CN111062103A - Metallurgical crane reducer gear service life assessment method with optimized parameters - Google Patents

Metallurgical crane reducer gear service life assessment method with optimized parameters Download PDF

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CN111062103A
CN111062103A CN201911346634.1A CN201911346634A CN111062103A CN 111062103 A CN111062103 A CN 111062103A CN 201911346634 A CN201911346634 A CN 201911346634A CN 111062103 A CN111062103 A CN 111062103A
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gear
wear
tooth profile
stage
teeth
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CN111062103B (en
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刘庆运
濮滔
丁克勤
刘涛
郑近德
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Anhui University of Technology AHUT
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

本发明公开一种优化参数的冶金起重机减速器齿轮寿命评估方法，属于设备寿命评估技术领域。该方法包括如下步骤：基于阿查德磨损计算模型构建齿廓磨损量计算公式；对减速器前后两级传动齿轮，保证总传动比与每级的主动轮齿数不变，在合理齿数范围内调整每级传动比，依次计算齿廓磨损量与整体寿命；针对减速器中同一级齿轮，保证传动中心距不变的情况下，调整模数和两轮齿数，计算齿廓磨损量，并观察其变化趋势；引入变位系数，达到减少齿廓磨损量，延长使用寿命的目的。本发明通过调节齿轮的基本参数，实现了对单个齿轮磨损率的减小，对同级齿轮的主、从动轮以及不同级齿轮之间的磨损量差值的缩小，实现了延长齿轮使用寿命和齿轮间的等磨损目的。

Figure 201911346634

The invention discloses a method for evaluating the life of a gear of a metallurgical crane reducer with optimized parameters, which belongs to the technical field of equipment life evaluation. The method includes the following steps: constructing a tooth profile wear calculation formula based on the Archard wear calculation model; for the two-stage transmission gears before and after the reducer, ensure that the total transmission ratio and the number of teeth of the driving gear of each stage remain unchanged, and adjust within a reasonable range of the number of teeth For the gear ratio of each stage, calculate the tooth profile wear amount and the overall life in turn; for the gears of the same stage in the reducer, when the transmission center distance is kept unchanged, adjust the module and the number of teeth of the two gears, calculate the tooth profile wear amount, and observe the Change trend; introduce the displacement coefficient to reduce the wear of the tooth profile and prolong the service life. By adjusting the basic parameters of the gear, the invention realizes the reduction of the wear rate of a single gear, the reduction of the wear amount difference between the main and driven wheels of the same-stage gear and the gears of different stages, and the prolongation of the service life of the gear and the reduction of the wear amount between the gears of different stages. Equal wear purpose between gears.

Figure 201911346634

Description

Metallurgical crane reducer gear service life assessment method with optimized parameters
The technical field is as follows:
the invention belongs to the technical field of equipment service life evaluation, relates to an Archimedes wear calculation model, and particularly relates to a parameter-optimized metallurgical crane reducer gear service life evaluation method for numerical calculation of tooth profile wear amount.
Background art:
the gear is used as a main structure in the speed reducer, has the advantages of large bearing capacity, high transmission precision, constant transmission power and the like, and the reliability and the service life of the gear have important significance on the normal operation of other moving parts and the state between friction pairs. There is often relative sliding of the contact surfaces between the gear pairs and wear is therefore unavoidable. Excessive tooth surface wear not only reduces the transmission accuracy and efficiency, but also causes additional shock and noise, and even tooth breakage and damage. At present, the main research means is to carry out actual measurement by an experimental method, the experimental period is long, and a large amount of manpower and financial resources are consumed, so that theoretical derivation and wear simulation by a numerical calculation and software simulation method are necessary to develop.
The invention content is as follows:
the invention aims to provide a method for evaluating the service life of a metallurgical crane reducer gear with optimized parameters.
The invention provides a method for evaluating the service life of a gear of a reducer of a metallurgical crane by optimizing parameters, which comprises the following steps:
(1) and constructing a tooth profile wear amount calculation formula based on an Archard (Archard) wear calculation model.
(2) And the transmission gears at the front and rear stages of the speed reducer ensure that the total transmission ratio is unchanged from the number of teeth of the driving wheel at each stage, the transmission ratio at each stage is adjusted within a reasonable range of the number of teeth, and the tooth profile abrasion loss and the whole service life are calculated in sequence.
(3) Aiming at the same-stage gear in the speed reducer, under the condition of ensuring that the transmission center distance is not changed, the modulus and the number of teeth of two wheels are adjusted, the tooth profile abrasion loss is calculated, and the change trend of the tooth profile abrasion loss is observed.
(4) The modification coefficient is introduced to achieve the purposes of reducing the tooth profile abrasion loss and prolonging the service life.
The method for constructing the tooth profile wear amount calculation formula based on the Archimedes wear calculation model in the step (1) comprises the following steps:
(1) due to the relative sliding speed existing between tooth profiles, a sliding coefficient expression is constructed according to a gear meshing schematic diagram:
Figure BDA0002333554210000011
in the formula: lambda [ alpha ]1Sliding coefficient at meshing point K on the driving wheel, λ2Slip coefficient at meshing point K on the driven wheel, i-transmission ratio, α -meshing angle, αk1-pressure angle of the engagement point K on the driving wheel;
(2) according to the geometrical relationship in the gear meshing principle diagram, the pressure angle range at the meshing point is calculated:
Figure BDA0002333554210000021
in the formula: r is1,r2Is the radius of two wheels,
Figure BDA0002333554210000022
is the crest factor, m is the gear module, αk2The pressure angle of the engagement point K on the driven wheel.
(3) Calculating the tooth thickness at any point on the tooth profile:
rK,sK,αKand thetaKThe radius, tooth thickness, pressure angle and spread angle of any circle,
Figure BDA0002333554210000023
is s isKThe subtended central angle.
Figure BDA0002333554210000024
Wherein theta is tan α - α and thetaK＝tanαK-αK
Figure BDA0002333554210000025
In the formula:
Figure BDA0002333554210000026
(4) and (3) calculating the contact ratio: epsilona＝[z1(tanαa1-tanα)+z2(tanαa2-tanα)]/2π
In the formula αa1＝cos-1(rb1/ra1),αa2＝cos-1(rb2/ra2)
(5) Calculating the contact half width:
Figure BDA0002333554210000027
in the formula: t-input torque, μ1，μ2Poisson ratio of two rounds of material, E1，E2-the modulus of elasticity of the material of the two wheels,
Figure BDA0002333554210000028
-the tooth width factor;
(6) calculating the wear rate:
Figure BDA0002333554210000029
in the formula: i ish1，Ih2Wear rate of driving and driven wheels, k1，k2Two wheels wear factor, n1，n2-the rotational speed of both wheels;
(7) calculating tooth profile abrasion loss: h isI＝2aλntεaIh。
Guarantee total drive ratio and every level action wheel number of teeth unchangeable, adjust every level drive ratio in reasonable number of teeth within range, calculate flank profile wearing and tearing volume and whole life-span in proper order and include following step:
(1) set rotational speed n1A torque value T;
(2) setting allowable tooth surface wear: in the lifting structure, the abrasion loss of the gear tooth profile on the first shaft is not more than 10% of the original tooth thickness, and the abrasion loss of the gear tooth profile on the other shafts is not more than 20% of the original tooth thickness. When the abrasion loss reaches the set value, the gear reaches the service life;
(3) set appropriate iGeneral assembly＝i1·i2，i1、i2The transmission ratios of the high-speed gear and the low-speed gear of the speed reducer are respectively; z1，Z2Number of teeth of high-speed step pinions, Z3，Z4The number of teeth of the low-speed big and small gears is i1＝Z2/Z1，i2＝Z4/Z3；
(4) Holding Z1，Z3And iGeneral assemblyUnchanged by changing i appropriately1To obtain a corresponding Z2，Z4And i2。
(5) Calculate each i1And (4) recording and observing the change trend of the service life of the high-speed gear and the low-speed gear corresponding to the value.
The method for calculating the tooth profile abrasion loss comprises the following steps of:
(1) setting the modulus of high-speed stage as m1，Z1，Z2The number of teeth of the high-speed big gear and the high-speed small gear;
(2) change modulus to miTo obtain a correspondence Z1i，Z2iGuarantee mi(Z1i+Z2i)＝m1(Z1+Z2)；
(3) Calculate each m in turniAnd recording and observing the change trend of the corresponding wear life.
The method for introducing the deflection coefficient comprises the following steps:
(1) according to the gear meshing diagram, a sliding coefficient expression is derived through a geometrical relation:
Figure BDA0002333554210000031
(2) setting of lambda1max＝max(λ1)，λ2max＝max(λ2)，u＝λ1max/λ2max；
(3) The coefficient of variation is x, e ═ mx, i.e. when λ1And λ2In the image N2N1When the gear is translated to the right by a distance of e (the rightward translation is positive deflection, and the leftward translation is negative deflection), the value of u is close to 1, and at this time, the two gears are considered to be in an approximate equal wear state.
The invention realizes the reduction of the wear rate of a single gear, the reduction of the tooth profile wear difference between the driving wheel and the driven wheel of the same gear and gears of different stages by adjusting the basic parameters of the gears, and the aims of prolonging the service life of the gears and the equal wear among the gears are fulfilled.
Description of the drawings:
FIG. 1 is one of the tooth profile engagement illustrations of the present invention;
FIG. 2 is a second schematic view of the inventive tooth profile engagement;
FIG. 3 is a schematic illustration of the calculated tooth thickness of the present invention;
FIG. 4 is a graph of slip coefficient versus pressure angle for the present invention;
FIG. 5 is a tooth thickness curve at any meshing point of the tooth surfaces of the present invention;
FIG. 6(a) is a schematic view showing the amount of wear at any meshing point of the tooth surfaces of the driving wheels according to the present invention;
FIG. 6(b) is a schematic view showing the amount of wear at any meshing point of the tooth surfaces of the driven wheel in the present invention;
FIG. 7 shows a diagram of the present invention iGeneral assemblyWear life of two-stage gear at 5.6 hours and i1A relation curve of the ratio;
FIG. 8 shows a diagram of the present invention iGeneral assemblyWear life of two-stage gear at 7.2 hours and i1A relation curve of the ratio;
FIG. 9 shows a diagram of the present invention iGeneral assemblyWear life of two-stage gear at 9.6 hours and i1A relation curve of the ratio;
FIG. 10 is a graph showing the relationship between the wear loss and the modulus after changing the parameters of the high-speed gear according to the present invention;
FIG. 11 is a graph showing the relationship between the wear loss and the modulus after changing the parameters of the intermediate gear in the present invention;
FIG. 12 is a graph showing the relationship between the wear loss and the modulus after changing the parameters for the low-speed gear according to the present invention;
FIG. 13 is a graph showing the relationship between the wear loss and the modulus after the parameters of the three-stage gear are changed;
FIG. 14 is a graph of the initial slip coefficient of the high speed stage gear of the present invention;
FIG. 15 is a graph of the initial slip coefficient of the low speed stage gear of the present invention;
FIG. 16 is a graph of the slip coefficient of a high speed gear after it has been indexed according to the present invention;
fig. 17 is a sliding coefficient curve of the low gear according to the present invention after being shifted.
The specific implementation mode is as follows:
the present invention will be described in detail below with reference to the accompanying drawings and examples.
Firstly, constructing a tooth profile abrasion amount calculation formula based on an Archimedes abrasion calculation model; secondly, for the front and rear two-stage transmission gears of the speed reducer, the total transmission ratio is ensured to be unchanged with the number of teeth of the driving wheel at each stage, the transmission ratio at each stage is adjusted within a reasonable range of the number of teeth, and the tooth profile abrasion loss and the whole service life are calculated in sequence; then, aiming at the same-stage gear in the reducer, under the condition of ensuring that the transmission center distance is not changed, adjusting the modulus and the number of teeth of two wheels, calculating the tooth profile abrasion loss, and observing the change trend of the tooth profile abrasion loss; finally, the modification coefficient is introduced, so that the purposes of reducing the tooth profile abrasion loss and prolonging the service life are achieved.
Preferably, a ZSC-400 vertical speed reducer is selected as an embodiment, a metallurgical crane speed reducer gear life evaluation method based on optimized parameters is carried out, and the original parameters of a three-stage involute straight toothed cylindrical gear are shown in the following table.
TABLE 1 initial parameters of the three-stage gear of the reducer
Parameter name High speed stage Intermediate stage Low speed stage
Number of teeth Z Z1＝18，Z2＝42 Z3＝14，Z4＝56 Z5＝20，Z6＝48
Modulus m 3 4 5
Normal pressure angle α (°) 20 20 20
Normal tooth crest height coefficient h a * 1 1 1
Coefficient of normal clearance* 0.25 0.25 0.25
Theoretical center distance a (mm) 90 140 170
Tooth width b (mm) 30 40 50
Modulus of elasticity E (GPa) E1＝210，E2＝206 E1＝210，E2＝206 E1＝210，E2＝206
Poisson ratio upsilon 0.3 0.3 0.3
In order to perform the following calculation, the above basic parameters are used to calculate the intermediate quantities of the gear, such as the reference circle, the base circle, the addendum circle, the dedendum circle, and the like, and the specific calculation process is as shown in the following formula:
radius of reference circle: r is1＝Z1m1/2＝27mm，r2＝Z2m1/2＝63mm，r3＝Z3m2/2＝28mm，r4＝Z4m2/2＝112mm，r5＝Z5m3/2＝50mm，r6＝Z6m3/2＝120mm
Radius of base circle: r isb1＝r1cos(α)＝25.372mm，rb2＝r2cos(α)＝59.201mm，rb3＝r3cos(α)＝26.311mm，rb4＝r4cos(α)＝105.246mm，rb5＝r5cos(α)＝46.985mm，rb6＝r6cos(α)＝112.763mm
Pressure angle range at meshing point on each gear tooth profile:
high speed stage gear αk1∈(5.922°，32.249°)，αk2∈(14.943°，26.235°)；
Intermediate stage gear αk1∈(3.220°，32.252°)，αk2∈(15.744°，22.866°)；
Low gear αk1∈(5.112°，31.321°)，αk2∈(14.687°，25.564°)。
The result of the contact ratio calculation is: epsilon1＝1.626，ε2＝1.618，ε3＝1.543。
Setting input power to 4kw, and rotation speed n1720r/min, and 51000N mm of input torque.
Selecting high-speed stage and low-speed stage gears of a ZSC-400 vertical speed reducer as research objects of step two, and setting a total transmission ratio to be iGeneral 1＝5.6，iGeneral 2＝7.2，iTotal 3The calculations were performed sequentially for the three cases of 9.6.
In calculating step (2), the total transmission ratio i is ensured in each caseGeneral assemblyAnd two stages of driving wheels with constant number of teeth, Z1＝18，Z 320, independent variable is i1With a dependent variable of i2，Z2，Z4. The calculation process can be divided into the following steps:
step A: get iGeneral assembly5.6 with i1Making changes in the life of the two-stage gear and i1The occupancy relationship curve is shown in fig. 7.
And B: get iGeneral assembly7.2 with i1Making changes in the life of the two-stage gear and i1The occupancy relationship curve is shown in fig. 8.
And C: get iGeneral assembly9.6 with i1Making changes in the life of the two-stage gear and i1The occupancy relationship curve is shown in fig. 9.
The change trends of the two curves in the three graphs are contrastively analyzed, and a proper transmission ratio formula is selected to achieve the purposes of prolonging the service life of the gear and enabling the service lives of the gears of different stages to be close to each other.
And (4) regarding the step (3), selecting a three-level gear of the ZSC-400 vertical speed reducer as a research object, ensuring that the center distance is constant, wherein the independent variable is the modulus m, and the dependent variable is the tooth number of the two gears. The calculation process is divided into the following steps.
Step A: for high speed gears, the center distance a is maintained1Constant at 90mm, taking multiple values for modulus m to obtain corresponding Z1，Z2The life of the gear is calculated in turn, and the corresponding s ═ max (h)2)/max(h1) The calculation result, which is the ratio of the maximum wear amount of the driven wheel tooth profile to the maximum wear amount of the driving wheel tooth profile, is shown in table 2.
TABLE 2 calculated values of the life of the high-speed gears with different moduli
Modulus m Number of teeth of driving gear Z1 Number of driven gear teeth Z2 Life t/(h) Wear loss ratio s
2.4 23 52 13130 0.1813
2.5 22 50 11580 0.1648
2.6 21 48 10040 0.1487
2.7 20 47 8760 0.1222
2.9 19 43 7400 0.1256
3.0 18 42 6120 0.0989
The data in the table are fitted to a curve as presented in fig. 10.
And B: for intermediate stage gears, the center distance a is maintained2Constant 140mm, taking multiple values for modulus m, to obtain the corresponding Z1，Z2The life of the gear is calculated in turn, and the corresponding s ═ max (h)2)/max(h1) The calculation result, which is the ratio of the maximum wear amount of the driven wheel tooth profile to the maximum wear amount of the driving wheel tooth profile, is shown in table 3.
TABLE 3 calculated values of the service life of the intermediate gear with different moduli
Modulus m Number of teeth of driving gear Z1 Number of driven gear teeth Z2 Life t/(h) Wear loss ratio s
3.0 19 74 54790 0.0313
3.1 18 72 43960 0.0247
3.3 17 68 35280 0.0207
3.5 16 64 26620 0.0167
3.7 15 61 18750 0.0119
4.0 14 56 11660 0.0084
The data in the table are fitted to a curve as presented in fig. 11.
And C: for intermediate stage gears, the center distance a is maintained2Constant 170mm, taking multiple values for modulus m, to obtain the corresponding Z1，Z2The life of the gear is calculated in turn, and the corresponding s ═ max (h)2)/max(h1) The calculation result, which is the ratio of the maximum wear amount of the driven wheel tooth profile to the maximum wear amount of the driving wheel tooth profile, is shown in table 4.
TABLE 4 calculated values of life of low-speed gears with different modulus
Modulus m Number of teeth of driving gear Z1 Number of driven gear teeth Z2 Life t/(h) Wear loss ratio s
4.0 25 60 53290 0.0648
4.2 24 57 48240 0.0631
4.3 23 56 42730 0.0524
4.5 22 53 37170 0.0520
4.8 21 50 32830 0.0491
5.0 20 48 27510 0.0425
The data in the table are fitted to a curve as presented in fig. 12.
The three steps can reflect the rule that the gear life is increased along with the reduction of the modulus, which shows that the tooth profile abrasion loss is reduced.
It is stated that the tooth profile wear can be reduced by changing the number of teeth and the modulus.
For step (4), the tooth profile wear amount is reduced by introducing the modification coefficient, which can be divided into the following steps.
Step A: the tooth profile meshing schematic diagram 10 is obtained by taking high-speed gears and low-speed gears of a ZSC-400 vertical speed reducer as research objects, and a calculation formula of a sliding coefficient is converted into the following components through a geometrical relation:
Figure BDA0002333554210000071
the trend of the change can be judged more clearly according to the movement of the mesh point K, and the graphs are shown in fig. 14 and 15.
Calculated, in FIG. 11, the high speed stage gear λ1max＝6.7907，λ2max＝0.6550，μ1＝λ1max/λ2max10.37, that is to say the wear of the tooth root of the pinion is 10.37 times that of the gearwheel;
in FIG. 12, the low gear λ1max＝4.3463，λ2max＝0.5508，μ1＝λ1max/λ2max7.89, namely the wear degree of the tooth root part of the pinion is 7.89 times that of the gear wheel;
to achieve a close degree of wear of the two gears, i.e. a ratio μ close to 1, we wish to reduce λ1maxIs increased by2maxAnd therefore starting from the sliding coefficient calculation equations (11) and (12).
When the tooth profile meshing point K is closer to the point N1While, KN1Reduced length, KN2Increased length, λ1maxIs correspondingly smaller, λ2maxThe increase is made accordingly.
As can be seen from the tooth profile meshing schematic diagram, the transmission center distance is kept unchanged and overlappedOn the premise that the gear tooth depth is not less than 1.2, the radius r of the addendum circle of the large gear is gradually reduceda2Time, theoretical mesh point N2N1And the actual line of engagement B2B1All shift to the right, then1maxIs reduced therewith, and2maxwith this increase, the value of μ will be closer and closer to 1, achieving equal wear of both gears at the tooth root location.
Set the addendum circle radius r of the big geara2The reduction value of e, i.e. the gearwheel is a negative profile shifted gearwheel, the profile shift coefficient x2The pinion is a positive modified gear with modification coefficient x1＝+e/m。
The Matlab programming calculation shows that under the condition of ensuring that the transmission ratio is not less than 1.2, the change value e of the radius of the top circle of the gear of the high-speed gear is 3.308, and the contact ratio epsilon is at the momenta1.290, pinion index x11.103, large gear deflection coefficient x2＝-1.103；
The change value e of the radius of the addendum circle of the gear of the low-speed gear is 5.724, and the contact ratio epsilon isa1.301, pinion shift coefficient x11.145, large gear deflection coefficient x2＝-1.145。
At this time, as shown in fig. 16 and 17, the slip coefficient curves of the pinion and the pinion are observed, and the maximum wear amounts on the tooth profiles of the driving wheel and the driven wheel are almost equal and both values are much smaller than those before the displacement in each gear stage. After the displacement treatment, the service lives of the driving wheel and the driven wheel are close to each other, the tooth profile abrasion loss can be reduced, and the service life is prolonged.

Claims (5)

1.一种优化参数的冶金起重机减速器齿轮寿命评估方法，其特征在于该评估方法包括如下具体步骤：1. a metallurgical crane reducer gear life evaluation method of optimization parameter is characterized in that this evaluation method comprises the following concrete steps: (1)基于阿查德磨损计算模型构建所述减速器齿轮的齿廓磨损量计算公式；(1) Constructing the calculation formula of the tooth profile wear amount of the reducer gear based on the Archard wear calculation model; (2)对所述减速器前后两级传动齿轮，保证总传动比与每级的主动轮齿数不变，在合理齿数范围内调整每级传动比，依次计算齿廓磨损量与整体寿命；保证传动中心距不变的情况下，调整模数和前后两级传动齿轮的齿数，计算齿廓磨损量，并观察其变化趋势；(2) For the two-stage transmission gears before and after the reducer, ensure that the total transmission ratio and the number of teeth of the driving gear of each stage remain unchanged, adjust the transmission ratio of each stage within a reasonable range of teeth, and calculate the tooth profile wear amount and overall life in turn; ensure that Under the condition that the transmission center distance is unchanged, adjust the module and the number of teeth of the front and rear transmission gears, calculate the tooth profile wear amount, and observe the change trend; (3)引入变位系数，达到减少齿廓磨损量，延长使用寿命的目的。(3) The displacement coefficient is introduced to reduce the wear of the tooth profile and prolong the service life. 2.根据权利要求1所述的优化参数的冶金起重机减速器齿轮寿命评估方法，其特征在于步骤(1)中所述基于阿查德磨损计算模型构建齿廓磨损量计算公式包括如下步骤：2. The metallurgical crane reducer gear life evaluation method of optimizing parameters according to claim 1, is characterized in that described in step (1), constructing tooth profile wear calculation formula based on Archard wear calculation model comprises the following steps: (1)由于齿廓间存在的相对滑动速度，根据齿轮啮合示意图构建滑动系数表达式：(1) Due to the relative sliding speed between the tooth profiles, the sliding coefficient expression is constructed according to the schematic diagram of gear meshing:
Figure FDA0002333554200000011
Figure FDA0002333554200000011
 式中：λ1—主动轮上啮合点K处的滑动系数，λ2—从动轮上啮合点K处的滑动系数，i—传动比，α—啮合角，αk1—啮合点K在主动轮上的压力角；In the formula: λ 1 - the sliding coefficient at the meshing point K on the driving wheel, λ 2 - the sliding coefficient at the meshing point K on the driven wheel, i - the transmission ratio, α - the meshing angle, α k1 - the meshing point K at the driving wheel pressure angle on; (2)根据齿轮啮合原理图中的几何关系，计算啮合点处的压力角范围：(2) Calculate the pressure angle range at the meshing point according to the geometric relationship in the gear meshing schematic diagram:
Figure FDA0002333554200000012
Figure FDA0002333554200000012
 式中：r1,r2为两轮半径，
Figure FDA0002333554200000013
为齿顶高系数，m为齿轮模数，αk2—啮合点K在从动轮上的压力角。In the formula: r 1 , r 2 are the radius of the two wheels,
Figure FDA0002333554200000013
is the tooth tip height coefficient, m is the gear modulus, α k2 - the pressure angle of the meshing point K on the driven wheel. (3)计算齿廓上任意点处的齿厚：(3) Calculate the tooth thickness at any point on the tooth profile: rK,sK,αK和θK则分别为任意圆的半径、齿厚、压力角和展角，
Figure FDA0002333554200000014
为sK所对的圆心角。r K , s K , α K and θ K are the radius, tooth thickness, pressure angle and spread angle of any circle, respectively,
Figure FDA0002333554200000014
is the central angle opposite to s K.
Figure FDA0002333554200000015
Figure FDA0002333554200000015
 式中：θ＝tanα-α，θK＝tanαK-αK In the formula: θ = tanα-α, θ K = tanα K -α K
Figure FDA0002333554200000016
Figure FDA0002333554200000016
 式中：
Figure FDA0002333554200000021
where:
Figure FDA0002333554200000021
 (4)重合度计算：εa＝[z1(tanαa1-tanα)+z2(tanαa2-tanα)]/2π(4) Calculation of coincidence degree: ε a =[z 1 (tanα a1 -tanα)+z 2 (tanα a2 -tanα)]/2π 式中：αa1＝cos-1(rb1/ra1),αa2＝cos-1(rb2/ra2)In the formula: α a1 =cos -1 (r b1 /r a1 ), α a2 =cos -1 (r b2 /r a2 ) (5)计算接触半宽：
Figure FDA0002333554200000022
(5) Calculate the contact half width:
Figure FDA0002333554200000022
 式中：T—输入转矩，μ1，μ2—两轮材料的泊松比，E1，E2—两轮材料的弹性模量，
Figure FDA0002333554200000023
—齿宽系数；where: T—input torque, μ 1 , μ 2 —Poisson’s ratio of the two-wheel material, E 1 , E 2 —the elastic modulus of the two-wheel material,
Figure FDA0002333554200000023
- tooth width coefficient; (6)计算磨损率：
Figure FDA0002333554200000024
(6) Calculate the wear rate:
Figure FDA0002333554200000024
 式中：Ih1，Ih2—主、从动轮的磨损率，k1，k2—两轮的磨损系数，n1，n2—两轮的转速；In the formula: I h1 , I h2 - the wear rate of the main and driven wheels, k 1 , k 2 - the wear coefficient of the two wheels, n 1 , n 2 - the rotational speed of the two wheels; (7)计算齿廓磨损量：hI＝2aλntεaIh。(7) Calculate the tooth profile wear amount: h I =2aλntε a I h . 3.根据权利要求1所述优化参数的冶金起重机减速器齿轮寿命评估方法，其特征在于步骤(2)中所述的保证总传动比与每级的主动轮齿数不变，在合理齿数范围内调整每级传动比，依次计算齿廓磨损量与整体寿命包括如下步骤：3. the metallurgical crane reducer gear life evaluation method according to the described optimization parameter of claim 1 is characterized in that the guaranteed total transmission ratio described in the step (2) and the number of teeth of the driving gear of each stage are constant, within a reasonable range of the number of teeth Adjusting the transmission ratio of each stage and calculating the tooth profile wear amount and overall life in turn includes the following steps: (1)设定转速n1、转矩值T；(1) Set the rotational speed n 1 and the torque value T; (2)设置齿面许用磨损量：在起升结构中，第一根轴上的齿轮齿廓磨损量不超过原齿厚的10％，其余各轴上齿轮齿廓磨损量不超过原齿厚的20％。当磨损量达到该设定值时，齿轮即达到使用寿命；(2) Set the allowable wear amount of the tooth surface: in the lifting structure, the wear amount of the gear tooth profile on the first shaft does not exceed 10% of the original tooth thickness, and the gear tooth profile wear amount on the other shafts does not exceed the original tooth thickness. 20% thicker. When the wear amount reaches the set value, the gear will reach the service life; (3)设置合适的i总＝i1·i2，i1、i2分别为减速器高速级齿轮与低速级齿轮的传动比；Z1，Z2为高速级大、小齿轮的齿数，Z3，Z4为低速级大、小齿轮的齿数，则i1＝Z2/Z1，i2＝Z4/Z3；(3) Set the appropriate i total = i 1 ·i 2 , i 1 and i 2 are the transmission ratios of the high-speed gear and the low-speed gear of the reducer respectively; Z 1 and Z 2 are the number of teeth of the high-speed gear and the pinion, Z 3 , Z 4 are the number of teeth of the large and small gears of the low-speed stage, then i 1 =Z 2 /Z 1 , i 2 =Z 4 /Z 3 ; (4)保持Z1，Z3和i总不变，通过适当改变i1，得到对应的Z2，Z4和i2。(4) Keep Z 1 , Z 3 and i unchanged, and obtain corresponding Z 2 , Z 4 and i 2 by appropriately changing i 1 . (5)计算各个i1值所对应的高速级和低速级齿轮寿命，记录并观察变化趋势。(5) Calculate the life of the high-speed and low-speed gears corresponding to each i 1 value, and record and observe the change trend. 4.根据权利要求1所述的优化参数的冶金起重机减速器齿轮寿命评估方法，其特征在于步骤(2)所述的保证传动中心距不变的情况下调整模数和两轮齿数，计算齿廓磨损量包括如下步骤：4. the metallurgical crane reducer gear life evaluation method of the optimized parameter according to claim 1 is characterized in that the described in step (2) guarantees that under the condition of constant transmission center distance, adjust the modulus and the number of teeth of two wheels, calculate the tooth Profile wear includes the following steps: (1)设置高速级模数为m1，Z1，Z2为高速级大、小齿轮的齿数；(1) Set the high-speed stage module as m 1 , Z 1 , Z 2 are the number of teeth of the high-speed stage large and small gears; (2)改变模数为mi，得到对应Z1i，Z2i，保证mi(Z1i+Z2i)＝m1(Z1+Z2)；(2) Change the modulus to m i , obtain corresponding Z 1i , Z 2i , ensure that m i (Z 1i +Z 2i )=m 1 (Z 1 +Z 2 ); (3)依次计算各个mi所对应的磨损寿命，记录并观察其变化趋势。(3) Calculate the wear life corresponding to each mi in turn, record and observe its changing trend. 5.权利要求1所述优化参数的冶金起重机减速器齿轮寿命评估方法，其特征在于所述的引入变位系数包括如下步骤：5. the metallurgical crane reducer gear life evaluation method of the described optimization parameter of claim 1, is characterized in that described introduction displacement coefficient comprises the steps: (1)根据齿轮啮合图，通过几何关系推导出滑动系数表达式：(1) According to the gear meshing diagram, the slip coefficient expression is derived through the geometric relationship:
Figure FDA0002333554200000031
Figure FDA0002333554200000031
 (2)设置λ1max＝max(λ1)，λ2max＝max(λ2)，u＝λ1max/λ2max；(2) Set λ 1max =max(λ 1 ), λ 2max =max(λ 2 ), u=λ 1max /λ 2max ; (3)变位系数为x，e＝mx，即当λ1和λ2的曲线在图像N2N1的范围内向右平移e的距离时，u的取值接近1，此时认为两齿轮接近等磨损状态。(3) The displacement coefficient is x, e=mx, that is, when the curves of λ 1 and λ 2 are shifted to the right by the distance e within the range of image N 2 N 1 , the value of u is close to 1, and it is considered that the two gears near equal wear condition.
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