CN112989665A - Fatigue life analysis method for differential shell of electric drive assembly - Google Patents

Fatigue life analysis method for differential shell of electric drive assembly Download PDF

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CN112989665A
CN112989665A CN202110309875.XA CN202110309875A CN112989665A CN 112989665 A CN112989665 A CN 112989665A CN 202110309875 A CN202110309875 A CN 202110309875A CN 112989665 A CN112989665 A CN 112989665A
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electric drive
drive assembly
stress
differential
fatigue life
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邹喜红
苟林林
袁冬梅
熊锋
王超
蒋明聪
凌龙
王占飞
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Chongqing University of Technology
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Abstract

The invention relates to a fatigue life analysis method of a differential shell of an electric drive assembly, which comprises the following steps: establishing a differential shell finite element model of the differential shell of the electric drive assembly; verifying the accuracy of the differential shell finite element model; calculating the stress relation of the differential case finite element model under the unit torque load, which is successfully verified; calculating a material S-N curve of the differential shell of the electric drive assembly, and calculating a corresponding relation between the fatigue life and the stress according to the material S-N curve; taking an actually measured load spectrum of a differential shell of the electric drive assembly as load input, and calculating corresponding equivalent stress according to a stress relation under a unit torque load; and then calculating and evaluating the fatigue life of the differential shell of the electric drive assembly according to the equivalent stress and the relation between the fatigue life and the stress. The fatigue life analysis method can fully consider the impact of impact load and better combine the actual bearing torque condition, thereby improving the accuracy of the fatigue life analysis of the differential shell.

Description

Fatigue life analysis method for differential shell of electric drive assembly
Technical Field
The invention relates to the technical field of fatigue life analysis of a differential shell, in particular to a fatigue life analysis method of a differential shell of an electric drive assembly.
Background
The differential case is an intermediate link for connecting the main speed reducer and the half shaft to transmit power, and fatigue failures such as fatigue failure at the position of a planetary shaft hole and fatigue failure at the upper part of a window of the differential case are easy to occur, so that vehicle faults and personnel damage are caused. Therefore, the prior art has conducted many studies on the strength, mode, and fatigue life of the differential case. For example, a foreign document equally divides the rotational position of the input shaft of the final drive into 18 parts around the circumference, and analyzes the stress of the differential case under the rotational cyclic load to find the damage accumulation and the fatigue life of the differential case.
However, the above-described prior art does not consider the influence of the impact load of the differential case, and therefore the accuracy of the fatigue life analysis of the differential case is not high. Therefore, chinese patent publication No. CN105488298B discloses "a transmission differential impact strength and fatigue analysis method", which is a method of dividing the meshing position of a main reduction gear into twenty parts circumferentially, combining the quasi-static analysis results to form a transient stress history of one rotation of a differential housing, so as to simulate the transient stress of the differential housing of one actual rotation, linearly scaling the stress analysis results according to the load ratio of the load and the stress analysis by combining the torque levels and the corresponding rotation numbers of the load spectrum of the entire vehicle, and finally superposing the fatigue losses of the torque levels, so as to calculate the fatigue endurance life of the differential housing in the working process, i.e., the load spectrum.
The impact strength and fatigue analysis method for the transmission differential in the existing scheme can also be used for fatigue life analysis of the differential shell, namely the fatigue life analysis method for the differential shell can improve the accuracy of fatigue life analysis of the differential shell to a certain extent. However, the applicant finds that the existing differential case fatigue life analysis method is designed for the traditional fuel oil automobile, and the method cannot be completely suitable for the existing pure electric automobile. Compared with a fuel automobile, the pure electric automobile has the advantages that the output torque of the motor is larger, the main reduction ratio is improved, the dynamic response of the torque of the differential shell of the electric drive assembly is faster, and the impact problem is more prominent. In addition, the rotating speed of the motor is wider during operation during acceleration and deceleration, so that the reduction gear is influenced by a large amount of small loads, the transmission load fluctuation of the differential shell of the electric drive assembly is large, and the fatigue damage generated by the differential shell is difficult to determine. Therefore, the applicant thought to devise a fatigue life analysis method that could be better adapted to the differential case of the electric drive assembly.
Disclosure of Invention
Aiming at the defects of the prior art, the technical problems to be solved by the invention are as follows: how to provide a fatigue life analysis method which can be better suitable for an electric drive assembly differential case so as to fully consider the impact load influence and better combine the actual bearing torque condition, thereby improving the accuracy of the fatigue life analysis of the differential case.
In order to solve the technical problems, the invention adopts the following technical scheme:
a fatigue life analysis method for a differential case of an electric drive assembly comprises the following steps:
s1: establishing a differential shell finite element model of the differential shell of the electric drive assembly;
s2: verifying the accuracy of the differential shell finite element model;
s3: calculating the stress relation of the differential case finite element model under the unit torque load, which is successfully verified;
s4: calculating a material S-N curve of the differential shell of the electric drive assembly, and calculating a corresponding relation between the fatigue life and the stress according to the material S-N curve;
s5: taking an actually measured load spectrum of the electric drive assembly differential shell under a typical road surface as load input, and calculating corresponding equivalent stress according to a stress relation under a unit torque load; and then calculating and evaluating the fatigue life of the differential shell of the electric drive assembly according to the equivalent stress and the relation between the fatigue life and the stress.
Preferably, in step S1, the differential case finite element model is created by:
s11: establishing a three-dimensional model of the differential shell of the electric drive assembly by using three-dimensional software;
s12: importing the three-dimensional model into HyperWorks software; and then, carrying out mesh division and mesh encryption on the three-dimensional model by adopting a second-order tetrahedral unit to obtain a corresponding differential case finite element model.
Preferably, in step S2, the accuracy of the differential case finite element model is verified by:
s21: arranging a test bed structure for applying a torsional load to the electric drive assembly differential shell, and arranging a plurality of strain measuring points on the electric drive assembly differential shell;
s22: applying a torsional load to the differential shell of the electric drive assembly through a test bed structure, and recording the strain and stress of each strain measuring point to obtain a corresponding bed test result;
s23: establishing a finite element simulation model which is used for applying a torsion load to the differential case finite element model and corresponds to the test bench structure, and arranging simulation measuring points corresponding to a plurality of strain measuring points arranged on the differential case of the electric drive assembly on the differential case finite element model;
s24: applying a torsion load to the differential shell finite element model through the finite element simulation model, and recording the strain and stress of each simulation measuring point to obtain a corresponding simulation test result;
s25: calculating an error value of the simulation test result relative to the bench test result, and if the error value is less than or equal to a set error threshold, successfully verifying the accuracy of the finite element model of the differential case; otherwise, the verification fails.
Preferably, in step S3, the S-N curve of the material of the differential case of the electric drive assembly is calculated by the following formula:
s41: estimating a material S-N curve estimation formula of a differential shell of the electric drive assembly by an approximate calculation method;
s42: correcting the material S-N curve pre-estimation formula according to the notch effect, the surface roughness and the loading mode;
s43: the load borne by the differential shell of the electric drive assembly is counted circularly by a rotating rain flow counting method;
s44: correcting the load borne by the differential housing of the electric drive assembly through a Goodman algorithm;
s45: and obtaining the S-N curve of the material of the differential shell of the electric drive assembly.
Preferably, the S-N curve of the material of the differential case of the electric drive assembly is represented by the following formula:
Figure BDA0002989274570000031
in the formula: s1、S2Representing a stress value; b1、b2Respectively representing a first fatigue strength index and a second fatigue strength index; sigmabRepresents the ultimate strength of the material; SRI1 represents a stress phase range; nc1 denotes the fatigue transition point.
Preferably, the material S-N curve prediction formula is modified by the following formula:
Figure BDA0002989274570000032
in the formula: kfRepresents the fatigue notch coefficient; sigmafRepresents the fatigue limit of the optical slider; sigmacIndicating the fatigue limit of the notched part; sigmaaRepresenting an equivalent zero mean stress; saIndicating the total electric driveForming the stress amplitude of an S-N curve of the differential shell material; β represents a surface mass coefficient; ε represents the size factor; cLThe loading mode is indicated, and 0.58 is taken.
Preferably, the load borne by the differential case of the electric drive assembly is corrected by the following formula:
Figure BDA0002989274570000033
in the formula: sigmaa' represents the corrected load; sigma-1Representing the stress fatigue limit under symmetric cycles; sigmamIs the stress mean value; sigmabIndicating the ultimate strength of the material.
Preferably, the S-N curve of the material of the differential case of the electric drive assembly is represented by the following formula:
Figure BDA0002989274570000034
in the formula: s1′、S2' represents the corrected stress value; b1′、b2' means the corrected first and second fatigue strength indexes, respectively; sigmabRepresents the ultimate strength of the material; SRI1 represents a stress phase range; nc1 denotes the fatigue transition point.
Preferably, in step S4, the relationship between fatigue life and stress is expressed by the following formula:
Figure BDA0002989274570000041
in the formula: sigmaaRepresenting the equivalent stress; n is a radical offRepresents the fatigue life; β represents a surface mass coefficient; ε represents the size factor; cLRepresenting the loading mode, and taking 0.58; kfRepresents the fatigue notch coefficient; sigmaf' represents a fatigue strength coefficient; b represents a fatigue strength coefficient.
Preferably, in step S3, the stress relationship under unit torque load of the finite element model of the differential case is expressed by the following formula:
∑UiMi＝∫Ω{ε}TσidΩ(ii) a In the formula: miRepresenting a virtual external force, namely torque, and taking 1 during calculation; u shapeiRepresenting the true displacement; Ω represents the field of integration; { ε } represents the true strain induced by the torque load; t represents transposition; sigmaiThe imaginary stress, i.e., the stress corresponding to the unit torque, is represented.
Compared with the prior art, the fatigue life analysis method has the following beneficial effects:
1. according to the invention, the differential shell finite element model is established and the accuracy of the differential shell finite element model is verified, so that the differential shell finite element model can be well adapted to an actual electric drive assembly differential shell, and the analysis effect of the fatigue life of the electric differential shell can be ensured.
2. According to the method, the fatigue life of the differential shell is calculated and evaluated according to the actually measured load spectrum, the stress relation under the unit torque load and the S-N curve (fatigue life and stress relation) of the material, the actual torque bearing condition of the differential shell is combined, the influence of impact load on the fatigue life of the differential shell is fully considered, the method is better suitable for analyzing the fatigue life of the differential shell of the electric drive assembly, meanwhile, the life analysis mode is completed based on the fatigue of the actually measured load spectrum, and the accuracy of the fatigue life analysis of the differential shell can be further improved.
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For purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made in detail to the present invention as illustrated in the accompanying drawings, in which:
FIG. 1 is a logic diagram of a fatigue life analysis method in an embodiment;
FIG. 2 is a schematic structural view of an embodiment of a load transfer assembly;
FIG. 3 is a schematic structural diagram of an embodiment of a torque actuated assembly;
FIG. 4 is a schematic graph showing the strain of the first axis of the triaxial strain relief sensor as a function of time in an embodiment;
FIG. 5 is a schematic diagram showing the strain of the second shaft of the triaxial strain-relief sensor as a function of time in an embodiment;
FIG. 6 is a schematic diagram of the strain of the third shaft of the three-shaft strain gage sensor in an embodiment as a function of time;
FIG. 7 is a schematic diagram showing the change of stress with time at the strain measuring point 2 in the example;
FIG. 8 is a schematic structural diagram of a finite element simulation model in an embodiment;
FIG. 9 is a diagram illustrating the stress analysis results of the simulation test point 1 and the strain test point 1 in the embodiment;
FIG. 10 is a diagram illustrating the stress analysis results of the simulation test point 2 and the strain test point 2 in the embodiment;
FIG. 11 is a diagram illustrating the stress analysis results of the simulation test point 3 and the strain test point 3 in the embodiment;
FIG. 12 is a diagram illustrating the stress analysis results of the simulation test point 4 and the strain test point 4 in the embodiment;
FIG. 13 is a diagram showing relative errors at respective measurement points in the example;
FIG. 14 is a graph showing the simulation results of the stress per unit torque in the examples;
FIG. 15 is a schematic representation of a measured load spectrum in an example;
FIG. 16 is a cloud plot of differential case fatigue life for an embodiment.
Detailed Description
The following is further detailed by the specific embodiments:
example (b):
the embodiment of the invention discloses a fatigue life analysis method for a differential shell of an electric drive assembly.
As shown in fig. 1, a method for analyzing fatigue life of a differential case of an electric drive assembly includes the following steps:
s1: establishing a differential shell finite element model of the differential shell of the electric drive assembly;
s2: verifying the accuracy of the differential shell finite element model;
s3: calculating the stress relation of the differential case finite element model under the unit torque load, which is successfully verified;
s4: calculating a material S-N curve of the differential shell of the electric drive assembly, and calculating a corresponding relation between the fatigue life and the stress according to the material S-N curve;
s5: taking an actually measured load spectrum of the electric drive assembly differential shell under a typical road surface as load input, and calculating corresponding equivalent stress according to a stress relation under a unit torque load; and then calculating and evaluating the fatigue life of the differential shell of the electric drive assembly according to the equivalent stress and the relation between the fatigue life and the stress.
According to the invention, the differential shell finite element model is established and the accuracy of the differential shell finite element model is verified, so that the differential shell finite element model can be well adapted to an actual electric drive assembly differential shell, and the analysis effect of the fatigue life of the electric differential shell can be ensured. Secondly, the fatigue life of the differential shell is calculated and evaluated according to the actually measured load spectrum, the stress relation under the unit torque load and the S-N curve (fatigue life and stress relation) of the material, the actual torque bearing condition of the differential shell is combined, the influence of impact load on the fatigue life of the differential shell is fully considered, the method is better suitable for analyzing the fatigue life of the differential shell of the electric drive assembly, meanwhile, the fatigue life analysis mode is completed based on the actually measured load spectrum, and the accuracy of the fatigue life analysis of the differential shell can be further improved.
In the specific implementation process, the relation between the fatigue life and the stress is expressed by the following formula:
Figure BDA0002989274570000061
in the formula: sigmaaRepresenting the equivalent stress; n is a radical offRepresents the fatigue life; β represents a surface mass coefficient; ε represents the size factor; cLRepresenting the loading mode, and taking 0.58; kfRepresents the fatigue notch coefficient; sigmaf' represents a fatigue strength coefficient; b represents a fatigue strength coefficient. Wherein σfBoth' and b are material dependent and are known values.
In the specific implementation process, in step S1, a differential case finite element model is established by the following steps:
s11: establishing a three-dimensional model of the differential shell of the electric drive assembly by using three-dimensional software;
s12: importing the three-dimensional model into HyperWorks software; and then, carrying out mesh division and mesh encryption on the three-dimensional model by adopting a second-order tetrahedral unit to obtain a corresponding differential case finite element model.
In this embodiment, a Hypermesh preprocessing function is used to perform mesh division, and a proper amount of mesh encryption can be performed on a concerned part of the differential case. Parameters of the three-dimensional model are checked by means of the jacobian coefficient, the amount of warp angle, the stretch value, and the like, so that the mesh quality can be ensured. The differential case finite element model is co-discretized into 641677 second order tetrahedral elements and 956052 nodes. The planet gear shaft is simulated by using an RBE2 unit, so that torque is conveniently applied, and the torque between the differential shell and the main speed reducer gear is transmitted by bolts between the differential shell and the main speed reducer gear; the local coordinate system and RBE2 cells for the simulated bolts were set for applying torque at each bolt hole. The differential case material is given a material property of QT600-3, which is shown in table 1.
TABLE 1
Figure BDA0002989274570000062
In the invention, the differential case finite element model can be well established through the steps.
In the specific implementation process, in step S2, the accuracy of the differential case finite element model is verified through the following steps:
s21: arranging a test bed structure for applying a torsional load to the electric drive assembly differential shell, and arranging a plurality of strain measuring points on the electric drive assembly differential shell;
s22: applying a torsional load to the differential shell of the electric drive assembly through a test bed structure, and recording the strain and stress of each strain measuring point to obtain a corresponding bed test result;
s23: establishing a finite element simulation model which is used for applying a torsion load to the differential case finite element model and corresponds to the test bench structure, and arranging simulation measuring points corresponding to a plurality of strain measuring points arranged on the differential case of the electric drive assembly on the differential case finite element model;
s24: applying a torsion load to the differential shell finite element model through the finite element simulation model, and recording the strain and stress of each simulation measuring point to obtain a corresponding simulation test result;
s25: calculating an error value of the simulation test result relative to the bench test result, and if the error value is less than or equal to a set error threshold, successfully verifying the accuracy of the finite element model of the differential case; otherwise, the verification fails.
As shown in fig. 2 and 3, the test bench structure in step S21 includes a load conversion assembly and a torque actuator assembly.
The load conversion component comprises a connecting piece 1 and a rocker arm 2; the connecting piece 1 is used for connecting the linear load generator with the rocker arm 2; one end of the rocker arm 2 is provided with a flange plate for fixedly connecting a differential case flange 4, the flange plate is provided with a hole structure, and the hole structure is sleeved on a planetary gear mounting section of the differential case and can be tightly attached to the position of the differential case flange plate; a differential bearing 3 is arranged in the main body structure of the differential shell; the other end of the rocker arm 2 is a hinged plate hinged at one end of the connecting piece 1. The hole structure is a through hole arranged in the center of the flange plate, and the diameter of the through hole is larger than that of the main structure of the differential case and smaller than that of the flange 4 of the differential case; the pore structure edge is equipped with the bolted connection hole corresponding with the bolt hole on differential mechanism casing flange 4 to can connect the flange board of rocking arm 2 on differential mechanism casing flange 4 through bolt 5, realize dismantling the connection, simple to operate has avoided causing the motion to interfere with two semi-axles of differential mechanism owing to connect on differential mechanism casing flange 4 moreover.
The torque actuating assembly comprises a linear load generator and a load conversion assembly for the differential shell; the linear load generator is connected with one end of the connecting piece 1, the connecting piece 1 is not in the same straight line with the rocker arm 2 (the included angle between the connecting piece 1 and the rocker arm 2 is not 0 degree and 180 degrees), and the included angle between the connecting piece 1 and the rocker arm 2 is 90 degrees in order to improve the conversion efficiency. Specifically, the tested differential is loaded by adopting a hydraulic servo linear cylinder actuator of MTS company 244, and converting force or displacement in a linear direction into torque on a tested differential shell through a load conversion assembly. Clamping grooves are formed in two ends of the connecting piece 1, the clamping groove in one end of the connecting piece 1 is used for accommodating the hinged plate, and the connecting piece 1 is connected with the hinged plate through a pin; the clamping groove at the other end of the connecting piece 1 is used for accommodating the output end of the linear load generator, and the connecting piece 1 is connected with the output end of the linear load generator through a spherical hinge. The main effect of ball pivot is for connecting actuator and connecting piece 1, and power and displacement that the transmission actuator sent ensure that the actuator still can protect the actuator not to take place to damage when the actuator normally works in the test process. The pin can ensure that the connecting piece 1 and the rocker arm 2 can normally and flexibly transmit load in the test process. The rocker arm 2 plays a role of a force arm and is connected with a flange of the tested differential through a fastening bolt, so that the actual operating environment of the tested differential can be greatly reproduced. The linear cylinder actuator 13 is supported by the actuator support 6; the input end of the linear cylinder actuator 13 and the two half shafts of the differential are respectively fixed by corresponding fixing devices, refer to an L plate 11 and an L plate 9 in FIG. 2.
The complete working process of the test bed structure is as follows: the controller is used as a load control device through hole to control the servo valves 7 and 8 to send signal commands to a load generating device consisting of a hydraulic station and a hydraulic servo linear cylinder actuator, the actuator outputs force or displacement load signals in the linear direction, the force or displacement load signals are transmitted to the rocker arm 2 through the spherical hinge 10 and the connecting piece 1 and are converted into torque to be applied to a tested differential shell, and meanwhile, the force sensor 14 and the displacement sensor 12 feed back signals to the controller so as to realize the cyclic reciprocating torsional impact fatigue test of the tested differential.
Strain measuring points are arranged at the window and the root position of the window of the differential shell of the electric drive assembly, and a triaxial strain pattern sensor is correspondingly arranged; strain measuring points are arranged at the positions of planetary gear shaft holes of the differential shell of the electric drive assembly, and strain gauge sensors are correspondingly arranged. And polishing the selected strain measuring point positions to meet the strain gauge arrangement requirement, and performing work such as strain gauge pasting and protection, wherein the strain gauge group bridge method adopts 1/4 bridges and adopts a SoMateDAQ data acquisition system to acquire strain signals of 20 channels.
In step S22, when the structure is subjected to a performance test, the load loading waveform includes loading modes such as a pulse wave, a sine wave, a half sine wave, a rectangular wave, and the like, and the sine wave loading is adopted in the present invention. The transmission ratio of a main speed reducer of the hydraulic linear motor is 12.91, the rated torque, the peak torque and the transmission ratio of the main speed reducer of the motor are comprehensively considered, the amplitude is loaded to 5500 N.m from 1500 N.m, the dynamic response of a differential shell is examined through loads of different grades, and the loading frequency is selected to be 1Hz in combination with the actual situation of a test bed. The strain and stress values of one of the stress points (stress point 2) under 4300N m amplitude loading are shown in FIG. 4, FIG. 5, FIG. 6 and FIG. 7. The strain values of all levels of loads acquired by the strain gauge sensors are solved through the following formula to obtain the main stress values of all positions of all levels of loads:
Figure BDA0002989274570000081
in the formula, σ1Or σ2Denotes the principal stress value, E denotes the modulus of elasticity of the material of the differential case, v denotes the Poisson's ratio of the material of the differential case, ε1、ε2、ε3Respectively, the three-axis strain value of the three-axis strain rosette. Wherein E and v are both known values.
σ ═ E ∈; in the formula, σ represents a stress value of the uniaxial strain sensor.
In step S23, the CATIA software and the finite element software are used, the boundary, the constraint load and the load condition of the test bench structure are combined, the contact between the components is established, the loads of various grades are applied to the actuator, the output ends of the two half shafts of the differential case are fully constrained, and a finite element simulation model based on the bench test is established, as shown in fig. 8.
In step S24, the simulation analysis results of the simulation measuring point 2 and the simulation measuring point 4 under the loads of each level are shown in table 2 through finite element simulation analysis.
TABLE 2
Figure BDA0002989274570000082
In step S25, the error threshold is set to 10%; fig. 9, fig. 10, fig. 11, and fig. 12 are comparisons of simulation test results and bench test results, and it can be seen that under a load of 1500N · m to 5500N · m torque, the matching degree of the simulation analysis results of stresses at positions from the simulation measuring points 1 to the simulation measuring points 4 and the bench test results is high, as shown in fig. 13, the relative error value of each measuring point is within 10%, the maximum relative error is 9.64%, and the established differential case finite element model has high accuracy and can be used for fatigue life analysis of the differential case of the electric drive assembly.
According to the invention, the differential case finite element model is established, and the bench test result and the simulation test result are compared and analyzed in combination with the test of the test bench structure and the finite element simulation model, so that the accuracy of the differential case finite element model can be well ensured, namely the differential case finite element model can be well adapted to the actual electric drive assembly differential case, and the analysis effect of the fatigue life of the electric differential case can be ensured.
In the specific implementation process, in step S3, a S-N curve of the material of the differential case of the electric drive assembly is calculated by the following formula:
s41: estimating a material S-N curve estimation formula of a differential shell of the electric drive assembly by an approximate calculation method;
s42: correcting the material S-N curve pre-estimation formula according to the notch effect, the surface roughness and the loading mode;
s43: the load borne by the differential shell of the electric drive assembly is counted circularly by a rotating rain flow counting method;
s44: correcting the load borne by the differential housing of the electric drive assembly through a Goodman algorithm;
s45: and obtaining the S-N curve of the material of the differential shell of the electric drive assembly.
In step S41, a nominal stress method (i.e., S-N curve) is used to calculate the fatigue life, and the S-N curve expresses the relationship between the fatigue life and the stress as:
σa＝σf′(2Nf)b(ii) a In the formula, σaDenotes the equivalent stress (stress amplitude), σf' denotes the fatigue strength coefficient, NfRepresents the number of load cycles (i.e., fatigue life), and b represents the fatigue strength index. Wherein σfBoth' and b are material dependent and are known values.
Meanwhile, the fatigue life is calculated and evaluated by combining a linear accumulated damage theory, the linear accumulated damage theory considers that when the material or the part bears the stress action higher than the fatigue limit, each cycle causes certain damage to the material, and the damage can be accumulated, and when the damage accumulation reaches a limit, the material or the part is damaged.
According to the method, a material S-N curve pre-estimation formula is estimated based on a nominal stress method, then the material S-N curve pre-estimation formula is corrected according to a gap effect, surface roughness and a loading mode, random loads are circularly counted through a rotating rain flow counting method, and average stress correction is performed on the random loads through a Goodman algorithm, so that the finally obtained material S-N curve is closer to the material S-N curve under the real working environment of the differential shell of the electric drive assembly, and the accuracy of fatigue life analysis of the differential shell can be improved in an auxiliary mode.
In the specific implementation process, the S-N curve of the material of the differential shell of the electric drive assembly is represented by the following formula:
Figure BDA0002989274570000101
in the formula: s1、S2Representing a stress value; b1、b2Respectively representing a first fatigue strength index and a second fatigue strength index; sigmabRepresents the ultimate strength of the material; SRI1 represents a stress phase range; nc1 denotes the fatigue transition point. Wherein σbMaterial dependent, is a known value; both SRI1 and Nc1 can be obtained from the S-N curve of the material.
In the specific implementation process, the material S-N curve estimation formula is corrected through the following formula:
Figure BDA0002989274570000102
in the formula: kfRepresents the fatigue notch coefficient; sigmafRepresents the fatigue limit of the optical slider; sigmacIndicating the fatigue limit of the notched part; sigmaaRepresenting an equivalent zero mean stress; saRepresenting the stress amplitude of an S-N curve of a differential shell material of the electric drive assembly; β represents a surface mass coefficient; ε represents the size factor; cLThe loading mode is indicated, and 0.58 is taken.
In the specific implementation process, the load borne by the differential shell of the electric drive assembly is corrected through the following formula:
σa′＝σ-1(1-σm/σb) (ii) a In the formula: sigmaa' represents the corrected load; sigma-1Representing the stress fatigue limit under symmetric cycles; sigmamIs the stress mean value; sigmabIndicating the ultimate strength of the material.
In the specific implementation process, the S-N curve of the material of the differential shell of the electric drive assembly is represented by the following formula:
Figure BDA0002989274570000103
in the formula: s1′、S2' represents the corrected stress value; b1′、b2' means the corrected first and second fatigue strength indexes, respectively; sigmabRepresents the ultimate strength of the material; SRI1 represents a stress phase range; nc1 denotes the fatigue transition point. Wherein σbMaterial dependent, is a known value; both SRI1 and Nc1 can be obtained from the S-N curve of the material.
In the specific implementation process, the stress relation of the differential case finite element model under the unit torque load is expressed by the following formula:
∑UiMi＝∫Ω{ε}TσidΩ(ii) a In the formula: miRepresenting a virtual external force, namely torque, and taking 1 during calculation; u shapeiRepresenting the true displacement; Ω represents the field of integration; { ε } represents the true strain induced by the torque load; t represents transposition; sigmaiThe virtual stress is represented as a function of,i.e. the stress per unit torque. Wherein, UiRelating epsilon to the material properties, it can be solved by finite element software and is considered as a known value.
The unit torque stress analysis is carried out by applying the differential case finite element model which is successfully verified, the simulation analysis result is shown in figure 14, and the maximum stress value is 2.0 MPa. The unit load method is a static force permission field with imaginary external force and internal force as structures, and is a method led out by an imaginary force principle (a residual imaginary work principle).
Specifically, the combined stress can also be calculated by the following formula:
Figure BDA0002989274570000111
in the formula, σeqDenotes the combined stress, σx、σy、σzRespectively represent the positive stress components in the x, y and z directions, tauxy、τyz、τzxRespectively, representing the tangential stress component acting on the build. Because the differential shell material is a brittle material, has little plastic deformation and has the characteristic of motion hardening, the Von Mises criterion is adopted for stress combination.
Specifically, in step S5, the actual road load spectrum of the left and right half shafts of the pure electric vehicle is collected in a certain field of test by using the wireless telemetry, the sum of the torques of the left and right half shafts is approximately equivalent to the differential case torque, and the actual load spectrum is as shown in fig. 15.
In order to satisfy the 2 σ principle, the survival rate is set to 95.4% according to normal probability distribution; the fatigue life of the differential shell of the electric drive assembly is analyzed based on the measured differential shell load spectrum, and a cloud chart of the service life of the differential shell obtained through analysis is shown in fig. 16. As can be seen from the fatigue life cloud chart of the differential shell, the minimum fatigue life of the differential shell of the electric drive assembly, namely the position where fatigue failure easily occurs, is formed at the position of the planetary gear shaft hole and the upper part of the differential shell window, and the position is the same as the position of the fatigue failure of the differential shell during actual vehicle running, so the test result is credible.
From table 4, it can be seen that the maximum cell damage value is 851466 cells, the damage value is 7.82E +08, the cycle number is 1.28E +07 times, and the fatigue life of the automobile parts is required to be more than 10 kilometers in the durability road test by converting the length of the reinforced road surface and the driving distance of the automobile on the test road surface into the fatigue life of the differential case to be 2.56E +05 km.
TABLE 4
Figure BDA0002989274570000112
Figure BDA0002989274570000121
In conclusion, the method and the device not only combine the actual bearing torque condition of the differential shell, but also fully consider the influence of the impact load on the fatigue life of the differential shell, and simultaneously complete the life analysis mode based on the fatigue of the measured load spectrum, and can assist in improving the accuracy of the fatigue life analysis result of the differential shell.
The foregoing is merely an example of the present invention, and common general knowledge in the field of known specific structures and characteristics is not described herein in any greater extent than that known in the art at the filing date or prior to the priority date of the application, so that those skilled in the art can now appreciate that all of the above-described techniques in this field and have the ability to apply routine experimentation before this date can be combined with one or more of the present teachings to complete and implement the present invention, and that certain typical known structures or known methods do not pose any impediments to the implementation of the present invention by those skilled in the art. It should be noted that, for those skilled in the art, without departing from the structure of the present invention, several changes and modifications can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicability of the patent. The scope of the claims of the present application shall be determined by the contents of the claims, and the description of the embodiments and the like in the specification shall be used to explain the contents of the claims.

Claims (10)

1. A fatigue life analysis method for a differential case of an electric drive assembly is characterized by comprising the following steps:
s1: establishing a differential shell finite element model of the differential shell of the electric drive assembly;
s2: verifying the accuracy of the differential shell finite element model;
s3: calculating the stress relation of the differential case finite element model under the unit torque load, which is successfully verified;
s4: calculating a material S-N curve of the differential shell of the electric drive assembly, and calculating a corresponding relation between the fatigue life and the stress according to the material S-N curve;
s5: taking an actually measured load spectrum of the electric drive assembly differential shell under a typical road surface as load input, and calculating corresponding equivalent stress according to a stress relation under a unit torque load; and then calculating and evaluating the fatigue life of the differential shell of the electric drive assembly according to the equivalent stress and the relation between the fatigue life and the stress.
2. The method for analyzing fatigue life of an electrically driven assembly differential case according to claim 1, wherein in step S1, the differential case finite element model is established by:
s11: establishing a three-dimensional model of the differential shell of the electric drive assembly by using three-dimensional software;
s12: importing the three-dimensional model into HyperWorks software; and then, carrying out mesh division and mesh encryption on the three-dimensional model by adopting a second-order tetrahedral unit to obtain a corresponding differential case finite element model.
3. The method for fatigue life analysis of an electrically driven assembly differential case of claim 1, wherein in step S2, the accuracy of the differential case finite element model is verified by:
s21: arranging a test bed structure for applying a torsional load to the electric drive assembly differential shell, and arranging a plurality of strain measuring points on the electric drive assembly differential shell;
s22: applying a torsional load to the differential shell of the electric drive assembly through a test bed structure, and recording the strain and stress of each strain measuring point to obtain a corresponding bed test result;
s23: establishing a finite element simulation model which is used for applying a torsion load to the differential case finite element model and corresponds to the test bench structure, and arranging simulation measuring points corresponding to a plurality of strain measuring points arranged on the differential case of the electric drive assembly on the differential case finite element model;
s24: applying a torsion load to the differential shell finite element model through the finite element simulation model, and recording the strain and stress of each simulation measuring point to obtain a corresponding simulation test result;
s25: calculating an error value of the simulation test result relative to the bench test result, and if the error value is less than or equal to a set error threshold, successfully verifying the accuracy of the finite element model of the differential case; otherwise, the verification fails.
4. The method for analyzing fatigue life of an electrically driven assembly differential case according to claim 1, wherein in step S4, the S-N curve of the material of the electrically driven assembly differential case is calculated by the following formula:
s41: estimating a material S-N curve estimation formula of a differential shell of the electric drive assembly by an approximate calculation method;
s42: correcting the material S-N curve pre-estimation formula according to the notch effect, the surface roughness and the loading mode;
s43: the load borne by the differential shell of the electric drive assembly is counted circularly by a rotating rain flow counting method;
s44: correcting the load borne by the differential housing of the electric drive assembly through a Goodman algorithm;
s45: and obtaining the S-N curve of the material of the differential shell of the electric drive assembly.
5. The method for fatigue life analysis of an electric drive assembly differential case according to claim 4, wherein the S-N curve of the material of the electric drive assembly differential case is represented by the following formula:
Figure FDA0002989274560000021
in the formula: s1、S2Representing a stress value; b1、b2Respectively representing a first fatigue strength index and a second fatigue strength index; sigmabRepresents the ultimate strength of the material; SRI1 represents a stress phase range; nc1 denotes the fatigue transition point.
6. The method for analyzing fatigue life of a differential case of an electric drive assembly according to claim 4, wherein the material S-N curve prediction formula is modified by the following formula:
Figure FDA0002989274560000022
in the formula: kfRepresents the fatigue notch coefficient; sigmafRepresents the fatigue limit of the optical slider; sigmacIndicating the fatigue limit of the notched part; sigmaaRepresenting an equivalent zero mean stress; saRepresenting the stress amplitude of an S-N curve of a differential shell material of the electric drive assembly; β represents a surface mass coefficient; ε represents the size factor; cLThe loading mode is indicated, and 0.58 is taken.
7. The method for fatigue life analysis of an electric drive assembly differential case of claim 4, wherein the load experienced by the electric drive assembly differential case is corrected by the formula:
σa′＝σ-1(1-σm/σb) (ii) a In the formula: sigmaa' represents the corrected load; sigma-1Representing symmetrical cyclesLower stress fatigue limit; sigmamIs the stress mean value; sigmabIndicating the ultimate strength of the material.
8. The method for fatigue life analysis of an electric drive assembly differential case according to claim 4, wherein the S-N curve of the material of the electric drive assembly differential case is represented by the following formula:
Figure FDA0002989274560000031
in the formula: s1′、S2' represents the corrected stress value; b1′、b2' means the corrected first and second fatigue strength indexes, respectively; sigmabRepresents the ultimate strength of the material; sigmacIndicating the fatigue limit of the notched part; β represents a surface mass coefficient; ε represents the size factor; cLRepresenting the loading mode, and taking 0.58; SRI1 represents a stress phase range; nc1 denotes the fatigue transition point.
9. The method for analyzing fatigue life of a differential case of an electric drive assembly according to claim 8, wherein in step S4, the relationship between fatigue life and stress is expressed by the following formula:
Figure FDA0002989274560000032
in the formula: sigmaaRepresenting the equivalent stress; n is a radical offRepresents the fatigue life; β represents a surface mass coefficient; ε represents the size factor; cLRepresenting the loading mode, and taking 0.58; kfRepresents the fatigue notch coefficient; sigmaf' represents a fatigue strength coefficient; b represents a fatigue strength coefficient.
10. The method for analyzing fatigue life of a differential case of an electric drive assembly according to claim 1, wherein in step S3, the stress relationship under unit torque load of the finite element model of the differential case is expressed by the following formula:
∑UiMi＝∫Ω{ε}TσidΩ(ii) a In the formula: miRepresenting a virtual external force, namely torque, and taking 1 during calculation; u shapeiRepresenting the true displacement; Ω represents the field of integration; { ε } represents the true strain induced by the torque load; t represents transposition; sigmaiThe imaginary stress, i.e., the stress corresponding to the unit torque, is represented.
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