CN105973983A - Method for designing ultrasonic torsion fatigue testing specimen with uniform section - Google Patents

Abstract

The invention provides a method for designing an ultrasonic torsion fatigue testing specimen with uniform section. The method comprises the following steps: a resonance length of the torsion fatigue testing specimen is obtained according to specimen material parameters and geometric design dimensions by a resonance length analytic formula of the torsion fatigue testing specimen; a finite element method is used for analyzing a natural frequency corresponding to a specimen torsional vibration mode; the resonance length of the torsion specimen is corrected according to an analysis result, so that the actual natural frequency of the specimen approaches the design frequency in the range of F+/-0.5kHz; and a segment with a gauge length obtains an equal maximum torsional stress. Requirements of ultrasonic torsion fatigue testing are satisfied, and accuracy of test data is improved. The method enriches specimen types of the ultrasonic torsion fatigue testing, expands applied range of the ultrasonic fatigue testing method, improves accuracy of the ultrasonic fatigue testing, and establishes a base for researching ultra-high cycle torsion fatigue performance of metal materials.

Description

Uiform section ultrasonic torsional fatigue sample design method

Technical field

The present invention relates to metal material torsional fatigue performance, durability test field, specifically a kind of ultrasonic torsion of uiform section Turn the method for designing of fatigue testing specimen.

Background technology

Fatigue be material under the repeated action of stress or strain, certain point or local produce permanent damage, necessarily follow Ring loads and forms crackle after cycle, crackle further expands to rupture completely, this is caused material by ess-strain repeated action Performance changes, and causes the phenomenon of material failure to be referred to as the fatigue of material.Fatigue failure is that structural member is bearing repeat load Failure mode main under lotus effect, such as components such as axle, crank, blade, gear etc. and pressure vessel, pipeline, vehicle, aircrafts Main failure forms be all tired broken ring, along with production practices develop, it has been found that, according to cycle-index 10⁷Left and right is really The endurance made and the component designed, when bearing higher cycle Circulation, still can occur fatigue rupture, and this promotees Vast researcher and engineering staff is made to seek the fatigue limit of structural material under higher circulation cycle.But according to traditional Testing fatigue means, test frequency, typically at about 100Hz, if as a example by this test frequency, is circulated number of times more than 10⁹Week Fatigue test, need time-consuming more than 100 days, this can not accept in engineering completely, but last century Ultrasonic fatigue testing system Occurring, test loading frequency reaches 20kHz, carries out 10 equally⁹The fatigue test in week, only needs 13.9 hours so that be performed for more than 10⁹The super high cycle fatigue test of cycle is possibly realized, and applies Ultrasonic fatigue testing technology, has carried out a lot of metal material both at home and abroad Very High Cycle repeated tension and compression test, its tension and compression Fatigue Life in Very High Cycle is studied, but in practical engineering application, as axle, The Main Load that the structural members such as crank, blade, gear bear, not axial push-pull load, but torsional shear load, owing to being subject to The impact of the factors such as Ultrasonic fatigue testing device and torsional fatigue sample design, the domestic Very High Cycle seldom carrying out material reverses tired Labor test and performance study.

The tired fatigue test of Very High Cycle and device for material have carried out a lot of work, wherein, patent of invention both at home and abroad CN201520691782.8 and CN201510828131.3 has separately designed uiform section circular arc and uiform section plate-shaped metal material draws Specimen for Fatigue Test at Ultrasonic Frequency under compressive load, it is achieved that the Very High Cycle drawingand pressing fatigue performance test of difformity metal material is practical new Type patent CN201320391869.4 devises a kind of ultrasonic torsional displacement caliberating device, solves in ultrasonic torsional fatigue test The mensuration problem of torsional displacement, but in place of yet suffering from some shortcomings for the ultrasonic torsional fatigue test of metal material, super Sound torsional fatigue test generally uses dog bone ultrasonic torsional fatigue sample, and obtaining maximum twist at middle smallest cross-sectional should Power, but for the great majority material containing defective (be mingled with, shrinkage cavity, interior tissue uneven), maximum equal stress zone is too small, difficult To obtain test data accurately, therefore, in order to obtain Ultrasonic fatigue testing data accurately, need to strengthen ultrasonic torsional fatigue The maximum twist stressed zone of sample.

Summary of the invention

For solving in prior art owing to lacking uiform section ultrasonic torsional fatigue sample design method, it is difficult to obtain super The problem of high all torsional fatigue test data, the present invention proposes the uiform section ultrasonic torsional fatigue sample being applicable to different materials Method for designing, in the sample between uiform section district (gauge length section) obtain equal peak torque, strengthen maximum twist stressed zone, and make Natural frequency corresponding to its torsion vibration mode is near ultrasonic reverse torsion machine operating frequency, it is possible to try in ultrasonic torsional fatigue Test and on machine, realize torsional resonances loading.

The technical scheme is that

A kind of described uiform section ultrasonic torsional fatigue sample design method, it is characterised in that: comprise the following steps:

Step 1: obtain shear modulus G and the density p of the metal material making ultrasonic torsional fatigue sample；

Step 2: according to making the performance of metal material and the fatigue strength of ultrasonic torsional fatigue sample, determine sample design Natural frequency f, smallest cross-sectional radius R₁, maximum cross-section radius R₂, gauge length segment length L₁With transition section length L₂, the most intrinsic In the range of frequency f is in F ± 0.5kHz, wherein F is ultrasonic reverse torsion machine operating frequency；

Step 3: according to formula

$L_3=\frac{1}{K}arctan\{\frac{1}{K}\[\mathrm{\β}\frac{\mathrm{\β}sin\left({\mathrm{KL}}_1\right)\sinh \left({\mathrm{KL}}_2\right)-Kcos\left({\mathrm{KL}}_1\right)\cosh \left({\mathrm{KL}}_2\right)}{\mathrm{\β}\sin \left({\mathrm{KL}}_1\right)\cosh \left({\mathrm{KL}}_2\right)+Kcos\left({\mathrm{KL}}_1\right)\sinh \left({\mathrm{KL}}_2\right)}\]\}$

Calculate ultrasonic torsional fatigue sample resonance length L₃, whereinω=2 π f, c are in material Velocity of wave, ω is angular frequency,

Step 4: according to step 1,2, the 3 ultrasonic torsional fatigue sample parameters obtained, set up ultrasonic in finite element software Torsional fatigue sample model, and carry out model analysis, obtain natural frequency f that sample torsion vibration mode is corresponding₁, according to model analysis The physical dimension of ultrasonic torsional fatigue sample is modified by result:

Step a: if natural frequency f that sample torsion vibration mode is corresponding₁Less than design natural frequency f-20Hz, then reduce examination Sample resonance length L₃, then carry out model analysis again by finite element software, until the sample that model analysis obtains reverses and shakes Natural frequency f that type is corresponding₁Till being in the range of f ± 20Hz, finally determine the physical dimension of sample, complete sample design；

Step b: if natural frequency f that sample torsion vibration mode is corresponding₁More than design natural frequency f+20Hz, then increase examination Sample resonance length L₃, then carry out model analysis again by finite element software, until the sample that model analysis obtains reverses and shakes Natural frequency f that type is corresponding₁Till being in the range of f ± 20Hz, finally determine the physical dimension of sample, complete sample design.

Further preferred version, a kind of described uiform section ultrasonic torsional fatigue sample design method, it is characterised in that: step Sample resonance length L is reduced or increased in rapid 4₃Time, the length range of fine setting is 0.02mm～0.6mm every time.

Beneficial effect

Employing this method can realize the design of the uiform section ultrasonic torsional fatigue sample of different metal material, by limited The natural frequency that unit's methods analyst sample torsion vibration mode is corresponding, according to analysis result correction torsional specimen resonance length, makes sample Actual natural frequency in the range of F ± 0.5kHz close to design frequency, and obtain equal maximum twist stress in gauge length section, Meet the requirement of ultrasonic torsional fatigue test, improve the accuracy of test data.The present invention enriches the examination of Ultrasonic fatigue testing Sample type, extends the range of application of Ultrasonic fatigue testing method, improves the accuracy of ultrasonic fatigue fatigue test, for metal The Very High Cycle torsional fatigue performance study of material is laid a good foundation.

The additional aspect of the present invention and advantage will part be given in the following description, and part will become from the following description Obtain substantially, or recognized by the practice of the present invention.

Accompanying drawing explanation

Above-mentioned and/or the additional aspect of the present invention and advantage are from combining the accompanying drawings below description to embodiment and will become Substantially with easy to understand, wherein:

Fig. 1: dog bone ultrasonic torsional fatigue sample torsional displacement and distorting stress schematic diagram；

Fig. 2: uiform section ultrasonic torsional fatigue sample torsional displacement and distorting stress schematic diagram；

Fig. 3: uiform section ultrasonic torsional fatigue sample schematic diagram；

Fig. 4: cast aluminium ZL114A uiform section torsional specimen analytical Calculation physical dimension；

Fig. 5: cast aluminium ZL114A uiform section torsional specimen torsional natural frequency is with the situation of change of resonance length；

Fig. 6: physical dimension after cast aluminium ZL114A uiform section torsional specimen correction.

Detailed description of the invention

Embodiments of the invention are described below in detail, and the embodiment of description is exemplary, it is intended to be used for explaining the present invention, And be not considered as limiting the invention.

Current ultrasonic torsional fatigue test mainly uses dog bone ultrasonic torsional fatigue sample, as it is shown in figure 1, in centre Maximum twist stress is obtained at small bore, but for the great majority material containing defective (be mingled with, shrinkage cavity, interior tissue uneven) Material, dog bone ultrasonic torsional fatigue sample maximum equal stress zone is too small, it is difficult to obtain test data accurately, therefore, in order to obtain Obtain Ultrasonic fatigue testing data accurately, need to strengthen the maximum twist stressed zone of ultrasonic torsional fatigue sample, so the present invention A kind of uiform section ultrasonic torsional fatigue sample of design, as in figure 2 it is shown, between in the sample uiform section district (gauge length section) obtain equal High pulling torque, increases maximum twist stressed zone.

In the present invention designs uiform section ultrasonic torsional fatigue specimen, in order to solve uiform section ultrasonic torsional fatigue examination Producing during sample ruler cun Analytical Solution and calculate error, the natural frequency that sample torsion vibration mode may be made corresponding is unsatisfactory for ultrasonic The frequency requirement of torsional fatigue machine, it is impossible to realize the problem that resonance loads, The present invention gives uiform section ultrasonic torsional fatigue examination Natural frequencies analysis method that sample torsion vibration mode is corresponding and the modification method of physical dimension.

Analytical analysis principle process be given below:

Uiform section ultrasonic torsional fatigue sample material is uniform, isotropism, ignores the plastic deformation of material, according to linear elasticity Vibration mechanics, the one-dimensional twisting vibration differential equation is expressed as:

In formula, G is material modulus of shearing, J_pX () is rotary inertia, ρ is density, J_TX () is the torsional resistance of material.Right In the continuous sample of symmetrical circular section, have:

J_p(x)=J_T(x) (2)

$J_T\left(x\right)=\frac{\mathrm{\π}}{2}{R}^4\left(x\right)=\frac{S^2\left(x\right)}{2\mathrm{\π}}---\left(3\right)$

(2) and (3) are brought into (1), and the one-dimensional twisting vibration differential equation is represented by:

At a resonant condition, for one-dimensional continuum, angular displacement ripple is represented by:

(5) are brought into (4) and can obtain one-dimensional twisting vibration model:

$\frac{d^2\mathrm{\ξ}\left(x\right)}{{\mathrm{dx}}^2}+\frac{d\left(ln\right(S^2\left(x\right)\left)\right)}{dx}\frac{d\mathrm{\ξ}\left(x\right)}{\∂x}+K^2\mathrm{\ξ}\left(x\right)=0---\left(6\right)$

In formula,ω=2 π f, c are the velocities of wave in material, and ω is angular frequency, and f is shaking of torsional specimen Dynamic frequency.

As it is shown on figure 3, using the symmetrical centre of ultrasonic for uiform section torsional fatigue sample as the initial point of cartesian coordinate system, R₁ And R₂It is | x | L respectively₁And L₁+L₂Radius during | x | L, L₁It is uiform section segment length (sample marking distance segment length), L₂It is to become to cut Face segment length (transition section length), L₃Being uiform section segment length (sample resonance length), the sectional area of torsional fatigue sample can table It is shown as:

$S\left(x\right)=\left\{\begin{array}{cc}{S}_1& 0<\left|x\right|<L_1\\ S_{2}cos\left(\mathrm{\&alpha;}x\right)& L_1<\left|x\right|<L_1+L_2\\ S_2& L_1+L_2<\left|x\right|<L\end{array}\right.---\left(7\right)$

In formula,Arccosh () represents more than anti-hyperbolic String.

(7) are brought in one-dimensional twisting vibration model (6), and vibration displacement is represented by:

In formula:

ξ₀=ξ (x) |_X=L,

Being tried to achieve by analytic method, the resonance length of torsional fatigue sample is:

$L_3=\frac{1}{K}arctan\{\frac{1}{K}\&lsqb;\mathrm{\&beta;}\frac{\mathrm{\&beta;}sin\left({\mathrm{KL}}_1\right)\sinh \left({\mathrm{KL}}_2\right)-Kcos\left({\mathrm{KL}}_1\right)\cosh \left({\mathrm{KL}}_2\right)}{\mathrm{\&beta;}sin\left({\mathrm{KL}}_1\right)\cosh \left({\mathrm{KL}}_2\right)+Kcos\left({\mathrm{KL}}_1\right)\sinh \left({\mathrm{KL}}_2\right)}\&rsqb;\}---\left(9\right)$

Obtain ultrasonic torsional fatigue sample resonance length L₃Analytic expression after, carry out specific design process below, with cast aluminium As a example by ZL114A:

Step 1: obtain shear modulus G and the density p of the metal material cast aluminium ZL114A making ultrasonic torsional fatigue sample； Shear modulus G=46.8GPa, density p=2270kg/m³。

Step 2: according to making the performance of metal material and the fatigue strength of ultrasonic torsional fatigue sample, determine sample design Natural frequency f, smallest cross-sectional radius R₁, maximum cross-section radius R₂, gauge length segment length L₁With transition section length L₂, the most intrinsic In the range of frequency f is in F ± 0.5kHz, wherein F is ultrasonic reverse torsion machine operating frequency；The present embodiment F=20kHz, Sample design natural frequency f=20kHz that determines, smallest cross-sectional radius R₁=2.5mm, maximum cross-section radius R₂=10mm, gauge length Segment length L₁=3.5mm and transition section length L₂=2.5mm,

Step 3: according to formula

$L_3=\frac{1}{K}arctan\{\frac{1}{K}\&lsqb;\mathrm{\&beta;}\frac{\mathrm{\&beta;}sin\left({\mathrm{KL}}_1\right)\sinh \left({\mathrm{KL}}_2\right)-Kcos\left({\mathrm{KL}}_1\right)\cosh \left({\mathrm{KL}}_2\right)}{\mathrm{\&beta;}\sin \left({\mathrm{KL}}_1\right)\cosh \left({\mathrm{KL}}_2\right)+Kcos\left({\mathrm{KL}}_1\right)\sinh \left({\mathrm{KL}}_2\right)}\&rsqb;\}$

Calculate ultrasonic torsional fatigue sample resonance length L₃, whereinω=2 π f, c are in material Velocity of wave, ω is angular frequency,The present embodiment It is calculated ultrasonic torsional fatigue sample resonance length L₃=7.6mm.

Step 4: according to step 1,2, the 3 ultrasonic torsional fatigue sample parameters obtained, build in finite element software ABAQUS Vertical ultrasonic torsional fatigue sample model, and carry out model analysis, obtain natural frequency f that sample torsion vibration mode is corresponding₁, according to mould The physical dimension of ultrasonic torsional fatigue sample is modified by state analysis result:

Step a: if natural frequency f that sample torsion vibration mode is corresponding₁Less than design natural frequency f-20Hz, then reduce examination Sample resonance length L₃, fine setting reduces length range preferably every time is 0.02mm～0.6mm, improves the intrinsic frequency of sample torsion vibration mode Rate, then carries out model analysis again by finite element software ABAQUS, until the sample torsion vibration mode pair that model analysis obtains Natural frequency f answered₁Till being in the range of f ± 20Hz, finally determine the physical dimension of sample, complete sample design；

Step b: if natural frequency f that sample torsion vibration mode is corresponding₁More than design natural frequency f+20Hz, then increase examination Sample resonance length L₃, fine setting increases length range preferably every time is 0.02mm～0.6mm, reduces corresponding the consolidating of sample torsion vibration mode There is frequency, then carry out model analysis again by finite element software ABAQUS, until the sample that model analysis obtains reverses and shakes Natural frequency f that type is corresponding₁Till being in the range of f ± 20Hz, finally determine the physical dimension of sample, complete sample design.

This example carries out model analysis as a example by cast aluminium ZL114A sample, determines the natural frequency that torsion vibration mode is corresponding, examination The natural frequency of sample torsion vibration mode is with resonance length L₃Adjust and change, finally determine the dimensioning of cast aluminium ZL114A torsional specimen Very little.

Although above it has been shown and described that embodiments of the invention, it is to be understood that above-described embodiment is example Property, it is impossible to be interpreted as limitation of the present invention, those of ordinary skill in the art is without departing from the principle of the present invention and objective In the case of above-described embodiment can be changed within the scope of the invention, revise, replace and modification.

Claims (2)

1. a uiform section ultrasonic torsional fatigue sample design method, it is characterised in that: comprise the following steps:

Step 1: obtain shear modulus G and the density p of the metal material making ultrasonic torsional fatigue sample；

Step 2: according to making the performance of metal material and the fatigue strength of ultrasonic torsional fatigue sample, determine consolidating of sample design There are frequency f, smallest cross-sectional radius R₁, maximum cross-section radius R₂, gauge length segment length L₁With transition section length L₂, wherein natural frequency f In the range of being in F ± 0.5kHz, wherein F is ultrasonic reverse torsion machine operating frequency；

Step 3: according to formula

$L_3=\frac{1}{K}\arctan \{\frac{1}{K}\&lsqb;\mathrm{\&beta;}\frac{\mathrm{\&beta;}sin\left({\mathrm{KL}}_1\right)\sinh \left({\mathrm{KL}}_2\right)-Kcos\left({\mathrm{KL}}_1\right)\cosh \left({\mathrm{KL}}_2\right)}{\mathrm{\&beta;}\sin \left({\mathrm{KL}}_1\right)\cosh \left({\mathrm{KL}}_2\right)+Kcos\left({\mathrm{KL}}_1\right)\sinh \left({\mathrm{KL}}_2\right)}\&rsqb;\}$

Calculate ultrasonic torsional fatigue sample resonance length L₃, whereinω=2 π f, c are the velocities of wave in material, ω is angular frequency,

Step 4: according to step 1,2, the 3 ultrasonic torsional fatigue sample parameters obtained, set up ultrasonic torsion in finite element software Fatigue testing specimen model, and carry out model analysis, obtain natural frequency f that sample torsion vibration mode is corresponding₁, according to modal analysis result The physical dimension of ultrasonic torsional fatigue sample is modified:

Step a: if natural frequency f that sample torsion vibration mode is corresponding₁Less than design natural frequency f-20Hz, then reduce sample humorous Shake length L₃, then carry out model analysis again by finite element software, until the sample torsion vibration mode pair that model analysis obtains Natural frequency f answered₁Till being in the range of f ± 20Hz, finally determine the physical dimension of sample, complete sample design；

Step b: if natural frequency f that sample torsion vibration mode is corresponding₁More than design natural frequency f+20Hz, then increase sample humorous Shake length L₃, then carry out model analysis again by finite element software, until the sample torsion vibration mode pair that model analysis obtains Natural frequency f answered₁Till being in the range of f ± 20Hz, finally determine the physical dimension of sample, complete sample design.

A kind of uiform section ultrasonic torsional fatigue sample design method, it is characterised in that: in step 4 Sample resonance length L is reduced or increased₃Time, the length range of fine setting is 0.02mm～0.6mm every time.