CN116882230A - Method for calculating fatigue life of drive axle housing - Google Patents
Method for calculating fatigue life of drive axle housing Download PDFInfo
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Abstract
The invention discloses a method for calculating fatigue life of a drive axle shell, which comprises the following steps: establishing a finite element model of a drive axle system; defining material properties; defining the contact and connection modes of the parts of the drive axle; applying a bolt pretightening force; the fatigue test load spectrum is simplified; defining boundary conditions; solving and calculating; preliminary evaluation; calculating the fatigue safety coefficient of the driving axle housing; a component material fatigue life curve; calculating the total damage of the drive axle housing; and judging the fatigue life and the failure position. According to the invention, the finite element model directly related to the stress of the driving axle housing is established, so that the result of the stress-strain analysis process of the driving axle is attached to the actual stress state, the fatigue life analysis is carried out by judging the stress or the fatigue life analysis is carried out by the strain, the fatigue life of the driving axle housing calculated by the method is more consistent with the actual state, and the calculation precision is higher.
Description
Technical Field
The invention belongs to the field of calculation of fatigue life of a vehicle transmission system, and particularly relates to a calculation method of fatigue life of a driving axle shell.
Background
The drive axle is used as an important component of a vehicle transmission system, plays roles of reducing speed and increasing torque, changing the torque transmission direction and the like in the running process of the vehicle, and the low cycle fatigue life of the drive axle shell directly influences the service performance of the drive axle shell. The fatigue life and the failure position of the driving axle housing are calculated efficiently and accurately, the weak point of the driving axle housing can be found timely and effectively, the housing can be designed optimally in time, cost is saved, and the research and development period is shortened.
At present, two main methods for analyzing the fatigue life of the driving axle housing are as follows:
a fatigue life test of a drive axle assembly is carried out under a specified load spectrum by a test means to obtain the fatigue life and failure position of a drive axle shell.
Secondly, by means of simulation, stress strain analysis of a certain working condition is carried out on the driving axle housing, fatigue safety performance of the driving axle housing is calculated, and a weak position is found. For example, in the simulation analysis method for fatigue life of a battery module structure and application thereof (CN 114282409 a), fatigue life analysis is performed on the battery module through an expansion working condition and a random vibration working condition, and only the expansion working condition and the random vibration working condition are aimed at, so that fatigue damage of a component in a fatigue life test process is not considered, and impact received by the component in different stages of load change processes under a multi-stage load spectrum is not considered. The method for analyzing the load of the flange bolt of the helicopter and predicting the low cycle fatigue life (CN 114091177A) calculates the low cycle fatigue life of the bolt by calculating the low cycle fatigue static stress of the flange bolt of the helicopter, and does not consider the strain in the fatigue life calculation or the impact received by the component in the load change process of different stages under a multistage load spectrum.
The driving axle housing directly bears the reaction force of the gear in the working process, and in the process of carrying out a multi-stage load spectrum fatigue life test, the change of different stages of loads can cause certain impact on the driving axle housing, and the stress condition of the housing is severe. The effect of shell impacts caused by different levels of load variation should therefore be considered in conducting the analysis of the fatigue life of the drive axle shell.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method for calculating the fatigue life of a driving axle shell, which is characterized in that a finite element model directly related to the stress of the driving axle shell is established, so that the result of the stress-strain analysis process of the driving axle is attached to the actual stress state, the fatigue life analysis by stress or the fatigue life analysis by strain is judged, the fatigue life of the driving axle shell calculated by the method is more consistent with the actual stress, and the calculation precision is higher.
The invention aims at realizing the following technical scheme:
a method for calculating fatigue life of a drive axle housing comprises the following steps:
s1, establishing a finite element model of a drive axle system, and modeling the parts of the drive axle system by adopting a solid grid unit;
s2, defining material properties of a finite element model, including defining material elastic modulus, poisson' S ratio and stress-strain relation;
s3, defining contact and connection modes of components of the drive axle:
according to the actual installation position of the drive axle system, assembling a model, and creating a drive axle shell bolt-drive axle left shell, a drive axle left shell-drive axle right shell, a differential first bearing outer ring-drive axle left shell, a differential first bearing inner ring-differential shell, a differential second bearing outer ring-drive axle right shell, a differential second bearing inner ring-differential shell, a drive axle right shell-drive axle support, a drive axle support-support bolt, a drive gear first bearing inner ring-drive gear shaft, a drive gear second bearing inner ring-drive gear shaft, a drive gear first bearing outer ring-drive axle right shell, and a drive gear second bearing outer ring-drive axle right shell; connecting a driving axle shell bolt and a driving axle right shell into a whole, and connecting a bracket bolt and the driving axle right shell into a whole;
s4, applying bolt pretightening force:
the bolt pretightening force is obtained by a relational expression between the bolt pretightening force and the bolt tightening torque and is applied to the shell bolt and the bracket bolt of the drive axle;
the bolt pretightening force is calculated by the following formula:
wherein F is 1 For pretightening force of the driving axle housing bolt, T 1 For the screw tightening torque of the shell of the driving axle, K is the screw tightening torque coefficient, D 1 The diameter of the bolts is the diameter of the bolts of the shell of the driving axle; f (F) 2 For pretightening force of the bracket bolt, T 2 D is the tightening torque of the bracket bolt 2 The diameter of the bracket bolt is the diameter of the bracket bolt; f (F) 1 、F 2 To calculate the amount, T 1 、T 2 、D 1 、D 2 Is a known quantity; the acting direction of the bolt pretightening force is along the axial direction of the bolt;
s5, simplifying a fatigue test load spectrum, and selecting a typical working condition in the fatigue test load spectrum as an input condition for calculation and analysis;
s6, defining boundary conditions
All degrees of freedom of the joint of the drive axle and the frame are restrained, gear force is applied by means of a local coordinate system defined on a drive gear axis, a Z axis of the coordinate system is along the axis direction of the drive gear, an R axis is along the radial direction of the drive gear, and a t axis is determined by the Z axis and the R axis according to right-hand criteria;
the driving and driven gears of the drive axle are hyperboloid gears, and the stress of the driving gears under two working conditions is calculated by combining the axial force and radial force calculation table of the hyperboloid gears according to the following formula, and the stress is applied to the driving gears in a form of concentrated force:
hyperboloid gear axial force and radial force calculation meter
Wherein T is the output torque, i is the gear ratio, F t 、F r 、F a The circumferential force, the radial force and the axial force of the driving gear are respectively calculated, d is the pitch circle diameter of the middle point of the tooth face width of the driving gear, alpha is the normal pressure angle of the driving gear, beta is the helix angle of the driving gear, and gamma is the pitch angle of the driving gear;
the stress of the driven gear is equal to that of the driving gear, the direction of the stress is opposite, and the stress is applied to the driven gear in a form of concentrated force;
s7, solving and calculating the finite element model to obtain stress values and strain values of all positions of the driving axle housing under the working condition of the maximum torque of the forward gear and the working condition of the maximum torque of the reverse gear;
s8, carrying out preliminary evaluation on the fatigue strength of the shell according to the MISES stress of the shell of the drive axle;
s9, calculating fatigue safety coefficients of the driving axle shell: if the shell MISES stress is smaller than the shell material yield strength limit in the step S8, calculating a shell fatigue safety coefficient according to the following formula, and evaluating the shell fatigue life:
s10, constructing a material fatigue life curve: if the shell MISES stress is greater than the shell material yield strength limit in the step S8, carrying out low cycle fatigue analysis on the driving axle shell according to a Manson-Coffin low cycle fatigue formula, and constructing a plastic strain-life curve of the material according to the following formula:
ε pa ＝ε’ f (2N) c
wherein ε pa For the plastic strain value of the component ε' f C is the fatigue ductility index;
s11, calculating low-cycle fatigue damage of a driving axle shell under the cycle of a fatigue life load spectrum;
s12, calculating the total damage of the shell of the drive axle under the cycle of the load spectrum of the specified fatigue life, wherein the calculation formula is as follows:
D total ＝n×d 1
wherein D is total N is the fatigue life load spectrum cycle number for total damage;
and finally judging the low cycle fatigue life and failure position of the drive axle housing according to the total damage result of the drive axle housing.
Further, in the step S1, the left casing of the drive axle, the driven gear, the differential casing, the right casing of the drive axle, and the drive axle bracket are modeled by adopting a second order tetrahedron unit; the driving axle housing connecting bolt, the differential mechanism No. one bearing, the differential mechanism No. two bearing, the bracket bolt, the driving gear No. one bearing, the driving gear shaft and the driving gear No. two bearing adopt a first order hexahedral unit for modeling; the driven gear and the driving gear shaft adopt a simplified model; the driven gear is connected with the differential housing in a common node mode.
Further, in the step S2, the elastic modulus and poisson ratio of the materials of the left shell and the right shell of the driving axle are defined, the plastic data of the materials of the shells of the driving axle are obtained according to the following formula, and the plastic data of the materials of the shells of the driving axle are added into an analysis model:
σ＝σ nom (1+ε nom )
ε＝ln(1+ε nom )
ε pl ＝ε-ε el
wherein sigma is true stress, epsilon is true strain, sigma nom For nominal stress, ε nom For nominal strain, ε pl For plastic strain, epsilon el Is elastic strain, E is elastic modulus of the material.
Further, in the step S3, to simplify the model, the number of contact pairs is reduced, and corresponding simplification is performed for the bearing: connecting the bearing rolling bodies and the bearing inner ring into a whole, and establishing contact between the bearing rolling bodies and the bearing outer ring; the first differential bearing, the second differential bearing, the first driving gear bearing and the second driving gear bearing are connected in the mode.
Further, in the step S5, a forward gear maximum torque working condition and a reverse gear maximum torque working condition in a fatigue test load spectrum are selected as typical working conditions, and a forward gear maximum torque working condition outputs a torque T +max Output torque T under the working condition of maximum torque of reverse gear -max As input conditions.
Further, in the step S8, if the shell MISES stress is less than the shell material yield strength limit, the fatigue life of the drive axle shell is evaluated by calculating the shell fatigue safety factor from the shell stress; if the shell MISES stress is larger than the shell material yield strength limit, calculating different stages of load impact based on a multi-stage load spectrum, and evaluating the fatigue life of the drive axle shell by using a low-cycle fatigue life analysis method.
Further, in the step S9, if the fatigue safety coefficient of the shell is greater than 1, the fatigue life of the shell of the drive axle meets the requirement, and if the fatigue safety coefficient of the shell is less than 1, the fatigue life of the shell of the drive axle does not meet the requirement, and optimization is required for the weak position.
Further, in the step S10, in order to accurately calculate the low cycle fatigue life of the transaxle housing, the formula ε is calculated pa ＝ε’ f (2N) c Correcting, and constructing an actual strain-life curve of the material according to a corrected formula, wherein the corrected formula is as follows:
wherein Δγ is the actual strain amplitude of the part, ε ea For elastic strain of the part, sigma' f For the fatigue strength coefficient, b is the fatigue strength index and E is the elastic modulus of the material.
Further, in the step S11, in order to ensure that the impact of the shell caused by different level of load changes can be considered in the damage calculation process, according to the material strain-life curve constructed in the step S9, based on the fatigue life test load spectrum, the maximum torque working condition output torque T of the forward gear is calculated according to the following formula +max Output torque T under the working condition of maximum torque of reverse gear -max Single damage to the transaxle housing under two-stage load impact:
wherein d 1 N is a single injury 1 And calculating the circulation times corresponding to the actual strain amplitude delta gamma of the component according to the working condition of the maximum torque of the forward gear and the working condition of the maximum torque of the reverse gear.
Further, in the step S12, if the driving axle housing has a position with a total damage value greater than 1, the low cycle fatigue life of the driving axle housing does not meet the requirement, and the failure position is a position with a total damage value greater than 1, and structural optimization is required to improve the fatigue strength of the housing; if the total damage value of the driving axle housing is less than 1, the low cycle fatigue life of the driving axle housing meets the requirement.
The invention has the following beneficial effects:
(1) By establishing a finite element model directly related to the stress of the driving axle housing, such as a bearing, a differential housing, an input shaft and the like, a reasonable driving axle finite element model is established, so that the result of the stress-strain analysis process of the driving axle is relatively attached to the actual stress state
(2) The fatigue life analysis is carried out by judging the fatigue life analysis by stress or strain through the comparison of the stress of the driving axle housing and the yield limit of the material, the fatigue life of the driving axle housing calculated by the method is more consistent with the actual service, and the calculation precision is higher.
(3) The evaluation standards of the driving axle housing with different calculation methods are provided, and guidance is provided for the calculation of the subsequent driving axle housing.
Drawings
The invention is described in further detail below with reference to the drawings and the detailed description.
FIG. 1 is a schematic illustration of a drive axle assembly configuration;
FIG. 2 is a schematic diagram of bearing modeling;
FIG. 3 is a schematic diagram of a fatigue life test load spectrum;
FIG. 4 is a schematic diagram of fatigue life load spectrum of an embodiment
FIG. 5 is a transaxle housing MISSES stress distribution for forward gear torque capacity conditions
FIG. 6 is a graph of the drive axle housing MISES stress distribution under reverse maximum torque conditions
FIG. 7 is a schematic diagram of an actual strain-life curve of a material;
FIG. 8 is a schematic diagram of an actual strain-life curve of an aluminum alloy material;
FIG. 9 is a schematic illustration of total damage to a drive axle housing;
FIG. 10 is a flowchart of a method for calculating fatigue life of a drive axle housing according to an embodiment of the present invention;
in the figure:
1-a drive axle housing connecting bolt; 2-left drive axle housing; 3-a first differential bearing; 4-driven gears; 5-differential housing; 6-a second bearing of the differential mechanism; 7-a right drive axle housing; 8-a drive axle bracket; 9-a bracket bolt; 10-a first bearing of a driving gear; 11-a drive gear shaft; 12-a driving gear bearing II; 13-bearing outer ring; 14-bearing rolling bodies; 15-bearing inner ring.
Detailed Description
The method for calculating the fatigue life of the shell of the drive axle is characterized by comprising the following steps of:
s1, establishing a finite element model of a drive axle system:
the components of the drive axle system are modeled by using solid grid cells.
In the step S1, in order to ensure the number of model nodes and simulation accuracy, a left shell of a drive axle device, a driven gear, a differential shell, a right shell of the drive axle, and a drive axle bracket are modeled by adopting a second order tetrahedron unit. The driving axle housing connecting bolt, the differential mechanism No. one bearing, the differential mechanism No. two bearing, the bracket bolt, the driving gear No. one bearing, the driving gear shaft and the driving gear No. two bearing adopt a first order hexahedral unit for modeling. The driven gear and the driving gear shaft adopt a simplified model, and the driven gear and the differential housing are connected in a common node mode.
S2, defining finite element model material properties
And defining the relation among the elastic modulus, poisson ratio and stress strain of the material.
In the step S2, the elastic modulus and poisson ratio of the materials of the left shell and the right shell of the driving axle are defined, the plastic data of the materials of the shells of the driving axle are obtained according to formulas (1) - (4), and the plastic data of the materials of the shells of the driving axle are added into an analysis model.
σ＝σ nom (1+ε nom ) (1)
ε＝ln(1+ε nom ) (2)
ε pl ＝ε-ε el (3)
Wherein sigma is true stress, epsilon is true strain, sigma nom For nominal stress, ε nom For nominal strain, ε pl For plastic strain, epsilon el Is elastic strain, E is elastic modulus of the material.
S3, defining contact and connection modes of parts of drive axle
And assembling the model according to the actual installation position of the drive axle system, and creating the contact of a drive axle shell bolt-drive axle left shell, a drive axle left shell-drive axle right shell, a differential first bearing outer ring-drive axle left shell, a differential first bearing inner ring-differential shell, a differential second bearing outer ring-drive axle right shell, a differential second bearing inner ring-differential shell, a drive axle right shell-drive axle support, a drive axle support-support bolt, a drive gear first bearing inner ring-drive gear shaft, a drive gear second bearing inner ring-drive gear shaft, a drive gear first bearing outer ring-drive axle right shell and a drive gear second bearing outer ring-drive axle right shell. The driving axle shell bolt is connected with the driving axle right shell into a whole, and the bracket bolt is connected with the driving axle right shell into a whole.
In the step S3, in order to simplify the model, the number of contact pairs is reduced, and corresponding simplification is performed for the bearing: the bearing rolling bodies and the bearing inner rings are connected into a whole, the contact between the bearing rolling bodies and the bearing outer rings is established, and the first differential bearing, the second differential bearing, the first driving gear bearing and the second driving gear bearing are all connected in the mode.
S4, applying bolt pretightening force
The bolt pretightening force is obtained by a relational expression between the bolt pretightening force and the bolt tightening torque, and is applied to the shell bolt and the bracket bolt of the drive axle.
And (3) calculating according to formulas (5) and (6) to obtain the bolt pretightening force, wherein the acting direction of the bolt pretightening force is along the axial direction of the bolt.
Wherein F is 1 For pretightening force of the driving axle housing bolt, T 1 For the screw tightening torque of the shell of the driving axle, K is the screw tightening torque coefficient, D 1 Is the diameter of the driving axle housing bolt. F (F) 2 For pretightening force of the bracket bolt, T 2 D is the tightening torque of the bracket bolt 2 Is the diameter of the bracket bolt. F (F) 1 、F 2 To calculate the amount, T 1 、T 2 、D 1 、D 2 Is a known quantity;
s5, load spectrum simplification of fatigue test
And selecting a typical working condition in a fatigue test load spectrum as an input condition for calculation and analysis.
In the step S5, since the fatigue test load spectrum is a multi-stage load, and in the fatigue test process, the drive axle housing receives a certain impact due to the different stage load changes, in order to ensure that the selected typical working condition can cover the fatigue test load spectrum, the working condition of the maximum forward gear torque and the working condition of the maximum reverse gear torque in the fatigue test load spectrum are selected as typical working conditions, and the working condition of the maximum forward gear torque outputs the torque T +max Output torque T under the working condition of maximum torque of reverse gear -max As input conditions.
S6, defining boundary conditions
All degrees of freedom at the joint of the drive axle and the frame are constrained, gear force is applied by means of a local coordinate system defined on the axis of the drive gear, the Z axis of the coordinate system is along the axis direction of the drive gear, the R axis is along the radial direction of the drive gear, and the t axis is determined by the Z axis and the R axis according to right-hand criteria. The driving and driven gears of the drive axle are hyperboloid gears, and the stress of the driving gears is calculated according to the formula (7) and the table 1 under two working conditions and is applied to the driving gears in a form of concentrated force. The stress of the driven gear is equal to that of the driving gear, the direction of the stress is opposite, and the stress is applied to the driven gear in a form of concentrated force;
table 1 hyperboloid gear axial force and radial force calculations
Wherein T is the output torque, i is the gear ratio, F t 、F r 、F a The circumferential force, the radial force and the axial force of the driving gear are respectively calculated, d is the pitch circle diameter of the middle point of the tooth face width of the driving gear, alpha is the normal pressure angle of the driving gear, beta is the helix angle of the driving gear, and gamma is the pitch angle of the driving gear.
S7, solving and calculating the finite element model by using ABAQUS/Standard
And obtaining stress values and strain values of all positions of the driving axle housing under the working condition of the maximum torque of the forward gear and the working condition of the maximum torque of the reverse gear.
S8, result analysis
The shell fatigue strength was initially evaluated based on transaxle shell mis stress.
In the step S8, if the shell MISES stress is smaller than the shell material yield strength limit, the fatigue life of the shell of the drive axle is evaluated by calculating the shell fatigue safety coefficient through the shell stress; if the shell MISES stress is larger than the shell material yield strength limit, calculating different stages of load impact based on a multi-stage load spectrum, and evaluating the fatigue life of the drive axle shell by using a low-cycle fatigue life analysis method.
S9, calculating fatigue safety coefficient of driving axle shell
If the shell MISES stress in S8 is smaller than the shell material yield strength limit, calculating a shell fatigue safety coefficient according to a formula (8), and evaluating the shell fatigue life;
in SF a Sigma, the fatigue safety coefficient of the component E For the material fatigue limit, sigma a Is part stress.
In the step S9, if the fatigue safety coefficient of the shell is greater than 1, the fatigue life of the shell of the drive axle meets the requirement, and if the fatigue safety coefficient of the shell is less than 1, the fatigue life of the shell of the drive axle does not meet the requirement, and the drive axle needs to be optimized for the weak position.
S10, constructing a material fatigue life curve
If the shell MISES stress is larger than the shell material yield strength limit in the step S8, the shell is required to be subjected to low cycle fatigue life calculation, the driving axle shell is subjected to low cycle fatigue analysis according to a Manson-Coffin low cycle fatigue formula, and a material plastic strain-life curve is constructed according to a formula (9);
ε pa ＝ε’ f (2N) c (9)
wherein ε pa For the plastic strain value of the component ε' f For the fatigue ductility factor, c is the fatigue ductility index and 2N is the number of cycles on the material strain-life curve.
In the step S10, in order to accurately calculate the low cycle fatigue life of the driving axle housing, the formula (9) is modified, and an actual strain-life curve of the material is constructed according to the formula (10);
wherein Δγ is the actual strain amplitude of the part, ε ea For elastic strain of the part, sigma' f For the fatigue strength coefficient, b is the fatigue strength index and E is the elastic modulus of the material.
S11, calculating low-cycle fatigue damage of the shell of the drive axle under the cycle of a fatigue life load spectrum
In the step S11, in order to ensure that the impact of the shell caused by different levels of load changes can be considered in the damage calculation process, the maximum torque working condition output torque T of the forward gear is calculated according to the material strain-life curve constructed in the step S9, the fatigue life test load spectrum and the formula (11) +max Torque output torque T under the working condition of maximum torque of reverse gear -max Single damage to the transaxle housing under two-stage load impact:
wherein d 1 N is a single injury 1 And calculating the circulation times corresponding to the actual strain amplitude delta gamma of the component according to the working condition of the maximum torque of the forward gear and the working condition of the maximum torque of the reverse gear.
S12, calculating the total damage of the shell of the drive axle according to a formula (12) under the condition of calculating the load spectrum cycle of the specified fatigue life:
D total ＝n×d 1 (12)
wherein D is total N is the fatigue life load spectrum cycle number for total damage;
and judging the low cycle fatigue life and failure position of the driving axle housing according to the total damage result of the driving axle housing.
In the step S12, if the drive axle housing has a position with a total damage value greater than 1, the low cycle fatigue life of the drive axle housing does not meet the requirement, and the failure position is a position with a total damage value greater than 1, and structural optimization is required to improve the fatigue strength of the housing; if the total damage value of the driving axle housing is less than 1, the low cycle fatigue life of the driving axle housing meets the requirement.
Examples
As shown in fig. 10, the present embodiment is a method for calculating fatigue life of a driving axle housing, including the steps of:
s1, establishing a finite element model of a drive axle system
The main structure of the drive axle system is shown in fig. 1, and the components of the drive axle system are modeled by adopting solid grid cells.
In step S1, in order to ensure the number of model nodes and simulation accuracy, the left casing 2, the driven gear 4, the differential casing 5, the right casing 7 and the drive axle bracket 8 of the drive axle are modeled by adopting a second order tetrahedron unit. The driving axle housing connecting bolt 1, the differential first bearing 3, the differential second bearing 6, the bracket bolt 9, the driving gear first bearing 10, the driving gear shaft 11 and the driving gear second bearing 12 are modeled by adopting a first order hexahedral unit. The driven gear 4 and the driving gear shaft 11 adopt a simplified model, and the driven gear 4 and the differential housing 5 are connected in a common node mode.
S2, defining finite element model material properties
Including defining the material elastic modulus, poisson's ratio and stress-strain relationship.
a) The materials of the driving gear and the driven gear are 20CrMnTi, the elastic modulus of the 20CrMnTi material is 210000Mpa, and the Poisson ratio is 0.3.
b) The material of the differential case is QT600, the elastic modulus of the QT600 material is 172000Mpa, and the Poisson ratio is 0.3.
c) The elastic modulus of the material properties of the rest parts is 210000Mpa, and the Poisson ratio is 0.3.
In the step S2, the driving axle housing is made of aluminum alloy, the elastic modulus of the aluminum alloy is 210000Mpa, and the Poisson ratio is 0.3. Defining the elastic modulus and poisson ratio of the materials of the left shell 2 and the right shell 7 of the driving axle, obtaining the plastic data of the materials of the shells of the driving axle according to formulas (1) - (4), and adding the plastic data of the materials of the shells of the driving axle into an analysis model as shown in table 2.
σ＝σ nom (1+ε nom ) (1)
ε＝ln(1+ε nom ) (2)
ε pl ＝ε-ε el (3)
Wherein sigma is true stress, epsilon is true strain, sigma nom For nominal stress, ε nom For nominal strain, ε pl For plastic strain, epsilon el The elastic strain is adopted, and E is the elastic modulus of the material;
table 2 plastic mechanical properties of transaxle housing materials
| Sequence number | Nominal stress sigma nom | Nominal strain epsilon nom | True stress sigma | True strain ε | Elastic strain epsilon el | Plastic strain epsilon pl |
| 1 | 1.00E+02 | 1.36E-03 | 1.00E+02 | 1.36E-03 | 1.35E-03 | 0 |
| 2 | 1.20E+02 | 1.65E-03 | 1.20E+02 | 1.65E-03 | 1.62E-03 | 2.43E-05 |
| 3 | 1.30E+02 | 1.81E-03 | 1.30E+02 | 1.81E-03 | 1.76E-03 | 4.84E-05 |
| 4 | 1.40E+02 | 2.00E-03 | 1.40E+02 | 2.00E-03 | 1.90E-03 | 1.02E-04 |
| 5 | 1.50E+02 | 2.22E-03 | 1.50E+02 | 2.22E-03 | 2.03E-03 | 1.86E-04 |
| 6 | 1.60E+02 | 2.50E-03 | 1.60E+02 | 2.50E-03 | 2.17E-03 | 3.29E-04 |
| 7 | 1.70E+02 | 2.89E-03 | 1.70E+02 | 2.89E-03 | 2.30E-03 | 5.82E-04 |
| 8 | 1.80E+02 | 3.42E-03 | 1.81E+02 | 3.41E-03 | 2.44E-03 | 9.73E-04 |
| 9 | 1.88E+02 | 4.01E-03 | 1.89E+02 | 4.00E-03 | 2.55E-03 | 1.45E-03 |
| 10 | 1.94E+02 | 4.51E-03 | 1.94E+02 | 4.50E-03 | 2.63E-03 | 1.87E-03 |
| 11 | 1.98E+02 | 5.00E-03 | 1.99E+02 | 4.99E-03 | 2.69E-03 | 2.30E-03 |
| 12 | 2.07E+02 | 6.23E-03 | 2.08E+02 | 6.21E-03 | 2.81E-03 | 3.40E-03 |
| 13 | 2.10E+02 | 6.77E-03 | 2.11E+02 | 6.75E-03 | 2.86E-03 | 3.89E-03 |
| 14 | 2.14E+02 | 7.51E-03 | 2.15E+02 | 7.48E-03 | 2.91E-03 | 4.58E-03 |
| 15 | 2.20E+02 | 8.96E-03 | 2.22E+02 | 8.92E-03 | 3.00E-03 | 5.92E-03 |
| 16 | 2.20E+02 | 9.11E-03 | 2.22E+02 | 9.07E-03 | 3.00E-03 | 6.07E-03 |
| 17 | 2.31E+02 | 1.25E-02 | 2.34E+02 | 1.24E-02 | 3.16E-03 | 9.26E-03 |
| 18 | 2.40E+02 | 1.64E-02 | 2.44E+02 | 1.63E-02 | 3.30E-03 | 1.30E-02 |
| 19 | 2.50E+02 | 2.25E-02 | 2.56E+02 | 2.23E-02 | 3.45E-03 | 1.88E-02 |
| 20 | 2.59E+02 | 3.04E-02 | 2.67E+02 | 2.99E-02 | 3.61E-03 | 2.63E-02 |
| 21 | 2.63E+02 | 3.46E-02 | 2.72E+02 | 3.40E-02 | 3.68E-03 | 3.03E-02 |
S3, defining contact and connection modes of parts of drive axle
The method comprises the steps of assembling a model according to the actual installation position of a drive axle system, creating a drive axle shell bolt 1-a drive axle left shell 2, a drive axle left shell 2-a drive axle right shell 7, a differential first bearing 3 outer ring-a drive axle left shell 2, a differential first bearing 3 inner ring-a differential shell 5, a differential second bearing 6 outer ring-a drive axle right shell 7, a differential second bearing 6 inner ring-a differential shell 5, a drive axle right shell 7-a drive axle bracket 8, a drive axle bracket 8-a bracket bolt 9, a drive gear first bearing 10 inner ring-a drive gear shaft 11, a drive gear second bearing 12 inner ring-a drive gear shaft 11, a drive gear first bearing 10 outer ring-a drive axle right shell 7 and a drive gear second bearing 12 outer ring-drive axle right shell 7. The drive axle housing bolt 1 is connected with the drive axle right shell 7 into a whole, and the bracket bolt 9 is connected with the drive axle right shell 7 (figure 1) into a whole.
In the step S3, in order to simplify the model, the number of contact pairs is reduced, and corresponding simplification is performed for the bearing: the bearing rolling bodies 14 and the bearing inner ring 15 are connected into a whole, the contact between the bearing rolling bodies 14 and the bearing outer ring 13 (figure 2) is established, and the first differential bearing 3, the second differential bearing 6, the first driving gear bearing 10 and the second driving gear bearing 12 are all connected in the mode.
S4, applying bolt pretightening force
The bolt pretightening force is obtained by a relational expression between the bolt pretightening force and the bolt tightening torque, and is applied to the shell bolt and the bracket bolt of the drive axle.
And (3) calculating according to formulas (1) and (2) to obtain the bolt pretightening force, wherein the acting direction of the bolt pretightening force is along the axial direction of the bolt.
Wherein F is 1 For pretightening force of the driving axle housing bolt, T 1 For the screw tightening torque of the shell of the driving axle, K is the screw tightening torque coefficient, D 1 Is the diameter of the driving axle housing bolt. F (F) 2 For pretightening force of the bracket bolt, T 2 D is the tightening torque of the bracket bolt 2 Is the diameter of the bracket bolt. F (F) 1 、F 2 To calculate the amount, T 1 、T 2 、D 1 、D 2 Is a known quantity;
T 1 ＝70Nm，D 1 ＝10mm，T 2 ＝100Nm，D 2 =12mm, k=0.2. Calculating to obtain the pretightening force F of the driving axle housing bolt 1 =35000N, support bolt pretension force F 2 = 41667N. Applying the calculated bolt pretightening force to each bolt;
s5, load spectrum simplification of fatigue test
Typical working conditions in a fatigue test load spectrum are selected as input conditions for calculation and analysis
In the step S5, since the fatigue test load spectrum is a multi-stage load, as shown in fig. 3, and in the fatigue test process, the drive axle housing receives a certain impact due to the different stage load changes, in order to ensure that the selected typical working condition can cover the fatigue test load spectrum, the working condition of the maximum forward gear torque and the working condition of the maximum reverse gear torque in the fatigue test load spectrum are selected as typical working conditions, and the working condition of the maximum forward gear torque outputs the torque T +max Output torque T under the working condition of maximum torque of reverse gear -max As input conditions.
The fatigue test load spectrum of the drive axle is shown in figure 4, wherein T is +max ＝4200Nm，T -max = -4200Nm as a computational analysis input condition.
S6, defining boundary conditions
All degrees of freedom at the joint of the drive axle and the frame are constrained, gear force is applied by means of a local coordinate system defined on the axis of the drive gear, the Z axis of the coordinate system is along the axis direction of the drive gear, the R axis is along the radial direction of the drive gear, and the t axis is determined by the Z axis and the R axis according to right-hand criteria. The driving and driven gears of the drive axle are hyperboloid gears, and the stress of the driving gears is calculated according to the formula (7) and the table 4 under two working conditions and is applied to the driving gears in a form of concentrated force. The stress of the driven gear is equal to that of the driving gear, the direction is opposite, and the driven gear is applied with concentrated force
Table 4 hyperboloid gear axial force and radial force calculations
Wherein T is the output torque, F t 、F r 、F a The circumferential force, the radial force and the axial force of the driving gear are respectively calculated, d is the pitch circle diameter of the middle point of the tooth face width of the driving gear, alpha is the normal pressure angle of the driving gear, beta is the helix angle of the driving gear, and gamma is the pitch angle of the driving gear.
Drive axle hypoid gear parameters: i=3.9, d=180 mm, α=20°, β=40°, γ=12°, and gear forces for forward and reverse gear torque capacities are calculated and applied to the analytical model in the form of concentrated forces:
F +t 、F +r 、F +a the circumferential force, the radial force and the axial force of the driving gear under the working condition of maximum torque of the forward gear are respectively;
F -t 、F -r 、F -a the circumferential force, the radial force and the axial force of the driving gear under the working condition of the reverse maximum torque are respectively calculated;
s7, solving and calculating the finite element model by using ABAQUS/Standard
Obtaining stress values and strain values of all positions of a driving axle housing under the working condition of maximum torque of a forward gear and the working condition of maximum torque of a reverse gear;
s8, result analysis
Preliminary evaluation of Shell fatigue Strength according to drive axle Shell MISES stress
In the step S8, if the shell MISES stress is smaller than the shell material yield strength limit, the fatigue life of the shell of the drive axle is evaluated by calculating the shell fatigue safety coefficient through the shell stress; if the shell MISES stress is larger than the shell material yield strength limit, calculating different stages of load impact based on a multi-stage load spectrum, and evaluating the fatigue life of the drive axle shell by using a low-cycle fatigue life analysis method.
Under the working condition of maximum torque of the forward gear, the maximum stress of the MIESS of the driving axle shell is 197Mpa, as shown in figure 5; under the working condition of reverse gear maximum torque, the maximum value of MISES stress of the driving axle housing is 221Mpa, as shown in figure 6, is greater than 150Mpa of the yield strength limit of the aluminum alloy material, different stages of load impact are calculated based on a multi-stage load spectrum, and fatigue life evaluation is carried out on the driving axle housing by using a low cycle fatigue life analysis method.
S9, calculating fatigue safety coefficient of driving axle shell
If the shell MISES stress in S8 is smaller than the shell material yield strength limit, calculating the shell fatigue safety coefficient according to the formula (8), and evaluating the shell fatigue life
In the middle of，SF a Sigma, the fatigue safety coefficient of the component E For the material fatigue limit, sigma a Is part stress.
In the step S9, if the fatigue safety coefficient of the shell is greater than 1, the fatigue life of the shell of the drive axle meets the requirement, and if the fatigue safety coefficient of the shell is less than 1, the fatigue life of the shell of the drive axle does not meet the requirement, and the drive axle needs to be optimized for the weak position;
since the driving axle housing MISES stress is greater than the yield strength limit of the material, no fatigue safety coefficient calculation is required.
S10, constructing a material fatigue life curve
If the shell MISES stress is larger than the shell material yield strength limit in the step S8, the shell is required to be subjected to low cycle fatigue life calculation, the driving axle shell is subjected to low cycle fatigue analysis according to a Manson-Coffin low cycle fatigue formula, and a material plastic strain-life curve is constructed according to a formula (9);
ε pa ＝ε’ f (2N) c (9)
wherein ε pa For the plastic strain value of the component ε' f For the fatigue ductility coefficient, c is the fatigue ductility index.
In the step S10, in order to accurately calculate the low cycle fatigue life of the driving axle housing, the formula (9) is modified, and an actual strain-life curve of the material is constructed according to the formula (10);
wherein Δγ is the actual strain amplitude of the part, ε ea For elastic strain of the part, sigma' f For the fatigue strength coefficient, b is the fatigue strength index, E is the elastic modulus of the material, and 2N is the number of cycles on the strain-life curve of the material.
Sigma 'of aluminum alloy material' f ＝323Mpa，b＝-0.091，ε’ f =0.286, c= -0.83, resulting in an actual strain-life curve of the aluminum alloy material, as shown in fig. 8;
s11, calculating low-cycle fatigue damage of the shell of the drive axle under the cycle of a fatigue life load spectrum
In the step S11, in order to ensure that the impact of the shell caused by different levels of load changes can be considered in the damage calculation process, the maximum torque working condition output torque T of the forward gear is calculated according to the material strain-life curve constructed in the step S9, the fatigue life test load spectrum and the formula (11) +max Output torque T under the working condition of maximum torque of reverse gear -max Single damage of the drive axle housing under two-stage load impact;
wherein d 1 N is a single injury 1 Calculating the circulation times corresponding to the actual strain amplitude delta gamma of the component according to the working condition of the maximum torque of the forward gear and the working condition of the maximum torque of the reverse gear;
s12, calculating total damage of a shell of the drive axle under the cycle of a load spectrum with specified fatigue life
And (3) calculating the total damage of the driving axle housing according to a formula (12).
D total ＝n×d 1 (12)
Wherein D is total N is the fatigue life load spectrum cycle number for total damage;
judging the low cycle fatigue life and failure position of the drive axle housing according to the total damage result of the drive axle housing
In the step S12, if the drive axle housing has a position with a total damage value greater than 1, the low cycle fatigue life of the drive axle housing does not meet the requirement, and the failure position is a position with a total damage value greater than 1, and structural optimization is required to improve the fatigue strength of the housing; if the total damage value of the driving axle housing is less than 1, the low cycle fatigue life of the driving axle housing meets the requirement.
The fatigue life load spectrum cycle number n=60, the damage distribution of the driving axle housing is shown in fig. 9, the position (such as the position of the total damage value 1.2 scale value in fig. 9) where the total damage is greater than 1 exists around the first bearing hole of the driving axle housing input shaft, the low cycle fatigue life of the driving axle housing does not meet the requirement, the failure position is around the first bearing hole of the driving axle housing input shaft, structural optimization is needed, and the fatigue strength of the housing is improved.
Claims (10)
1. The method for calculating the fatigue life of the driving axle shell is characterized by comprising the following steps of:
s1, establishing a finite element model of a drive axle system, and modeling the parts of the drive axle system by adopting a solid grid unit;
s2, defining material properties of a finite element model, including defining material elastic modulus, poisson' S ratio and stress-strain relation;
s3, defining contact and connection modes of components of the drive axle:
according to the actual installation position of the drive axle system, assembling a model, and creating a drive axle shell bolt-drive axle left shell, a drive axle left shell-drive axle right shell, a differential first bearing outer ring-drive axle left shell, a differential first bearing inner ring-differential shell, a differential second bearing outer ring-drive axle right shell, a differential second bearing inner ring-differential shell, a drive axle right shell-drive axle support, a drive axle support-support bolt, a drive gear first bearing inner ring-drive gear shaft, a drive gear second bearing inner ring-drive gear shaft, a drive gear first bearing outer ring-drive axle right shell, and a drive gear second bearing outer ring-drive axle right shell; connecting a driving axle shell bolt and a driving axle right shell into a whole, and connecting a bracket bolt and the driving axle right shell into a whole;
s4, applying bolt pretightening force:
the bolt pretightening force is obtained by a relational expression between the bolt pretightening force and the bolt tightening torque and is applied to the shell bolt and the bracket bolt of the drive axle;
the bolt pretightening force is calculated by the following formula:
wherein F is 1 For pretightening force of the driving axle housing bolt, T 1 For the screw tightening torque of the shell of the driving axle, K is the screw tightening torque coefficient, D 1 The diameter of the bolts is the diameter of the bolts of the shell of the driving axle; f (F) 2 For pretightening force of the bracket bolt, T 2 D is the tightening torque of the bracket bolt 2 The diameter of the bracket bolt is the diameter of the bracket bolt; f (F) 1 、F 2 To calculate the amount, T 1 、T 2 、D 1 、D 2 Is a known quantity; the acting direction of the bolt pretightening force is along the axial direction of the bolt;
s5, simplifying a fatigue test load spectrum, and selecting a typical working condition in the fatigue test load spectrum as an input condition for calculation and analysis;
s6, defining boundary conditions
All degrees of freedom of the joint of the drive axle and the frame are restrained, gear force is applied by means of a local coordinate system defined on a drive gear axis, a Z axis of the coordinate system is along the axis direction of the drive gear, an R axis is along the radial direction of the drive gear, and a t axis is determined by the Z axis and the R axis according to right-hand criteria;
the driving and driven gears of the drive axle are hyperboloid gears, and the stress of the driving gears under two working conditions is calculated by combining the axial force and radial force calculation table of the hyperboloid gears according to the following formula, and the stress is applied to the driving gears in a form of concentrated force:
hyperboloid gear axial force and radial force calculation meter
Wherein T is the output torque, i is the gear ratio, F t 、F r 、F a The circumferential force, the radial force and the axial force of the driving gear respectively,d is the pitch circle diameter of the gear face width midpoint of the driving gear, alpha is the normal pressure angle of the driving gear, beta is the helix angle of the driving gear, and gamma is the pitch angle of the driving gear;
the stress of the driven gear is equal to that of the driving gear, the direction of the stress is opposite, and the stress is applied to the driven gear in a form of concentrated force;
s7, solving and calculating the finite element model to obtain stress values and strain values of all positions of the driving axle housing under the working condition of the maximum torque of the forward gear and the working condition of the maximum torque of the reverse gear;
s8, carrying out preliminary evaluation on the fatigue strength of the shell according to the MISES stress of the shell of the drive axle;
s9, calculating fatigue safety coefficients of the driving axle shell: if the shell MISES stress is smaller than the shell material yield strength limit in the step S8, calculating a shell fatigue safety coefficient according to the following formula, and evaluating the shell fatigue life:
s10, constructing a material fatigue life curve: if the shell MISES stress is greater than the shell material yield strength limit in the step S8, carrying out low cycle fatigue analysis on the driving axle shell according to a Manson-Coffin low cycle fatigue formula, and constructing a plastic strain-life curve of the material according to the following formula:
ε pa ＝ε’ f (2N) c
wherein ε pa For the plastic strain value of the component ε' f C is the fatigue ductility index;
s11, calculating low-cycle fatigue damage of a driving axle shell under the cycle of a fatigue life load spectrum;
s12, calculating the total damage of the shell of the drive axle under the cycle of the load spectrum of the specified fatigue life, wherein the calculation formula is as follows:
D total ＝n×d 1
wherein D is total N is the fatigue life load spectrum cycle number for total damage;
and finally judging the low cycle fatigue life and failure position of the drive axle housing according to the total damage result of the drive axle housing.
2. The method for calculating the fatigue life of a driving axle housing according to claim 1, wherein in the step S1, a driving axle left housing, a driven gear, a differential housing, a driving axle right housing, and a driving axle bracket are modeled by using a second order tetrahedron unit; the driving axle housing connecting bolt, the differential mechanism No. one bearing, the differential mechanism No. two bearing, the bracket bolt, the driving gear No. one bearing, the driving gear shaft and the driving gear No. two bearing adopt a first order hexahedral unit for modeling; the driven gear and the driving gear shaft adopt a simplified model; the driven gear is connected with the differential housing in a common node mode.
3. The method for calculating fatigue life of a driving axle housing according to claim 1, wherein in the step S2, the elastic modulus and poisson ratio of the materials of the left and right driving axle housings are defined, the plastic data of the driving axle housing material is obtained according to the following formula, and the plastic data of the driving axle housing material is added to the analysis model:
σ＝σ nom (1+ε nom )
ε＝ln(1+ε nom )
ε pl ＝ε-ε el
wherein sigma is true stress, epsilon is true strain, sigma nom For nominal stress, ε nom For nominal strain, ε pl For plastic strain, epsilon el Is elastic strain, E is elastic modulus of the material.
4. The method for calculating fatigue life of a driving axle housing according to claim 1, wherein in the step S3, in order to simplify the model, the number of contact pairs is reduced, and the bearing is correspondingly simplified: connecting the bearing rolling bodies and the bearing inner ring into a whole, and establishing contact between the bearing rolling bodies and the bearing outer ring; the first differential bearing, the second differential bearing, the first driving gear bearing and the second driving gear bearing are connected in the mode.
5. The method for calculating the fatigue life of a shell of a driving axle according to claim 1, wherein in the step S5, a forward gear maximum torque working condition and a reverse gear maximum torque working condition in a fatigue test load spectrum are selected as typical working conditions, and a forward gear maximum torque working condition outputs a torque T +max Output torque T under the working condition of maximum torque of reverse gear -max As input conditions.
6. The method for calculating fatigue life of a shell of a drive axle according to claim 1, wherein in the step S8, if the shell MISES stress is less than the shell material yield strength limit, the fatigue life of the shell of the drive axle is evaluated by calculating a shell fatigue safety factor by the shell stress; if the shell MISES stress is larger than the shell material yield strength limit, calculating different stages of load impact based on a multi-stage load spectrum, and evaluating the fatigue life of the drive axle shell by using a low-cycle fatigue life analysis method.
7. The method for calculating the fatigue life of the shell of the driving axle according to claim 1, wherein in the step S9, if the fatigue safety coefficient of the shell is greater than 1, the fatigue life of the shell of the driving axle meets the requirement, and if the fatigue safety coefficient of the shell is less than 1, the fatigue life of the shell of the driving axle does not meet the requirement, and the optimization is required for the weak position.
8. The method for calculating fatigue life of a driving axle housing according to claim 1, wherein in the step S10, for accurately calculating the low cycle fatigue life of the driving axle housing, the formula ε is calculated pa ＝ε’ f (2N) c Correcting, and constructing an actual strain-life curve of the material according to a corrected formula, and correctingThe following formula is given:
wherein Δγ is the actual strain amplitude of the part, ε ea For elastic strain of the part, sigma' f For the fatigue strength coefficient, b is the fatigue strength index and E is the elastic modulus of the material.
9. The method for calculating fatigue life of a driving axle housing according to claim 1, wherein in step S11, in order to ensure that the housing is impacted by different levels of load changes during the damage calculation, the driving gear maximum torque condition output torque T is calculated according to the following formula based on the fatigue life test load spectrum according to the material strain-life curve constructed in S9 +max Output torque T under the working condition of maximum torque of reverse gear -max Single damage to the transaxle housing under two-stage load impact:
wherein d 1 N is a single injury 1 And calculating the circulation times corresponding to the actual strain amplitude delta gamma of the component according to the working condition of the maximum torque of the forward gear and the working condition of the maximum torque of the reverse gear.
10. The method for calculating the fatigue life of the driving axle housing according to claim 1, wherein in the step S12, if the driving axle housing has a position with a total damage value greater than 1, the low cycle fatigue life of the driving axle housing does not meet the requirement, and the failure position is a position with a total damage value greater than 1, and structural optimization is required to improve the fatigue strength of the housing; if the total damage value of the driving axle housing is less than 1, the low cycle fatigue life of the driving axle housing meets the requirement.
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