In a fast-paced global economy, the ability of induction heating manufacturers to minimize time between a customer’s request for a quotation and a prepared quote based on efficient computer modeling is critical to their customer’s success.

A competitive industrial environment does not offer the luxury of several months, weeks or even days of waiting in order to prove feasibility of certain processes through trial and error. Market demands for obtaining quick and reliable results regarding critical design parameters are now an everyday, normal occurrence. 

Computer simulation allows induction heating specialists to determine the details of a process that could be costly, time consuming and, in some instances, difficult or impossible to resolve experimentally. It provides the ability to predict how different, interrelated and nonlinear factors may impact the transitional and final thermal conditions of the heated component. 

Simulation helps determine what must be accomplished to improve the effectiveness of the process in order to establish the most appropriate process recipes. Results of computer modeling serve as a comfort factor when designing new systems, avoiding unpleasant surprises, shortening the learning curve and reducing development time. Computer modeling is not just a useful tool anymore, assisting in improving system performance. It has become a vital necessity.[1-3]

Scan Induction Hardening

Scan inductors are often used to induction harden steel components. The main advantages of scan hardening compared to single-shot hardening or static hardening are associated with the superior process flexibility for hardening parts of various lengths and diameters. Scan coils may consist of one or more turns, and its copper can be profiled to better accommodate geometrical irregularities (e.g., fillet hardening). 

To illustrate, Figure 1 shows the computer-modeling results of an initial stage of induction scan hardening a 64-mm (2.5-inch) diameter medium-carbon-steel hollow shaft with an inside diameter of 25 mm (1 inch) using a two-turn inductor. The frequency is 1 kHz.

The inductor moves along a shaft during scan hardening. Coil power and scan rate are varied to accommodate the geometry of the shaft (including shoulders, diameter changes, wall thickness, etc.). To properly harden the shaft’s fillet area, a short dwell is often incorporated at the beginning of scan hardening where the inductor is energized but does not move. Quenching is not applied during the dwell stage. 

Achieving a case depth with a minimum required hardness in the shaft fillet without exceeding the maximum case depth in regions next to the fillet might present certain challenges. Those challenges can be associated with several phenomena.[1, 2]

From an electromagnetic perspective, it is challenging to induce a sufficient heat source (power density) into the fillet without creating excessive temperatures in regions next to the fillet. Smaller fillets with smaller radiuses are even more challenging due to electromagnetic proximity, and ring effects becoming more pronounced.

From a heat-transfer perspective, the presence of various cold areas adjacent to the fillet during heating creates an appreciable irregular cooling effect (cold-sink effect) in the fillet region compared with other areas of the shaft. During induction heating, there-fore, more heat is removed from the fillet area due to thermal conduction than is removed from other areas of the shaft. This re-quires an inductor designed to generate more heat in the fillet to compensate for the intensive heat-sink effect. 

From a design perspective, the shaft geometry may have certain features (e.g., edges, sharp corners, cuts, thin walls, etc.) located near the fillet that are not permitted to be re-austenitized or through hardened during the fillet hardening cycle.

Figure 1 shows temperature pattern and magnetic-field distribution at the end of the dwell stage of the fillet’s preheating. Per the customer’s request, a bare two-turn coil (white color) should be used in this application. 

In order to increase power density into the fillet region, the bottom turn was deformed, providing a favorable condition for a selective preheating of the fillet. Closer coupling of the bottom turn to the fillet compared to the shaft’s body complements copper-tube profiling in focusing the heating effect. Upon completion of the dwell stage, the shaft fillet is sufficiently preheated and scanning begins. Sometimes when the coil and/or shaft first begins to move, a faster speed is initially used to quickly move the coil in position so that the spray will strike the area heated during the dwell.

Two-Step Process

It is important to remember that induction hardening of steel components is a two-step process involving heating and quenching. When scanning outside surfaces (e.g., shaft’s outside diameter) the quenching device is typically positioned next to the coil in order to spray-quench the area that has been heated. In other cases, a machine integral-quench (MIQ) inductor can be used. In either case, a quenching device consists of a quench chamber with numerous holes (orifices) that allow the quenchant to impinge on the part at a specific angle and distance. 

Therefore, it is imperative to be able to simulate not only the heating but also the quenching stages. As an example, Figure 2 shows the results of computer modeling of heating and quenching during an intermediate stage of a vertical scan surface hardening of the hollow shaft using a two-turn MIQ inductor with an “L”-shaped flux concentrator ring (frequency  9 kHz).[2] 

Preheating and post-heating phenomena caused by electromagnetic end effects are clearly visible. Note that appreciable heating of the shaft begins considerably in front of the coil top turn (leading turn), creating the preheating effect. An electromagnetic end effect of an induction coil is primarily responsible for that preheating. It is the propagation of the external magnetic field that causes the generation of the heat sources outside the induction coil. 

The presence of an external magnetic field behind the bottom turn (trailing turn) is responsible for post-heating of shaft areas located immediately below the coil and, in some cases, even in the regions where the quenchant impinges on the surface of the shaft. It is very important to take end effects into consideration to properly design a quench device and determine an appropriate process recipe. Computer modeling helps to obtain critical information in this respect. 

The comet-tail effect is also clearly visible and manifests itself as a heat accumulation in shaft subsurface regions below the scan inductor. Upon quenching, the temperature of the shaft surface can be cooled sufficiently below the Ms temperature. At the same time, the heat accumulated in the shaft subsurface might be sufficient for the tempering back of as-quenched surface regions and could potentially result in the appearance of soft spots within the case depth. Sufficient quench-out is essential to prevent this undesirable phenomenon. 


Localized Heating

Many applications (induction brazing, soldering, hardening, tempering, stress relieving, annealing, shrink fitting, localized warm and hot forming, and bending) require induction heating of only selected areas of the workpiece. Compared to applications that require heating the entire workpiece, selective heating involves several important process characteristics that affect electrical parameters, frequency selection and coil design. These characteristics include the existence of electromagnetic end effects and a thermal cooling phenomenon, which occurs due to the heat-sink effect from colder regions adjacent to the heated area. 


FEA Computer Simulation

An FEA computer simulation of induction heating a selected area of a steel rail from ambient to hot-forming temperatures is shown (Fig. 3). Butterfly inductors positioned on both sides of a steel rail provide selective heating. Current flowing in the center turns is in the same direction, generating the main heating effect. Top and bottom turns represent the so-called “return legs of the inductor” with current flowing in a direction opposite to the current of the center turns. The main heating effect is provided by the center turns, while heating generated by return legs helps compensate the thermal cold-sink effect of adjacent regions, particularly during rail transportation to the subsequent operation in the manufacturing process.

U-shape lamination stacks positioned around the center turns have a twofold impact on performance of butterfly-type inductors. First, they serve as magnetic flux-concentrators to boost the heating intensity of center turns. Second, they provide electromagnetic decoupling of coil turns with currents flowing in opposite directions, which also increases overall electrical efficiency.

Some process requirements specify not only required minimum temperature for the sequential forming operation but also maximum temperatures of adjacent areas (e.g., selective heating of rails). Computer modeling shortens development time and helps reveal important process subtleties of selective induction heating.

In many cases, it is effective to simulate an induction heating process, taking advantage of the component’s rotational symmetry. This is often the case for induction heating of cylindrical components (shafts, Figs. 1 and 2). 


3-D Simulation

In some cases, however, the part’s geometry does not permit such simplification. 3-D electromagnetic and thermal software is used in these cases. 3-D simulation allows taking all critical geometrical features of the process into consideration. It is imperative to remember that any FEA computational analysis can, at best, produce only results that are derived from the correctly defined theoretical model, governing equations, boundary conditions and proper meshing. At the end of the simulation, modern 3-D software does not usually provide any information regarding an accuracy of obtained results. 

Experience shows that proper FEA meshing is one of the most crucial factors affecting the accuracy of numerical simulations. Regions of high current concentration and areas where the electromagnetic field has measurable gradients must be properly meshed using a sufficient number of elements. As an example, Figure 4 shows a 3-D mesh generation when radio-frequency hardening a complex-geometry component (red) using a hairpin inductor (yellow) and magnetic flux concentrator (black). Coil copper edge effect as well as the skin effect were properly addressed. The use of higher frequencies increases the importance of proper meshing.



Years of experience leveraged by recent advancements in high-performance computers have improved the cost-effectiveness of the development stage for induction heating equipment by shortening the learning curve, reducing development time and allowing quick and reliable feasibility estimates of novel processes. It continues to play an increasingly critical role in optimizing performance of induction systems. 

It is important that the analyst has a clear understanding of the process specifics, however, as well as experience in the real world of heat treating because it is a complicated art. Computer simulation must be used in conjunction with experience in numerical computation, proper education and engineering knowledge to achieve the required accuracy of the mathematical simulation. When the right people use these tools, the end-user request can be efficiently handled with precision and in a cost-effective way. IH



1. V. Rudnev, “Computer Modeling Helps Prevent Failures of Heat Treated Components,” Advanced Materials & Processes, October 2011, 6-11p. 

2. V. Rudnev, “Computer Modeling of Induction Heating: Things to be Aware of, Things to Avoid,” Industrial Heating, May 2011, 41-45p.

3. G. Doyon, D. Brown, V. Rudnev, C. Van Tyne, “Ensuring the Quality of Inductively Heated Billets,” Forge, April 2010, 14-17p.