CN105138734B - A kind of improved speed changer helical gear principal parameter noise optimization design method - Google Patents
A kind of improved speed changer helical gear principal parameter noise optimization design method Download PDFInfo
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- CN105138734B CN105138734B CN201510460240.4A CN201510460240A CN105138734B CN 105138734 B CN105138734 B CN 105138734B CN 201510460240 A CN201510460240 A CN 201510460240A CN 105138734 B CN105138734 B CN 105138734B
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Abstract
A kind of improved helical gear noise optimization design method, belongs to the optimization design field of transmission gear.The present invention provides a kind of improvement Ishikawa method speed changer helical gear principal parameter optimum design method based on theory of mechanics of materials, this method can reduce the transmission error of gear engagement, to reduce the vibration and noise in engagement process, improve service life and ride comfort.The present invention includes following steps：Step 1 establishes the computation model of the engagement dynamic stiffness and dynamic transmission error in helical gear engagement process, and dynamic transmission error undulating value is engaged for calculating helical gear；Step 2, computation model based on step 1 and design of gears laws and regulations requirement, it establishes to reduce noise, reduction volume as target, while the mathematical optimization models of the speed changer helical gear principal parameter of the reliability during proof strength and use, speed changer helical gear is optimized；Step 3 tests to the optimized parameter that optimization design obtains, it is ensured that the correctness of optimum results.
Description
Technical field
The invention belongs to the noise optimization design fields of transmission gear, are based on changing more precisely, the present invention is one kind
Into the helical gear principal parameter noise optimization design method of Ishikawa method.
Background technology
Due to the noise of the generations such as deformation, gap in transmission gear engagement process, all have a significant impact to vehicle noise,
Noise-reducing design is carried out to transmission gear, gear engagement impact can be reduced, improve reliability of gears and service life, and vapour can be promoted
The comfort and driving quality of vehicle.Currently, research circle and engineering circles are nibbled by carrying out correction of the flank shape processing raising gear to gear
It closes quality, reduce meshing noise, belong to the late design after gear major parameter determines and processing.In fact, in speed changer tooth
Design initial stage is taken turns, the number of teeth, modulus, helical angle of gear etc. also have a major impact the noise in Meshing Process of Spur Gear, do not look over so as to check
The preceding processing to design of gears principal parameter is all to be used as the means of reduction meshing noise by improving registration as much as possible.
The study found that the dynamic transmission error in engagement process, is the noise directly affected in speed changer engagement process
Main cause, and can be used as the direct measurement index of its meshing noise.In general, it is special by transmission design to calculate transmission error
It is calculated with software, such as MASTA, or is open FEM-software ANSYS.These softwares, which have, calculates accurately spy
Point, but the special designs such as MASTA software cannot optimize transmission error, and manual modification parameter is needed in design repeatedly
It attempts, to obtain acceptable transmission error fluctuation range, and to speed changer, other indexs also have shadow in modification parametric procedure
It rings, therefore the cumbersome and result of modification is unsatisfactory, and Computing Principle of the finite element softwares such as ANSYS based on finite element, modeling are multiple
It is miscellaneous, calculating process is very long, single calculation can also receive, and if to carry out sensitivity analysis or optimization design, extremely heavy
Parameter iteration during, time span is too long.It is suitable for straight-tooth based on theory of mechanics of materials, the faster Ishikawa method of calculating speed
The dynamic transmission error of wheel calculates and now most of transmission gear uses helical gear, but there is no and passed for helical gear
Pass the research of error quick calculation method.
Invention content
The problem to be solved in the present invention be to provide it is a kind of calculate quickly, the convenient speed changer helical gear principal parameter of modification makes an uproar
Sound optimum design method, auxiliary gear box design.Place in view of the shortcomings of the prior art, the present invention is to traditional spur gear
Ishikawa method is improved, and obtains the improvement Ishikawa method suitable for helical gear dynamic transmission error, this method have calculating speed it is fast,
Parameter changes convenient feature, and uses it in the helical gear principal parameter optimization design of speed changer, is designed in transmission gear
Initial stage just improves noise qualities as far as possible, and ensures the necessary reliability of gear, intensity and corresponding laws and regulations requirement.Specifically,
The present invention adopts the following technical scheme that, a kind of improved speed changer helical gear principal parameter noise optimization design method, including following
Several steps：
Step 1：Using Ishikawa method is improved, the engagement dynamic stiffness and dynamic transmission error in helical gear engagement process are established
Computation model, and calculate the maximum fluctuation value of dynamic transmission error；
Step 2：Based on helical gear pair dynamic transmission error undulating value computation model and design of gears laws and regulations requirement, establish
To reduce noise, reduction volume as target, at the same during proof strength and use reliability speed changer helical gear principal parameter
Mathematical optimization models；
Step 3：, calculated by will optimize in the forward and backward professional Gear calculation software MASTA of gear parameter input
And comparison, examine Optimized model to obtain feasibility and validity, after ensuring that the parameter after optimization can meet constraints, optimization
The transmission error of gear has reduction before comparing optimization.
In technical solution, the improvement Ishikawa method described in step 1 calculates helical gear dynamic transmission error maximum fluctuation value and includes
Following steps：
1. based on traditional Ishikawa method and wheel body circumferential deformation, the shape of the single gear teeth of helical gear corresponding end surface spur gear is calculated
Variable δj, the rectangular segment bending deformation quantity δ of Ishikawa method consideration gear teeth approximate trapezoidBr, trapezoidal portions bending deformation quantity δBt、
Shear the deflection δ generatedsThe deflection δ generated is tilted with foundationG, wheel body circumferential deformation δωConsider that wheel compound plate is approximate bent
Side trapezoidal shear deformation and bending deformation quantity, calculation formula are：δj=(δBr+δBt+δs+δG+δω)j；
2. according to the interaction force F of gear teeth meshingN(hx,ωx) and a pair of of gear teeth meshing total deformation δ (hx,ωx),
Calculate the engagement dynamic stiffness k (h of the single gear teeth pairx,ωx)：Wherein
Be engaged to 3. calculating helical gear corresponding end surface spur gear and leave engagement from entering, that is, the base pitch of passing by it is complete
During whole, which integrally engages dynamic stiffness function of time KDirectly(t), include the following steps：
4. helical gear pair approximation regards N number of superposition with identical transverse parameters small Spur gear pair, each pair of small straight-tooth as
The width of wheel set is B/N, and the angular phase difference of adjacent small Spur gear pair engagement isAccording to the of claim 2 the 3) step
The whole engagement dynamic stiffness function of time K of helical gear corresponding end surface spur gear pairDirectly(t), the engagement of each small Spur gear pair is calculated
Dynamic stiffness ki(t)；
5. the engagement dynamic stiffness k of pair all small Spur gear pairsi(t) summation takes the limit, and it is dynamic to obtain helical gear whole engagement
Stiffness KTiltedly(t), calculation formula is as follows：
6. according to helical gear whole engagement dynamic stiffness KTiltedly(t) the peripheral force F being subject to entire gearn, calculate helical gear
Dynamic transmission error TE (t)：
7. calculating the dynamic transmission error maximum fluctuation value of helical gear engagement：Δ TE0=maxTE (t)-minTE (t)；
8. the transmission error based on FEM calculation is calculated by MASTA, correction factor η is obtained, the present invention is carried
The helical gear dynamic transmission error undulating value that the improvement Ishikawa method gone out calculates is modified：Δ TE=η (maxTE-minTE).
The secondary engagement of 3rd step of above-mentioned technical proposal step 1, the complete engagement process of helical gear corresponding end surface spur gear is dynamic
Rigidity time function KDirectly(t) calculating specifically includes following steps：
(1) transverse contact ratio ε is calculatedα, according to εαSize, path of action is divided into three sections：Double-teeth toothing region B2C, it is single
Tooth engagement area CD and double-teeth toothing region DB1；
(2) three sections of engagement sections are divided into n parts (n needs of certain scale) respectively, certain in engagement point sequence is indicated with i
A bit, according to geometrical relationship, the engagement dynamic stiffness calculation formula of the 2) the single gear teeth pair that step calculates of claim 2 is utilized
The mesh stiffness for calculating the gear teeth pair at the point, if B2C sections of meshing point E1The rigidity at place is kE1(i), the rigidity of CD sections of meshing point E is
kE(i), DB1Section meshing point E2The rigidity at place is kE2(i)；
(3) according to the mesh stiffness of each section gear teeth pair, the whole engagement for calculating helical gear corresponding end surface spur gear pair is dynamic
Stiffness KDirectly(i)：Double-teeth toothing region B2C and DB1Section KDirectly(i)=kE1(i)+kE2(i), monodentate region of engagement CD sections：KDirectly(i)=kE(i)；
(4) the engagement moment function of each meshing point is calculated：
(5) according to KDirectly(i) with the one-to-one relationship of t (i), fitting of a polynomial is carried out, you can obtain helical gear corresponding end
The whole engagement dynamic stiffness function of time K of face spur gear pairDirectly(t)。
In technical solution, the helical gear principal parameter mathematical optimization models described in step 2 include following optimized variable, optimization
Target and constraints：
1. optimized variable：Active tooth number, modulus, pressure angle, helical angle, driving wheel modification coefficient, the facewidth, the active gear teeth
Rise coefficient, driven wheel addendum coefficient, driving wheel tip clearance coefficient, driven wheel tip clearance coefficient；
2. optimization aim：Including reduce as possible can characterize grating of gears transmission error undulating value and reduce gear to the greatest extent
Two targets of volume convert double optimization aims to comprehensive single optimization aim using linear weight weighting method, and mathematic(al) representation is：
Wherein f1(X) it is that helical gear engages transmission error maximum fluctuation value, f1 *(X) it is that transmission error fluctuates single object optimization knot
Fruit, f2(X) it is the volume of helical gear pair,For volume single object optimization result；
3. constraints：The upper and lower limits of optimized variable constrain；Nominal center distance constrains；Jackshaft axial force balance is about
Beam；The minimum modification coefficient constraint that root is cut does not occur；Tooth top transverse tooth thickness constrains；Control the noise objective of slip ratio and frictional force mutation
Constraint；Teeth bending strength constrains；Contact strength of tooth surface constrains.
Compared with prior art, beneficial effects of the present invention：
1. the present invention is established suitable for helical gear dynamic transmission error rapid calculation model, which is based on spur gear
Ishikawa method calculates the thought of mesh stiffness, and it is supplemented and is improved, and has the characteristics that calculating speed is fast, while also having
The characteristics of capable of reflecting the relationship and effect tendency between the main basic parameter of gear and helical gear dynamic transmission error is helical teeth
Model basis is established in wheel principal parameter noise optimization design.
2. the present invention has carried out noise optimization design to speed changer helical gear major parameter, influencing source with main noise passes
Error and the minimum target of gear volume are passed, under the premise of ensureing necessary intensity, reliability requirements, in rules and regulations
In range, the helical gear main structure parameters of speed changer are optimized, in this way, in main structure parameters design just by noise
Optimization take into account, to just ensure that the noise qualities of engagement process to a certain extent at gear structure design initial stage.
Description of the drawings
The present invention will be further described below with reference to the drawings：
Fig. 1 is to design general flow chart based on the speed changer helical gear principal parameter noise optimization for improving Ishikawa method；
Fig. 2 is based on the helical gear dynamic transmission error undulating value calculation flow chart for improving Ishikawa method；
Fig. 3 is the geometric representation that Ishikawa method calculates spur gear engagement deformation；
Fig. 4 is the Computing Principle geometric representation of the circumferential deformation of gear wheel body；
Fig. 5 is the change in location schematic diagram of meshing point；
Fig. 6 is the relationship between helical gear and small Spur gear；
Fig. 7 is the angular phase difference relationship between adjacent small Spur gear；
Fig. 8 is the speed changer helical gear dynamic transmission error-engagement time curve for improving Ishikawa method and calculating；
Fig. 9 is speed changer helical gear dynamic transmission error-engagement time curve that MASTA softwares calculate；
Figure 10 is helical gear engagement dynamic transmission error undulating value computation model data flow；
Figure 11 is to carry out helical gear principal parameter noise optimization design flow diagram using GAs Toolbox.
Specific implementation mode
With reference to the accompanying drawings and examples, improved speed changer helical gear principal parameter noise optimization of the present invention is set
The process of meter is described in detail.
The overview flow chart of improved speed changer helical gear principal parameter noise optimization design of the present invention as shown in Figure 1,
Key step includes：It is primarily based on and improves Ishikawa method, establish the computation model of helical gear dynamic transmission error and its undulating value；So
Afterwards with one of minimum optimization aim of helical gear transmission error maximum fluctuation value, with the minimum another optimization mesh of helical gear volume
Mark, and consider that national standard to the requirement of the strength of gear teeth and other constraintss, establishes the speed changer helical gear based on genetic algorithm
Principal parameter noise optimization design mathematic model, optimizes the helical gear main structure parameters of speed changer；Finally, before to optimization
Parameter afterwards carries out the calculating such as intensity, noise, is verified to optimum results.
Preferably, select the fourth gear cylindric spiral gear of a vapour hybrid power passenger car speed changer 5BB080 as embodiment,
It carries out based on the helical gear principal parameter noise optimization design for improving Ishikawa method, it is assumed that the parameter of the input shaft gear pair of speed changer is
Through determination, the initial parameter of fourth gear pair is as shown in the table.
1 helical gear initial parameter of table
To carry out subsequent calculating, needs using the basic circle of the above Parameter Calculation gear, outside circle, root circle, nibbles
The intermediate quantities such as the radius of chalaza, shown in specific calculating process such as formula (1~13)：
Transverse pressure angle：αt=arctan (tan (αη)/cos(β)) (1)
Transverse module：mt=mn/cos(β) (2)
Reference diameter：d1=mt×z1,d2=mt×z2 (3)
Base circle diameter (BCD)：db1=d1×cos(αt),db2=d2×cos(αt) (4)
Position limiting length：
Pressure angle at pitch circle：αt'=arctan (2 × N1N2/(db1+db2)) (6)
The sum of open top container ship overlap arc：xxn=(z1+z2)×(inv(αt')-inv(αt))/tan(αη)/2 (7)
Driven wheel modification coefficient：xn2=xxn-xn1 (8)
Height of teeth top：
Height of teeth root：
Base radius：rb1=d1/2,rb2=d2/2 (11)
Radius of addendum：ra1=d1/2+ha1,ra2=d2/2+ha2 (12)
Root radius：rf1=d1/2-hf1,rf2=d2/2-hf2 (13)
Wherein, number of teeth z, reference diameter, base circle diameter (BCD), modification coefficient, height of teeth top, height of teeth root, base radius rb, tooth top
Radius of circle ra, root radius rfLower footnote 1 and 2 respectively indicate be driving wheel and driven wheel relative dimensions.
Step 1：Establish the engagement dynamic stiffness and dynamic transmission error computation model in helical gear engagement process
It is summarized by research it is found that the transmission error of gear engagement is missed by the elastic deformation of the stand under load gear teeth and the manufacture of gear
Poor two parts composition.In the design process, do not consider foozle, therefore present invention contemplates that under ideal gear state only by
Transmission error caused by gear teeth stand under load elastic deformation.
As shown in Fig. 2, to the calculating of engagement dynamic stiffness and dynamic transmission error in helical gear engagement process can be divided into
Under several steps：A calculates the single of helical gear corresponding end surface spur gear based on the considerations of Ishikawa method and wheel body circumferential deformation amount
Gear tooth deformation situation；B, according to the deformation of the single gear teeth and the load applied, the engagement for calculating single gear mesh is dynamic rigid
Degree；C considers that there are monodentate, bidentates (or even three teeth) in helical gear corresponding end surface spur gear engagement process according to transverse contact ratio
The case where engagement, calculates the end face spur gear and is engaged to a base pitch of passing by and leaves in the complete procedure of engagement from entering,
The engagement dynamic stiffness of helical gear corresponding end surface spur gear pair entirety；D will be engaged according to factors such as helical gear helical angle, the facewidth
Process is discrete to turn to several small Spur gears, and considers the phase difference of meshing point, by the aforementioned helical gear corresponding end being calculated
Face spur gear pair integrally engages dynamic stiffness and calculates the whole engagement dynamic stiffness of helical gear pair, and calculates corresponding dynamic and transmit mistake
Difference；E considers error caused by some hypothesis for the theoretical calculation that the present invention uses, is repaiied to helical gear dynamic transmission error
Just.
Step A：It calculates in engagement process, the deformation of the single gear teeth of the helical gear corresponding end surface spur gear.
In end face spur gear parameter corresponding to helical gear, the number of teeth, centre-to-centre spacing, addendum coefficient, tip clearance coefficient, basic circle half
Diameter, radius of addendum, root radius are all as helical gear, and pressure angle, modulus, the tooth of helical gear corresponding end surface spur gear
It is wide then consistent with helical gear transverse pressure angle, transverse module, effective facewidth.
As shown in figure 3, calculating the geometric representation of spur gear engagement deformation for Ishikawa method, wherein hrIt is high for bottom rectangle,
sFWide for rectangle, h is rectangle and trapezoidal total height, skFor the trapezoidal upper length of side, ωx、hxRespectively load FNAction direction and position
To the height on rectangle bottom edge.When Ishikawa method calculates spur gear engagement deformation, using the basic thought of the mechanics of materials, gear is regarded as
It is rectangle and trapezoidal combination, considers under load effect rectangle and trapezoidal bending and shear-deformable.According to gear base
The calculating of this parameter and formula (14~19), to the crucial geometric parameter of rectangular, trapezoidal and load position and action direction
It calculates as shown in formula (20~24)：
αa=arccos (rb/ra),αf=arccos (rb/rf) (14)
S=r π/z (15)
αF1=arccos (rb1/rF1),αF2=arccos (rb2/rF2) (effective root circle pressure angle) (19)
sk=ra· (s/r+2×(inv(αt)-inv(αa))) (20)
sF=2rf1·sin(π/2z+inv(αt)-tan(αF1)+αF1) (21)
Wherein, z is the number of teeth, rbFor base radius, raFor radius of addendum, α0For pressure angle of graduated circle；rfFor root circle half
Diameter；rxFor the distance of load position and gear centre point.
Deflection δ of the gear in load position along path of contact direction is calculated by Ishikawa methodStoneIt is specific to calculate such as formula
(25)：
δStone=δBr+δBt+δs+δG (25)
Wherein, δBr、δBt、δsAnd δGRespectively rectangular segment bending deformation quantity, the bending variable of trapezoidal portions, shearing production
Raw deflection and foundation tilt the deflection generated, specific to calculate as shown in formula (26~29)：
Wherein,FNFor the independent stress of each gear teeth.
The present invention considers the circumferential deformation of gear wheel body, changes as the first step to Ishikawa method on the basis of Ishikawa method
Into.
As shown in figure 4, the Computing Principle geometric representation of the circumferential deformation for gear wheel body, by the trunnion axis in the gear center of circle
It is reduced to that a curl is trapezoidal to the gear compound plate between gear teeth dangerouse cross-section, trapezoidal following a length of root diameter db, on
Length of side tail dangerouse cross-section width sF, by load FNIt moves at dangerouse cross-section, then web flexural deformation is by tangential force FNcosωxAnd load
Lotus FNMoment M caused by mobilex(Mx=FNcosωxhx) effect generation.
Web arbitrary section inertia is to the moment of inertia in facewidth direction：
It is trapezoidal a height of：
Tangential force effect bottom web is deformed into
The deformation of Moment bottom web is
The total deformation δ of webω=δω1+δω2, can obtain after integral shown in total deformation such as formula (34)：
Deflection in the Meshing Process of Spur Gear calculated according to Ishikawa method and wheel body circumferential deformation, you can obtain the helical gear
Corresponding end face spur gear is in load position along the deflection δ in path of contact directionjSuch as formula (35)：
δj=(δBr+δBt+δs+δG+δω)j (35)
Wherein, j=1,2, that take 1 expression calculating is the deflection of driving wheel, δ thereinBr、δBt、δsAnd δGIt is all made of master
The calculation of design parameters of driving wheel, that take 2 expressions calculating is the deflection of driven wheel, δ thereinBr、δBt、δsAnd δGIt is all made of driven
The calculation of design parameters of wheel.
Step B：According to the result of calculation of the single gear engagement deformation of helical gear corresponding end surface spur gear, helical gear pair is calculated
Answer the time-variant mesh stiffness such as formula (36) of a pair of meshing gear teeth pair of end face spur gear：
Wherein, FN(hx,ωx) be a pair of of gear teeth meshing interaction force, as the active force that the single gear teeth are subject to；Including two teeth of driving wheel and driven wheel
The deformation of wheel.
Step C：The spur gear pair of the corresponding end face spur gear of helical gear pair is calculated in engagement process according to transverse contact ratio
In whole time-variant mesh stiffness.
Dynamic mesh stiffness calculating is carried out to helical gear corresponding end surface spur gear pair, considers to enter to be engaged to from gear to turn over
One base pitch is a complete procedure.According to the basic parameter of helical gear corresponding end surface spur gear, end face weight is calculated
It is right to be：
Transverse contact ratio illustrates that there are double-teeth toothing regions and monodentate region of engagement in gear mesh engagement process between 1~2.
As shown in figure 5, for the change in location schematic diagram of meshing point E, B in figure2C and DB1For double-teeth toothing region, CD is monodentate
Region of engagement, in practical engagement process, meshing point E is from B2Into engagement, double-teeth toothing region B is first passed around2C is nibbled using monodentate
Area CD is closed, using double-teeth toothing region DB1, then in B1Point exits engagement.Wherein, as the meshing point E of a pair of of gear teeth1In B2C
(or DB1) section when, must have another gear teeth to being engaged in DB1(or B2C) section, if meshing point is E2。
By formula (34) it is found that above-mentioned mesh stiffness k (hx,ωx) it is to use load position hxWith action direction ωxTo count
It calculates, but hxAnd ωxAnd change with engagement process, it needs to be indicated with the position of meshing point and time.Here by B2C、
CD is respectively divided into 100 parts, when E at an arbitrary position when, ωx、hxIt can be by O1E indicates that the gear teeth enter B2When C sections of engagements, while having two
Meshing state is in the gear teeth, need to be calculated separately in B2C sections of first pair of tooth and DB1Second pair of tooth of section.
First, meshing point is calculated to limit of contact point N according to formula (38~40)1Distance：
Double-teeth toothing region：If E1In B2C, E2In DB1Section, E1、E2At a distance of a tooth pitch Pb, then
Wherein, i=1~100, n=100, with meshing point E1From B2Start to be moved to C points, i is gradually increased to 100 from 1.
Monodentate region of engagement：If E is in the sections CD, then
Wherein, i=1~100, n=100, as meshing point E is moved to D points since C, i is gradually increased to 100 from 1.
Utilize N1E1、N1E2And N1E can calculate the center of circle to the distance O of meshing point according to formula (41)1E (or O1E1With
O1E2), and then corresponding ω is calculated according to formula (42~44)x、hx：
The mesh stiffness for each section gear teeth pair being finally calculated by Ishikawa method in this way is available to be expressed as：
B2C sections of meshing point E1The rigidity at place：kE1(i)
CD sections of meshing point E：kE(i)
DB1Section meshing point E2Rigidity：kE2(i)
To the whole engagement dynamic stiffness K of helical gear corresponding end surface spur gear pairDirectly(i) each section mesh stiffness can be passed through
It directly acquires, for CD sections of monodentate region of engagement, gear pair integrally engages dynamic stiffness KDirectly(i) gear teeth at meshing point E are equal to
Mesh stiffness, and double-teeth toothing region B2C and DB1Section, while the two pairs of teeth engaged can be regarded as two springs in parallel, so
Whole engagement dynamic stiffness KDirectly(i) it is added for the rigidity of two pairs of teeth, specifically as shown in formula (45~46)：
Double-teeth toothing region B2C and DB1Section：KDirectly(i)=kE1(i)+kE2(i) (45)
CD sections of monodentate region of engagement：KDirectly(i)=kE(i) (46)
The rotating speed of driving wheel is set as nz, then the time of a tooth is turned overIf certain gear is from B2Into engagement
When be 0 moment, then with the progress of engagement, shown in engagement moment function such as formula (47)：
Wherein, with the progress of engagement, each section of i=1~100.
In this way, the corresponding i of meshing point all has one-to-one relationship with three period functions in each engage in section,
And monotonic increase.To KDirectly(i) being engaged at three with t (i) has one-to-one relationship in section, to B2C, CD and DB1Three sections
Mesh stiffness and engagement the moment be fitted respectively, you can show that helical gear corresponding end surface spur gear pair integrally engages dynamic stiffness
Function of time KDirectly(t), which is piecewise function.
Step D：Improvement Ishikawa method based on phase delay calculates helical gear engagement dynamic stiffness and dynamic transmission error.
The tooth profile of spur gear is generating surface when doing pure rolling on base cylinder, in generating surface one it is equal with gear shaft
The involute surface that capable straight line KK is transformed into, formation basic theory and the straight spur gear phase of helical gear teeth contour curved surface
Seemingly, the straight line KK but in generating surface is not parallel to the axis of base cylinder, but there are one helixangleβs with it.So in model
On, as shown in fig. 6, it is N number of, which can to regard the helical gear pair approximation that a pair of of width is B, helical angle is β as, for we has same side
The width of the superposition of face parameter small Spur gear pair, each pair of small Spur gear pair isFrom the perspective of engagement, as each pair of in Fig. 7
Small Spur gear pair (being indicated with i+1) is than previous to secondary (being indicated with the i) leading angle of small Spur gear(48) formula as follows：
Wherein, AB, A ' B ' are respectively the end face reference circle arc length of two adjacent small Spur gears, and r is end face reference radius.
Then, the time phase difference of two small Spur gear pairs of initial and end (the 1st and n-th) is：
Shown in the time phase difference of adjacent small Spur gear secondary i and i+1 such as formula (49)：
Wherein T is mesh cycle, and turns over a tooth required time, and z is the number of teeth.
Dynamic stiffness K is integrally engaged according to the helical gear corresponding end surface spur gear pair that the width being the previously calculated is BDirectly(t),
Width, which can be obtained, isThe secondary whole engagement dynamic stiffness of the 1st small Spur gear
Shown in the secondary whole engagement dynamic stiffness such as formula (50) of i-th of small Spur gear：
The limit is taken to N and is summed, the whole mesh stiffness K of helical gear pair is obtainedTiltedly(t) as shown in formula (51)：
Then dynamic transmission error TE (t) and transmission error maximum fluctuation value Δ TE0 is respectively as formula (52) and (53) calculate：
Δ TE0=maxTE (t)-minTE (t) (53)
Wherein, FnThe peripheral force being subject to for entire gear.
As shown in Figure 8 and Figure 9, the helical gear engagement process respectively of the present invention for improving Ishikawa method and MASTA calculating
In dynamic transmission error, it can be seen that its variation tendency is consistent, therefore computational methods of the present invention are feasible.
Step E improves the amendment that Ishikawa method calculates transmission error.
Based on the transmission error for improving the calculating of Ishikawa method, there are certain gap between actual transfer error, reason is main
Including following factor：
Ishikawa method formula is handled the gear teeth as trapezoidal, so the rigidity calculated in gear teeth intermediate region can be inclined
Greatly, the deformation values being calculated in this way are less than normal；
For helical gear, the present invention by its it is discrete turn to more parts of wide small Spur gears, and counted by considering delayed phase
The whole engagement dynamic stiffness of helical gear pair is calculated, it is rigid that such computational methods do not account for the tension and compression connected between two small Spur gears
The problem of degree and shearing rigidity, therefore have further influence to whole mesh stiffness and dynamic transmission error.
Consider these influences, the transmission error based on FEM calculation is calculated by MASTA, the present invention is carried
The improvement Ishikawa method gone out calculates transmission error and is modified.
The result of calculation of 2 MASTA of table and Ishikawa method compares
Based on table 2, it is modified to improving the helical gear transmission error maximum fluctuation value that Ishikawa method calculates, correction factor
For：η=2.55
Therefore, revised improvement Ishikawa method helical gear transmission error maximum fluctuation value Δ TE such as formulas (54)：
Δ TE=η (maxTE-minTE) (54)
As shown in Figure 10, for based on the helical gear engagement process dynamic transmission error for improving Ishikawa method and phase delay consideration
The data flow diagram of undulating value computation model.First, the helical gear basic parameter provided according to table 1, to helical gear corresponding end
Face spur gear calculates the rectangle of basic Ishikawa method and geometric parameter and engagement that trapezoidal geometric parameter, variable cross-section wheel body are trapezoidal
The position of point and load action direction；Then, according to the locality of geometric parameter and active force, helical gear corresponding end surface is calculated
The deformation quantity of the single gear teeth of the single gear of spur gear；According to driving wheel and the respective deflection of driven wheel, helical gear is calculated
The engagement dynamic stiffness of corresponding end surface spur gear a pair of gear teeth；According to helical gear transverse contact ratio, helical gear corresponding end surface is determined
Rodent population number in spur gear engagement process calculates helical gear corresponding end surface straight-tooth using the engagement dynamic stiffness of a pair of of gear teeth
The whole engagement dynamic stiffness in a complete engagement process of wheel set, and by the transformation of independent variable, obtain with the engagement moment
The helical gear corresponding end surface spur gear pair entirety dynamic stiffness function of time indicated for independent variable；Based on helical gear corresponding end surface straight-tooth
The engagement dynamic stiffness of wheel set considers that it is small Spur gear that helical gear, which is divided into multiple pinion gears and approximately equivalent, introduces meshing point
Between phase difference concept, engage dynamic stiffness computation model using helical gear corresponding end surface spur gear pair, consider different small straight
The engagement time phase difference of gear obtains the whole engagement dynamic stiffness of helical gear pair to the limit summation of all small Spur gear consequent poles；Profit
With helical gear pair engagement dynamic stiffness and practical engagement process in interaction force, obtain helical gear engage dynamic transmission error and
Its maximum fluctuation value；Consider the deviation that calculating and equivalent small Spur gear based on the mechanics of materials generate, helical gear engagement is moved
State transmission error maximum fluctuation value is modified, and obtains helical gear dynamic engagement transmission error maximum fluctuation value to the end.
Step 2 is established to reduce noise, reduction volume as target, while the reliability during proof strength and use
Speed changer helical gear principal parameter mathematical optimization models.
It optimizes, it is necessary first to it determines optimized variable and its variation range, initial value, determines optimization aim, with
And enough constraints, then according to optimization problem the characteristics of, select optimization algorithm optimize.In view of helical gear ginseng
In number, not only there are the continuous variables such as modulus, helical angle, but also there are discrete variables as the number of teeth, meanwhile, the target of optimization it
One, transmission error undulating value computation model is non-linear, non-differentiability, therefore this example is optimized using genetic algorithm.
As shown in figure 11, for using the flow chart of genetic algorithm progress helical gear principal parameter noise optimization design.
In matlab GAs Toolboxes, the number of optimized variable is inputted, optimization object function title, the upper and lower limit of variable, linearly
Equality constraint, inequality constraints condition, Nonlinear Constraints and other necessary configurations, you can carry out based on something lost
The optimization of propagation algorithm.
Selection for optimized variable and optimized variable range, from the independence ensured as possible between parameter, the present invention
Consider the helical gear major design structural parameters in table 3.
3 helical gear Optimal Structure Designing variable of table and optimization range
Wherein, modulus range, pressure angular region, spiral angular region, addendum coefficient range and tip clearance coefficient range are all
Pass through engineering practice and rules and regulations.
Since transmission ratio has usually had been contemplated that in economy, dynamic property analysis and design, active and passive wheel
What the ratio between number of teeth was to determine, you can pass through transmission ratio and the driven tooth number of driving wheel Tooth Number Calculation：Z2=iZ1 (55)
Consider in this example, only optimized by taking fourth gear as an example, transmission ratio is influenced by direct high gear ratio,
And with the relatively prime requirement of the number of teeth, therefore the driving and driven number of gear teeth of fourth gear does not change substantially, therefore the number of teeth is fixed in example,
It does not do and optimizes.
Meanwhile the modification coefficient of driven wheel is also to be determined according to operating center distance, reference center distance etc., such as formula (56) institute
Show：
Determination about object function.The main target of optimization of the present invention is to realize the helical gear principal parameter noise reduction of speed changer
Design, therefore first optimization aim is to try to reduce the transmission error undulating value of enough characterization gratings of gears, specific calculating process
Using the helical gear transmission error undulating value computation model of step 1；Meanwhile in the premise for ensureing necessary intensity and reliability
Under, it should reduce the volume and quality of gear to the greatest extent, therefore second optimization aim of the present invention is to reduce gear volume to the greatest extent.
Using linear weight weighting method, two optimization aims are converted into one, specific weighting scheme such as formula (57) indicates：
F (X)=s [W1f1(X)+W2f2(X)] (57)
Wherein：
W1=1/|f1 *(X)|--- -- volume weighting coefficient, f1 *(X) --- --- volume single goal optimal value；
--- -- transmission error fluctuates weighting coefficient,--- --- gear dynamic transmission error wave
Dynamic value single goal optimal value.
About optimization constraints.In addition to the bound to range of variables for describing and determining in the range of optimized variable
Constraint, in helical gear optimization, it is also necessary to consider to the intensity of gear, reliability, main driven gear centre-to-centre spacing, axial force etc.
It is required that.
1) nominal center distance constrains：
It is constrained by complete vehicle structure design, transmission input shaft, jackshaft and position of output axle, centre-to-centre spacing is to have determined
, the nominal center distance of present example is 135, obtains Nonlinear Constraints g1(X) as shown in formula (58)：
2) jackshaft axial force balance constrains：
Helical gear will produce axial force during power transmission, because these power can be applied on bearing, increase bearing
Load, reduce bearing life.So being considered as this factor in the design process, power makes axial resultant force close to zero.Root
According to jackshaft axial force balance condition, Nonlinear Constraints g can be obtained2(X) and g3(X) as shown in formula (59~60)：
3) the minimum modification coefficient constraint that root is cut does not occur：
To prevent from working as z < zminWhen root do not occur cut, regulation minimum modification coefficient is needed, to obtain constraints g4(X)
As shown in formula (61)：
4) tooth top transverse tooth thickness constrains：
Outside circle normal plane circular tooth thickness Sntk0.3m should be not less thannk, to obtain constraints g5(X) and g6(X) such as formula
Shown in (62~63)：
g5(X)=0.3mn-Snt1≤0 (62)
g6(X)=0.3mn-Snt2≤0 (63)
5) constraint of other noise objectives：
It summarizes known to achievement in research and engineering practice result：1, the starting point of meshing can reduce noise far from basic circle, and 2, gear
Secondary engaging-in section is less than and nibbles out segment length and can reduce noise., two noise objectives, β are determined respectively at 2 points accordinglycgSlip ratio is controlled,
βzFrictional force mutation is controlled, shown in definition such as formula (64~65),：
Wherein：dfaCircular diameter is originated for engagement,D'And db'Respectively
The outer diameter and base circle diameter (BCD) of phase selective gear.dbFor base circle diameter (BCD), tnFor normal pitch, tn=π mn, ρ1max,ρ2maxBased on, driven tooth
Take turns maximum curvature radius, db1,db2Based on, driven gear base circle diameter (BCD), αsFor the end face angle of engagement.
For βcgAnd βz, it is desirable that βcg< 1, βz< 0.9 obtains the constraints g for needing to meet7(X)~g9(X) such as formula (66
~68) shown in：
6) strength constraint
There are many kinds of the failure modes of gear, such as tooth surface abrasion, tooth face agglutination and tooth surface plastic deformation etc., wherein most heavy
The two kinds of failure modes wanted are break of gear tooth and rippling.Break of gear tooth is generally all since root, because of root at work
The bending stress in portion is maximum, and since the factors such as the abrupt change of cross-section are also easy to produce stress concentration.And spot corrosion refers to then the gold of gear surface
Category falls off, and easily appears near nodel line, because when being engaged near nodel line, contact stress is big, is not likely to produce oil film.And both
Failure mode is constrained by teeth bending strength and tooth face contact fatigue strength respectively.According to GB3480-1997, the flank of tooth is obtained
The formula of contact and tooth root bending-fatigue strength constraint.
A, contact strength of tooth surface constrain g10(X) such as formula (69)：
g10(X)=σH-σHP≤0 (69)
Wherein, σHFor the calculating contact stress of gear, σHPFor the allowable contact stress of gear.
Wherein, ZBFor single pair tooth engagement coefficient, KAFor coefficient of utilization, KVFor dynamic load factor, KHβFor load distribution along width system
Number, KHαIt is related with the accuracy of manufacture for load share between teeth, σH0To calculate the basic value of contact stress at node.
Wherein, σHlim·ZNTThe experiment face fatigue limit obtained according to S-N Curve, SHminFor face
Intensity minimum safety factor, ZL、ZV、ZR、ZWAnd ZXRespectively lubricant coefficient, velocity coeffficient, roughness value, work hardening system
Number and coefficient.
B, tooth root bending-fatigue strength constrain g11(X)、g12(X) as formula (72) indicate：
gj(X)=σFi-σFPi≤0 (72)
Wherein, σFFor the calculating root stress of gear, σFPFor the root stress allowable of gear, j=11,12, i=1,2.
σF=σF0·KA·KV·KFβ·KFα (73)
Wherein, KAFor coefficient of utilization, KVFor dynamic load factor, KFβFor the Longitudinal Load Distribution Factors that bending strength calculates, KFα
For the load share between teeth of bending strength, σF0For root stress basic value.
Wherein, SFminFor bending strength minimum safety factor, σFlim·YNTFor the experiment tooth obtained according to S-N Curve
Root bending fatigue limit, YSTFor Stress Correction Coefficient, YXFor size factor, YδrelTFor opposite root fillet sensitivity coefficient, here
Using the sensitivity coefficient of creep rupture life, YRrelTFor opposite root surface situation coefficient, the root surface of creep rupture life is used here
Situation coefficient.
More than, the calculating of formula (70), (71), (73), parameter involved in (74), with reference to the formula in GB3480-1997
Or it tables look-up.
Step 3 verifies the feasibility of optimum results.
By the calculating and optimization of step 1 and step 2, the speed changer helical gear principal parameter noise optimization of this example is obtained
Design result is as shown in table 4.
The helical gear principal parameter that table 4 optimizes
It, will to verify the validity of improved speed changer helical gear principal parameter noise optimization design method proposed by the present invention
In helical gear principal parameter input MASTA business softwares after original helical gear parameter and optimization, to being produced in helical gear engagement process
Raw transmission error and its undulating value is calculated, and obtains that the results are shown in Table 5, and the loaded load used is maximum load
1261.5NM。
Table 5 optimizes front and back gear performance
| Performance indicator | maxTE(μm) | ΔTE(μm) | Gear volume (dm3) |
| Before optimization | 60.3908 | 5.2946 | 1.7 |
| After optimization | 57.2715 | 3.1279 | 1.6772 |
| The front and back variation of optimization | It is empty | - 41% | - 1.34% |
As can be seen from Table 5, transmission error undulating value of the helical gear after optimization in engagement process reduces 41%, together
When gear volume reduce 1.34%, this illustrates improved speed changer helical gear principal parameter noise optimization side proposed by the present invention
Method is effective.
Claims (3)
1. a kind of improved speed changer helical gear principal parameter noise optimization design method, which is characterized in that the improved change
Fast device helical gear principal parameter noise optimization design method includes the following steps：
Step 1：Using Ishikawa method is improved, the meter of the engagement dynamic stiffness and dynamic transmission error in helical gear engagement process is established
Model is calculated, and calculates the maximum fluctuation value of dynamic transmission error；
Step 2：Based on helical gear pair dynamic transmission error undulating value computation model and design of gears laws and regulations requirement, establish to subtract
Small noise, reduction volume be target, while during proof strength and use the speed changer helical gear principal parameter of reliability it is excellent
Change designs a model；
Step 3：The correctness for the Optimum Design Results that inspection Optimized model obtains；
Wherein, step 1 specifically comprises the following steps：
1) it is based on traditional Ishikawa method and wheel body circumferential deformation, calculates the deformation quantity of the single gear teeth of helical gear corresponding end surface spur gear
δj, the rectangular segment bending deformation quantity δ of Ishikawa method consideration gear teeth approximate trapezoidBr, trapezoidal portions bending deformation quantity δBt, shearing
The deflection δ of generationsThe deflection δ generated is tilted with foundationG, wheel body circumferential deformation δωConsider wheel compound plate approximation curl ladder
The shear deformation and bending deformation quantity of shape, calculation formula are：δj=(δBr+δBt+δs+δG+δω)j, wherein j=1,2 take 1 table
Show calculating is the deflection of driving wheel, δ thereinBr、δBt、δsAnd δGIt is all made of the calculation of design parameters of driving wheel, takes 2 expressions
That calculate is the deflection of driven wheel, δ thereinBr、δBt、δsAnd δGIt is all made of the calculation of design parameters of driven wheel；
2) according to the interaction force F of gear teeth meshingN(hx,ωx) and a pair of of gear teeth meshing total deformation δ (hx,ωx), it calculates
The engagement dynamic stiffness k (h of the single gear teeth pairx,ωx)：WhereinωxFor load
FNAction direction, hxFor FNPosition to rectangle bottom edge height；
3) calculating helical gear corresponding end surface spur gear is engaged to from entrance and leaves engagement, that is, the complete mistake for a base pitch of passing by
Cheng Zhong, end face spur gear pair integrally engage dynamic stiffness function of time KDirectly(t), include the following steps：
(1) transverse contact ratio ε is calculatedα, according to εαSize, path of action is divided into three sections：Double-teeth toothing region B2C, monodentate are nibbled
Close area CD and double-teeth toothing region DB1；
(2) three sections of engagement sections are divided into n parts respectively, certain point in engagement point sequence are indicated with i, according to geometrical relationship, profit
The mesh stiffness of the gear teeth pair at the point is calculated with the engagement dynamic stiffness calculation formula of the 2) the single gear teeth pair that step calculates, if
B2C sections of meshing point E1The rigidity at place is kE1(i), the rigidity at CD sections of meshing point E is kE(i), DB1Section meshing point E2The rigidity at place
For kE2(i)；
(3) the whole engagement dynamic stiffness K of helical gear corresponding end surface spur gear pair is calculated to mesh stiffness according to each section gear teethDirectly
(i)：
Double-teeth toothing region B2C and DB1Section：KDirectly(i)=kE1(i)+kE2(i),
CD sections of monodentate region of engagement：KDirectly(i)=kE(i)；
(4) the engagement moment function of each meshing point is calculated：
Wherein, B2C, CD indicates region of engagement B respectively2C, CD sections of line segment length, PbFor a tooth pitch, TzOne is turned over for driving wheel
The time of tooth；
(5) according to KDirectly(i) and the one-to-one relationship of t (i), progress fitting of a polynomial obtain helical gear corresponding end surface spur gear
Secondary whole engagement dynamic stiffness function of time KDirectly(t)；
4) the helical gear pair approximation that width is B is regarded as N number of superposition with identical transverse parameters small Spur gear pair, Mei Dui little
The width of spur gear pair is B/N, and the angular phase difference of adjacent small Spur gear pair engagement isAccording to the helical gear pair of the 3) step
Answer the whole engagement dynamic stiffness function of time K of end face spur gear pairDirectly(t), the engagement dynamic stiffness k of each small Spur gear pair is calculatedi
(t)；
5) to the engagement dynamic stiffness k of all small Spur gears pairi(t) summation takes the limit, obtains helical gear whole engagement dynamic stiffness KTiltedly
(t), calculation formula is as follows：
Wherein Δ T is the engagement time phase difference of two small Spur gear pairs of head and the tail；
6) according to helical gear whole engagement dynamic stiffness KTiltedly(t) the peripheral force F being subject to entire gearn, calculate helical gear dynamic
Transmission error TE (t)：
7) the dynamic transmission error maximum fluctuation value of helical gear engagement is calculated：Δ TE0=max TE (t)-min TE (t)；
8) transmission error based on FEM calculation is calculated by MASTA, obtains correction factor η, to the improvement stone of proposition
The helical gear dynamic transmission error undulating value that river method calculates is modified：Δ TE=η (max TE-min TE).
2. improved speed changer helical gear principal parameter noise optimization design method as described in claim 1, which is characterized in that institute
The helical gear principal parameter mathematical optimization models stated include following optimized variable, optimization aim and constraints：
1) optimized variable：Active tooth number, modulus, pressure angle, helical angle, driving wheel modification coefficient, the facewidth, driving wheel height of teeth top
Coefficient, driven wheel addendum coefficient, driving wheel tip clearance coefficient, driven wheel tip clearance coefficient；
2) optimization aim：Including reduce as possible can characterize grating of gears transmission error undulating value and reduce gear volume to the greatest extent
Two targets convert double optimization aims to comprehensive single optimization aim using linear weight weighting method, and mathematic(al) representation is：
Wherein f1(X) it is that helical gear engages transmission error maximum fluctuation value, f1 *(X) it is that transmission error fluctuates single object optimization knot
Fruit, f2(X) it is the volume of helical gear pair,For volume single object optimization result；
3) constraints：The upper and lower limits of optimized variable constrain；Nominal center distance constrains；Jackshaft axial force balance constrains；
The minimum modification coefficient constraint that root is cut does not occur；Tooth top transverse tooth thickness constrains；Control the noise objective of slip ratio and frictional force mutation
Constraint；Teeth bending strength constrains；Contact strength of tooth surface constrains.
3. improved speed changer helical gear principal parameter noise optimization design method as described in claim 1, which is characterized in that institute
The correctness for the Optimum Design Results that the inspection Optimized model stated obtains is special by that will optimize forward and backward gear parameter input
It is calculated and is compared in industry Gear calculation software MASTA, after ensuring that the parameter after optimization can meet constraints, optimization
The transmission error of gear has reduction before comparing optimization.
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| CN106326555B (en) * | 2016-08-23 | 2019-10-01 | 温州大学 | A kind of automobile speed-changing device robust Fatigue Design Methods |
| CN106326564A (en) * | 2016-08-25 | 2017-01-11 | 辽宁科技学院 | Modification method for gearbox bevel gear engagement and noise reduction |
| CN106407546B (en) * | 2016-09-09 | 2019-04-30 | 上海理工大学 | A method of utilizing origin dynamic stiffness specificity analysis case of transmission local deformation feature |
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| CN106763642B (en) * | 2017-02-22 | 2020-09-04 | 北京新能源汽车股份有限公司 | Noise reduction method for electric automobile speed reducer and electric automobile speed reducer |
| CN107194124B (en) * | 2017-06-23 | 2020-08-07 | 重庆长安汽车股份有限公司 | Design method of transmission helical gear |
| CN107273637B (en) * | 2017-07-06 | 2020-04-10 | 济南大学 | Volume optimization design method for single-stage straight bevel gear |
| CN110056639A (en) * | 2019-04-25 | 2019-07-26 | 浙江吉利控股集团有限公司 | Calculation method and system for gear train |
| CN111414667B (en) * | 2020-04-28 | 2023-09-12 | 西安渐开机械传动技术有限责任公司 | Design method of involute cylindrical gear end face macroscopic parameters based on meshing line |
| CN112711853B (en) * | 2020-12-31 | 2022-04-01 | 石家庄国祥运输设备有限公司 | Train air conditioner structure noise simulation method |
| CN113221261B (en) * | 2021-02-09 | 2022-12-13 | 重庆大学 | Method for formulating vibration limit value of aviation transmission system |
| CN113283032B (en) * | 2021-06-01 | 2023-01-03 | 哈尔滨工程大学 | Marine gear subsurface stress calculation method related to mixed lubrication-contact state |
| CN113255084B (en) * | 2021-07-07 | 2022-05-06 | 盛瑞传动股份有限公司 | Rapid optimization method of gear noise radiation based on response surface method |
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