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Hardness Testing of Detail's Internal Surfaces by Higher Harmonic Method N.Gusak, A.Chernyshev, S.Murlin Institute of Applied Physics, National Academy of Sciences, 16, Academicheskaya str., 220072, Minsk, Belarus Contact

1. Introduction

Nowadays the high demands to the quality of machine-building factories products are presented. One of the parameters describing the quality of machines'details after thermal processing and also after surface hardening (high-frequency hardening, chemical-thermal processing, laser processing, etc.) is the hardness. In many cases the hardness determines reliability and lasting of machines'details. At the industrial enterprises the standard methods of Brinell, Vickers, Rockwell, etc. are basically used for hardness determination. These methods are destroying. Among the nondestructive methods of the hardness testing the greatest spreading have received ultrasonic, shock, magnetic, etc. The installation for the hardness nondestructive testing, based on use of the analysis of materials several electromagnetic parameters, is described in [1]. However, area of application of devices based on these methods is limited. In particular, they can't be used for the hardness testing in hard-to-reach places of the complex form details and also with a low class of surface cleanliness.
The most difficult is the internal surfaces hardness testing of details after surface hardening. Such details are pipes, couplings, hubs, etc. The hardness testing of details with a small internal diameter (approximately 20 mm), internal surfaces of the complex form, for example, spline, and internal surfaces of extended products is especially difficult.

2. Experimental results

The opportunity of use the higher harmonic method for the hardness testing of details' internal surfaces after the high-frequency hardening was investigated. It is known, if a controllable detail or site of a detail is reverse magnetized by a-c harmonic field, generated by an exciting coil of the transducer, then owing to a ferromagnet nonlinear properties the magnetic induction and output signal, proportional to it,of the measuring coil will be sinusoidal and contain the higher odd harmonics and at constant bias magnetization - even harmonics,also.The amplitude and phase of these higher harmonics depend on the magnetic characteristics of the testing details. For example, as it was shown in [2], at magnetic reversal of ferromagnet in Rayleigh's area by a-c harmonic field by intensity H=H_mcos(wt) the amplitude of the magnetic induction third harmonic component was written as:
B_3m = m ₀(4/15p )kH_m²/H_c²
where m ₀ = 4p·10^-7H/m, k - coefficient, H_c - coercive force.
In turn, magnetic characteristics and, in particular, coercive force H_c depend on thermal processing and surface hardening. Therefore the higher harmonics are sensitive parameters to the hardened layer hardness. The characteristic correlation dependences of the third harmonic component amplitude of the superimposed transducer e.m.f. on the hardness of samples made of different steels after the induction hardening by the high-frequency currents are submitted in Fig.1.

Fig 1: U3 dependence on the sample hardness after hardening by high frequency currents. 1 - 45 steel, 2 - 40H steel (0,4 wt% C, ~1,0 wt% Cr, 3 - 65G steel (0,65 wt% C, ~1 wt% Mn)

Fig 2: An arrangement of the transducer at the control of an internal surface: 1 - transducer, 2 - controllable detail.


The hardness testing of internal surfaces with superimposed electromagnetic transducers by the higher harmonic method has its peculiarities. In this case change of radius of curvature of the testing surface influences essentially over the character of the higher harmonics dependences on the hardness. The radius of curvature R decrease is similar to the lift-off d (between the transducer and detail) increase (Fig. 2) and results in harmonic amplitude decrease. As an example, in Fig.3 the third harmonic amplitude dependence of the superimposed transducer e.m.f., its outside diameter is 10 mm, on radius of curvature R of an internal surface of details with identical hardnesses is submitted. It is visible, that by radius decrease from 40 mm up to 10 mm the harmonic amplitude decreases under the nonlinear law more than four times. It is possible to reduce influence of radius of curvature change reducing an outside diameter of the transducer.

Fig 3: Dependence of the third harmonic amplitude of the superimposed transducer e.m.f. on radius of curvature of samples internal surfaces.

Fig 4: Dependence of the relation) U3/U3', where U3' - the third harmonic amplitude on a sample with hardness 60 HRC, on hardness of samples made of steel 40XH for various excitation frequencies : - 2500Hz; -160Hz


However, with the transducer diameter decrease the exciting field decreases also, that results in decrease of sensitivity and hardness testing accuracy. Therefore it is necessary to make up the tuning-off the influence of R change at optimum parameters of the superimposed transducer. As an additional parameter sensitive to change of radius of curvature, as well as in [3] to a lift-off, a summary signal U_s effective meaning of the superimposed transducer measuring coil was chosen. The effective meaning of a summary signal U_s, unlike the third harmonic amplitude U₃, depends basically on the lift-off and unsignificantly on physical-mechanical properties and hardness. The U₃ changes for all investigated marks of steels did not exceed 5 % at hardness changes from 20 up to 62 HRC.
As the summary signal and the third harmonic are decreased with the radius of curvature decreasing, the opportunity to compensate this change by increase the transducer exciting current was investigated. In order to choice a character of exciting current change at which U₃ would not depend on R, the transducer was primary established on a flat sample (d = 0), then U_s and U₃ were measured at the chosen exciting current I_e. Then the transducer was put on samples with various radiuses of curvature and various hardnesses and at each putting an exciting current I_e was increased up to U₃ had achieved its initial meaning, i.e. the meaning U₃ which was on a flat sample, and then U_s was measured. At the same time the radius of curvature of an internal surface was reduced up to 10 mm and samples hardnesses were changed from 20 up to 62 HRC. In result, for each set of samples the curves of an optimum exciting current I_e and of a summary signal U_s changes have been received, at which U₃ did not depend on radius of curvature R. After processing the received dependences the algorithm of an exciting current change was developed at which the third harmonic amplitude did not depend on radius of curvature of a sample internal surface.
For the successful decision of a task of the hardness nondestructive testing of details internal surfaces by the higher harmonic method the correct choice of an a-c magnetic field excitation frequency has the important meaning. At choice of frequency we proceeded from the following reasons:
• the level of the measuring harmonic in the transducer output signal should be sufficient for its measurement, and sensitivity to hardness - sufficient for use in the device;
• the depth of a-c magnetic field penetration should be less than the hardened layer thickness in order to exclude influence of a detail "core";
• the exciting field frequency should be such, that can reduce influence of a testing surface roughness and others local inhomogeneities.

Taking into account that in practice it is necessary to carry out the hardness testing of details with various thicknesses of a hardened layer and various roughness of a testing surface, i.e. to use various excitation frequencies, the estimation of sensitivity of the third harmonic amplitude of the superimposed transducer e.m.f. to hardness at various frequencies of a-c magnetic field was carried out. For this purpose the samples were made of steel 40XH, were hardened and were tempered from various temperatures to receive different hardnesses. The a-c magnetic field excitation was changed from 2500 Hz up to 160 Hz. It is known, with the excitation frequency decrease the influence of eddy currents decreases and as a percentage of the higher harmonics in an output signal of the transducer falls. However, as have shown researches at the exciting field frequency change in the indicated interval the sensitivity of the third harmonic amplitude of the superimposed transducer e.m.f. and hardnesses of samples remained practically constant (Fig. 4).

3. Practical use

On the basis of researches the devices for nondestructive testing of details internal surfaces hardness by the higher harmonic method were developed. The devices can be used for testing of details after surface hardening, and after volume thermal processing, also. The third harmonic component amplitude of the measuring coil e.m.f. is used as a testing parameter. The devices are supplied with replaceable transducers, both with ferromagnetic cores and without them. The minimal outside diameter of the transducer - 5 mm, height - 10 mm. The internal diameter of a testing surface is from 15 mm and more. The calibration of the device is carried out on samples.

Fig 5: An example of a detail with an internal surface of the complex geometrical form controlled by the developed device.

The graduation curves for each mark of steels are stored in the device memory. The hardness testing can be carried out in HRC, HB and HV units. The devices allow to carry out the hardness testing of internal surfaces and also in difficult of access places of the complex form details, for example, pathes of rolling hinges of equal angular velocities (Fig.5). The devices are used at the industrial enterprises for the hardness testing of responsible machine details.

4. Reference

1. W.A. Theiner et. al., Process Integrated Nondestructive Testing for Evaluation of Hardness. 14^th World Conference on Non-Destructive Testing, New-Delhi, India, December 8-13, 1996, p. 573 - 576.
2. N. Gusak, A. Chernyshev, S. Murlin. Usage of Magnetic Induction Higher Harmonic Components for Hardness Nondestructive Testing of Details after Surface Hardening. In book Non - Liner Electromagnetic Systems. Advanced Techniques and Mathematical Methods, Edited by V. Kose and J. Sievert, IOS Press, 1998, p. 181 - 184.
3. Gusak N.O. Research of an Opportunity for Tuning-off from Lift-off when Testing Products by Higher Harmonic Method with Superimposed Transducer. Defectoscopy, 1989, No.12, p.60-64.

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