CN103808806A - Ultrasonic non-destructive testing method for measuring circumference residual stress at gear root - Google Patents

Abstract

The invention provides an ultrasonic non-destructive testing method for measuring circumference residual stress at root, the method is suitable for the non-destructive measurement of residual stress at the gear root. An LCR (critically refracted longitudinal) wave which is most sensitive to the stress is motivated through the combination of an ultrasonic stress measurement system, an ultrasonic transducer and a wedge block, and the residue stress at the region is precisely computed by using acoustic time difference of the LCR wave for detecting whether the stress is near to the root. The method is capable of accurately, fast and non-destructively detecting the residue stress value.

Description

An Ultrasonic Nondestructive Testing Method for Measuring the Circumferential Residual Stress of Gear Dedendum

1. Technical field

The invention provides an ultrasonic non-destructive testing method for measuring the residual stress of the tooth root of the gear, and the method is suitable for the non-destructive measurement of the residual stress of the tooth root of the gear.

2. Background technology

Gears are important parts in machines such as automobiles, tractors, and machine tools. They are responsible for the important tasks of transmitting motion, changing the speed and direction of motion. Therefore, whether it is the stress situation during the manufacturing process of the gear or the stress situation during work, it is an important subject for people to study.

Literature search found that the paper: (Zhao Xiyong. Determination of tooth root stress of worn traction gear) mentioned the method of sticking strain gauges to measure the stress of the tooth root, but this method is limited to measuring the tooth root stress during the motion process. In the case of stress, the residual stress of the tooth root due to processing and other factors cannot be detected. Paper: (Dai Jin. Dynamic stress analysis of gear tooth root and its structural optimization design [D]. Changsha: Central South University, 2008.) The article mentioned the calculation of tooth root stress by finite element analysis method, which is a kind of The computer-based simulation method has a lot of human factors, and the difference in grid division will greatly affect the final detection results of stress. Patent: (Jiang Chuanhai, et al. Detection method for residual stress of shot peening layer at the root of small curved gears [P]. Patent No.: CN102628815A, 2012) discloses a rectangular diffraction baffle with different sizes prepared according to the curvature radius of the gear. Under the condition of different sizes of baffles, the residual stress value of the root of the curved gear is obtained, and the relationship between the width of the rectangular baffle and the residual stress value is obtained. This is an X-ray-based stress detection method, which requires that the gear root surface is basically flat and must be Appropriate chemical treatment exposes the lattice, and repeatedly adjusts the incident angle of X-rays to obtain a certain intensity at a suitable diffraction angle. The operation is complicated, there are many influencing factors, and the accuracy is not high. Practical applications are greatly affected. big limit.

This paper proposes a method of using ultrasonic technology to detect the residual stress of the tooth root of the gear. This method is highly sensitive to the residual stress, and the measurement operation is convenient and fast. It can not only measure the axial residual The root axial residual stress is very suitable for field use.

3. Contents of the invention

The purpose of the present invention is to provide an ultrasonic non-destructive testing method for measuring the residual stress of the tooth root of the gear, which is used to accurately and quickly detect the residual stress of the gear root. To achieve accurate, non-destructive, fast goals.

Concrete technical scheme of the present invention is as follows:

(1) According to the special size and curved surface structure of the gear, a method of measuring the residual stress of the tooth root with two wedges respectively placed on the two tooth surfaces is studied.

(2) According to the special size and surface structure of gears, an acoustic wedge that can be used for root residual stress measurement is designed. The sound velocity of the specially designed acoustic wedge material is lower than that of the tested gear material.

(3) According to Snell's law, when the ultrasonic longitudinal wave propagates from a medium with a slower wave velocity to a medium with a faster wave velocity (for example, from the acoustic wedge incident to the tooth surface), refraction will occur. When the longitudinal wave refraction angle is equal to 90 ^° The corresponding incident angle is called the first critical angle, and the refracted longitudinal wave will propagate along the surface of the gear, that is, the critical refracted longitudinal wave (English: Longitudinal critically refracted wave—English abbreviation L _CR wave). According to the theoretical characteristics of the L _CR wave, the propagation law of the L _CR on the special curved surface of the gear is verified by experiments.

4. Description of drawings

Fig. 1 Schematic diagram of gear tooth root stress measurement;

Figure 2 Tensile sample diagram;

Figure 3 Compression sample diagram;

Figure 4 copper wedge diagram.

5. Specific implementation

The specific embodiment of the present invention is described in detail below:

1. Excitation of L _CR wave

According to Snell's law, when the ultrasonic longitudinal wave propagates from the slower acoustic wedge to the faster gear material, refraction will occur. When the longitudinal wave refraction angle is equal to 90°, the corresponding incident angle is called the first critical angle. Calculate The formula is shown below.

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; cr</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

In the formula:

V ₁ —propagation velocity of ultrasonic longitudinal wave in medium with slow wave velocity (m/s);

V ₂ —propagation velocity of ultrasonic longitudinal wave in medium with faster wave velocity (m/s).

θ _cr —the first critical angle (°);

The refracted longitudinal wave will propagate along the propagating surface of the gear.

According to the shape of the tooth profile of the gear, find the tangent of the involute at the position where the sound wedge is placed on the tooth surface, and calculate the first at this point according to Snell's law and the speed of sound in the sound wedge material and the gear material critical angle.

2. The principle of ultrasonic stress measurement

According to the basic principle of acoustoelasticity, when ultrasonic waves propagate in isotropic elastic media, when the polarization direction of the wave particle is consistent with or opposite to the direction of residual stress (that is, 0 degrees or 180 degrees), the change of ultrasonic wave velocity and the change of residual stress Quantities are in a linear relationship. Therefore, the ultrasonic critical refraction longitudinal wave can be used to detect the residual stress in this direction. When the critical refracted longitudinal wave velocity increases, it means that there is compressive residual stress in the material; otherwise, there is tensile residual stress. Under the condition of certain material properties, the relationship between critical refracted longitudinal wave velocity dV and residual stress change dσ is as follows:

$\mathrm{<span\; class="notranslate">\; d\&sigma;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; dV</span>}$

In the formula:

dσ—change of residual stress (MPa);

dV—the change of critical refracted longitudinal wave propagation velocity (m/s);

V ₀ —propagation velocity of critical refracted longitudinal wave under zero stress condition (m/s);

k—acoustoelastic coefficient (ns/m ² );

When the critical refracted longitudinal wave propagation distance L is determined, the sound velocity change in the measured medium can be replaced by the sound time change equivalently, as follows:

$\mathrm{<span\; class="notranslate">\; d\&sigma;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}\mathrm{<span\; class="notranslate">\; dt</span>}$

In the formula:

dt—the variation (s) of critically refracted longitudinal waves propagating sound;

T ₀ —the time (s) required for the critical refracted longitudinal wave to propagate a fixed distance L under the condition of zero stress;

Let the stress constant K=2/kt ₀ where T ₀ is the propagation of the longitudinal wave under the condition of zero stress. At this time, the stress change and the sound time change of the ultrasonic wave have an approximately linear relationship, that is, Δσ=KΔt.

3. Calculation of stress constant K value

Make the same tensile and compression samples as the gear material, and use an electronic tension and compression testing machine, an ultrasonic pulse transceiver, and an oscilloscope to calibrate the K value. Specific steps are as follows:

Within the yield limit of the gear material, use a tensile testing machine to pull and compress the tensile and compressive test pieces, and record the time difference t _i displayed on the oscilloscope and the tensile testing machine at intervals of a certain stress value (this method uses every 30MPa). Displayed stress values σ _i . Curve fitting was carried out by least square method, and the value of stress constant K was calculated.

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}$

4. Measurement of gear tooth root stress

记应力状态下超声纵波在齿轮中的声速为Vi，则齿轮中的应力大小为

Firstly, the sound path between the two wedges is measured and denoted as S, then in the state of zero stress, the propagation time of the ultrasonic longitudinal wave between the two wedges is

Note that the sound velocity of the ultrasonic longitudinal wave in the gear under the stress state is Vi, then the stress in the gear is

Claims (8)

1. The present invention proposes a method for measuring the circumferential residual stress of the tooth root, which is characterized in that it comprises: a gear, an ultrasonic stress measurement system, a residual stress ultrasonic detection transducer, and an acoustic wedge. 2. The method for measuring the circumferential residual stress of the dedendum according to claim 1, first carrying out the calibration of the stress constant K value. 3. According to the K value calibration described in claim 2, first formulate a tensile test piece identical to the material to be tested and with the same heat treatment method, stretch it with a stretching machine and record the stress values σ _i at different times, and pass ultrasonic The stress measurement system measures the acoustic time difference t _i of different stress values, and performs linear fitting through the least square method to obtain the K value. $\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}$ 4. According to the method for measuring the circumferential residual stress of the dedendum according to claim 1, a special acoustic wedge is designed so that the ultrasonic detection transducer can excite and receive critical refracted longitudinal waves through the wedge. 5. According to the method for measuring the circumferential residual stress of the tooth root according to claim 1, when the wedge is designed, it needs to be well coupled with the tooth surface of the gear, so the bottom surface of the wedge should be made to match the involute of the tooth surface of the gear. line surface. 6. The method for measuring the circumferential residual stress of the dedendum according to claim 1, according to the special structural size of the gear, the material whose sound velocity is slower than the sound velocity of the gear material is selected as the acoustic wedge material. 7. The method for measuring the circumferential residual stress of the dedendum according to claim 1, when measuring the stress, perform zero stress calibration first, and record the zero stress waveform. 8. The method for measuring the circumferential residual stress of the dedendum according to claim 1, when measuring the residual stress of the dedendum, the time difference of sound is calculated by the system through the comparison between the waveform during measurement and the zero stress waveform, and the formula σ=K× (t _i -t ₀ ).

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