CN110069867B - Method for calculating comprehensive fatigue safety coefficient of parts of drive axle transmission system under multiple working conditions - Google Patents

Method for calculating comprehensive fatigue safety coefficient of parts of drive axle transmission system under multiple working conditions Download PDF

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CN110069867B
CN110069867B CN201910342472.8A CN201910342472A CN110069867B CN 110069867 B CN110069867 B CN 110069867B CN 201910342472 A CN201910342472 A CN 201910342472A CN 110069867 B CN110069867 B CN 110069867B
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范子杰
王琪
周驰
桂良进
丁炜琦
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Tsinghua University
Shaanxi Hande Axle Co Ltd
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Shaanxi Hande Axle Co Ltd
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Abstract

The invention discloses a method for calculating comprehensive fatigue safety coefficient of a drive axle transmission system under multiple working conditions of parts, which comprises the following steps: establishing a statics analysis model of a drive axle transmission system, and calculating the stress of parts under a certain single working condition; calculating the comprehensive limited life fatigue safety coefficient of the shaft under a plurality of working conditions; calculating comprehensive fatigue safety coefficients of each bearing in the transmission system under a plurality of working conditions; and calculating comprehensive fatigue safety factors of each gear in the transmission system under a plurality of working conditions. The method for calculating the comprehensive fatigue safety coefficient of the drive axle transmission system parts under the multi-working-condition comprehensive condition can ensure that the fatigue safety performance of the drive axle transmission system can meet the design requirement without influencing the service life of the drive axle transmission system parts, improve the stability of the product performance and further improve the qualification rate of products.

Description

Method for calculating comprehensive fatigue safety coefficient of parts of drive axle transmission system under multiple working conditions
Technical Field
The invention relates to the technical field of automobiles, in particular to a method for calculating comprehensive fatigue safety coefficients of drive axle transmission system parts under multiple working conditions.
Background
The drive axle transmission system comprises important parts such as a shaft, a bearing, a gear and the like. When designing a transaxle transmission system, the current design method includes the steps of: firstly, establishing a statics analysis model of a transmission system; then, carrying out stress analysis on the typical working condition of the device to obtain the load of each part; and finally, carrying out fatigue safety check on parts such as shafts, bearings, gears and the like according to related technical standards, calculating the fatigue safety coefficient of the parts under a single working condition, and modifying the size and the model of the parts if the safety coefficient does not meet the requirements until the requirements are met.
The existing design method of the drive axle transmission system only calculates the safety coefficient under a single working condition when fatigue safety coefficient calculation is carried out, although a product can meet the requirement of service life through checking of the single working condition, the design method usually faces various working conditions when in actual use, and the existing design method of the drive axle transmission system does not check and calculate the comprehensive fatigue safety coefficient according to the comprehensive influence of all working conditions on parts. Under the influence of multiple working conditions, the safety coefficient of a product is generally lower than a single working condition checking result, so that the use requirement of the safety coefficient is met when the single working condition checking is used, but the safety coefficient is reduced under the multiple working conditions, so that the use requirement is not met, the fatigue safety performance of a drive axle transmission system sometimes cannot meet the design requirement, the service life of the drive axle transmission system is influenced, the product performance is unstable, and the qualified rate is low.
Disclosure of Invention
The invention aims to provide a method for calculating a comprehensive fatigue safety coefficient of a drive axle transmission system under multiple working conditions, which is used for solving the problems that the fatigue safety performance of the drive axle transmission system sometimes cannot meet the design requirement to influence the service life of the drive axle transmission system, and the product performance is unstable and the qualification rate is low.
The invention provides a method for calculating comprehensive fatigue safety coefficient of parts of a drive axle transmission system under multiple working conditions, wherein the parts comprise a shaft, a bearing and a gear, and the number of the working conditions of the parts of the drive axle transmission system is set to be NL(NLIs a natural number greater than 1), the calculation method includes the steps of:
step A: establishing a statics analysis model of a drive axle transmission system, and calculating a single working condition N of partsi(i is 1 to N)LNatural number of) stress;
and B: is calculated at NLThe comprehensive limited service life fatigue safety factor of the shaft under each working condition;
and C: calculate each bearing in the drive train at NLComprehensive fatigue safety factors under individual working conditions;
step D: calculate each gear in the drive train at NLComprehensive fatigue safety factor under individual working condition.
Further, the step B includes the steps of:
step B1: calculating a single operating mode NiLower axis damage rate:
according to the condition of the component in a single working condition NiUnder stress and by referring to infinite life fatigue safety coefficient calculation formula in standard 'selection and design of closed gear transmission device' to calculate single working condition NiThe infinite life fatigue safety coefficient of the lower shaft;
Figure GDA0002658678590000021
wherein, FsfRepresenting a safety factor of the system,
Figure GDA0002658678590000022
is the alternating stress of the rice-diesel,
Figure GDA0002658678590000023
is the mean stress in Milsses, SfFor fatigue strength, SyIs the tensile yield strength.
Step B2: calculating the total damage rate of the shaft and the equivalent cycle times of all working conditions under the working condition with the maximum damage rate,
wherein N isLTotal damage ratio D of individual working conditionsAThe calculation formula of (2) is as follows:
Figure GDA0002658678590000024
calculating the maximum damage rate D of the working condition corresponding to the maximum damage rate in all the working conditionsEThe calculation formula is
DE＝max{D1，D2，…Di，…DNL}
In the formula, DiThe damage rate is the damage rate of a single working condition.
Setting the maximum Damage Rate DECorresponding cycle number NEAll the working conditions are at the maximum damage rate DEEquivalent cycle number N of total damage rateAThe calculation formula of (2) is as follows:
Figure GDA0002658678590000025
step B3: repeating the equivalent cycle times N according to the infinite life fatigue safety coefficient calculation formulaAAt the maximum damage rate DEAnd checking the shaft under the working condition, and calculating the comprehensive fatigue safety coefficient of the shaft under multiple working conditions.
Further, in the step B1, if the infinite life fatigue safety factor is greater than 1, it indicates that the damage rate of the shaft under the working condition is 0; if the infinite life fatigue safety coefficient is less than 1, the damage rate DiIs composed of
Figure GDA0002658678590000026
Wherein N isiThe number of cycles of the shaft under the working condition i is N0iThe calculation formula of (a) is as follows:
Figure GDA0002658678590000027
where the coefficients c and m are related to the tensile strength limit of the material, σaAnd σmRespectively, the Misses alternating stress and the mean stress, SyIs the tensile yield strength.
Further, for the bearings in the transaxle drive train, the step C includes the steps of:
step C1: according to the international standard rolling bearing: calculating the damage rate of the bearing under each working condition by using a calculation formula of the basic rated service life of the rolling bearing of rated dynamic load and rated service life; wherein the basic rated life L10Is calculated by the formula
Figure GDA0002658678590000031
Wherein, CdIs the basic rated dynamic load of the bearing, k is the bearing index, PrThe radial equivalent dynamic load is obtained;
if the operation frequency of the bearing under the ith working condition is LiThen, the fatigue safety coefficient S under the ith working condition is utilizediThe damage rate D of the bearing under the ith working condition can be calculatediIs composed of
Figure GDA0002658678590000032
Step C2: calculating the total damage rate and comprehensive fatigue safety coefficient of the bearing
The calculation formula of the total damage rate D of all working conditions of the bearing is as follows:
Figure GDA0002658678590000033
the calculation formula of the multi-working-condition comprehensive fatigue safety coefficient S is as follows:
Figure GDA0002658678590000034
further, the step D includes the steps of:
step D1: calculating the damage rate D of the gear fatigue under each working conditioniWherein the gear bending fatigue damage rate D under the ith working conditioniThe calculation formula of (2) is as follows:
Figure GDA0002658678590000035
in the formula, NiFor the number of actual runs, NHRiIs the rated operation times;
step D2: calculating the total damage rate of the gear and the equivalent cycle times of all forward working conditions A and all reverse working conditions B under the maximum damage rate;
step D3: respectively using equivalent cycle times
Figure GDA0002658678590000036
And
Figure GDA0002658678590000037
at the maximum damage rate DEChecking and calculating under the load under the working condition, and solving a new fatigue safety coefficient S under the working condition A of driving againHANew fatigue safety factor S under reverse working condition BHBAnd then the comprehensive fatigue safety coefficient of the multiple working conditions takes the smaller value of the two as follows:
SHM＝min(SHA,SHB)
further, in the step D1, if the static fatigue cycle number boundary point N is setH0The corresponding fatigue safety coefficient is less than 1, and then the fatigue damage rate D under the working conditioniIs infinite; if the number of cycles NH0+ N Δ N to infinite life fatigue cycle number demarcation point NHCThe post-fatigue safety coefficient is still more than 1, and then the bending fatigue damage rate D under the working conditioniIs zero.
The invention has the beneficial effects that:
the invention discloses a method for calculating the comprehensive fatigue safety coefficient of parts of a drive axle transmission system under multiple working conditions, which realizes the calculation of the comprehensive fatigue safety coefficient of key parts such as shafts, bearings, gears and the like in the transmission system under multiple working conditions, so that a designer can check the comprehensive fatigue safety coefficient of the parts under the comprehensive conditions under multiple working conditions during design, thereby ensuring that the fatigue safety performance of the drive axle transmission system reaches the design requirement without influencing the service life of the drive axle transmission system, improving the stability of the product performance and further improving the qualification rate of products. The calculation method is easy to realize programming in various common programming language environments, has high calculation efficiency, and can be widely applied to multi-working-condition comprehensive design check of various multi-support shaft system transmission structures.
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FIG. 1 is a schematic structural diagram of a drive axle transmission system provided by the present invention;
FIG. 2 is a graph showing the variation of the bending fatigue stress with the cycle number according to the present invention.
Detailed Description
The following examples are intended to illustrate the invention, but are not intended to limit the scope of the invention.
The drive axle transmission system comprises 3 shafts, 5 bearings and a pair of hypoid gear pairs, as shown in fig. 1, wherein the 3 shafts are a small wheel shaft 31, a large wheel shaft 32 and a differential shaft 33 respectively; the 5 bearings are respectively a first roller bearing 51, a second roller bearing 52, a third roller bearing 53, a fourth roller bearing 54 and a fifth roller bearing 55, a hypoid gear pair 2 comprises a pinion and a bull gear, and the two ends of the drive axle transmission system are respectively provided with an input torque 10 and an output torque 11; wherein the parts sequentially arranged from top to bottom on the pinion shaft are a first roller bearing, a second roller bearing, a pinion of a hypoid gear pair and a third roller bearing; the torque input position is the small axle end, inputting torque as shown in FIG. 1; the parts sequentially arranged from left to right on the differential shaft are a fifth roller bearing, a bull wheel shaft, a bull wheel of a hypoid gear pair and a fourth roller bearing.
Example 1
The method for calculating the comprehensive fatigue safety coefficient of the bearing in the main speed reducer gear under multiple working conditions comprises the following steps:
step A: establishing a static analysis model of the system, wherein the static analysis model comprises 3 shafts, 5 bearings and a pair of hypoid gear pairs, and calculating the N of parts under a certain single working conditioni(i is 1 to N)LNatural number of) is applied. For the establishment of the static analysis model, refer to "finite element analysis of support stiffness of main reducer of automobile drive axle" (by weekly writer, etc.), which is published in "automobile engineering" 2016, volume 38, phase 8.
Force calculation for 3 axes:
the small wheel shaft has 23 nodes and 22 beam units, the elastic modulus of the material is 200GPa, the Poisson ratio is 0.252, and the density is 7880kg/m3And the rigidity matrixes of the beam units are grouped to obtain an integral rigidity matrix of the small wheel shaft.
The large wheel shaft has 7 nodes and 6 beam units, the elastic modulus of the material is 207GPa, the Poisson ratio is 0.29, and the density is 7800kg/m3And the rigidity matrixes of the beam units are grouped to obtain an integral rigidity matrix of the large wheel shaft. The differential shaft has 21 nodes and 20 beam units, the elastic modulus of the shaft material is 207GPa, the Poisson ratio is 0.29, and the density is 7800kg/m3And the stiffness matrixes of the beam units are combined to obtain an overall stiffness matrix of the differential shaft.
Force calculation for 5 bearings:
the first roller bearing is FAG31312, the inner diameter is 60mm, the outer diameter is 130mm, the width is 33.5mm, the average diameter is 95mm, the number of rollers is 16, the diameter of the rollers is 17.18mm, the effective length of the rollers is 19.8mm, and the bearing contact angle is 28.81 degrees;
the second roller bearing model is FAG546439, the inner diameter is 70mm, the outer diameter is 165mm, the width is 57mm, the average diameter is 117.5mm, the number of rollers is 15, the diameter of the rollers is 22.6mm, the effective length of the rollers is 39.556mm, and the bearing contact angle is 25 degrees;
the third roller bearing is FAG575867, the inner diameter is 40mm, the outer diameter is 94mm, the width is 30mm, the average diameter is 67mm, the number of rollers is 13, the diameter of the rollers is 16mm, and the effective length of the rollers is 19 mm;
the model of the fourth roller bearing is SKF33021, the inner diameter is 105mm, the outer diameter is 160mm, the width is 43mm, the average diameter is 132.5mm, the number of rollers is 28, the diameter of the roller is 13.74mm, the effective length of the roller is 29.76mm, and the contact angle of the bearing is 10.67 degrees;
the fifth roller bearing is FAG32021, the inner diameter is 105mm, the outer diameter is 160mm, the width is 35mm, the average diameter is 132.5mm, the number of rollers is 28, the diameter of the rollers is 13.4mm, the effective length of the rollers is 23.48mm, and the bearing contact angle is 16.5 degrees. Furthermore, the elastic modulus of all bearing materials is 210GPa, and the Poisson ratio is 0.3.
And according to a nonlinear stiffness calculation formula of the roller bearing, calculating to obtain a respective nonlinear stiffness matrix of each bearing.
And (3) calculating the stress of a hypoid gear pair:
the transmission system comprises an hypoid gear pair, the parameters of which are shown in table 1, and a gear unit stiffness matrix and an equivalent meshing stiffness matrix are obtained through calculation according to a mechanical model calculation formula of the hypoid gear.
TABLE 1 design parameters for hypoid gear pairs
Figure GDA0002658678590000051
Figure GDA0002658678590000061
The number of total operating modes being NLThe input loads corresponding to 4 working conditions are shown in table 2, and the stress of the part under each working condition can be calculated by using a static analysis model. The comprehensive fatigue safety coefficient of each part of the gear transmission system after sequentially operating 4 working conditions is calculated by using the method.
TABLE 2 input load situation for the operating conditions
Input torque (Nm) Input rotation speed (rpm) Number of cycles input
First working condition (full loaded in the right side of the vehicle) -5385 -200 0.5e6
Second operating mode (full reverse) 5385 200 0.5e6
Third operating mode (full vehicle) -5385 -200 0.5e6
Fourth operating mode (full reverse) 5385 200 0.5e6
And B: and calculating the comprehensive limited life fatigue safety factor of the shaft in the transmission system after 4 working conditions of operation. The small wheel axle is taken as an example in the embodiment, and the method comprises the following 3 steps.
Step B1: and calculating the damage rate of the shaft under each working condition.
According to the condition of the component in a single working condition NiStress and reference to Infinite Life fatigue safety factor calculation formula in Standard selection and Design of Enclosed Gear drives (Design and selection of Components for closed Gear drives, in particular, U.S. Standard ANSI/AGMA6001-D97, page 5)iLower shaft infinite life fatigue safety factor FsfThe calculation expression is;
Figure GDA0002658678590000062
wherein, FsfThe infinite life fatigue safety factor is shown,
Figure GDA0002658678590000063
is the alternating stress of the rice-diesel,
Figure GDA0002658678590000064
is the mean stress in Milsses, SfFor fatigue strength, SyIs the tensile yield strength.
For example, under the first operating condition, the infinite life fatigue safety factor of the shaft is calculated to be 1.0918 according to equation 1. The infinite life fatigue safety coefficient is more than 1, which indicates that the damage rate of the shaft under the working condition is 0, namely D1＝0。
The infinite life fatigue safety factor for this shaft under the second condition was calculated to be 0.5257. The infinite life fatigue safety coefficient is less than 1, and the cycle number N when the infinite life fatigue safety coefficient is 1 under the working condition is calculated02
Figure GDA0002658678590000065
Where the coefficients c and m are related to the tensile strength limit of the material, σaAnd σmRespectively, the Misses alternating stress and the mean stress, SyFor tensile yield strength, the specific values of these parameters are referenced in ANSI/AGMA6001-D97, where σaSee page 8 equation 13, σmSee page 8 formula 14, SySee page 9 formula 31.
The damage rate D under this condition2Is composed of
Figure GDA0002658678590000071
The third working condition is the same as the first working condition, and the fourth working condition is the same as the second working condition, so D3＝D1，D4＝D2。
Step B2: and calculating the total damage rate and the equivalent cycle times of all the working conditions under the maximum damage rate working condition.
For 4 conditions, the total damage rate DAIs composed of
Figure GDA0002658678590000072
Calculating the maximum damage rate D of the working condition corresponding to the maximum damage rate in all the working conditionsEI.e. by
DE＝max{D1，D2，…Di，…DNL}
In the formula, DiThe damage rate is the damage rate of a single working condition.
The second working condition and the fourth working condition in this embodiment are the same, and are the maximum damage rate DETaking the second working condition as an example, the corresponding cycle number NE＝0.5e6The damage rate is DE6.8823. At the maximum damage rate DETotal damage rate equivalent cycle number N under working conditionsAIs composed of
Figure GDA0002658678590000073
Step B3: using equivalent number of cycles NA＝1e6And under the working condition of the maximum damage rate, re-checking and calculating the shaft according to the infinite life fatigue safety coefficient calculation formula to obtain a new finite life fatigue safety coefficient of 0.526, wherein the coefficient is the multi-working-condition comprehensive finite life fatigue safety coefficient of the shaft.
And C: and calculating the comprehensive fatigue safety coefficient of each bearing in the transmission system after 4 working conditions are operated.
The second roller bearing is taken as an example in the present embodiment, and includes the following 2 steps.
Step C1: and calculating the damage rate of the bearing under each working condition.
First, the rolling bearing is manufactured by international standard rolling bearing: basic rated life L of Rolling bearing on page 10 of Rolling bearings-Dynamic load rating and rating life (ISO 281-2007)10The calculation formula calculates the basic rated service life L of the rolling bearing under the first working condition101Is composed of
Figure GDA0002658678590000074
The bearing operating frequency under the working condition is L1＝0.5e5And then the damage rate D of the bearing under the first working condition1Is composed of
Figure GDA0002658678590000081
Secondly, calculating the basic rated service life L of the rolling bearing under the second working condition102Is composed of
Figure GDA0002658678590000082
The bearing operating frequency under the working condition is L2＝0.5e5And then the damage rate D of the bearing under the second working condition2Is composed of
Figure GDA0002658678590000083
The third working condition is the same as the first working condition, and the fourth working condition is the same as the second working condition, so D3＝D1，D4＝D2。
Step C2: calculating the total damage rate D and the comprehensive fatigue safety coefficient S of the bearing
Total damage ratio D of bearing
Figure GDA0002658678590000084
When multiple working conditions are considered, the comprehensive fatigue safety coefficient S of the multiple working conditions is calculated according to the total damage rate
S＝D-1/k＝0.1566-1/(10/3)Becoming 1.744 (formula 11)
Step D: and calculating the comprehensive fatigue safety factor of each gear in the transmission system under 4 working conditions.
Since the gears relate to two safety factors of bending fatigue and contact fatigue during checking, the comprehensive fatigue safety factors of the pinion and the gearwheel are calculated by the same method no matter the gears are subjected to bending fatigue or contact fatigue, and the embodiment takes the bending fatigue of the pinion as an example, so that the calculation of the comprehensive fatigue safety factor of the hypoid gear pair comprises the following steps:
step D1: and calculating the fatigue damage rate of the gear under each working condition.
Referring to fig. 2, in a curve of bending fatigue stress S versus cycle number N, the abscissa represents the number of rotation cycles of the part, the ordinate represents the stress value, and each point on the curve represents the stress value for bending fatigue failure at a certain number of cycles.
For the first working condition, the rated operation times when the safety factor is 1 are calculated, and two key points contained in the bending fatigue SN curve of the gear material are respectively a static fatigue cycle time dividing point N shown in figure 2H0＝0.001e6And infinite life fatigue cycle number demarcation point NHC＝3e6。
Firstly, the larger step size Δ N is 1e4Number of slave cycles NH0The method comprises the steps of starting to adopt a Gleason fatigue safety coefficient calculation formula to check a standard to calculate the gear fatigue safety coefficient, wherein the Gleason fatigue safety coefficient calculation standard refers to the Gleason bevel gear strength analysis and calculation in the third subsection of the Gleason bevel gear technical data translation set translated by the Beijing Gear factory, the obtained fatigue safety coefficient is gradually reduced along with the increase of the cycle number, and when the cycle number is increased to 7e4When the fatigue safety coefficient is less than 1, the corresponding cycle number is 6e when the safety coefficient is 14And 7e4To (c) to (d); then accurately finding out the corresponding cycle times N when the safety coefficient is closest to 1 by taking 1 as the step lengthHR1＝62580。
After the rated operation times are obtained, the bending fatigue damage rate of the gear is
Figure GDA0002658678590000091
In the formula, NiFor the number of actual runs, NHRiIs a rated operation number NHRiThe method comprises the steps of carrying out fatigue checking on the gear by adopting a Gleason fatigue safety coefficient Calculation formula and a check standard or an international standard fatigue safety coefficient Calculation formula, and calculating the operation times when the safety coefficient is 1, wherein the international standard fatigue safety coefficient Calculation formula refers to the international standard of Calculation of bearing capacity of straight gears and helical gears (ISO 6336-2006 for short).
For the second operating condition, the number of operations when the safety factor is 1 is calculated. Firstly, the larger step size Δ N is 1e4Number of slave cycles NH0The fatigue safety coefficient of the gear is calculated by adopting the Gleason calculation and checking standard, the obtained fatigue safety coefficient is gradually reduced along with the increase of the cycle number, and when the cycle number is increased to 1e4When the fatigue safety coefficient is less than 1, the safety coefficient is1 the corresponding cycle number should be 0.001e6And 1e4To (c) to (d); then accurately finding out the corresponding cycle times N when the safety coefficient is closest to 1 by taking 1 as the step lengthHR2＝7575。
After the rated operation times are obtained, the bending fatigue damage rate of the gear is
Figure GDA0002658678590000092
The third working condition is the same as the first working condition, and the fourth working condition is the same as the second working condition, so D3＝D1，D4＝D2。
Step D2: and calculating the total damage rate of the gear and the equivalent cycle times of all the forward working conditions A and all the reverse working conditions B under the working condition of the maximum damage rate.
If the 4 working conditions include 2 working conditions A of driving and 2 working conditions B of reversing, the damage D of all working conditions of driving is calculated respectivelyAAnd damage to all reverse operating conditions DBAs follows
Figure GDA0002658678590000093
Figure GDA0002658678590000094
In all working conditions, the working condition with the largest damage rate in the forward working condition and the reverse working condition is the third working condition and the fourth working condition, and the corresponding damage rates are D respectively3And D4The corresponding original cycle times are respectively NAmax＝0.5e6And NBmax＝0.5e6. Equivalent cycle times of all vehicle-driving working conditions under maximum damage rate working conditions
Figure GDA0002658678590000095
Equivalent cycle times of all reverse working conditions under maximum damage rate working conditions
Figure GDA0002658678590000096
Is calculated as follows
Figure GDA0002658678590000097
Figure GDA0002658678590000101
Step D3: respectively using equivalent cycle times according to a Gleason fatigue safety coefficient calculation formula or an international standard fatigue safety coefficient calculation formula
Figure GDA0002658678590000102
And
Figure GDA0002658678590000103
at the maximum damage rate DEChecking and calculating under the load under the working condition, and solving a new fatigue safety coefficient S under the working condition A of driving againHANew fatigue safety factor S under reverse working condition BHBAnd then the comprehensive fatigue safety coefficient of the multiple working conditions takes the smaller value of the two as follows:
SHM＝min(SHA,SHB) (formula 18)
The grisson fatigue safety coefficient calculation formula is as follows:
Figure GDA0002658678590000104
Figure GDA0002658678590000105
wherein S isPAnd SGRepresenting the safety factors of the small wheel and the big wheel respectively, StPAnd StGRespectively representing calculated stress values, S, of the small and large wheelswtPAnd SwtGRespectively representing allowable working stress values of the small wheel and the large wheel.
The international standard fatigue safety coefficient calculation formula is as follows:
Figure GDA0002658678590000106
Figure GDA0002658678590000107
wherein S isF1And SF2Representing the safety factors, sigma, of the small and large wheels, respectivelyFG1,σFG2Representing allowable stress values, σ, of small and large wheels, respectivelyF1,σF2The calculated stress values are represented for the small and large wheels, respectively.
The multi-condition comprehensive calculation results of the checking parts can be obtained through the calculation, and are listed in the following table 3 together with the single-condition calculation results. The table shows that the safety coefficient is reduced after the influence of multiple working conditions is considered in the design process, and a designer can adopt the method to more closely consider the main operation working conditions (load, speed, cycle times and the like) to be in practical operation use conditions when designing a transmission system, so that the comprehensive fatigue safety check of the multiple working conditions on each part is efficiently and accurately carried out.
TABLE 3 comparison of the multi-condition comprehensive calculation results of each checking part with the single condition
Figure GDA0002658678590000108
Figure GDA0002658678590000111
Although the invention has been described in detail above with reference to a general description and specific examples, it will be apparent to one skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.

Claims (3)

1. A method for calculating comprehensive fatigue safety coefficient of drive axle transmission system parts under multiple working conditions includes that the parts include a shaft, a bearing and a gear, and the number of the working conditions of the drive axle transmission system parts is NLIn which N isLIs a natural number greater than 1, characterized in that the calculation method comprises the steps of:
step A: establishing a statics analysis model of a drive axle transmission system, and calculating a single working condition N of partsiUnder a force of i from 1 to NLA natural number of (2);
and B: is calculated at NLThe comprehensive limited service life fatigue safety factor of the shaft under each working condition;
step B1: calculating a single operating mode NiLower axis damage rate:
according to the condition of the component in a single working condition NiUnder stress and by referring to infinite life fatigue safety coefficient calculation formula in standard 'selection and design of closed gear transmission device' to calculate single working condition NiThe infinite life fatigue safety coefficient of the lower shaft;
Figure FDA0002658678580000011
wherein, FsfRepresenting a safety factor of the system,
Figure FDA0002658678580000012
is the alternating stress of the rice-diesel,
Figure FDA0002658678580000013
is the mean stress in Milsses, SfFor fatigue strength, SyIs the tensile yield strength;
step B2: calculating the total damage rate of the shaft and the equivalent cycle times of all working conditions under the working condition with the maximum damage rate,
wherein N isLTotal damage ratio D of individual working conditionsAThe calculation formula of (2) is as follows:
Figure FDA0002658678580000014
calculating the maximum damage rate D of the working condition corresponding to the maximum damage rate in all the working conditionsEThe calculation formula is
DE＝max{D1，D2，…Di，…DNL}
In the formula, DiThe damage rate is of a single working condition;
setting the maximum Damage Rate DECorresponding cycle number NEAll the working conditions are at the maximum damage rate DEEquivalent cycle number N of total damage rateAThe calculation formula of (2) is as follows:
Figure FDA0002658678580000015
step B3: repeating the equivalent cycle times N according to the infinite life fatigue safety coefficient calculation formulaAAt the maximum damage rate DEChecking the shaft under the working condition, and calculating the comprehensive fatigue safety coefficient of the shaft under multiple working conditions;
and C: calculate each bearing in the drive train at NLComprehensive fatigue safety factors under individual working conditions;
step C1: according to the international standard rolling bearing: calculating the damage rate of the bearing under each working condition by using a calculation formula of the basic rated service life of the rolling bearing of rated dynamic load and rated service life;
wherein the basic rated life L10Is calculated by the formula
Figure FDA0002658678580000021
Wherein, CdIs the basic rated dynamic load of the bearing, k is the bearing index, PrFor radial equivalent of movementLoading;
if the operation frequency of the bearing under the ith working condition is LiThen, the fatigue safety coefficient S under the ith working condition is utilizediThe damage rate D of the bearing under the ith working condition can be calculatediIs composed of
Figure FDA0002658678580000022
Step C2: calculating the total damage rate and comprehensive fatigue safety coefficient of the bearing;
the calculation formula of the total damage rate D of all working conditions of the bearing is as follows:
Figure FDA0002658678580000023
the calculation formula of the multi-working-condition comprehensive fatigue safety coefficient S is as follows:
Figure FDA0002658678580000024
step D: calculate each gear in the drive train at NLComprehensive fatigue safety factors under individual working conditions;
step D1: calculating the damage rate D of the gear fatigue under each working conditioniWherein the gear bending fatigue damage rate D under the ith working conditioniThe calculation formula of (2) is as follows:
Figure FDA0002658678580000025
in the formula, NiFor the number of actual runs, NHRiIs the rated operation times;
step D2: calculating the total damage rate of the gear and the equivalent cycle times of all forward working conditions A and all reverse working conditions B under the maximum damage rate;
step D3: respectively using equivalent cycle times
Figure FDA0002658678580000026
And
Figure FDA0002658678580000027
at the maximum damage rate DEChecking and calculating under the load under the working condition, and solving a new fatigue safety coefficient S under the working condition A of driving againHANew fatigue safety factor S under reverse working condition BHBAnd then the comprehensive fatigue safety coefficient of the multiple working conditions takes the smaller value of the two as follows:
SHM＝min(SHA,SHB)。
2. the method for calculating the comprehensive fatigue safety coefficient of the drive axle transmission system under the multiple working conditions, as claimed in claim 1, wherein in the step B1, if the infinite life fatigue safety coefficient is greater than 1, the damage rate of the shaft under the working condition is 0; if the infinite life fatigue safety coefficient is less than 1, the damage rate DiIs composed of
Figure FDA0002658678580000031
Wherein N isiThe number of cycles of the shaft under the working condition i is N0iThe calculation formula of (a) is as follows:
Figure FDA0002658678580000032
where the coefficients c and m are related to the tensile strength limit of the material, σaAnd σmRespectively, the Misses alternating stress and the mean stress, SyIs the tensile yield strength.
3. The method for calculating the comprehensive fatigue safety coefficient under the multi-condition of the parts of the drive axle transmission system according to claim 1, wherein in the step D1,
if the number of static fatigue cycles is dividedPoint NH0The corresponding fatigue safety coefficient is less than 1, and then the fatigue damage rate D under the working conditioniIs infinite; if the number of cycles NH0+ N Δ N to infinite life fatigue cycle number demarcation point NHCThe post-fatigue safety coefficient is still more than 1, and then the bending fatigue damage rate D under the working conditioniIs zero.
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