CN112989665B - Fatigue life analysis method for electric drive assembly differential mechanism shell - Google Patents

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

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CN112989665B
CN112989665B CN202110309875.XA CN202110309875A CN112989665B CN 112989665 B CN112989665 B CN 112989665B CN 202110309875 A CN202110309875 A CN 202110309875A CN 112989665 B CN112989665 B CN 112989665B
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electric drive
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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 influence of impact load and better combine the actual bearing torque condition, thereby improving the accuracy of the fatigue life analysis of the differential case.

Description

Fatigue life analysis method for differential shell of electric drive assembly
Technical Field
The invention relates to the technical field of differential shell fatigue life analysis, in particular to a fatigue life analysis method for an electric drive assembly differential shell.
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, fatigue failure at the upper part of a window of the differential case and the like easily 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, one 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 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 method for analyzing impact strength and fatigue of a transmission differential", which is to divide the meshing position of a main reduction gear into twenty parts around the circumferential direction, combine the quasi-static analysis results to form a transient stress history of one rotation of the differential case, so as to simulate the transient stress of the differential case of one actual rotation, and combine each torque level and corresponding rotation number of the load spectrum of the entire vehicle, perform linear scaling on the stress analysis results according to the load ratio of the load and the stress analysis, finally superimpose the fatigue loss of each torque level, and calculate the working process of the differential case, i.e., the fatigue endurance life of the differential case under 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 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.
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 torsional load to the differential shell finite element model and corresponds to the test bench structure, and setting simulation measuring points corresponding to a plurality of strain measuring points arranged on the differential shell of the electric drive assembly on the differential shell finite element model;
s24: applying a torsional 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 shell 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: s. the 1 、S 2 Representing a stress value; b 1 、b 2 Respectively representing a first fatigue strength index and a second fatigue strength index; sigma b Represents the ultimate strength of the material; SRI1 represents the stress phase range; nc1 denotes a fatigue transition point.
Preferably, the material S-N curve prediction formula is modified by the following formula:
Figure BDA0002989274570000032
in the formula: k f Represents the fatigue notch coefficient; sigma f Represents the fatigue limit of the optical slider; sigma c Indicating the fatigue limit of the notched part; sigma a Representing an equivalent zero mean stress; s a Representing 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; c L The loading mode is indicated, and 0.58 is taken.
Preferably, the load experienced by the differential case of the electric drive assembly is corrected by the following equation:
Figure BDA0002989274570000033
in the formula: sigma a ' represents the corrected load; sigma -1 Representing stress fatigue limit under symmetrical cycle; sigma m Is the stress mean value; sigma b Indicating 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: s 1 ′、S 2 ' represents the corrected stress value; b 1 ′、b 2 ' means the corrected first and second fatigue strength indexes, respectively; sigma b Represents the ultimate strength of the material; SRI1 represents the stress phase range; nc1 denotes a 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: sigma a Representing the equivalent stress; n is a radical of hydrogen f Represents the fatigue life; β represents a surface mass coefficient; ε represents the size factor; c L Representing the loading mode, and taking 0.58; k f Represents the fatigue notch coefficient; sigma f ' 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:
∑U i M i ＝∫ Ω {ε} T σ i d Ω (ii) a In the formula: m is a group of i Representing a virtual external force, namely torque, and taking 1 during calculation; u shape i Representing the true displacement; Ω represents the field of integration; { ε } represents the true strain induced by the torque load; t represents transposition; sigma i The 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. in 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 the 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 (the relation between the fatigue life and the stress) of the material, the actual bearing torque 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 diagram 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 in an example.
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 a finite element model of the differential shell;
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: sigma a Representing the equivalent stress; n is a radical of f Represents the fatigue life; β represents a surface mass coefficient; ε represents the size factor; c L Representing a loading mode, and taking 0.58; k f Represents the fatigue notch coefficient; sigma f ' represents a fatigue strength coefficient; b represents a fatigue strength coefficient. Wherein σ f Both' 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 through 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 units 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 a bolt between the differential shell and the main speed reducer gear; a local coordinate system and an RBE2 unit for simulating a bolt are set in each bolt hole for applying torque. The differential case material properties are given, and are QT600-3, and are 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 bench structure, and recording the strain and stress of each strain measuring point to obtain a corresponding bench test result;
s23: establishing a finite element simulation model which is used for applying a torsional load to the differential shell finite element model and corresponds to the test bench structure, and setting simulation measuring points corresponding to a plurality of strain measuring points arranged on the differential shell of the electric drive assembly on the differential shell finite element model;
s24: applying a torsional 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 differential case finite element model; otherwise, the verification fails.
As shown in fig. 2 and 3, the test bench structure in step S21 includes a load conversion member and a torque actuator member.
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 and 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 corresponding bolted connection hole 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-axises of differential mechanism moreover owing to connect on differential mechanism casing flange 4.
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. The tested differential is loaded by a load conversion assembly in a way that a force or displacement in a linear direction is converted into a torque on a shell of the tested differential by adopting a 244 type hydraulic servo linear cylinder actuator of MTS company. 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 a 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 take place to damage when the normal work of test in-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 of the linear cylinder actuator 13, the two half-shafts of the differential are each fixed by a respective fixing device, see L- plates 11, 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 a 1/4 bridge is adopted in a strain gauge bridging method, and a SoMateDAQ data acquisition system is adopted to acquire strain signals of 20 channels.
In step S22, when the structure is subjected to the performance test, the loading waveforms include loading modes such as pulse wave, sine wave, half sine wave, rectangular wave, and the like, and 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 5500N m from 1500N m, the dynamic response of a differential shell is checked through loads of different grades, and the loading frequency is selected to be 1Hz in combination with the actual condition 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 the strain gauge sensors under all levels of loads are acquired, and the main stress values of all positions under all levels of loads are obtained by solving through the following formula:
Figure BDA0002989274570000081
in the formula, σ 1 Or σ 2 Denotes 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, ε 1 、ε 2 、ε 3 Respectively, the three-axis strain value of the three-axis strain rosette. Wherein E and v are both known values.
σ = E ε; 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, and the boundary, the constraint load and the load condition of the test bench structure are combined to establish contact between the components, apply loads of various grades to the actuator, perform full constraint on the output ends of the two half shafts of the differential case, and establish a finite element simulation model based on the bench test, as shown in fig. 8.
In step S24, through finite element simulation analysis, the simulation analysis results of the simulation measuring points 2 and the simulation measuring points 4 under the loads of each level are shown in table 2.
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 material S-N curve 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:
σ a ＝σ f ′(2N f ) b (ii) a In the formula, σ a Denotes the equivalent stress (stress amplitude), σ f ' denotes the fatigue strength coefficient, N f Represents the number of load cycles (i.e., fatigue life), and b represents the fatigue strength index. Wherein σ f Both' 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: s 1 、S 2 Representing a stress value; b 1 、b 2 Respectively representing a first fatigue strength index and a second fatigue strength index; sigma b Represents the ultimate strength of the material; SRI1 represents the stress phase range; nc1 denotes a fatigue transition point. Wherein σ b Material 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 S-N curve estimation formula of the material is corrected through the following formula:
Figure BDA0002989274570000102
in the formula: k f Represents the fatigue notch coefficient; sigma f Represents the fatigue limit of the optical slider; sigma c Indicating the fatigue limit of the notched part; sigma a Representing an equivalent zero mean stress; s. the a Representing 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; c L The 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:
σ a ′＝σ -1 (1-σ m /σ b ) (ii) a In the formula: sigma a ' represents the corrected load; sigma -1 Representing the stress fatigue limit under symmetric cycles; sigma m Is the stress mean value; sigma b Indicating 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: s 1 ′、S 2 ' represents the corrected stress value; b 1 ′、b 2 ' means the corrected first and second fatigue strength indexes, respectively; sigma b Represents the ultimate strength of the material; SRI1 represents the stress phase range; nc1 denotes a fatigue transition point. Wherein σ b Material 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:
∑U i M i ＝∫ Ω {ε} T σ i d Ω (ii) a In the formula: m is a group of i Representing a virtual external force, namely torque, and taking 1 during calculation; u shape i Representing the true displacement; Ω represents the field of integration; { ε } represents the true strain induced by the torque load; t represents transposition; sigma i The imaginary stress, i.e. the stress corresponding to a unit torque, is indicated. Wherein, U i Relating 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 2.0MPa. The unit load method is a static force permission field taking 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, σ eq Denotes the combined stress, σ x 、σ y 、σ z Respectively represent the positive stress components in the x, y and z directions, tau xy 、τ yz 、τ zx Respectively, 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 sigma 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 actually measured load spectrum of the differential shell, and a cloud chart of the service life of the differential shell obtained by analyzing 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 3, the maximum unit of the unit damage value is 851466 unit, the damage value is 7.82e +08, the cycle number is 1.28e +07 times, and the fatigue life of the automobile parts in the durability road test is 2.56e +05km which is converted into the fatigue life of the differential housing according to the length of the reinforced road surface and the driving distance of the automobile on the tested road surface, thereby meeting the requirement that the fatigue life of the automobile parts is more than 10 kilometres.
TABLE 3
Figure BDA0002989274570000112
Figure BDA0002989274570000121
In conclusion, the method and the device not only combine the actual bearing torque condition of the differential case, but also fully consider the influence of impact load on the fatigue life of the differential case, and meanwhile, the method for analyzing the fatigue service life is completed based on the actual measurement load spectrum, and the accuracy of the analysis result of the fatigue life of the differential case can be improved in an auxiliary manner.
The foregoing are embodiments of the present invention and are not intended to limit the scope of the invention to the particular forms set forth in the specification, which are set forth in the claims below, but rather are to be construed as the full breadth and scope of the claims, as defined by the appended claims, as defined in the appended claims, in order to provide a thorough understanding of the present invention. 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 defined by 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 (7)

1. A method for analyzing the fatigue life of a differential shell 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;
the stress relationship under unit torque load of the finite element model of the differential shell is expressed by the following formula:
∑U i M i ＝∫ Ω {ε} T σ i d Ω (ii) a In the formula: m is a group of i Representing a virtual external force, namely torque, and taking 1 in calculation; u shape i Representing the true displacement; Ω represents the field of integration; { ε } represents the true strain induced by the torque load; t represents transposition; sigma i The virtual stress is expressed, namely the stress corresponding to unit torque;
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;
calculating the S-N curve of the material of the differential shell of the electric drive assembly 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 an S-N curve prediction formula of the material 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: obtaining a material S-N curve of a differential shell of the electric drive assembly;
the fatigue life versus stress relationship is expressed by the following equation:
Figure FDA0003918427910000011
in the formula: sigma a Representing the equivalent stress; n is a radical of f Represents the fatigue life; β represents a surface mass coefficient; ε represents the size factor; c L Representing the loading mode, and taking 0.58; k f Represents the fatigue notch coefficient; sigma f ' represents a fatigue strength coefficient; b represents a fatigue strength coefficient;
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 the 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 according to 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 bench structure, and recording the strain and stress of each strain measuring point to obtain a corresponding bench test result;
s23: establishing a finite element simulation model which is used for applying a torsional load to the differential shell finite element model and corresponds to the test bench structure, and setting simulation measuring points corresponding to a plurality of strain measuring points arranged on the differential shell of the electric drive assembly on the differential shell finite element model;
s24: applying a torsional 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 fatigue life analysis of an electric drive assembly differential case according to claim 1, wherein an S-N curve of a material of the electric drive assembly differential case is represented by the following formula:
Figure FDA0003918427910000021
in the formula: s. the 1 、S 2 Representing a stress value; b 1 、b 2 Respectively representing a first fatigue strength index and a second fatigue strength index; sigma b Represents the ultimate strength of the material; SRI1 represents the stress phase range; nc1 denotes a fatigue transition point.
5. A method of analyzing fatigue life of an electrically driven assembly differential case as defined in claim 1, wherein the material S-N curve prediction formula is modified by the formula:
Figure FDA0003918427910000022
in the formula: k is f Represents the fatigue notch coefficient; sigma f Represents the fatigue limit of the optical slider; sigma c Indicating the fatigue limit of the notched part; sigma a Representing an equivalent zero mean stress; s. the a Representing 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; c L The loading mode is indicated, and 0.58 is taken.
6. The method for fatigue life analysis of an electric drive assembly differential case of claim 1, wherein the load experienced by the electric drive assembly differential case is corrected by the formula:
σ a ′＝σ -1 (1-σ m /σ b ) (ii) a In the formula: sigma a ' represents the corrected load; sigma -1 Representing the stress fatigue limit under symmetric cycles; sigma m Is the stress mean value; sigma b Indicating the ultimate strength of the material.
7. The method for analyzing the fatigue life of an electrically driven assembly differential case according to claim 1, wherein the S-N curve of the material of the electrically driven assembly differential case is represented by the formula:
Figure FDA0003918427910000031
in the formula: s. the 1 ′、S 2 ' represents the corrected stress value; b is a mixture of 1 ′、b 2 ' means the corrected first and second fatigue strength indexes, respectively; sigma b Represents the ultimate strength of the material; sigma c Indicating the fatigue limit of the notched part; β represents a surface mass coefficient; ε represents the size factor; c L Representing the loading mode, and taking 0.58; SRI1 represents the stress phase range; nc1 denotes a fatigue transition point.
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