IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010 1821 Nonlinear Eddy Current Technique for Characterizing Case Hardening Profiles Shiu Chuen Chan , Raimond Grimberg , Jose A. Hejase , Zhiwei Zeng , Peter Lekeakatakunju , Lalita Udpa , Fellow, IEEE, and Satish S. Udpa , Fellow, IEEE Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824 USA National Institute of R&D for Technical Physics, Iasi, Romania Department of Aeronautics, Xiamen University, Fujian, 361005 China Industrial components are often case hardened to improve their strength and wear characteristics. Traditionally, component sam- ples are collected from the production line at specific intervals and destructively tested for case depth profile assessment. This process is time-consuming, laborious, and can potentially allow an improperly treated component to escape detection. This paper presents a novel nonlinear eddy current technique for assessing the case hardening profile based on the premise that the magnetic characteristic of the case hardened region is different from that of the host material. A custom electromagnetic excitation-sensor array is used to both apply sinusoidal excitations to the component and measure the nonlinear response at multiple excitation frequencies and spatial loca- tions, taking advantage of the different penetration regions due to the skin depth phenomenon. Each response signal obtained from the component under test is compared with that from a reference component subjected to the same excitation. Two pattern recognition algo- rithms (an artificial neural network and the Iterative Dichotomiser 3 (ID3) algorithm) are then used to process selected characteristics of the difference signal to determine the case depth profile of the component. The nonlinear eddy current technique has been applied to evaluate the case hardening profile of automotive bearing assemblies. This problem is challenging due to the variations in geometry across assemblies as well as the limited accessibility to the case hardened surface. In the neural network test, the system achieved a 95.77% accuracy. For the ID3 algorithm, the system achieved a 95.65% accuracy. These results demonstrate that the nonlinear eddy current inspection technique is highly promising in characterizing the case profile of induction hardened parts. Index Terms—Automotive bearing assembly, case hardening profile evaluation, Iterative Dichotomiser 3 (ID3) algorithm, neural net- work, nondestructive testing, nonlinear eddy current. I. INTRODUCTION I NDUSTRIAL components are often case hardened to im- prove their strength and wear characteristics. An industrial component whose case hardening profile is of great importance is the automotive wheel bearing assembly shown in Fig. 1. The bearing assembly is made from 1050 steel and consists of a forged core (Fig. 2) surrounded by ball bearings that are held in place by an inner and outer retaining ring. The exterior sur- face of the core is case hardened to reduce mechanical wear due to contact with the ball bearings. The case depth, in this case, is critical: a case profile that is too shallow provides inade- quate protection against wear, which may in turn lead to bearing failure and wheel lock-up. An over-penetrated case profile (i.e., too deep) may render the core brittle and prone to fracture when in use. Both of these scenarios lead to important safety concerns. As a result, there is a significant interest in characterizing the case hardened profile and evaluating the case depth of the wheel bearing assembly nondestructively. The bearing assembly poses significant challenges for classical nondestructively evaluation approaches (e.g., the magneto-acoustic [1], [2], photothermal [3], or ultrasound [4], [8] methods) for determining either the surface hardness or case profile as these approaches are better-suited for applications where the hardened surface is readily accessible. Unfortu- nately, this is not the case with the wheel bearing assembly. In practice, any nondestructive case depth evaluation on the Manuscript received October 30, 2009; revised January 16, 2010; accepted February 23, 2010. Current version published May 19, 2010. Corresponding author: S. C. Chan (e-mail: schan@egr.msu.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2010.2044980 Fig. 1. Automotive wheel bearing assembly consisting of a core piece sur- rounded by ball bearings held in place by an inner and outer retaining ring. assembly must be carried out through the recessed opening of the inboard stem-end at the top of the core as shown in Fig. 1. To further complicate matters, the geometry of the recessed opening varies from one assembly to another as this area is considered non-functional and its dimensions are, therefore, not fully specified by the manufacturer. The proposed inspection system has been designed to address this challenging problem. The principle of the nonlinear eddy current inspection system [4], [8] is suitable for other case profile characterization appli- cations as well. Fig. 3 shows the cross-sectional profile of the wheel bearing core. The lateral exterior surface of the core is case hardened and the resulting hardening profile appears as darkened regions in the figure. The dimensions “L” and “D” in Fig. 3 represent the effective extent and maximum case depth, respectively, of 0018-9464/$26.00 © 2010 IEEE