Frequency selection has been the subject of discussion from the beginning of induction surface heat treating in 1935. At that time, the choice of power sources was limited to arc discharge generators, motor generators and tube generators. Arc generators had very low efficiency, and had become obsolete sources even at that time. Motor generators had high power (500 kW and more) and good efficiency with frequency up to 10 kHz (some generated frequencies of 50 kHz and higher). Tube oscillators were the only choice for frequencies above 50 kHz but had low efficiency and were large.

Over the years, many dramatic changes have transformed today's industrial environment. For example, almost any combination of power (up to several MW per unit) and frequency (up to several MHz) are available due to development of solid-state power supplies with high efficiency and small dimensions (Fig. 1). Small solid-state power supplies have frequencies up to 5 MHz and higher. Computer programs are available that can accurately simulate the induction heat treating process. These developments help to meet increased heat-treating demands with respect to production rate and part quality (hardness depth, pattern, distortion, etc.), as well as the demands of many new technologies and applications that set special requirements for frequency selection.

It is necessary to revise old recommendations for frequency selection and make corrections and additions. Without limitations on frequency level and the possibility to adjust the frequency of a solid-state power supply usually in a range of 3:1, it is easy to use the required optimal frequency.

The criteria and factors for frequency selection include:

- Inductor efficiency and installation in general

- Inductor power factor; characterizing the reactive power and, therefore, the dimensions of matching transformer and capacitor battery

- Heating time and corresponding production rate

- Hardness depth and heat pattern control

- Electrodynamic forces, which cause both vibration of the inductor and machine components and acoustic noise

- Equipment cost and size

The importance of each factor depends on the particular application. Frequency (F) must be selected in combination with power (P) and heating time (T). The values of F, P and T describe the induction process. Rigorous theoretical and experimental studies have resulted in the development of recommendations for frequency selection for different applications including contour hardening of gears and other parts of complex geometry [1].

## Surface hardening

All of the factors mentioned above may influence frequency selection for surface hardening, the most important and complicated induction heating process. It is difficult to give general recommendations for frequency selection due to the large variety of part geometries and heat treating specifications, and, therefore, different groups of parts must be considered separately.

For example, three possible options in the case of simultaneous contour hardening of gears are:

- Hardening at a well-defined combination of frequency, power and time; frequency must be in a narrow range, which is different for different tooth pitch, and power must be high and heating time short, especially for small gear pitch

- Hardening by successive application of low- and high-frequency power; this technology is more flexible for different gears

- Hardening using two simultaneously applied frequencies; the possibility to redistribute power between high and low frequency makes this technology the most flexible, but requires special equipment [2]

The best technology selection for each particular case must be based on detailed technical and economical analysis.

## Hardening cylindrical and thick, flat parts

For the most common case of hardening cylindrical parts (shafts, pins, etc.) or thick, flat parts, it is recommended to select frequency according to ratio of hardness depth (d) to penetration (reference) depth (p) of the eddy current in hot steel [1] in the range of 0.33

Computer simulation program Elta [3] was used to study deep (5 mm, or 0.2 in.) induction hardening of a 40 mm (~1.5 in.) diameter shaft. The recommended frequency range is 1.2 to 10 kHz with an optimal frequency around 2.5 kHz. It was assumed that the minimum temperature for steel austenitization is 800°C (1470°F) and the maximum permissible short-term temperature is 1000°C (1830°F), which approximately corresponds to an AISI 1045 carbon steel. Calculations show that the fastest heating and minimum required energy correspond to the maximum acceptable surface temperature of 1000°C. A constant inductor power mode was used in the simulation.

Simulation results in Table 1 and Fig. 2 confirm that a frequency corresponding to a ratio d/p = 0.5 provides the fastest, most energy-efficient heating (F = 2.5-3.0 kHz). Also, the power factor of the coil is at a maximum at this frequency, which means a smaller capacitor battery and more efficient transformer. Using a higher than optimal frequency gives a higher electrical efficiency, but minimum heating time increases significantly (up to 4 times longer at 30 kHz). Total energy consumption also increases, but less than 10%. At high frequency, it is better to heat the surface to the maximum acceptable temperature to reduce heating time and energy consumption. These calculations do not take into account heat transfer along the part axis. This assumption is accurate for a scanning process or simultaneous heating of the entire part length. For local static heating, additional axial heat losses can significantly increase energy demand for a longer high-frequency process.

Using a lower than optimal frequency can provide faster heating, but electrical efficiency and power factor decrease. Required coil power increases dramatically, and coil losses can reach an unacceptable value. For this reason, it is recommended to reduce power with the proper increase of heating time. Part surface temperature will be less than the acceptable maximum. At a frequency considerably lower than optimal (1,000 Hz in this case), the heating process becomes much less effective and more sensitive to variations in operating conditions.

The coil head voltage is approximately the same within the wide range of frequency variation around the optimal value. This means that transformer ratio can be the same if the frequency will be changed.

The influence of frequency on process parameters may be explained by considering the distribution of heat sources and temperature inside the part (Fig. 3). At optimal frequency, maximum power density occurs in magnetic material below the layer to be hardened. By comparison, at a higher frequency, power density drops in depth almost exponentially, thus requiring more time to achieve heat penetration to the required depth.

## Other factors influencing frequency selection

*Heat-pattern control* is usually more precise at higher frequency due to better power concentration, although a lower frequency may be required in some cases, such as achieving a continuous pattern in a shaft having several transition zones between different shaft diameters.

*Electrodynamic forces* are created by the mechanical effect of a magnetic field on magnetic and nonmagnetic conductive bodies (e.g., the workpiece, coil tubing and magnetic concentrators). These forces cause vibration of all affected components with a frequency that is double the electric frequency. Vibration can lead to reduced coil life and sometimes to coil geometry change (deformation). In addition to mechanical damage, vibration also causes acoustic noise, which affects operator working conditions. The most physiologically distressing is noise having a frequency of 2 to 4 kHz. In the case discussed above, selection of a frequency below optimal (1 to 2 kHz) will result in a noise having a frequency of 2 to 4 kHz-the most undesirable range. With an increase in frequency, vibration and noise levels drop very fast due to lower power demand. Even for the same power, electrodynamic forces and noise are smaller at higher frequency. An electric frequency above 5 kHz results in noise of low audibility.

*Size of equipment* is smaller for higher frequency, especially the size of capacitor battery and matching transformer.

*Cost of equipment* per kW is approximately the same in frequency range of 1to 30 kHz; more power supplies are available in a range 10 to 30 kHz than below 10 kHz.

## Conclusions

New power supplies make it possible and advantageous to more precisely select the optimal frequency for the application. A narrow optimal frequency range corresponds to hardness depth (d) equal to between 0.45 and 0.6 of the reference depth in hot steel. It results in frequency range of 40/d2

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