Method for predicting torsional fatigue life of torsion bar spring by considering residual stress gradient evolution
By considering the evolution of residual stress gradients in torsion rod spring specimens, a torsion fatigue life prediction model is established, which solves the problem of excessive prediction value in the prior art, improves the prediction accuracy, and extends the service life of the workpiece.
Patent Information
- Application Number
- CN202411800014.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-09
- Publication Date
- 2025-05-13
AI Technical Summary
The prior art fails to fully consider the impact of residual stress relaxation during the fatigue process when predicting the fatigue life of torsion bar spring specimens, resulting in excessive predicted value and early failure of the workpiece.
The torsional fatigue life prediction method considering the evolution of residual stress gradients is adopted, and the relationship curve between torsional residual shear stress and torsion angle is obtained through experiments and simulations, and combined with the plane assumption and least squares method, a fatigue life prediction model is established.
It improves the accuracy of fatigue life prediction, avoids workpiece failure prematurely, and provides a more reliable reference for fatigue life prediction of torsion bar springs.
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Figure CN119989555A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of key mechanical workpiece manufacturing processing technology and performance evaluation, relates to a fatigue life prediction technology for a torsion bar spring specimen, and specifically relates to a torsional fatigue life prediction method for a torsion bar spring considering residual stress gradient evolution. Background Art
[0002] The pre-twist process is an important process used in the manufacturing process of torsion bar springs. Reasonable pre-twist angle can improve the yield strength and elastic limit point of torsion bar springs, introduce residual compressive stress, and help reduce fatigue damage. When the pre-twist angle is set too large, it may have an adverse effect on the fatigue life of mechanical workpieces. Torsion bar springs are subjected to torsional fatigue loads during service. The fatigue performance of torsion bar springs is related to the residual stress distribution characteristics after pre-twist. There are many methods for predicting the fatigue life of torsion bar springs, including theoretical calculation methods, simulation methods, and experimental methods. However, the fatigue life of torsion bar spring specimens is currently predicted without fully considering the influence of residual stress relaxation during fatigue. The fatigue performance of torsion bar springs gradually weakens during service, which leads to excessive fatigue life values predicted by traditional prediction methods, which will cause the workpiece to fail prematurely during service. Summary of the invention
[0003] Purpose of the invention: In order to overcome the deficiencies in the prior art, a method for predicting the torsional fatigue life of a torsion bar spring taking into account the residual stress gradient distribution is provided. The residual stress evolution law of the pre-twisted torsion bar spring specimen is taken as the research object. The fatigue life of the torsion bar spring specimen under different pre-twisted angles can be predicted and evaluated. The method has good prediction accuracy and can provide a more favorable reference for the fatigue life prediction of the torsion bar spring.
[0004] Technical solution: To achieve the above object, the present invention provides a method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient, comprising the following steps:
[0005] S1: Perform pre-torsion tests on the torsion bar spring specimen at different pre-torsion angles to obtain torque-torsion angle curves M-θ at different pre-torsion angles;
[0006] S2: The torque-torsion angle curve M-θ is processed by elastic-plastic theory and Nadai formula to obtain the torsional residual shear stress τ r The relationship curve with the torsion angle θ;
[0007] S3: Based on the plane hypothesis theory, the distribution of shear stress from the center to the surface of the specimen and the calculation method are obtained, and then the torsional residual shear stress τ is obtained. r Relationship curve with specimen radius r;
[0008] S4: By simulating the evolution law of residual stress gradient during torsional fatigue loading, the magnitude and distribution curve of residual stress after evolution at different fatigue cycles are obtained;
[0009] S5: The evolved residual stress gradient curve is fitted using the least squares method, and the comprehensive parameter τ reflecting the residual stress gradient distribution is obtained according to the non-local stress method. rep ;
[0010] S6: Based on the comprehensive parameter τ rep , a fatigue life prediction model is established to predict the fatigue life of the specimens under different pre-twist angles.
[0011] Furthermore, in step S2, the torsional residual shear stress τ r The method for obtaining the relationship curve with the torsion angle θ includes:
[0012] The elastic-plastic theory states that during the torsion process, the specimen often undergoes elastic deformation first, and the torque increases linearly with the torsion angle. At this time, the torsional shear stress τ r The calculation of torque M is expressed by the following formula:
[0013]
[0014] Where, M is the torque and R is the diameter of the specimen;
[0015] When the load exceeds the elastic limit of the torsion bar, the material will enter the elastic-plastic deformation stage. At this time, there will be no linear relationship between the torsional shear stress and the torque. At this time, the relationship between the two is calculated by the Nadai formula, which is as follows:
[0016]
[0017] Where θ is the torsion angle;
[0018] Torsional shear stress τ during unloading cal The calculation formula is:
[0019]
[0020] The torsional residual shear stress τ is calculated using the above formula: r The relationship curve between the torsion angle θ.
[0021] Furthermore, the plane assumption in step S3 is expressed as follows: after the sample is deformed, its circular cross section remains a plane, its size and the distance between two adjacent cross sections remain unchanged, and the radius is still a straight line; when the sample is torsionally deformed, the cross section is like a rigid plane, rotated around the axis by an angle, and there is only shear stress on the cross section. At this time, the residual stress is the loading shear stress minus the unloading shear stress, and the circumferential residual stress presents a gradient distribution along the radial direction, gradually transitioning from the residual tensile stress in the core to the residual compressive stress on the surface, and as the pre-twist angle increases, the residual stress increases, and the distribution of the residual stress from the core to the surface is obtained by the plane assumption.
[0022] Furthermore, the least square method in step S5 is to perform an approximate fit on the residual stress gradient distribution curve to establish a cubic polynomial of the residual stress gradient distribution and depth variation, as shown in the following formula:
[0023] τ r (r) = C0 + C1r + C2r 2 +C3r 3
[0024] The residual stress gradient curve after relaxation is processed into a comprehensive parameter considering the stress value and the influence depth by the non-local method. The comprehensive parameter can represent the influence of the gradient residual compressive stress on the fatigue life. The residual compressive stress of the comprehensive parameter is defined as:
[0025]
[0026] Where: τ rep represents the equivalent compressive residual stress, τ(x) is the distribution polynomial of the residual stress along the depth, and L is the depth of the compressive residual stress.
[0027] Furthermore, the fatigue life prediction model in step S6 is established by combining the Goodman formula and the Basquin formula to establish the fatigue life N f , stress amplitude τ a , mean stress τ m and equivalent residual compressive stress τ rep The relationship formula.
[0028] Furthermore, the Goodman formula in step S6 is expressed as:
[0029]
[0030] Where: τ a is the stress amplitude, τ m is the mean stress, τ R is the stress amplitude, τ uss is the ultimate shear strength, m is the material parameter;
[0031] When the residual shear stress τ r When it exists on the surface of the specimen, the above formula is rewritten as:
[0032]
[0033] Where: is affected by τ r Affected stress amplitude.
[0034] Furthermore, in step S6, N f With τ R The relationship is described by the Basquin equation, as shown below:
[0035]
[0036] Where: τ' f is the fatigue strength coefficient, and b is the fatigue strength index.
[0037] Furthermore, the fatigue life prediction model in step S6 is to establish a fatigue life N f , stress amplitude τ a , mean stress τ m and equivalent residual compressive stress τ rep The relationship is as follows:
[0038]
[0039] in: is a constant 1.
[0040] Based on the above content, the scheme of the present invention can be summarized as follows: for the pre-twisted torsion bar spring specimen, obtain its torsion curve; establish the relationship curve between torsional shear stress and torsion angle based on elastic-plastic theory and Nadai formula; obtain the size distribution of torsional residual stress from the core to the surface through plane assumption, and obtain the residual stress gradient distribution after fatigue evolution through simulation; based on Goodman and Basquin formula, establish a fatigue life prediction formula considering the residual stress gradient distribution.
[0041] Beneficial effects: Compared with the prior art, the present invention establishes a relationship model between residual stress gradient and torsional fatigue life through experiments, numerical simulation and theoretical analysis. Compared with the prior art that directly obtains fatigue life through fatigue tests or simulations, a fatigue life prediction model that considers the evolution of residual stress gradient distribution is established, which effectively improves the prediction accuracy of fatigue life and avoids a large amount of experimental processes and resource waste. In addition, the present invention can predict the fatigue life of pre-torsed specimens under different processes. The establishment of the model has important guiding significance for the fatigue life prediction of torsion bar springs. BRIEF DESCRIPTION OF THE DRAWINGS
[0042] Figure 1 is a flow chart of the prediction method of the present invention;
[0043] Figure 2 It is a schematic diagram of the relationship between the pre-twist angle and the torque in this example;
[0044] Figure 3 This is the shear stress distribution diagram of the torsion bar spring specimen during loading and unloading in this example;
[0045] Figure 4 This is the residual stress distribution and calculation method diagram of the torsion bar spring specimen in this example;
[0046] Figure 5 This is a schematic diagram of the distribution of residual stress from the core to the surface of the torsion bar spring specimen in this example;
[0047] Figure 6 This is the stress gradient distribution diagram inside the torsion bar spring specimen after the residual stress evolution in this example. DETAILED DESCRIPTION
[0048] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.
[0049] The present invention provides a method for predicting the torsional fatigue life of a torsion bar spring taking into account the evolution of residual stress gradients, such as Figure 1 As shown, it includes the following steps:
[0050] S1: Perform pre-torsion tests on the torsion bar spring specimen at different pre-torsion angles to obtain torque-torsion angle curves M-θ at different pre-torsion angles;
[0051] S2: The torque-torsion angle curve M-θ is processed by elastic-plastic theory and Nadai formula to obtain the torsional residual shear stress τ r The relationship curve with the torsion angle θ;
[0052] The elastic-plastic theory states that during the torsion process, the specimen often undergoes elastic deformation first, and the torque increases linearly with the torsion angle. At this time, the torsional shear stress τ r The calculation of torque M is expressed by the following formula:
[0053]
[0054] Where, M is the torque and R is the diameter of the specimen;
[0055] When the load exceeds the elastic limit of the torsion bar, the material will enter the elastic-plastic deformation stage. At this time, there will be no linear relationship between the torsional shear stress and the torque. At this time, the relationship between the two is calculated by the Nadai formula, which is as follows:
[0056]
[0057] Where θ is the torsion angle;
[0058] Torsional shear stress τ during unloading cal The calculation formula is:
[0059]
[0060] The torsional residual shear stress τ is calculated using the above formula: r The relationship curve between the torsion angle θ.
[0061] S3: Based on the plane hypothesis theory, the distribution of shear stress from the center to the surface of the specimen and the calculation method are obtained, and then the torsional residual shear stress τ is obtained. r Relationship curve with specimen radius r;
[0062] The expression of the plane assumption is as follows: after the specimen is deformed, its circular cross section remains a plane, its size and the distance between two adjacent cross sections remain unchanged, and the radius is still a straight line; when the specimen is torsionally deformed, the cross section is like a rigid plane, rotated around the axis by an angle, and there is only shear stress on the cross section. At this time, the residual stress is the loading shear stress minus the unloading shear stress. The circumferential residual stress presents a gradient distribution along the radial direction, gradually transitioning from the residual tensile stress in the center to the residual compressive stress on the surface, and with the increase of the pre-twist angle, the residual stress increases. The distribution of residual stress from the center to the surface is obtained through the plane assumption.
[0063] S4: By simulating the evolution law of residual stress gradient during torsional fatigue loading, the magnitude and distribution curve of residual stress after evolution at different fatigue cycles are obtained;
[0064] S5: The evolved residual stress gradient curve is fitted using the least squares method, and the comprehensive parameter τ reflecting the residual stress gradient distribution is obtained according to the non-local stress method. rep ;
[0065] The least squares method is to approximate the residual stress gradient distribution curve and establish a cubic polynomial of residual stress gradient distribution and depth change, as shown in the following formula:
[0066] τ r (r) = C0 + C1r + C2r 2 +C3r 3
[0067] The residual stress gradient curve after relaxation is processed into a comprehensive parameter considering the stress value and the influence depth by the non-local method. The comprehensive parameter can represent the influence of the gradient residual compressive stress on the fatigue life. The residual compressive stress of the comprehensive parameter is defined as:
[0068]
[0069] Where: τ rep represents the equivalent compressive residual stress, τ(x) is the distribution polynomial of the residual stress along the depth, and L is the depth of the compressive residual stress.
[0070] S6: Based on the comprehensive parameter τ rep , a fatigue life prediction model is established to predict the fatigue life of the specimens under different pre-twist angles;
[0071] The fatigue life prediction model is established by combining the Goodman formula and the Basquin formula to establish the fatigue life N f , stress amplitude τ a , mean stress τ m and equivalent residual compressive stress τ rep The relationship between
[0072] The Goodman formula is expressed as:
[0073]
[0074] Where: τ a is the stress amplitude, τ m is the mean stress, τ R is the stress amplitude, τ uss is the ultimate shear strength, m is the material parameter;
[0075] When the residual shear stress τ r When it exists on the surface of the specimen, the above formula is rewritten as:
[0076]
[0077] Where: is affected by τ r Affected stress amplitude.
[0078] N f With τ R The relationship is described by the Basquin equation, as shown below:
[0079]
[0080] Where: τ' f is the fatigue strength coefficient, b is the fatigue strength index;
[0081] Establish fatigue life Nf , stress amplitude τ a , mean stress τ m and equivalent residual compressive stress τ rep The relationship is as follows:
[0082]
[0083] in: It is generally regarded as a constant of 1, b is generally between -0.02 and -0.15, and b is -0.11.
[0084] In this embodiment, the above method of the present invention is applied as an example, which specifically includes the following steps:
[0085] 1) According to the pre-twist test results, the experimental results under the pre-twist angles of 6°, 12° and 16° are processed respectively to obtain the curves of pre-twist torque and angle, such as Figure 2 shown.
[0086] 2) Process the torque-torsion angle curve, convert the torque in the torsion curve into shear stress through elastic-plastic theory and Nadai formula, and then obtain the shear stress-torsion angle curve, such as Figure 3 shown.
[0087] 3) Based on the plane assumption, the distribution of residual stress from the core to the surface is obtained. The residual stress is calculated by subtracting the unloading shear stress curve 2 from the loading shear stress curve 1, as shown in Figure 4 As shown in Figure 2, the relationship between residual shear stress and depth under different pre-twist angles is as follows: Figure 5 shown.
[0088] 4) According to the simulation, the relationship between residual stress and depth after different fatigue cycles is obtained, such as Figure 6 As shown in Figure 2, the residual compressive stress gradient is treated as a comprehensive parameter considering the stress value and the influence depth through the non-local method. The residual stress steady-state gradient distribution curve after different fatigue cycles is selected, and the residual stress steady-state gradient distribution curve after different fatigue cycles is selected. Figure 6 It can be seen that the relaxation of residual stress is mainly concentrated in the first fatigue cycle, and the subsequent fatigue cycles have little effect on the relaxation of residual stress. Therefore, the curve after the first fatigue cycle is fitted by the least squares method, and the fitting result is shown in the following formula:
[0089] τrep(9°)=34.58MPa, τrep(12°)=65.32MPa, τrep(16°)=105.22MPa
[0090] 5) Combine Goodman and Basquin formulas to establish a fatigue life prediction model that takes into account the residual stress gradient distribution. According to the Goodman formula, the following relationship is obtained:
[0091]
[0092] Where: τ a is the stress amplitude, τ m is the mean stress, τ R is the stress amplitude, τ uss is the ultimate shear strength and m is the material parameter.
[0093] After pre-twisting, the surface of the specimen undergoes plastic deformation, while the inner layer remains in an elastic deformation state. Due to the incompatible deformation between the surface and the inner layer, a negative residual stress τ is generated on the surface of the specimen. r When τ r When it exists on the surface of the specimen, the above formula can be rewritten as:
[0094]
[0095] Where: is affected by τ r Affected stress amplitude.
[0096] N f With τ R The relationship can be described by the Basquin equation:
[0097]
[0098] Where: τ' f is the fatigue strength coefficient, and b is the fatigue strength index.
[0099] Combining the above formulas, we get:
[0100]
[0101] Where: is 675MPa, τ m is 675MPa, τ rep are the parameters fitted in S4, τ uss It is 822.66MPa. is a constant of 1, and b is -0.11.
[0102] The fatigue life N of samples with different pre-twisted angles can be calculated by the above formula f As shown in Table 1:
[0103] Table 1 N calculated for samples with different pre-twisted angles f
[0104] Torsion Angle 9° 12° 16° Calculation results / cyc 92089 65568 59834
[0105] Based on the above content, in order to verify the effectiveness of the solution of the present invention, the torsional fatigue life verification of the samples under the pre-twisted angles of 9°, 12° and 16° was carried out. The pre-twisted test and torsional fatigue parameters are as follows:
[0106] This embodiment is used to predict the fatigue life of a torsion bar spring. The basic parameters are: (1) Instron 8874 torsion fatigue testing machine, (2) torsion bar spring sample material: 45CrMoVA steel, (3) pre-torsion parameters: torsion direction clockwise, torsion rate 15° / min, loading-unloading times three times; (3) torsion fatigue test parameters: fatigue stress amplitude σ a The stress ratio R is 1200MPa and the stress ratio R is -1. The fatigue life of the torsion bar spring specimens with different pre-twisted angles is shown in Table 2.
[0107] Table 2 N of torsional fatigue test with different pre-twist angles f
[0108] Torsion Angle 9° 12° 16° Experimental results / cyc 84743 66224 58993
[0109] Table 3 Comparison of N of samples with different pre-twisted angles f
[0110] Torsion Angle 9° 12° 16° Calculation results / cyc 92089 65568 59834 Experimental results / cyc 84743 66224 58993 Error rate / % 8.66 1.05 1.42
[0111] It can be seen from Table 3 that the error rate between the calculated results and the experimental results is controlled within 10%. The fatigue life prediction accuracy of the above fatigue considering the residual stress gradient evolution is relatively good.
Claims
1. A method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient, characterized in that: The steps include: S1: Perform pre-torsion tests on the torsion bar spring specimen at different pre-torsion angles to obtain torque-torsion angle curves M-θ at different pre-torsion angles; S2: The torque-torsion angle curve M-θ is processed by elastic-plastic theory and Nadai formula to obtain the torsional residual shear stress τ r The relationship curve with the torsion angle θ; S3: Based on the plane hypothesis theory, the distribution of shear stress from the center to the surface of the specimen and the calculation method are obtained, and then the torsional residual shear stress τ is obtained. r Relationship curve with specimen radius r; S4: By simulating the evolution law of residual stress gradient during torsional fatigue loading, the magnitude and distribution curve of residual stress after evolution at different fatigue cycles are obtained; S5: The evolved residual stress gradient curve is fitted using the least squares method, and the comprehensive parameter τ reflecting the residual stress gradient distribution is obtained according to the non-local stress method. rep ; S6: Based on the comprehensive parameter τ rep , a fatigue life prediction model is established to predict the fatigue life of the specimens under different pre-twist angles.
2. The method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient according to claim 1 is characterized in that: In step S2, the torsional residual shear stress τ r The method for obtaining the relationship curve with the torsion angle θ includes: The elastic-plastic theory states that during the torsion process, the specimen often undergoes elastic deformation first, at which point the torque increases linearly with the torsion angle. At this point, the torsional shear stress τ r The calculation of torque M is expressed by the following formula: Where, M is the torque and R is the diameter of the specimen; When the load exceeds the elastic limit of the torsion bar, the material will enter the elastic-plastic deformation stage. At this time, there will be no linear relationship between the torsional shear stress and the torque. At this time, the relationship between the two is calculated by the Nadai formula, which is as follows: Where θ is the torsion angle; Torsional shear stress τ during unloading cal The calculation formula is: The torsional residual shear stress τ is calculated using the above formula: r The relationship curve between the torsion angle θ.
3. The method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient according to claim 1 is characterized in that: The plane assumption in step S3 is expressed as follows: After the specimen is deformed, its circular cross section is still It remains a plane, its size and the distance between two adjacent cross sections remain unchanged, and the radius is still a straight line; when the specimen is torsionally deformed, the cross section rotates an angle around the axis like a rigid plane, and there is only shear stress on the cross section. The residual stress at this time is the loading shear stress minus the unloading shear stress. The circumferential residual stress presents a gradient distribution along the radial direction, gradually transitioning from the residual tensile stress in the core to the residual compressive stress on the surface, and with the increase of the pre-twist angle, the residual stress increases. The distribution of residual stress from the core to the surface is obtained through the plane assumption.
4. The method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient according to claim 1 is characterized in that: The least square method in step S5 is to perform approximate fitting on the residual stress gradient distribution curve to establish a cubic polynomial of residual stress gradient distribution and depth variation, as shown in the following formula: t r (r)=C0+C1r+C2r 2 +C3r 3 The residual stress gradient curve after relaxation is processed into a comprehensive parameter considering the stress value and the influence depth by the non-local method. The comprehensive parameter can represent the influence of the gradient residual compressive stress on the fatigue life. The residual compressive stress of the comprehensive parameter is defined as: Where: τ rep represents the equivalent compressive residual stress, τ(x) is the distribution polynomial of the residual stress along the depth, and L is the depth of the compressive residual stress.
5. The method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient according to claim 4 is characterized in that: The fatigue life prediction model in step S6 is established by combining the Goodman formula and the Basquin formula to establish the fatigue life N f , stress amplitude τ a , mean stress τ m and equivalent residual compressive stress τ rep The relationship formula.
6. The method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient according to claim 5, characterized in that: The Goodman formula in step S6 is expressed as: Where: τ a is the stress amplitude, τ m is the mean stress, τ R is the stress amplitude, τ uss is the ultimate shear strength, m is the material parameter; When the residual shear stress τ r When it exists on the surface of the specimen, the above formula is rewritten as: Where: is affected by τ r Affected stress amplitude.
7. The method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient according to claim 6, characterized in that: In step S6, N f With τ R The relationship is described by the Basquin equation, as shown below: t R =t′ f (2N f ) b Where: τ' f is the fatigue strength coefficient, and b is the fatigue strength index.
8. The method for predicting the torsional fatigue life of a torsion bar spring considering the evolution of residual stress gradient according to claim 7, characterized in that: The fatigue life prediction model in step S6 is to establish the fatigue life N f , stress amplitude τ a , mean stress τ m and equivalent residual compressive stress τ rep The relationship is as follows: in: is a constant.