1. A high-order tuning method capable of realizing near-zero fluctuation of time-varying meshing stiffness of a gear is characterized by comprising the following steps of:

1) determining target gear pair parameters and calculating the contact ratio epsilon_α(ii) a The target gear pair is an involute straight-tooth cylindrical gear pair; target gear pair parameters include number of drive gear teeth z₁Number of driven wheel teeth z₂Tooth width b of driving wheel₁Width b of driven wheel teeth₂Modulus m, reference circle pressure angle alpha and tooth crest height coefficient h_a ^*Coefficient of clearance and^*；

2) determining the proportion of a single-tooth meshing period and a double-tooth meshing period in one meshing cycle of gear meshing operation, and expressing the proportion in the form of a simplest fraction; the proportion of the bidentate meshing period is epsilon_α-1; the proportion of the single tooth meshing period is 2-epsilon_α(ii) a Dividing a meshing period into n time periods, wherein the l continuous time periods are that two pairs of gear teeth participate in meshing simultaneously, and the n-l continuous time periods are that one pair of gear teeth participate in meshing; l and n are positive integers, and l is less than n; wherein epsilon_α-1＝l/n，2-ε_α＝(n-l)/n；

3) And n-order axial phase tuning is carried out on the driving gear and the driven gear, and the number of the pairs of gear teeth participating in meshing in any time period is kept the same when the tuning gears are meshed through the meshing phase difference between the sub-gears.

2. The high-order tuning method capable of achieving near-zero fluctuation of time-varying meshing stiffness of the gear according to claim 1, is characterized in that: in step 1), the degree of coincidence ε_αThe formula (2) is shown as formula (1);

wherein α' is a meshing angle; alpha is alpha_a1The addendum circle pressure angle of the driving wheel; alpha is alpha_a2The addendum circle pressure angle of the driven wheel.

3. The high-order tuning method capable of achieving near-zero fluctuation of time-varying meshing stiffness of the gear according to claim 1, is characterized in that: in the step 3), the driving gear is averagely divided into n sub-gears along the tooth width direction; all the sub-gears are fixedly connected in the axial direction; the two adjacent sub-gears have a difference angle along the circumferential directionThe driven gear is averagely divided into n sub-gears along the tooth width direction; all the sub-gears are fixedly connected in the axial direction; the two adjacent sub-gears have a difference angle along the circumferential directionSelecting a phase angle of the driving gearIs 2 pi/nz₁Driven gear phase angleIs 2 pi/nz₂。

4. The high-order tuning method capable of achieving near-zero fluctuation of time-varying meshing stiffness of the gear according to claim 1, is characterized in that: and 3) after the step 3), verifying the time-varying meshing rigidity of the gear pair before and after tuning.

Background

The gear transmission depends on the engagement of a driving gear and a driven gear to transmit motion and power, and is the most widely applied transmission mode in the field of mechanical transmission. The meshing impact of the gears directly influences the reliability and the running smoothness of the gear transmission. The meshing stiffness fluctuation is a source of the meshing impact. Reducing gear meshing stiffness fluctuations can improve gear meshing impact and further reduce gear drive system vibration.

When the spur gear is meshed, no axial force is generated, but meshing impact is obvious, and vibration is relatively large. When the straight gear is in meshing operation, the number of teeth participating in meshing is changed from one pair to two pairs, and then the two pairs are changed into one pair, so that single-tooth and double-tooth meshing alternate change is formed, the meshing rigidity of the gear is caused to fluctuate periodically, a periodic impact is applied to the gear, and the meshing vibration of the gear is formed.

Therefore, it is of great significance to develop a method for reducing the fluctuation of the time-varying meshing stiffness of the gear.

Disclosure of Invention

The invention aims to provide a high-order tuning method capable of realizing near-zero fluctuation of time-varying meshing stiffness of a gear, so as to solve the problems in the prior art.

The technical scheme adopted for achieving the purpose of the invention is that the high-order tuning method capable of achieving near-zero fluctuation of the time-varying meshing stiffness of the gear comprises the following steps:

1) determining target gear pair parameters and calculating the contact ratio epsilon_α. The target gear pair is an involute straight-tooth cylindrical gear pair. Target gear pair parameters include number of drive gear teeth z₁Number of driven wheel teeth z₂Tooth width b of driving wheel₁Width b of driven wheel teeth₂Modulus m, reference circle pressure angle alpha and tooth crest height coefficient h_a ^*Coefficient of clearance and^*。

2) the proportion of the single-tooth meshing period to the double-tooth meshing period in one meshing period of the gear meshing operation is determined and expressed in the form of the simplest fraction. The proportion of the bidentate meshing period is epsilon_α-1. The proportion of the single tooth meshing period is 2-epsilon_α. A meshing cycle is divided into n time segments, wherein the l continuous time segments are two pairs of gear teeth simultaneously engaged, and n-l continuous time segments are a pair of gear teeth engaged. l and n are positive integers, and l is less than n. Wherein epsilon_α-1＝l/n，2-ε_α＝(n-l)/n。

3) And n-order axial phase tuning is carried out on the driving gear and the driven gear, and the number of the pairs of gear teeth participating in meshing in any time period is kept the same when the tuning gears are meshed through the meshing phase difference between the sub-gears.

Further, in step 1), the degree of coincidence ε_αThe formula (2) is shown in formula (1).

Wherein α' is the engagement angle. Alpha is alpha_a1The addendum circle pressure angle of the driving wheel. Alpha is alpha_a2The addendum circle pressure angle of the driven wheel.

Further, in step 3), the driving gear is evenly divided into n sub-gears along the tooth width direction. The sub-gears are fixedly connected in the axial direction. The two adjacent sub-gears have a difference angle along the circumferential directionThe driven gear is evenly divided into n sub-gears along the tooth width direction. The sub-gears are fixedly connected in the axial direction. The two adjacent sub-gears have a difference angle along the circumferential directionSelecting a phase angle of the driving gearIs 2 pi/nz₁Driven gear phase angleIs 2 pi/nz₂。

Further, after the step 3), a relevant step of verifying the time-varying meshing stiffness before and after the gear pair tuning is provided.

The technical effects of the invention are undoubted:

A. axial phase tuning is carried out on the gear, so that the number of pairs of gear teeth which participate in meshing in any time period of the tuned gear is kept the same;

B. when the tuning gear is meshed, axial component force is not generated, so that negative effects caused by the axial component force are avoided;

C. the time-varying meshing stiffness fluctuation of the tuning gear pair is close to zero, so that the meshing impact of the gears can be effectively improved, and the vibration caused by the meshing of the gears is further reduced;

D. the length of the average contact line of the tuning gear pair is prolonged, and the bearing capacity of the gear is improved.

Drawings

FIG. 1 is a schematic diagram of a spur gear axial phase tuning method;

FIG. 2 is a flow chart of a high-order tuning method for achieving near-zero fluctuation of time-varying meshing stiffness of a gear;

FIG. 3 is a schematic diagram of the meshing cycle of a spur gear pair;

FIG. 4 is a graph of time varying meshing stiffness approximated by a straight-toothed spur gear pair;

FIG. 5 is a schematic diagram of a second order harmonic gear with a time varying mesh stiffness that fluctuates near zero;

FIG. 6 is a schematic diagram of a second-order harmonic gear pair meshing cycle with time-varying meshing stiffness fluctuating near zero;

FIG. 7 is a schematic diagram of a meshing cycle of a third-order harmonic gear pair with time-varying meshing stiffness fluctuating near zero;

FIG. 8 shows a gear pair (degree of coincidence ε)_α1.75) time-varying meshing stiffness curve comparison graph before and after four-order tuning;

FIG. 9 shows a gear pair (coincidence degree ε)_α1.51) comparison plot of time varying mesh stiffness curves before and after second order tuning.

Detailed Description

The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.

Example 1:

referring to fig. 3 and 4, when the gears are in meshing operation, the number of teeth of the gears participating in meshing is changed from one pair to two pairs, and then the two pairs are changed to one pair, so that single-tooth and double-tooth meshing alternate change is formed, and the periodic fluctuation of the meshing rigidity of the gears is caused, and a periodic meshing impact is applied to the gears, so that vibration and noise are caused, and the transmission stability is influenced.

Referring to fig. 1, for a straight toothed spur gear with a certain number of teeth z and a tooth width b, the straight toothed spur gear is equally divided into n sub-gears with a tooth width b/n along the tooth width direction, the sub-gears are respectively numbered as sub-gears i (i is greater than or equal to 1 and is less than or equal to n), each sub-gear rotates a certain angle around the axis along the same rotation direction, and the difference angle between two adjacent sub-gears in the rotation direction isI.e. the angle of rotation of the sub-gear i isAll the sub-gears are fixedly connected in the axial direction, the same treatment is carried out on the gears matched with the original gear, the meshing of a pair of gear pairs is converted into the meshing of n pairs of sub-gear pairs, the meshing phase difference exists between different pairs of sub-gear pairs, but the conversion does not influence the gear transmission ratio, so the transmission performance can be improved by adjusting the meshing phase difference, the gears which comprise n sub-gears after conversion are called n-order harmonic gears, the conversion method is called axial phase tuning, and the angle difference between two adjacent sub-gears along the circumferential direction is called the angle differenceReferred to as the time-staggered phase angle.

Referring to fig. 2, the present embodiment provides a high-order tuning method capable of achieving near-zero fluctuation of time-varying meshing stiffness of a gear, including the following steps:

1) determining target gear pair parameters and calculating the contact ratio epsilon_α。

In the field of aviation gear transmission, for high-speed thin-web gears, the periodically-changed meshing force axial component can easily excite the traveling wave resonance of the gears to cause fatigue damage, and the excitation source brought to the traveling wave resonance of the gears is avoided without the axial force. In this embodiment, the target gear pair is an involute spur gear pair. The straight gear does not generate axial component force when engaged.

Target gear pair parameters include number of drive gear teeth z₁Number of driven wheel teeth z₂Tooth width b of driving wheel₁Width b of driven wheel teeth₂Modulus m, reference circle pressure angle alpha and tooth crest height coefficient h_a ^*Coefficient of clearance and^*。

coincidence degree epsilon_αThe formula (2) is shown in formula (1).

In the formula, α 'is a meshing angle, and the meshing angle of the involute standard spur gear is equal to a reference circle pressure angle, that is, α' is α. Alpha is alpha_a1The calculation formula is shown in formula (2) for the addendum circle pressure angle of the driving wheel. Alpha is alpha_a2The calculation formula is shown in formula (3) for the driven wheel addendum circle pressure angle.

2) The proportion of the single-tooth meshing period to the double-tooth meshing period in one meshing period of the gear meshing operation is determined and expressed in the form of the simplest fraction. The proportion of the bidentate meshing period is epsilon_α-1. The proportion of the single tooth meshing period is 2-epsilon_α. Dividing a meshing period into n time segments, wherein the l continuous time segments are that two pairs of gear teeth participate in meshing simultaneously and have n-l continuous timesThe segment is a pair of gear teeth engaged. l and n are positive integers, and l is less than n. Wherein epsilon_α-1＝l/n，2-ε_α＝(n-l)/n。

3) And n-order axial phase tuning is carried out on the driving gear and the driven gear, and the number of the pairs of gear teeth participating in meshing in any time period is kept the same when the tuning gears are meshed through the meshing phase difference between the sub-gears. After the straight gear is subjected to high-order tuning, the converted sub-gears are all straight gears, and axial component force is not generated during meshing, so that negative effects caused by the axial component force are avoided.

The driving gear is evenly divided into n sub-gears along the tooth width direction. The sub-gears are fixedly connected in the axial direction. The two adjacent sub-gears have a difference angle along the circumferential directionThe driven gear is evenly divided into n sub-gears along the tooth width direction. The sub-gears are fixedly connected in the axial direction. The two adjacent sub-gears have a difference angle along the circumferential directionSelecting a phase angle of the driving gearIs 2 pi/nz₁Driven gear phase angleIs 2 pi/nz₂。

4) And verifying the time-varying meshing stiffness before and after the gear pair tuning. As shown in fig. 4, the time-varying meshing stiffness variation law of the spur gear pair is also the time-varying meshing stiffness variation law of each sub-gear pair after the axial phase of the gear is tuned, and is approximately equivalent to a rectangular square wave. K_minFor minimum time-varying meshing stiffness, K_maxThe time-varying meshing stiffness K (t) is a mean value rewritably for the maximum time-varying meshing stiffnessAnd the sum of the variation amounts Δ K (t)Formula (II):

according to the proportion of the single-tooth meshing and the double-tooth meshing, the mean value of the meshing stiffness can be expressed as follows:

and expanding the meshing rigidity variation part according to Fourier series:

in the formula (6), ω ═ 2 π/τ_m，τ_mCoefficient a for meshing period^k、b^kRespectively as follows:

where Φ is understood to mean the phase of engagement, where Φ is ω t₀. When the gears are engaged, each time a pitch angle 2 pi/z is passed, a meshing period tau is passed_mCorresponding to a meshing phase change of 2 pi.

The pair of n-order harmonic gear pairs comprises n pairs of sub-gear pairs, and the time-varying meshing stiffness of each sub-gear pair is expressed as:

the n-order tuned gear pair overall time-varying mesh stiffness is expressed as:

and the integral meshing rigidity variation part of the n-order harmonic gear pair is expanded according to Fourier series:

n-order tuned gear mistiming phase angleTaking 2 pi/nz, the meshing phase difference between adjacent sub-gears is 2 pi/n, and the meshing phase of the sub-gear 1 is 0, the meshing phase of the sub-gear i is 2 pi (i-1)/n. Then, the coefficients of the variation part of the meshing stiffness of each sub-gear pair when expanded according to the Fourier series are respectively:

the trigonometric identity deformation of the formula (10) can be obtained:

II in formula (12)^kSatisfies the following conditions:

let A^kSatisfies the following conditions:

substituting formula (11) for formula (14) to obtain:

when the values of the parts on the right of the middle mark in the formula (15) are analyzed in sequence, the following are obtained:

a can be obtained by substituting formula (16), formula (17) and formula (18) for formula (15)^kWhen 0, Δ k (t) in formula (12) can be obtained as 0.

The embodiment enables the number of tooth pairs which participate in meshing of the tuned gear at any time interval to be kept the same by carrying out axial phase tuning on the gear. After the method in the embodiment is used for carrying out axial phase tuning on the driving gear and the driven gear of the target gear pair, the near-zero fluctuation of time-varying meshing rigidity can be realized, the vibration and the noise of a gear transmission system are reduced, and the bearing capacity is improved.

Example 2:

the embodiment provides a high-order tuning method capable of realizing near-zero fluctuation of time-varying meshing stiffness of a gear, which comprises the following steps of:

1) and determining parameters of the involute straight-tooth cylindrical gear pair and calculating the contact ratio of the involute straight-tooth cylindrical gear pair. Setting the tooth number z of the driving wheel of the target gear pair₁And number of driven wheel teeth z₂Width of driving wheel tooth b₁And width b of driven wheel teeth₂Modulus m, reference circle pressure angle alpha, crest height factor h_a ^*Coefficient of backlash c^*. The coincidence degree epsilon is calculated by looking up the mechanical design manual_αThe calculation formula is as follows:

in the formula, alpha 'is a meshing angle, and the meshing angle of the involute standard straight spur gear is equal to a reference circle pressure angle, namely alpha' is alpha, alpha_a1、α_a2Respectively is the addendum circle pressure angle of the driving wheel and the driven wheel, and the calculation formula is as follows:

2) when the gear is determined to be meshed, the proportion of the single-tooth meshing period to the double-tooth meshing period in one meshing period is represented in the form of the simplest fraction.

In the straight gear transmission, the contact ratio is directly related to the proportion of single-tooth and double-tooth meshing periods in a meshing period, and the contact ratio range of the standard straight-tooth cylindrical gear pair is 1<ε_α<2, the proportion of the bidentate meshing period is epsilon_α-1, the proportion of the single tooth meshing period is 2-epsilon_αThe proportion of the period of bidentate engagement is written as the simplest fraction, i.e. ε_α-1 ═ l/n (l, n are both positive integers, and l<n), the proportion of the single tooth engagement period can be written as (n-l)/n, which is understood to mean that a meshing cycle is divided into n time segments, of which l successive time segments are two pairs of teeth simultaneously engaged and n-l successive time segments are one pair of teeth engaged.

3) Performing n-order axial phase tuning on the driving gear and the driven gear (wherein n is consistent with the denominator n in the simplest fraction form in the previous step), and performing staggered phase angle on the driving gearTaking 2 pi/nz₁Driven gear phase angleTaking 2 pi/nz₂. When the gears are engaged, each time the gear rotates by one tooth pitchAt an angle of 2 pi/z, the gear undergoes a meshing cycle tau_mThe purpose of taking the staggered time phase angle of the tuning gear to be 2 pi/nz is to keep the number of pairs of gear teeth engaged in any time period to be the same when the tuning gear is engaged through the engagement phase difference between the sub-gears, so that the time-varying engagement rigidity is approximately zero fluctuation.

It should be noted that the main reason for the periodic fluctuation of the gear meshing stiffness is that the number of pairs of gear teeth participating in the meshing changes periodically when the gear is meshed, and the basic idea of this embodiment is to tune the axial phase of the gear, so that the number of pairs of gear teeth participating in the meshing in any time period of the tuned gear remains the same.

Example 3:

the main steps of this embodiment are the same as those of embodiment 2, specifically, in a pair of standard straight-tooth cylindrical gear pairs, the number of teeth of the driving gear is 20, the number of teeth of the driven gear is 29, the tooth width is 30mm, the modulus is 2mm, the reference circle pressure angle is 20 °, the crest height coefficient is 1, and the crest clearance coefficient is 0.25. The addendum circle pressure angles of the driving wheel and the driven wheel can be obtained as 31.32 degrees and 28.47 degrees respectively according to the formula (2) and the formula (3), and the contact ratio can be obtained as about 1.60 according to the formula (1).

Example 4:

the main steps of this embodiment are the same as those of embodiment 2, specifically, if the contact ratio of a certain pair of gear pairs is 1.5, the proportion of the double-tooth meshing period in one meshing cycle is 1.5-1-0.5, i.e., the double-tooth meshing period and the single-tooth meshing period each account for 1/2.

Example 5:

the main steps of this embodiment are the same as those of embodiment 2, specifically, if the contact ratio of a certain pair of gear pairs is 1.6, the proportion of the double-tooth meshing period in one meshing cycle is 1.6-1-0.6, that is, the double-tooth meshing period is 3/5, and the single-tooth meshing period is 2/5.

Example 6:

the main steps of this embodiment are the same as those of embodiment 2, specifically, if the contact ratio of a pair of gear pairs is 1.5, in one meshing cycle, the single-tooth and double-tooth meshing periods respectively account for 1/2, and the second-order axial phase tuning is performed on both the driving gear and the driven gear, and if the number of teeth of the driving gear is 17, the second-order phase tuning driving gear is used for tuning the driving gearThe time-staggered phase angle is pi/17. Referring to FIG. 5, the second order harmonic gear pitch angle is 2 π/17, and the timing phase angle π/17 is such that the two-tooth meshing periods of the two gear subsets are staggered τ_m/2. Referring to fig. 6, the meshing conditions of the two pairs of sub-gears are overlapped, and the second-order harmonic gear pair is formed by simultaneously meshing three pairs of gear teeth in each meshing period, so that the meshing rigidity fluctuation is close to zero.

Example 7:

the main steps of this embodiment are the same as embodiment 2, specifically, the gear pair contact ratio is 4/3, the single-tooth and double-tooth meshing periods respectively account for 2/3 and 1/3, and the gear is subjected to three-order axial phase tuning. Referring to fig. 7, three pairs of meshing conditions of the pair of gears are overlapped, and the three-order tuning gear pair is simultaneously meshed with four pairs of teeth in each meshing period, so that the meshing rigidity fluctuation is close to zero.

Example 8:

the main steps of this embodiment are the same as embodiment 2, specifically, the specific parameters of the gear pair are shown in table 1, tuning is performed according to the specific flow of the high-order tuning method for achieving near-zero fluctuation of the time-varying meshing stiffness of the gear, and finally the meshing stiffness of the tuned gear pair is verified.

TABLE 1 specific parameter table of gear pair

According to the formula (2) and the formula (3), the addendum circle pressure angles of the driving wheel and the driven wheel are 25.47 degrees, and then the contact ratio epsilon can be obtained according to the formula (1)_α1.75. According to the step (1), the contact ratio of the target gear pair is about 1.75, and the proportion of the double-tooth meshing period is epsilon_α-1-0.75, expressed in the form of the simplest fraction 3/4, i.e. the target gear pair has a ratio 3/4 for two pairs of teeth engaged simultaneously and a ratio 1/4 for one pair of teeth engaged during one engagement cycle. According to the fact that the denominator of the simplest true fraction in the step (2) is 4, four-order tuning is conducted on the driving gear and the driven gear of the gear pair, and the time-staggered phase angle of the driving gear and the driven gear is achievedAndare all pi/98. As shown in fig. 8, which is a comparison graph of time-varying meshing stiffness curves before and after the fourth-order tuning of the target gear pair, it can be seen that the fluctuation of the time-varying meshing stiffness of the target gear pair is greatly reduced after the method of the present invention is applied.

Example 9:

the main steps of this embodiment are the same as embodiment 2, specifically, the specific parameters of the gear pair are shown in table 2, tuning is performed according to the specific flow of the high-order tuning method for achieving near-zero fluctuation of the time-varying meshing stiffness of the gear, and finally the meshing stiffness of the tuned gear pair is verified.

TABLE 2 specific parameter table of gear pair

According to the formulas (2) and (3), addendum circle pressure angles of the driving wheel and the driven wheel are respectively 33.35 degrees and 32.78 degrees, and then the contact ratio epsilon can be obtained according to the formula (1)_α1.51. According to the step (1), the contact ratio of the target gear pair is about 1.51, and the proportion of the double-tooth meshing period is epsilon_α-1-0.51, expressed in the form of the simplest fraction, of about 1/2, i.e. the target gear pair has a ratio 1/2 for two pairs of teeth engaged simultaneously and a ratio 1/2 for one pair of teeth engaged during one engagement cycle. According to the fact that the denominator of the simplest true fraction in the step (2) is 2, the driving gear and the driven gear of the gear pair are subjected to second-order tuning, and the time-staggered phase angle of the driving gear and the driven gear is adjustedAndrespectively taking pi/16 and pi/17. As shown in fig. 9, is a graph comparing the time varying mesh stiffness curves before and after second order tuning of the target gear pair,as can be seen from the figure, the fluctuation of the time-varying meshing stiffness of the target gear pair is greatly reduced after the method is applied.