur for gear wheel root
Formula (3-2), (3-3) be gear engaged transmission general calculation formulas, because Double Involute Gear transmission be in the same direction gradually
Burst at the seams profile contact, and the value calculated is negative, it should be checked with absolute value, or directly calculate gear root and connect
Touch the pressure angle α of starting pointfcIt is checked, i.e.,
tanαfc≥tanαd
About αfcCalculation formula can be calculated according to starting point contact position
O in formula1B=rfc1It is pinion gear starting point of meshing radius, as shown in figure 9, in △ O1BO2In
O1O2=a
O2B=ra2
∠O1O2B=αat2–αwt
It is obtained according to triangle edges angle formula
Similarly available gear wheel root contacts starting point radius rfc2
Gear wheel root is anti-involute profile, cannot enough involutes calculation formula, therefore with formula (3-4)
Calculating is different, be according to formula
It calculates, i.e.,
According to formula (3-2), that (3-3) obtains calculation formulas is as follows:
Formula (3-8), (3-9) are suitable for Double Involute Gear engaged transmission Interference Check.
(2), the engaged transmission of the gear wheel basic circle flank profil is checked, and is comprised the concrete steps that,
When pinion gear flank profil passes through the basic circle of gear wheel, αat2=0, because the angle of engagement be it is constant, according to formula (1-4)
It can be in the hope of meshingangleαwt
Therefore pinion head is by the check formula interfered when the basic circle of gear wheel
If it is impossible to meet must choose the parameters such as modification coefficient, helical angle, the number of teeth to above formula again.
(3), the engaged transmission of anti-involute profile is checked in the gear wheel basic circle, and the curve in gear wheel basic circle is
Anti- involute, similar to internal gear transmission, tooth top and the gear wheel root of pinion gear are also intended to that easement curve is avoided to interfere,
The specific steps are,
1., the highest point in the process of gear wheel root
As shown in Figure 10, hob teeth effective depth hd, i.e., pinion gear flank profil height, hobboing cutter blade radius are ρf, rolling
Knife profile angle is αn, the highest point of anti-involute profile is then
rc=ra2–hd+(1–sinαn)ρf
2., the highest point of pinion head and engagement pass through condition
If gear sub-center is away from for a, then pinion head highest point is a-ra1, therefore the condition avoided interference with is
a–ra1≥rc
The highest point of anti-involute profile is processed according to hobboing cutter, then pinion gear engages the condition passed through
hd≥ra1+ra2–a+(1–sinαn)ρf (3–10)
hd=h1
Transverse tooth thickness s of the hobboing cutter when effective tooth is highdMeet condition
S in formulaa2It is gear wheel addendum circle arc transverse tooth thickness, can be acquired according to the calculation formula of involute gear, if s2It is big
Gear compound graduation circular thickness, αa2It is gear wheel outside circle pressure angle, αtIt is reference circle transverse pressure angle, xn2It is modification coefficient, β
It is helical angle, then has
In order to improve the intensity of flank profil root, it should increase hobboing cutter blade radius, in order to guarantee that engagement is not done
It relating to, to minimize hobboing cutter blade radius, therefore, to reasonably select hobboing cutter blade radius, this is related with modulus,
Usually calculated according to following formula
ρf=ρ*mn (3–12)
ρ * value 0.15~0.38, usually takes 0.25 in formula.
(4), contact ratio is calculated, contact ratio is the ratio of two gear actual line of action length and gear method section, point
It Suan Chu not the outer involute contact ratio ε of basic circlew, end face contact ratio εdWith involute contact ratio ε in basic circlen, such as Figure 11 institute
Show,
J1It is the basic circle of pinion gear, J2It is the basic circle of gear wheel, N1N2Common normal, 1-1 and 2-2 be respectively pinion gear and
The pitch circle of gear wheel, P are node, B1B is the path of contact of basic circle outer teeth profile, B1C is anti-involute profile and pinion gear in basic circle
The path of contact of flank profil, B1B is the outer involute engagement wire length of basic circle, B1C is anti-involute profile path of contact in gear wheel basic circle
It is long.∠ 1=αJt1It is pinion gear in " transverse pressure angle at gear wheel boundary circle ", ∠ 6=αat1It is " pinion head nose circle
Surface pressure angle ", ∠ 4=αat2It is " gear wheel outside circle transverse pressure angle " that ∠ 3 and ∠ 5 are equal to meshingangleαwt。
(1), the outer involute contact ratio ε of basic circlew
According to Figure 11, B1B is the outer involute engagement wire length of basic circle,
B1B=P B1+PB
PB1=rb1(tanαJt1–tanαwt)
PB=rb2(tanαat2–tanαwt)
In formula, αat2It is gear wheel outside circle transverse pressure angle, is calculated by following formula
αJt1It is transverse pressure angle of the pinion gear at gear wheel boundary circle, calculation formula
In formula, rJ1It is pinion gear boundary radius of circle, is calculated according to formula (1-25).It obtains
B1Registration outside ratio, that is, basic circle of B and method section
(2) end face contact ratio ε d
The calculating of transverse contact ratio is identical as involute calculating, i.e.,
In formula, b is gear tooth effective width.
(3), involute contact ratio ε n in basic circle
According to Figure 11, B1C is that involute engages wire length in basic circle
B1C=rb1(tanαat1–tanαJt1)
In formula, rb1 is pinion gear base radius, and α Jt1 is pinion gear top end surface pressure angle,
αat1It is transverse pressure angle of the pinion gear at gear wheel basic circle, is calculated by formula (3-14), i.e., calculation formula is
Gear method section is equal to basic circle transverse circular pitch
Therefore, involute contact ratio ε n in basic circle
(4), Total contact ratio (contact ratio)
εΣ=εw+εd+εn (3–18)
Because the engagement of anti-involute profile is different from involute profile mode, in order to guarantee engaged transmission reliability, one
As the registration of the main engagement of situation be greater than 1, in order to which popularity evaluates the situation of engagement with adaptability, if k is greater than 1 number,
Check registration condition be
εw+εd> k (3-19)
The numerical value of k is determined according to the primary condition of engaged transmission and transmission requirement.
(5), the calculating of the related slide coefficient is checked, and as shown in Figure 12 to Figure 13, step is, by slide coefficient
Formula, respectively calculate gear wheel tooth top slide coefficient formula are as follows:
When the flank profil of pinion gear is in contact with the basic circle of gear wheel, if phase of the pinion gear flank profil at gear wheel basic circle
When being η J1 to slide coefficient,
By ηJ1=tan αJt1 (3–22)
Derive the formula of slide coefficient at gear wheel basic circle are as follows:
The formula of pinion gear top slide coefficient are as follows:
Slide coefficient maximum three location points when being anti-involute gear engaged transmission above, position are different, it is desirable that sliding
The size of dynamic coefficient is also different, to check respectively.
(6), the check of total number of teeth and modification coefficient, step be,
Anti- involute gear is negative addendum modification gear, and net slip coefficient is negative value, and has the limit, this limit claims most
Small net slip coefficient.According to " flank profil engagement philosophy ", the pitch circle of a pair of of involute gear engaged transmission must basic circle with
Outside, i.e., the sum of two rolling circle radiuses are less than installation center away from obtaining conditional according to basic circle calculation formula
Therefore, the number of teeth of anti-Involute Gear Pair and to meet condition
As long as above formula show to have determined center away from and modulus, the maximum number of teeth of gear pair determines that, above formula is substituted into
Open top container ship equation (1-6) obtains
Limiting case, αwt=0, obtained limiting value
Here it is the conditions of minimum modification coefficient.
Four, ordinary circumstance, as long as guaranteeing that hobboing cutter is qualified, the outer involute of basic circle is qualified, also may determine that in basic circle and instead gradually opens
Line is qualified, if judge that a kind of involute is qualified, also may determine that two kinds of involute qualifications, main test content are specific
It is as follows:
1, base tangent length calculates
(1), the spanning measure tooth number calculation formula of the outer involute profile base tangent length of basic circle.
As shown in figure 14, number of gear teeth is z, and outside circle pressure angle is αat, common normal measurement distance in the number of teeth just by
Following formula is calculated, spanning measure tooth number kaIt indicates
Illustrate: pinion gear flank profil is involute profile, the spanning measure tooth number of base tangent length and base tangent length
Calculating and involute gear calculating are just the same, do not study here.Calculation formula
(2), base tangent length calculation formula
As the calculation method of involute gear, calculation formula is identical for the calculating of base tangent length, only spanning measure tooth number
Calculate different, the position difference of measurement.Base tangent length indicates with wk, calculation formula
wk=mncosαn[π(ka–0.5)+z invαt+2xntanαn] (4–3)
Spanning measure tooth number is that ka expression is Double Involute Gear, and spanning measure tooth number is that k expression is involute gear, it should be noted that ginseng
The meaning that number meets, substitutes into corresponding numerical value, in order to distinguish, the base tangent length w of double involute Tooth Profile GearskaIt indicates, gradually
The base tangent length of Tooth Profile Gears of bursting at the seams is indicated with wk.
2, boundary knuckle-tooth thickness calculates
Transverse tooth thickness is gear-driven significant dimensions, and manufacture hobboing cutter, processes the important parameter of gear, to double involute,
Boundary knuckle-tooth thickness is very important size, the calculation formula of large and small gear boundary circular thickness
(1), involute and anti-involute profile boundary circular thickness sJIt indicates, demarcate radius of circle rJIt indicates, for big
Gear demarcates radius of circle equal to base radius, that is,
rJ2=rb2
Then gear wheel boundary circular thickness sJ2
(2), pinion gear boundary radius of circle rJ1, it is related away from a to gear pair installation center,
rJ1=a-rb2 (4–5)
Pinion gear boundary circular thickness indicated with sJ1,
In formula, αJt1It is circle transverse pressure angle of demarcating
The boundary circular thickness of gear is not easy to measurement, but is an important inspection parameter, this point for cutter
It is different from involute gear.
Five, general gear Stress calculation and strength check, design calculating, modulus m including actual installation center away from an
Design calculating and Tooth Number Calculation, in addition, the force analysis and strength check of the double involute flank profil flank of tooth further include: main engagement
It is driven the strength check of gear wheel and the strength check of auxiliary engaged transmission pinion gear
Wherein, the strength check of main engaged transmission gear wheel, if input torque is Ne, the main engaged transmission of gear wheel
Pitch radius is rw2, the pitch radius of pinion gear is rw1, then the force of periphery F of the flank of tooth is acted ontWith NeAnd rw2And rw1Relationship
It is
Act on the force of periphery F of the flank of toothtWith flank of tooth normal pressure FnAnd axial force FzAnd βwRelationship be
The normal pressure of the flank of tooth is acted on perpendicular to the flank of tooth, therefore the stress of the gear teeth will be decomposed into tangential normal pressure FqAnd diameter
To power Fr, because of base radius rb=rwcosαwt=r cos αt, then tangential force FqWith radial force FrIt can calculate.
The gear teeth of gear are equivalent to a cantilever beam, and the moment of flexure that root portion is born is the largest, and stress point is in node, stress
Point arrives the distance h of rootwq2It is calculated by following formula
Teeth root root radius is equal to ra2–h2, the circular tooth thickness s of root is calculated according to formula (1-11), (1-12)wq2
In formula
Specifically, Bending strength check:
The section of the gear teeth is approximately a rectangle, and transverse tooth thickness approximation circular tooth thickness can calculate modulus of section (bending resistance according to formula
Modulus) W
B is gear tooth contact effective width in formula.The moment of flexure that teeth root is received
M=Fq hwq2
In main engaged transmission, canine tooth teeth root bending stress is the largest, and is substituted into relevant calculation and is obtained gear wheel
Bending stress σF2
Above calculate is calculated with dead load, really dynamic loading, and situation is more complex, therefore to consider
Load coefficient of colligation K (referred to as application factor), the power allocation proportion including main and auxiliary engaged transmission stress point, obtains actual stress
Ordinary circumstance, Torque unit use N.m, gear size Parameter units use mm, unit be it is skimble-scamble, in order to
It can directly be calculated with these units, unit of stress uses Mpa.According to gear ratio relation, gear wheel can also be all used
The bending stress of gear teeth of bull gear root when parameter calculates main engaged transmission, i.e.,
Gear drive torque is variation, meanwhile, the tooth force of gear is also clearance-type mechanical periodicity, and gear exists
The transmission process middle gear gear teeth just stress at the time of contact, stress is 0 when not contacting, it is therefore contemplated that the stress shape of flank profil
State is regular mechanical periodicity between 0 to σ Fmax, and according to fatigue strength theory, gear-tooth strength can be strong according to bending allowable
Degree is checked.I.e.
σF2≤[σ]F2 (5–10)
It is the permissible bending stress of gear material in formula, the high-quality conjunction of 20CrMnTi low-carbon is generallyd use for automobile gear
Golden Steel material carburizing and quenching, generally taking permissible bending stress is 420Mpa.
Contact strength is checked
The contact stress of anti-involute profile all uses hertz (H. Hertz) stress formula meter as involute profile
Calculate, gear engaged transmission all be roll band sliding, even if the pure rolling flank profil flank of tooth still by contact varying stress, therefore destroy shape
Formula is pitting corrosion.This is a kind of fatigue rupture, very big with material, hardness and stress-number of cycles relationship, to determine one
Circulation cardinal sum specification of heat treatment passes through experiment again and obtains the limit stress of contact fatigue failure.Calculating contact stress intensity is
It is necessary.
If the elasticity modulus of pinion gear material is E1, Poisson's ratio 1, the elasticity modulus of gear wheel material is E2, Poisson's ratio
It is 2, then the material property coefficient delta E of gear pair
Contact stress σ H is obtained according to hertz stress formula
It is composite curve radius ρ Σ in formula,
The radius of curvature of node is exactly pitch radius rw, if transmission ratio coefficient Zi
Then composite curve radius ρ Σ
Profile contact line length l
The flank profil flank of tooth is calculated by normal pressure according to formula (7-6), contact stress σ H calculation formula
Material property coefficient its numerical value for big pinion gear is carbon steel or steel alloy is a constant Δ E in formula
=8.84 × 10-6, therefore contact stress easily calculates.Likewise, above be calculated with uniform load, so
Still, there is load coefficient of colligation K in the case where considering dynamic load uneven load, then should be modified to
Large and small Gear Contact stress is identical, but the number of large and small Gear Contact is not identical, and possible material is different, therefore
Contact fatigue strength is different, and to carry out strength check respectively.It generally takes and removes the contact stress of pinion gear for canine tooth
The contact stress of wheel.I.e.
When gear wheel is identical as pinion gear material therefor, the contact strength for checking gear wheel is not needed generally.About comprehensive
Closing COEFFICIENT K is a complicated coefficient, is related to gear pair working characteristics, dynamic load variation, load distribution along width, Transverse Load point
Match, contact line length variation, factors, the choosing method such as tooth-face roughness, can be according to actual use as involute gear
It is required that choosing, do not discuss here.Profile contact intensity is checked according to permissible compression stress, i.e.,
σH≤[σ]H (5–15)
In formula [σ]HIt is the permissible compression stress of gear material, it is high-quality to generally use 20CrMnTi low-carbon for automobile gear
Alloy steel material carburizing and quenching, generally taking permissible compression stress is 730Mpa.
Likewise, auxiliary engaged transmission is also referred to as Inside gear drive for the strength check of auxiliary engaged transmission pinion gear, with
Internal gear transmission has similar place, but is different from the internal gear engaged transmission of involute gear.The auxiliary angle of engagement or internal messing angle
It is calculated according to formula (1-7) and (1-8), the node radius of gear wheel at interior nodes, abbreviation internal segment is calculated according to formula (1-11)
Radius of circle rwn2
The distance hwq1 of pinion gear stress point to root is calculated by following formula
hwq1=h1-(ra1-rwn1) (5–17)
Pinion gear root pressure angle α wq1
Pinion gear root circular tooth thickness swq1
Pinion gear is obtained in the tangential stress of interior nodes according to formula (7-8)
It is pinion gear root helical angle in formula
As gear wheel, the section of the gear teeth is approximately a rectangle, and transverse tooth thickness approximation circular tooth thickness can be calculated according to formula
Modulus of section (bending modulus)
B is gear tooth contact effective width in formula.The moment of flexure that teeth root is received
M=Fq hwq1
As gear wheel, consider that load coefficient of colligation K (referred to as application factor) obtains the bending stress σ of pinion gear rootF1
Calculation formulas is σF1≤[σ]F1
The contact of anti-involute profile be it is different from involute profile, i.e., the contact area of interior nodes is than involute teeth
Wide contact area is big, and contact strength is reliable, therefore the generally calculating without interior nodes contact strength and school
Core.
About addendum coefficient ha*, tip clearance coefficient c*, general involute gear take h*a=1, c*=0.25, double involute
Gear is determined still according to involute gear.About hobboing cutter corner radius coefficient ρ *, this has regulation in hobboing cutter standard,
In order to which tooth root smoothly transits, Double Involute Gear hobboing cutter is chosen still according to hobboing cutter standard, and hobboing cutter corner radius coefficient takes
*=0.25 ρ.In order to protect working flank, tooth top is using wedge angle burr chamfering is gone, and 45 ° of angle, chamfer height becomes according to modulus
Change, ca=c*amn, chamfering coefficient c*a=0.1.Transmission ratio i will change according to transmission speed to be required to determine, modulus mnIt will basis
Transmission power P and revolving speed n or torque NeIt determines, installation (reality) center away from a will be according to driving torque or mechanism space ruler
Very little determination.Therefore, addendum coefficient h*a, tip clearance coefficient c*, hobboing cutter corner radius coefficient ρ *, chamfering coefficient c*a, transmission
Than i, modulus mn, operating center distance a etc. is known conditions.The number of teeth obtains at first according to transmission ratio i, reference circle normal pressure
Angle αnWith spiral angle of graduated circle β and modification coefficient xnIt can also tentatively choose, check modification according still further to meshing condition and determine, so
Each portion's size of gear is calculated afterwards, determines machined parameters.
Embodiment 1: large transmission ratio gear drive calculates, as shown in Figure 15 and Figure 16
One shelves gear of 6T53 automobile gearbox is using a line gear Curve guide impeller.Transmission input torque 1516Nm (turn round by output
Square 7200Nm), installation center is away from a=123, it is desirable that transmission ratio i=4.5~5, material selection 20CrMnTi carburizing and quenching, material
Characteristic coefficient Δ E=8.84 × 10-6 characteristic system, permissible bending stress [σ]F=420Mpa, allowable contact stress [σ]H=
730Mpa, remaining parameter are chosen according to standard.It is practical to determine pinion gear z according to calculating1=8, gear wheel z2=38, modulus mn
=5.75, pressure angle αn=22.5 °, helixangleβ=7 °.Specific calculate is shown in Table 1-1.
Table 1-1 dotted line Gear Transmission Design computational chart
Table 1-2 gear parameter list (dotted line gear drive)
Table 1-3 hobboing cutter parameter list (pinion gear)
Table 1-4 hobboing cutter parameter list (gear wheel)
Embodiment 2: the gear drive that transmission ratio is 1 calculates (as shown in figure 17)
Steyr drive axle roller gear, center is away from a=193, and transmission ratio i=1 is true according to transmission output torque
Fixed modulus mn=5.25, pressure angle αn=20 °, number of gear teeth z1=z2=35, helixangleβ=15 °.Changed using a line gear
Into design, calculates and determine modulus mn=6.5, pressure angle αn=22.5 °, helixangleβ=15 °, number of gear teeth z1=z2=31,
It is constant to take turns tooth width 36.Calculating process is shown in Table 2-1.
The Gear Transmission Design computational chart of the table 2-1 number of teeth identical (i=1)
Table 2-2 gear parameter list (point line gear i=1)
Table 2-3 gear parameter list
The undescribed part of the invention is identical with the prior art, and this will not be repeated here.
The above is only embodiments of the present invention, are not intended to limit the scope of the invention, all to utilize the present invention
Equivalent structure made by specification and accompanying drawing content is directly or indirectly used in other related technical areas, similarly at this
Within the scope of patent protection of invention.
Claims (3)
1. a kind of design and calculation method of anti-Involutes Gears Transmission engagement, it is characterised in that: the design and calculation method includes
Following steps:
1): being modeled on the basis of rolling circle, establish the functional relation of anti-involute, and by involute profile engaged transmission nothing
Sideshake mesh equation derives anti-involute profile engaged transmission open top container ship equation；
2): according to the condition of anti-involute profile, confirming the calculating value of anti-Profile Shift Coefficient of Involute Gear.
3): calculating boundary radius of circle or diameter；
4): choosing fully teeth height and radius of addendum, it is high to calculate involute teeth；
5): engaged transmission Interference Check；
6): the calculating of related slide coefficient is checked；
7): the inspection of Gear Processing quality.
2. a kind of design and calculation method of anti-Involutes Gears Transmission engagement according to claim 1, it is characterised in that: institute
It states in step 1), on the rolling circle, the rectangular co-ordinate function expression of any point of contact P (x, y) geometric locus changes pole into
Coordinate function equation, obtains
invαk=tan αk-αk
In formula, αkFor pressure angle, βkFor helical angle, here it is infolute functions, and the starting point from basic circle of the curve in basic circle is opened
Begin to the curve of hobboing cutter point of a knife highest cutting point to be also involute, because in basic circle with involute outside basic circle about starting point pair
Claim, because of referred to herein as anti-involute.
3. a kind of design and calculation method of anti-Involutes Gears Transmission engagement according to claim 1, it is characterised in that: institute
It states in step 1), based on involute profile engaged transmission open top container ship equation, that is, involute gear open top container ship equation,
Its equation is
x∑n=xn1+xn2 (1-5)
Or
In conjunction with αt、αwt、αnThere is following relationship with spiral angle of graduated circle β:
Since the tooth curve of major-minor engaged transmission smoothly transits connection, modification coefficient is identical, only net slip system
Number is different, therefore open top container ship equation is also involute gear open top container ship equation, and equation is
x∑sn=xn1-xn2 (1-8)
x∑snIt is the total normal direction modification coefficient of auxiliary engaged transmission, because of xn2For negative value, it is clear that αwtn> αwt, this is anti-involute teeth
Wide engaged transmission open top container ship equation.
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