A Common Misassumption in Induction Hardening
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htprof.qxp 9/3/2004 11:22 AM Page 1 PPRROOFFEESSSSOORR IINNDDUUCCTTIIOONN by Valery I. Rudnev • Inductoheat Group Professor Induction welcomes comments, questions, and A common misassumption in suggestions for future columns. Since 1993, Dr. Valery Rudnev has been on the staff of induction hardening Inductoheat Group, where he Ω µ currently serves as group henever someone is talking about the metal ( ·m), r is the relative mag- director – science and Winduction heating, reference is netic permeability, and F is the fre- technology. In the past, he was an associate often made to the phenomenon of skin quency (Hz), or (in inches) as: professor at several universities, where he 1 effect. Skin effect is considered a fun- taught graduate and postgraduate courses. δ × ρ µ ½ damental property of induction = 3160 ( / rF) , (Eq. 3) His expertise is in materials science, heat treating, heating, representing a nonuniform applied electromagnetics, computer modeling, and distribution of an alternating current where electrical resistivity ρ is in units process development. He has 28 years of within the conductor cross section. This of Ω·in. experience in induction heating. effect will also be found in any electri- Thus, the value of penetration Credits include 15 patents and 118 scientific cally conductive body (workpiece) lo- depth varies with the square root of and engineering publications. cated inside an induction coil or in close electrical resistivity and inversely with proximity to the coil. According to this the square root of frequency and rel- Contact Dr. Rudnev at Inductoheat Group 32251 North Avis Drive phenomenon, eddy currents induced ative magnetic permeability. Mathe- Madison Heights, MI 48071 within the workpiece will primarily matically speaking, the penetration δ tel: 248/585-9393; fax: 248/589-1062 flow in the surface layer (the “skin”), depth, , in Eq. 1 is the distance from e-mail: [email protected] where 86% of all induced power will the surface of the conductor toward Web: www.inductoheat.com be concentrated. This layer is called the its core, at which the current decreases reference depth or current penetration exponentially to “1/exp” its value at depth, δ. The degree of skin effect de- the surface. The power density at this pends on the frequency and material distance will decrease to “1/exp2” its properties (electrical resistivity, ρ, and value at the surface. µ relative magnetic permeability, r) of Figure 1 illustrates the skin effect, the conductor.1 showing distribution of current Surface Core density from the workpiece sur- Traditional view of the skin effect face toward the core. At one It is often recommended to calcu- penetration depth from the sur- I = Isurface late the distribution of the current den- face (y = δ), the current will sity along the workpiece thickness equal 37% of its surface value. I = 0.368 Isurface (radius) using Bessel functions.2 How- However, the power density ever, for electromagnetically “thick” will equal 14% of its surface Current density δ workpieces, the following simplified value. From this, we can con- equation is frequently used: clude that about 63% of the cur- rent and 86% of the induced Distance from workpiece surface –y/δ I = I0·e , (Eq. 1) power in the workpiece will be concentrated within a surface layer of Fig. 1 — Current density distribution due where I is the current density (in to the skin effect. (Ref. 1) thickness δ. A/m2) at distance y (m) from the Analysis of Equations 2 and 3 workpiece surface toward the core, I 0 shows that the penetration depth has is the current density at the surface different values for different materials 2 δ (A/m ), and is the current penetra- and is a function of frequency. tion depth (m). According to this equation, an eddy current density in- Selecting case depth, frequency duced within an inductively heated Surface hardening of steels and cast workpiece has its maximum value at irons represents the most popular ap- the surface and falls off exponentially. δ plication of induction heat treatment. Current penetration depth, , is de- The goal in surface hardening is to scribed (in meters) as: provide a martensitic layer on specific δ × ρ µ ½ areas of the workpiece to increase the = 503 ( / rF) , (Eq. 2) hardness, strength, and fatigue and where ρ is the electrical resistivity of wear resistance, while allowing the re- HEAT TREATING PROGRESS • SEPTEMBER/OCTOBER 2004 23 htprof.qxp 9/3/2004 11:22 AM Page 2 PROFESSORPROFESSOR INDUCTIONINDUCTION mainder of the part to be unaffected ditional heating time is needed to some unique cases. For the great ma- by the process.1 The case depth, or allow heat to conduct to the desired jority of induction heating applica- hardness depth, is typically defined depth. Not only does this add unnec- tions, the current density (heat source) as the distance from the surface where essary time to the cycle, but there can distribution is not uniform and there the microstructure is at least 50% also be significant overheating of the always are thermal gradients within martensite. Below this depth the hard- surface, which can lead to excessive the heated workpiece. These thermal ness begins to decrease drastically. grain growth. Overheating of the sur- gradients result in nonuniform distri- Power and frequency are two of the face can also cause decarburization butions of electrical resistivity and most important factors that affect case and excessive scaling. magnetic permeability within the depth. In surface hardening applica- If the chosen frequency is too low workpiece. This nonlinearity means tions, the frequency can range from as (Fig. 2, center), the heating is deeper that the classical definition of current high as 4000 kHz (used for special ap- than necessary. The result is a large penetration depth often does not fully plications such as hardening of thin heat-affected zone, additional work- apply. wire) to as low as line frequency (used piece distortion, and unnecessary New explanation: An assumption for hardening large rolls). waste of energy. In some cases, the of exponential current density distri- In many instances, it is possible to penetration depth can be so large, bution can be used for rough engi- achieve the same desired case depth by compared with the required case neering estimates for induction using different combinations of power depth, that it will not be possible to heating nonmagnetic materials (alu- density and frequency. For example, meet the pattern specification. minum and copper, for example) and when a shallow case is required it In general, the optimum frequency through heating of carbon steels to might be possible to achieve the same will result in a current penetration forging temperature. results with a lower-than-optimal fre- depth that will be 1.2 to 2 times the re- However, in some applications, sur- quency in combination with a higher quired case depth. Maintaining this face hardening in particular, the power density applied for a shorter ratio compensates for the cooling/ power density distribution along the time. Conversely, if a deeper case is re- soaking effect of the workpiece’s cold radius/thickness has a unique “wave” quired with an existing system that uti- core. shape, which differs significantly from lizes a higher-than-optimal frequency, the commonly assumed, classical ex- then a lower power density in combi- Magnetic waves in hardening ponential distribution. Here, the nation with a longer heat time can be In most publications devoted to in- power density is maximum at the sur- used. Figure 2 compares a required duction heating and induction heat face, and decreases toward the core. case or hardness depth with the cur- treating, distributions of current den- But then, at a certain distance from the rent penetration depths obtained in hot sity and power density (heat source surface, the power density increases, steel using too high, too low, and op- distributions) along the workpiece reaching a maximum value before timal frequencies. thickness/radius are simplified, and again decreasing. If the frequency has been chosen described as exponentially decreasing This “magnetic-wave” phenom- correctly, the thickness of the non- from the surface into the workpiece enon was introduced by Davies and magnetic surface layer — the layer (see Eq. 1 and Fig. 1). It is important Simpson,2 and Losinskii.3 They intu- that is heated to above the Curie tem- to remember that this assumption is itively felt there should be situations perature — is somewhat less than the correct only for a solid body (work- where the power density (heat source) current penetration depth in hot steel piece) having constant electrical resis- distribution would differ from that of (Fig. 2, right). tivity and magnetic permeability. the traditionally accepted exponential If the frequency is too high for the Therefore, realistically speaking, this form. They provided a qualitative de- specified case depth (Fig. 2, left), ad- assumption can be made for only scription based on their intuition and understanding of the physics of the Current penetration depth in hot steel Required case depth Surface Core process. At the time, a quantitative descrip- tion of the phenomenon could not be developed due to limited computer power and the lack of software that could simulate the tightly coupled electrothermal phenomena of induc- tion heating processes. Of course, it Too high frequency Too low frequency Optimal frequency also was not possible to measure the Fig. 2 — How frequency affects current penetration depth in hot steel. If the frequency is too power/current density distribution high, left, surface overheating results, which can lead to excessive grain growth. If the frequency inside the solid body (workpiece). is too low, center, a higher power density and large heat-affected zone result, which can waste energy New software: Modern numerical and cause excessive distortion.