CN103761396A - Tooth direction line-type quantification designing method for cylindrical gear based on variable misalignment quantities - Google Patents

Abstract

The invention belongs to the technical field of drive control and provides a tooth direction line-type quantification designing method for a cylindrical gear based on variable quantities. The purposes are that the profiling quantity in the tooth direction is determined under the condition of variable loads, the problems that in the power transmission process of the cylindrical gear, contact stress is increased and distributed unevenly due to misalignment quantity are solved, and the bearing capacity of the cylindrical gear is improved. Contact stress values not profiled are calculated under all levels of loads, the number of circulation times of the stress is calculated under all the levels of loads, the allowable number of circulation times is calculated under all the levels of loads, an optimization objective function is set, with the maximum misalignment quantity and the minimum misalignment quantity as boundary conditions, the profiling quantity of the set optimization objective function is solved under the minimum value, and the profiling quantity is the solved value. The contact stress of the gear can be reduced under the variable loads, tooth surface stress values among all the levels of loads are equalized, tooth direction stress is equalized under all the levels of loads, the bearing capacity of the gear is improved, the gear size is reduced under the finite life condition, and the transmission power density is increased.

Description

Cylindrical gear teeth directional line style quantifying design method under a kind of change magnitude of misalignment

Technical field

The invention belongs to transmission control technology field, relate to cylindrical gear teeth directional line style quantifying design method under a kind of change magnitude of misalignment, be particularly related to a kind of under variable load the optimum line style correction of the flank shape of cylindrical gear teeth directional computing method in flexible support environment.

Background technology

The kinematic train such as military vehicle, engineering machinery middle gear has applying working condition complicated condition, the feature that load-bearing capacity variation range is wide, within the scope of gear carrying, be greater than the load at different levels of permanent fatigue limit allowable own, time history is enough large, the impact that fatigue damage is caused all can not be ignored, and the design of gear fatigue behaviour is finite lifetime by above conditional decision, designs.If said gear transmission adopts flexible support structure for improving power density, in becoming more meticulous design process, gear adopts the axial modification technology based on gear teeth magnitude of misalignment, can improve gear capacity by homogenizing flank of tooth stress.For multistage load geartooth correction problem, adopt that one-level load not yet to come to a conclusion at present as correction of the flank shape foundation both at home and abroad.Between gear teeth magnitude of misalignment and transmitted load, be nonlinear relationship on the other hand, increased in the definite difficulty of the meshing reason profiling quantity of variable load lower whorl.Therefore, to those skilled in the art, in the urgent need to studying cylindrical gear axial modification quantifying design method under a kind of change magnitude of misalignment.

Summary of the invention

(1) technical matters that will solve

The technical problem to be solved in the present invention is to be under variable load condition becoming magnitude of misalignment, calculating based on load at different levels to gear life damage, obtain load at different levels and affect the method that lower gear damages the optimum line style correction of the flank shape of minimum teeth directional, to determine the profiling quantity of teeth directional under variable load condition, solve the gear teeth and in transferring power process, by magnitude of misalignment, brought the problem of contact stress increase and stress distribution inequality, realize the raising of gear capacity.

(2) technical scheme

For solving the problems of the technologies described above, the invention provides cylindrical gear teeth directional line style quantifying design method under a kind of change magnitude of misalignment, it is characterized in that: this method for designing specifically comprises the steps:

Step 1, according to formula (1), calculate under load at different levels the not contact stress value of correction of the flank shape:

${\mathrm{\σ}}_{\mathrm{Hi}}=Z_B{\mathrm{\σ}}_{H0i}\sqrt{K_A{K}_{\mathrm{Vi}}{K}_{\mathrm{H\βi}}{K}_{H\∂i}}---\left(1\right)$

σ in formula (1) _hibe calculated stress value under i level load, Z _bfor list is to tooth contact radio, σ _h0ibe basic stress value under i level load, K _afor coefficient of performance, K _vibe dynamic load factor under i level load, K _{h β i}be teeth directional distribution coefficient under i level load, K _{h θ i}it is between cog distribution coefficient under i level load;

Step 2, according to formula (2), calculate stress-number of cycles under load at different levels:

N _ni＝60n _ih _i （2）

In formula (2)

be stress-number of cycles under i level load, n _ibe rotating speed under i level load, h _iit is lower service time of i level load;

Step 3, according to formula (3), calculate cycle index allowable under load at different levels:

$N_i={10}^{\frac{b-{\mathrm{\σ}}_{\mathrm{Hi}}}{a}}---\left(3\right)$

N in formula (3) _ibe cycle index allowable under i level load, a is material contact stress SN parameter of curve, σ _hibe calculated stress value under i level load, b is material contact stress SN parameter of curve;

Step 4, according to the given optimization aim function of formula (4):

$F=\mathrm{\Σ}\frac{N_{\mathrm{ni}}}{N_i}{10}^{-\frac{{\mathrm{\δ}}_i{\mathrm{\σ}}_{\mathrm{Hi}}}{a}}---\left(4\right)$

In formula (4), F is optimization aim function, N _ibe cycle index allowable under i level load, σ _hibe calculated stress value under i level load, N _nibe stress-number of cycles under i level load, a is material contact stress SN parameter of curve, δ _ibe under i level load after correction of the flank shape stress reduce ratio;

Step 5, the maximum that the gear of take produces in power transmission process, minimum magnitude of misalignment are boundary condition, solve the profiling quantity under given optimization aim minimum of a function value, this profiling quantity is the value of being solved.

Wherein, the magnitude of misalignment that described gear produces in power transmission process directly determines rational correction of the flank shape region, and maximum magnitude of misalignment equals maximum profiling quantity, and minimum magnitude of misalignment equals the minimum amount of practicing Buddhism or Taoism.

Wherein, described maximum magnitude of misalignment is that maximum profiling quantity is to be no more than the magnitude of misalignment that the maximum fatigue load of this gear transmission produces; Described minimum magnitude of misalignment is that minimum profiling quantity is to be not less than the magnitude of misalignment that the minimum fatigue load of the permanent fatigue load of this gear produces.

Wherein, the derivation method of described optimization aim function comprises the steps:

Step 1, according to formula (5), obtain the gear destruction rate under load impacts at different levels:

$U=\frac{n}{N}---\left(5\right)$

In formula (5), U is gear destruction rate, and N is cycle index allowable under load, and n is load lower gear stress-number of cycles;

Step 2, according to formula (6), obtain gear material SN parameter of curve:

σ＝-alog ₁₀N+b （6）

In formula (6), σ is Gear calculation stress, and a, b are material parameter, and N is cycle index allowable under this load;

Step 3, according to formula (7), obtain stress rate after gear modification:

$\mathrm{\δ}=\frac{{\mathrm{\σ}}_0-\mathrm{\σ}}{{\mathrm{\σ}}_0}---\left(7\right)$

In formula (7), δ is that after gear modification, stress reduces ratio, and σ is correction of the flank shape backgear calculated stress value, σ ₀for the front gear calculated stress value of practicing Buddhism or Taoism;

Step 4, establishing correction of the flank shape backgear cycle index allowable under this load is N', by formula (6) and formula (7), can obtain formula (8):

${\mathrm{\δ\σ}}_0=-a{\log }_{10}\frac{N}{N^{\′}}---\left(8\right)$

By formula (8), can obtain formula (9):

$N^{\′}=N/{10}^{-\frac{\mathrm{\δ\σ}}{a}}---\left(9\right)$

Formula (9) is brought formula (5) into and can be tried to achieve the back-geared damage ratio computing formula of correction of the flank shape (10) and be:

$U=\frac{n}{N^{\′}}=\frac{n}{N}{10}^{-\frac{\mathrm{\δ\σ}}{a}}---\left(10\right)$

By formula (10), can be drawn the damage ratio of multistage load lower gear, i.e. optimization aim function formula (4).

(3) beneficial effect

Compared with prior art, the present invention possesses following beneficial effect:

Cylindrical gear teeth directional line style quantifying design method under change magnitude of misalignment provided by the invention, can reduce the contact stress of variable load lower gear, flank of tooth stress value between homogenizing load at different levels, teeth directional stress under homogenizing load at different levels, improve gear capacity, reduce finite lifetime condition lower gear volume, improve transmission power density.

Accompanying drawing explanation

Fig. 1 is optimum correction of the flank shape areal map in cylindrical gear teeth directional line style quantifying design method under change magnitude of misalignment provided by the invention.

Embodiment

For making object of the present invention, content and advantage clearer, below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.

Cylindrical gear teeth directional line style quantifying design method under change magnitude of misalignment provided by the invention, this method for designing specifically comprises the steps:

Step 1, according to formula (1), calculate under load at different levels the not contact stress value of correction of the flank shape:

${\mathrm{\σ}}_{\mathrm{Hi}}=Z_B{\mathrm{\σ}}_{H0i}\sqrt{K_A{K}_{\mathrm{Vi}}{K}_{\mathrm{H\βi}}{K}_{H\∂i}}---\left(1\right)$

σ in formula (1) _hibe calculated stress value under i level load, Z _bfor list is to tooth contact radio, σ _h0ibe basic stress value under i level load, K _afor coefficient of performance, K _vibe dynamic load factor under i level load, K _{h β i}be teeth directional distribution coefficient under i level load, K _{h θ i}it is between cog distribution coefficient under i level load;

Step 2, according to formula (2), calculate stress-number of cycles under load at different levels:

N _ni＝60n _ih _i （2）

N in formula (2)

be stress-number of cycles under i level load, n _ibe rotating speed under i level load, h _iit is lower service time of i level load;

Step 3, according to formula (3), calculate cycle index allowable under load at different levels:

$N_i={10}^{\frac{b-{\mathrm{\σ}}_{\mathrm{Hi}}}{a}}---\left(3\right)$

N in formula (3) _ibe cycle index allowable under i level load, a is material contact stress SN parameter of curve, σ _hibe calculated stress value under i level load, b is material contact stress SN parameter of curve;

Step 4, according to the given optimization aim function of formula (4):

$F=\mathrm{\Σ}\frac{N_{\mathrm{ni}}}{N_i}{10}^{-\frac{{\mathrm{\δ}}_i{\mathrm{\σ}}_{\mathrm{Hi}}}{a}}---\left(4\right)$

In formula (4), F is optimization aim function, N _ibe cycle index allowable under i level load, σ _hibe calculated stress value under i level load, N _nibe stress-number of cycles under i level load, a is material contact stress SN parameter of curve, δ _ibe under i level load after correction of the flank shape stress reduce ratio;

Step 5, the maximum that the gear of take produces in power transmission process, minimum magnitude of misalignment are boundary condition, solve the profiling quantity under given optimization aim minimum of a function value, this profiling quantity is the value of being solved.

As shown in Figure 1, the magnitude of misalignment that described gear produces in power transmission process directly determines rational correction of the flank shape region, and maximum magnitude of misalignment equals maximum profiling quantity, and minimum magnitude of misalignment equals the minimum amount of practicing Buddhism or Taoism.

Gear modification is that the flexibility solving due to kinematic train causes gear in power transmission process, to produce magnitude of misalignment, and causes the flank of tooth to occur degradation problem under unbalance loading contact, stress raising, intensity.Therefore the magnitude of misalignment that reasonably correction of the flank shape region is directly produced in power transmission process by gear determines.

Determining of maximum profiling quantity: gear, at the torque load of transmission of power, can be divided into shock load and fatigue load according to the micromechanism of damage difference that gear is caused.It is few that shock load acts on number of times in power transmission process, and gear is not caused to fatigue damage, and failure mode main manifestations is undercapacity, and failure cause and surface microscopic stress distribution are without direct cause-effect relationship; Fatigue load is in gear transmission transmittance process, and its cycle index surpasses the minimum number that causes gear fatigue damage, and inefficacy main manifestations is fatigue failure, and failure cause and surface microscopic stress distribution are by direct cause-effect relationship.Therefore, becoming under magnitude of misalignment, gear teeth to maximum profiling quantity be to be no more than the magnitude of misalignment that the maximum fatigue load of this gear transmission produces.

Determining of minimum profiling quantity: in causing the load of gear fatigue damage, can be divided into finite lifetime fatigue load and permanent fatigue load according to cycle index allowable.Finite lifetime fatigue load causes the useful load of gear fatigue damage; Permanent fatigue load is not considering not cause under the factors such as macroscopic view wearing and tearing the load of gear fatigue damage.Therefore, becoming under magnitude of misalignment, gear teeth to minimum profiling quantity be to be not less than the magnitude of misalignment that the minimum fatigue load of the permanent fatigue load of this gear produces.

Wherein, the object of the invention is to calculate based on gear life damage, obtaining load at different levels affect lower gear and damages minimum teeth directional optimum line style modification curve, to solve the quantitative problem of axial modification under variable load, realizes the raising of gear capacity.

The derivation method of described optimization aim function comprises the steps:

Step 1, according to formula (5), obtain the gear destruction rate under load impacts at different levels:

$U=\frac{n}{N}---\left(5\right)$

In formula (5), U is gear destruction rate, and N is cycle index allowable under load, and n is load lower gear stress-number of cycles;

Step 2, according to formula (6), obtain gear material SN parameter of curve:

σ＝-alog ₁₀N+b （6）

In formula (6), σ is Gear calculation stress, and a, b are material parameter, and N is cycle index allowable under this load;

Step 3, according to formula (7), obtain stress rate after gear modification:

$\mathrm{\δ}=\frac{{\mathrm{\σ}}_0-\mathrm{\σ}}{{\mathrm{\σ}}_0}---\left(7\right)$

In formula (7), δ is that after gear modification, stress reduces ratio, and σ is correction of the flank shape backgear calculated stress value, σ ₀for the front gear calculated stress value of practicing Buddhism or Taoism;

Step 4, establishing correction of the flank shape backgear cycle index allowable under this load is N', by formula (6) and formula (7), can obtain formula (8):

${\mathrm{\δ\σ}}_0=-a{\log }_{10}\frac{N}{N^{\′}}---\left(8\right)$

By formula (8), can obtain formula (9):

$N^{\′}=N/{10}^{-\frac{\mathrm{\δ\σ}}{a}}---\left(9\right)$

Formula (9) is brought formula (5) into and can be tried to achieve the back-geared damage ratio computing formula of correction of the flank shape (10) and be:

$U=\frac{n}{N^{\′}}=\frac{n}{N}{10}^{-\frac{\mathrm{\δ\σ}}{a}}---\left(10\right)$

By formula (10), can be drawn the damage ratio of multistage load lower gear, i.e. optimization aim function formula (4).

After obtaining correction of the flank shape, stress reduces ratio:

From formula (1), Gear Contact stress and teeth directional distribution coefficient square with being directly proportional.According to ISO6336 cylindrical gear load-bearing capacity, calculate knownly, when meeting teeth directional load and be distributed as line style state, can be solved by formula (11).

Longitudinal Load Distribution Factors solution formula:

$K_{\mathrm{H\β}}=1+0.5\frac{(1.33f_{\mathrm{sh}}+f_{\mathrm{ma}}){\mathrm{\χ}}_{\mathrm{\β}}{c}_{\mathrm{\γ}}}{{\mathrm{\ω}}_m}---\left(11\right)$

K in formula (11) _{h β}for Longitudinal Load Distribution Factors, f _shfor the gear mesh error component that comprehensive deformation produces, f _mafor the gear mesh error component of manufacturing, installing, χ _βfor teeth directional running-in amount, c _γfor tooth mesh rigidity, ω _mfor unit facewidth average load.F _maavailable teeth directional tolerance F in calculating _βreplace, or calculate by the contact condition of actual measurement.

From formula (11), affecting correction of the flank shape front and back teeth directional distribution coefficient is the gear mesh error component f that comprehensive deformation produces _sh.By f _shdefine known, f before correction of the flank shape _shequate f after correction of the flank shape with magnitude of misalignment _shabsolute value for magnitude of misalignment and profiling quantity difference.

After correction of the flank shape, stress reduction ratiometer calculation formula (12) is:

$\mathrm{\δ}=1-\sqrt{\frac{{2\mathrm{\ω}}_m+\left(1.33\right|C-X|+f_{\mathrm{ma}}){\mathrm{\χ}}_{\mathrm{\β}}{c}_{\mathrm{\γ}}}{{2\mathrm{\ω}}_m+(1.33C+f_{\mathrm{ma}}){\mathrm{\χ}}_{\mathrm{\β}}{c}_{\mathrm{\γ}}}}---\left(12\right)$

In formula (12), δ is that after correction of the flank shape, stress reduces ratio, and C is magnitude of misalignment, and X is correction of the flank shape

Amount.

Embodiment

1) embodiment Basic parameters of gear

The number of teeth: 34/59

Modulus: 4.5

The facewidth: 45

Material parameter a:222.3

Teeth directional running-in amount: 0.85

Tooth mesh rigidity: 21.56

The gear mesh error component of manufacturing, installing: 11

2) basic load parameter

Load sequence number	Moment of torsion	Rotating speed	Time	Magnitude of misalignment
					1	4700	800	55.72	23.4949
2	3550	1200	77.4	19.7541
					3	3130	1800	238.93	18.0827
4	2710	2250	422.95	16.7676

3) performance parameter under not correction of the flank shape state

4) minimum magnitude of misalignment is as the performance parameter under profiling quantity state

5) maximum magnitude of misalignment is as the performance parameter under profiling quantity state

6) adopt the inventive method to obtain the performance parameter under profiling quantity state

7) result of calculation analysis

After adopting method provided by the invention to obtain profiling quantity, carry out performance parameter calculating, compare with correction of the flank shape under correction of the flank shape under not correction of the flank shape, maximum magnitude of misalignment state, minimum magnitude of misalignment state.

With respect to not correction of the flank shape state, under the profiling quantity that employing this method is obtained, its damage ratio has lowered 79%.

With respect to the correction of the flank shape of maximum magnitude of misalignment state, under the profiling quantity that employing this method is obtained, its damage ratio has lowered 4.8%.

With respect to the correction of the flank shape of minimum magnitude of misalignment state, under the profiling quantity that employing this method is obtained, its damage ratio has lowered 25.2%.

It is a kind of under change magnitude of misalignment condition that this method great advantage has been given, the computing method of gear teeth axial modification.

8) conclusion

The present invention is based on variable load lower gear damage ratio computing method, by theory, derive and obtained teeth directional line style profiling quantity quantifying design method, solved the problem of variable load lower gear axial modification quantitative design, achievement in research can effectively reduce gear destruction rate, improves the reliability of finite lifetime gear.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, do not departing under the prerequisite of the technology of the present invention principle; can also make some improvement and distortion, these improvement and distortion also should be considered as protection scope of the present invention.

Claims (4)

1. become a cylindrical gear teeth directional line style quantifying design method under magnitude of misalignment, it is characterized in that: this method for designing specifically comprises the steps:

Step 1, according to formula (1), calculate under load at different levels the not contact stress value of correction of the flank shape:

${\mathrm{\σ}}_{\mathrm{Hi}}=Z_B{\mathrm{\σ}}_{H0i}\sqrt{K_A{K}_{\mathrm{Vi}}{K}_{\mathrm{H\βi}}{K}_{H\∂i}}---\left(1\right)$

σ in formula (1) _hibe calculated stress value under i level load, Z _bfor list is to tooth contact radio, σ _h0ibe basic stress value under i level load, K _afor coefficient of performance, K _vibe dynamic load factor under i level load, K _{h β i}be teeth directional distribution coefficient under i level load, K _{h θ i}it is between cog distribution coefficient under i level load;

Step 2, according to formula (2), calculate stress-number of cycles under load at different levels:

N _ni＝60n _ih _i （2）

In formula (2) be stress-number of cycles under i level load, n _ibe rotating speed under i level load, h _iit is lower service time of i level load;

Step 3, according to formula (3), calculate cycle index allowable under load at different levels:

$N_i={10}^{\frac{b-{\mathrm{\σ}}_{\mathrm{Hi}}}{a}}---\left(3\right)$

N in formula (3) _ibe cycle index allowable under i level load, a is material contact stress SN parameter of curve, σ _hibe calculated stress value under i level load, b is material contact stress SN parameter of curve;

Step 4, according to the given optimization aim function of formula (4):

$F=\mathrm{\Σ}\frac{N_{\mathrm{ni}}}{N_i}{10}^{-\frac{{\mathrm{\δ}}_i{\mathrm{\σ}}_{\mathrm{Hi}}}{a}}---\left(4\right)$

In formula (4), F is optimization aim function, N _ibe cycle index allowable under i level load, σ _hibe calculated stress value under i level load, N _nibe stress-number of cycles under i level load, a is material contact stress SN parameter of curve, δ _ibe under i level load after correction of the flank shape stress reduce ratio;

Step 5, the maximum that the gear of take produces in power transmission process, minimum magnitude of misalignment are boundary condition, solve the profiling quantity under given optimization aim minimum of a function value, this profiling quantity is the value of being solved.

2. cylindrical gear teeth directional line style quantifying design method under change magnitude of misalignment according to claim 1, it is characterized in that: the magnitude of misalignment that described gear produces in power transmission process directly determines rational correction of the flank shape region, be that maximum magnitude of misalignment equals maximum profiling quantity, minimum magnitude of misalignment equals the minimum amount of practicing Buddhism or Taoism.

3. cylindrical gear teeth directional line style quantifying design method under change magnitude of misalignment according to claim 1 and 2, is characterized in that: described maximum magnitude of misalignment is that maximum profiling quantity is to be no more than the magnitude of misalignment that the maximum fatigue load of this gear transmission produces; Described minimum magnitude of misalignment is that minimum profiling quantity is to be not less than the magnitude of misalignment that the minimum fatigue load of the permanent fatigue load of this gear produces.

4. cylindrical gear teeth directional line style quantifying design method under change magnitude of misalignment according to claim 1, is characterized in that: the derivation method of described optimization aim function comprises the steps:

Step 1, according to formula (5), obtain the gear destruction rate under load impacts at different levels:

$U=\frac{n}{N}---\left(5\right)$

In formula (5), U is gear destruction rate, and N is cycle index allowable under load, and n is load lower gear stress-number of cycles;

Step 2, according to formula (6), obtain gear material SN parameter of curve:

σ＝-alog ₁₀N+b （6）

In formula (6), σ is Gear calculation stress, and a, b are material parameter, and N is cycle index allowable under this load;

Step 3, according to formula (7), obtain stress rate after gear modification:

$\mathrm{\δ}=\frac{{\mathrm{\σ}}_0-\mathrm{\σ}}{{\mathrm{\σ}}_0}---\left(7\right)$

In formula (7), δ is that after gear modification, stress reduces ratio, and σ is correction of the flank shape backgear calculated stress value, σ ₀for the front gear calculated stress value of practicing Buddhism or Taoism;

Step 4, establishing correction of the flank shape backgear cycle index allowable under this load is N', by formula (6) and formula (7), can obtain formula (8):

${\mathrm{\δ\σ}}_0=-a{\log }_{10}\frac{N}{N^{\′}}---\left(8\right)$

By formula (8), can obtain formula (9):

$N^{\′}=N/{10}^{-\frac{\mathrm{\δ\σ}}{a}}---\left(9\right)$

Formula (9) is brought formula (5) into and can be tried to achieve the back-geared damage ratio computing formula of correction of the flank shape (10) and be:

$U=\frac{n}{N^{\′}}=\frac{n}{N}{10}^{-\frac{\mathrm{\δ\σ}}{a}}---\left(10\right)$

By formula (10), can be drawn the damage ratio of multistage load lower gear, i.e. optimization aim function formula (4).