**Understanding induction heating efficiency and how it can be improved is critical for forgers pursuing the reduction of energy consumption and cost. This article presents a basic mathematical explanation of induction heating efficiency and discusses a variety of practical approaches to maximizing it.**

Due to the increasingly diverse and competitive nature of the overall manufacturing industry, the reduction of operational costs for the purpose of maximizing profits is a primary goal for manufacturing businesses. The forging industry is no exception. Because forging is a highly energy-intensive process, it is no surprise that reducing operational costs related to energy consumption is a high priority.

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**COMPONENTS OF ENERGY EFFICIENCY**

Regarding induction heating equipment and processes, minimizing energy consumption requires maximizing total efficiency. Because induction heating involves the transfer of both electromagnetic and thermal energy, total efficiency can be expressed instantaneously as a function of its electromagnetic- and thermal-efficiency components, h* _{el}*(

*t*) and h

*(*

_{th}*t*) respectively. (See top equation of "Equation List" in slideshow.)

Accordingly, maximizing total efficiency requires maximizing the product of its electromagnetic and thermal components.

**Electromagnetic Efficiency**

Because of the nature of alternating-current (AC) flow, the vast majority of electromagnetic losses in typical induction forging systems occur across the terminals of the coil(s). By assuming all appreciable sources of electromagnetic inefficiency occur across the coil terminals (neglecting conversion, transmission, load matching and control losses), electromagnetic efficiency can be expressed instantaneously as a function of the induced Joule losses (heat generation) in the workpiece and the Joule losses in the coil, *P _{ind}*

*(t)*and

*P*respectively. (See middle equation of "Equation List" in slideshow.)

_{coil}(t)Maximizing electromagnetic efficiency, therefore, requires maximizing the power induced in the workpiece while minimizing power losses in the coil(s).

**Thermal Efficiency**

The thermal component of total efficiency accounts for thermal energy transferred from the heated workpiece to its surroundings during heating by means of conduction, convection and radiation heat transfer. Thermal efficiency can be expressed instantaneously as a function of the induced Joule losses in the workpiece and the rate of thermal energy transfer (heat transfer) from the workpiece to its surroundings due to conduction, convection and radiation, *P _{ind} *

*(t)*and

*P*respectively. (See bottom equation of "Equation List" in slideshow.)

_{th}(t)Logically, maximizing the thermal component of total efficiency requires minimizing the transfer of thermal energy from the workpiece to its surroundings.

**Note Regarding Time-Dependence**

The equations presented thus far reflect time-dependence because a considerable number of induction forging systems operate at transient power levels due to type of system, the mode of power-supply control and the properties of the heated material.

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**MATERIAL PROPERTIES**

Before discussing equipment and process design factors, it is important to acknowledge how the workpiece material properties influence the maximum attainable efficiency of induction systems. Though there are many material properties that affect induction heating efficiency, two of the most critical are electrical resistivity and relative magnetic permeability.

**Electrical Resistivity**

Resistivity affects resistance, which influences the capacity of induced current to generate heat. While the relationship between heat generation in the workpiece and its resistivity is complex (due largely to the tendency for AC to flow near the surface of conductors, often called the “skin effect”), higher-resistivity materials tend to heat more efficiently than lower-resistivity materials. This is why, for example, 304 stainless steel can be heated more efficiently than copper or aluminum (Figure 1).

**Magnetic Permeability**

The aforementioned skin effect becomes much more pronounced in magnetic materials, resulting in higher effective electrical resistance and, consequently, more intense heat generation. Additionally, due to magnetic hysteresis, magnetic materials are subjected to internal frictional heat generation as well (due to the “flipping” of magnetic domains in the presence of an alternating magnetic field). As a result, heating efficiency is increased substantially when heating a magnetic material (relative to a nonmagnetic material with otherwise identical material properties). A practical implication of this phenomenon is shown in Figure 1. When heating carbon steel to hot/warm forming temperatures, there is an inherent reduction in efficiency when the material becomes nonmagnetic (at Curie temperature).

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**COIL DESIGN**

The simple mathematical equations presented thus far reveal a variety of coil-design factors that affect the efficiency of induction forging systems.

**Coupling and Refractory Thickness**

The design of induction forging coils is multifaceted. One of the most important design factors affecting electromagnetic efficiency is the coupling gap between the coil and workpiece. Analogously, one of the most important design factors affecting thermal efficiency is the thickness of the refractory between the coil and workpiece. Herein lies a paradox of induction coil design. Although decreasing the coupling gap between the coil and workpiece increases electromagnetic efficiency (a smaller coupling gap allows more flux lines to pass through the workpiece). Decreasing the coupling gap also forces a reduction in the thickness of refractory between the coil and workpiece and thus reduces thermal efficiency.

As already stated, maximizing the total efficiency of an induction forging system requires maximizing the product of its electromagnetic and thermal efficiency components. Consequently, coil design requires a balancing act of electromagnetic and thermal efficiency over the range of customers’ production requirements, while also considering system robustness and cost-effectiveness. Because of the complexity of induction heating, there is no universal coil design scheme that results in maximum efficiency for all induction forging processes. Leveraging numerical computer simulation, therefore, is an absolute necessity in the design of maximally efficient coils.

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**CASE STUDIES IN COIL DESIGN**

Factors including the geometry and material of the workpiece, the electrical frequency utilized for heating, and process temperature and production requirements influence the optimal coil design. Consider, for example, two different induction billet-heating systems designed for two different processes.

• A 3-kHz system heating 50 mm-diameter AISI 4140 steel billets to 1235 ± 40°C (2255 ± 72°F) at a production rate of 1,000 kg/hour

• A 1-kHz system heating 100 mm-diameter billets at a production rate of 2,220 kg/hour (same material and temperature requirements)

The effects of incremental increases in refractory thickness on heating efficiency can be illustrated in both cases using computer simulation software as shown in Figures 2 and 3 respectively. In each case, thermal efficiency increases and electrical efficiency decreases as the refractory thickness increases. However, due to differences between the two systems and processes, increasing the refractory thickness affects the net (total) efficiency of the two systems quite differently.

In the first case, while increasing the thickness of the refractory causes an increase in thermal efficiency, the increases in the electromagnetic coupling gap associated with the increases in refractory thickness result in a more substantial reduction in electromagnetic efficiency. As a result, the net efficiency decreases. In the second case, however, this is reversed. The increase in thermal efficiency is more significant than the decrease in electromagnetic efficiency, resulting in a net efficiency increase.

Again, the effects of varying refractory thickness are dissimilar because of differences between the two systems and processes. The billets in the second case have four times the cross-sectional area and twice the surface area (per unit length) than those in the first case. Because electromagnetic efficiency is greatly affected by the ratio of coil and workpiece cross-sectional areas (often called coil “fill factor”), the same incremental increases in refractory thickness. These more negatively affect electromagnetic efficiency in the first case than in the second. This is augmented by the fact that sensitivity to fill factor is generally more pronounced at higher frequencies.

Conversely, because convection and radiation losses from the billets to the surroundings are proportional to the external surface area of the billets, identical incremental increases in refractory thickness elicit a greater increase in thermal efficiency in the second case as opposed to the first.

**Copper Selection and Turn Spacing**

The cross-sectional geometry and spacing of coil turns can substantially affect the efficiency of induction forging systems composed of solenoidal multi-turn coils (the vast majority of induction heaters in forging applications). Copper-tube geometry, including the shape (square, round, etc.) and dimensions (wall thickness, width, diameter, etc.), as well as the spacing of the turns, affects the distribution of current in the coil and thus the magnetic field that induces current in the workpiece.

To illustrate the efficiency-related implications of copper selection and turn spacing, it is convenient to consider a single induction heating process and compare the electrical parameters associated with the use of two different coil designs. Figure 4 shows normalized current-density distributions associated with two different coil designs. The first design is shown at the top and the second at the bottom.

While the two coils share the same bore, length and number of turns, the copper tube comprising each coil is noticeably different. The smaller copper tube used in the first coil has an inappropriate wall thickness given the output frequency of the power supply, and the width of the turns is less than ideal.

The second coil is wound from a larger tube that is much more suitable for this system as evidenced by the significant reduction in maximum current density in the coil turns. Relative to the first, the second coil design improves electromagnetic efficiency by 11% and reduces Joule losses in the coil by 26%. The modified coil design provides a substantial reduction in energy consumption and a sharp decrease in water cooling demand (further reducing energy consumption and cost.)

**Selective-Heating Systems**

With regard to selective-heating systems, turn spacing also affects how much of the workpiece is heated. Considering conventional static bar-end heaters, typical heating requirements include uniformly heating a certain length (often called the “heated length”) of a bar to forming temperatures while minimizing the additional length of bar that is heated (the “transition region”). The presence of this transition region is unavoidable due to thermal conduction. By systematically varying coil-turn spacing (thereby locally increasing/decreasing heat generation along the length of the bar), however, the length of the transition region can be minimized. These so-called “variable-pitch coils” can provide a forger a number of quality-related benefits, and they can also be advantageous from an energy-consumption perspective.

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**PROCESS DESIGN**

Though easy to overlook, process design is an imperative part of engineering induction heating systems. The process recipe, including critical electrical parameters such as inverter output power and current setpoints, can profoundly affect the efficiency of induction forging systems.

**Effects of Power Distribution**

The distribution of power in modular progressive heating systems epitomizes the extent to which process design can affect efficiency. Consider a two-module system (consisting of two coils connected to two individual inverters) heating carbon steel billets 2.5 inches in diameter and 6.0 inches in length to 2280 ± 50°F at a production rate of 3,760 pounds/hour (nine-second cycle time). Given the process requirements, the number of combinations of inverter power setpoints that will result in acceptable heating of the billets is quite high. The number of combinations that will result in maximum efficiency, however, is much less – in fact, it is one. Calculating this optimal process recipe is virtually impossible without the use of numerical computer simulation.

For this specific system and process, our IHAZ simulation and control software is used to calculate the optimized first and second inverter outputs to be 357 kW and 203 kW respectively (for a total power requirement of 560 kW). A non-optimized recipe (for example, a recipe based on one of many outdated rules of thumb), requires a total of 577 kW to achieve a similar final temperature distribution in the workpiece (Figure 5).

Projected over a year of three-shift production, using this non-optimized process recipe could result in the consumption of an additional 110,000 kilowatt-hours of energy – and many thousands of dollars.

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