This article was written by Dr. Vadims Geza, chief scientist at CENOS. More information on CENOS Platform can be found here.
Induction is becoming an increasingly popular choice for heating steel billets prior to forging due to its ability to create high heat intensity quickly and within a billet, which leads to low process-cycle time (high productivity) with repeatable high quality, occupying minimal space on the shop floor. It is more energy-efficient and inherently more environmentally friendly than most other heat sources for steel billets.
In this article, the author demonstrates a simulation example on how to optimize a progressive induction heating system for a steel billet. The method used is CENOS Platform, a 3D simulation software which focuses specifically on induction heating and uses open source components and algorithms.
CENOS platform is capable of simulating various types of induction heating for forging. It is possible to simulate both static heating and progressive heating where the billet is moved through the coil with constant velocity. In accomplishing this simulation, coil design is not a limitation: both single coil and multi-coil are possible to simulate. Besides the coil, it is also possible to simulate any material and frequency.
The functional performance of the software
CENOS is a finite element method-based, computer-aided engineering desktop software for 2D and 3D physical process simulation and computational modeling of induction heating, induction hardening, brazing, annealing and tempering of steel, aluminum, copper, and other materials.
The simulation process consists of three steps:
Choose the workpiece geometry (from built-in templates or create your own CAD file).
Define induction heating parameters (frequency, voltage, time, etc.).
Run 2D or 3D simulation of your choice.
At the conclusion, results like temperature and magnetic field are displayed in 3D renderings, plots, and more. Apparent power, induced heat, and inductance are logged into an Excel file.
3D Simulation example—comparison of two heating systems
In the simulation, two systems under consideration—two-stage and three-stage systems—in the progressive heating of the billet. The target for the simulation was to reach 2192°F (1200°C) ± 122°F (50°C). To check both systems, the user has to create set up for both of them, set physical parameters (material properties, frequency, current, etc.), and start the simulation.
After the simulation is done, the user will have access to different output variables, including:
Temperature distribution
Current density and Joule heat distribution
Magnetic field lines
Total, reactive and apparent power
Inductance of the coil
Coil current, voltage
In our example of billet heating, it is possible to compare both cases and the output.
It is observable how a three-stage system can decrease power consumption and increase the production rate for this specific case. It is also possible to plot the distribution of temperature, Joule heat, magnetic field, etc. Resulting temperature distribution in the billet across the radius is shown in Figure 1. As can be seen, better temperature homogeneity is obtained in the three-stage system.
Figure 1. Temperature distribution along the billet radius at the outlet of the heating system
Figure 2. Temperature distribution in the long billet during scanning (progressive) induction heating.
Figure 2 shows how different systems lead to different temperature distribution. In the two-stage system, the temperature required for forging is reached with shorter coils, thus also with smaller scanning speed. This leads to worsened temperature uniformity and smaller production rates. On the other hand, the three-stage system heater gradually increases the temperature of the billet and the resulting temperature difference between core and surface is smaller.
Platform users are free to change all the input parameters and assemble the system of any number of stages required for their process.
Should the same system need to be used for scanning of shorter billets where end effects play a more significant role, it is possible to set up a simulation with a moving billet. An example of temperature dynamics in such simulation are shown in GIF images below:
A simulation with a moving billet in a two-stage system.
A simulation with a moving billet in a three-stage system.
Simulation helps make better decisions for production set-up and planning
As demonstrated in the simulation example, it is possible to compare two different systems and get results. The scope and variety of different simulations are unlimited; it all depends on what problem the user wants to solve:
Dr. Vadims Geza
Heating system design—to optimize induction heating performance, improve product quality, and avoid unpleasant surprises related to subsurface overheating
The selection of power, frequency, and coil length in induction billet heating applications
The selection of right forging temperatures for plain carbon and alloy steels to avoid possible damage by incipient melting or overheating.
Main Photo Image via CENOS, courtesy of efd-induction.com
This article continues the ongoing discussion on Equipment Selection for Induction Hardening by Dr. Valery Rudnev, FASM, IFHTSE Fellow. Six previous installments in Dr. Rudnev’s series on equipment selection addressed selected aspects of scan hardening and continuous/progressive hardening systems. This post is the second in a discussion on equipment selection for one of four popular induction hardening techniques focusing on single-shot hardening systems.
The first part on equipment selection for single-shot hardening is here; the third part is here. To see the earlier articles in the Induction Hardening series at Heat TreatToday as well as other news about Dr. Rudnev, click here.
Traditional Designs of Single-Shot Inductors
Figure 1 shows a typical shaft-like component (Figure 1,top-left) suitable for a single-shot hardening inductor, as well as a variety of traditionally designed single-shot inductors for surface hardening shaft-like workpieces. Sometimes, these inductors are also referred to as channel inductors.
A conventional single-shot inductor consists of two legs and two crossover segments, also known as bridges, “horseshoes,” or half-loops [1]. The induced eddy currents under the legs primarily flow along the length of the part (longitudinally/axially) with the exception of the regions of the workpiece located under the crossover segments where the flow of the eddy current is half circumferential. Unlike scanning inductors, traditional designs of single-shot inductors can be quite complicated.
Figure 1. A typical shaft-like component (top-left image) suitable for a single-shot hardening and a variety of traditionally designed single-shot inductors for surface hardening shaft-like workpieces (Courtesy of Inductoheat Inc., an Inductotherm Group company)
With a predominantly longitudinal eddy current flow, the heat uniformity in the diameter change areas of the stepped shafts is dramatically improved and the tendency of corners and shoulders to be overheated is reduced significantly compared to applying a single-turn or multi-turn solenoid coils commonly used in scan hardening and continuous/progressive hardening.
Because the copper of single-shot inductors does not completely encircle the entire region required to be heated, rotation must be used to create a sufficiently uniform austenitized surface layer along the workpiece perimeter. Upon quenching, a sufficiently uniform hardness case depth along the circumference of the part will be produced. For single-shot inductors, the rotation speed usually ranges from 120 to 500 rpm.
Different types of magnetic flux concentrators (also called flux intensifiers, flux controllers, flux diverters, magnetic shunts, etc.) complement the copper profiling of an inductor, helping to achieve the required hardness pattern. Flux concentrators may provide several considerable benefits when applied in single-shot inductors. This includes an increase of coil electrical efficiency, a noticeable reduction of coil current, and a significant reduction of the external magnetic field exposure.
As an example, Figure 2 shows a transverse cross-section of a single-shot inductor and a straight shaft. Computer-modeled electromagnetic field distribution of a bare inductor (Figure 2, left) compared to an inductor with a U-shaped flux concentrator (Figure 2, right) is shown. Note that the magnitude of magnetic field intensity on both images is different. The use of U-shaped magnetic flux concentrators in single-shot hardening applications typically results in a 16% to 27% coil current reduction compared to using a bare inductor while having a similar heating effect. A reduction of the external magnetic field exposure while applying flux concentrator is even more dramatic (Figure 2, right).
Figure 2. Computer-modeled EMF distribution in the transverse cross-section of a bare inductor (left) compared to an inductor with U-shaped flux concentrator (right). Note: the scale of magnetic field intensity on both images is different [1].Different applications may call for various materials used to fabricate magnetic flux concentrators including stacks of silicon-steel laminations, pure ferrites, and various proprietary multiphase composites. The selection of a particular material depends on a number of factors, including the following [1]:
applied frequency, power density, and duty cycle;
operating temperature and ability to be cooled;
geometries of workpiece and inductor;
machinability, formability, structural homogeneity, and integrity;
an ability to withstand an aggressive working environment resisting chemical attack by quenchants and corrosion;
brittleness, density, and ability to withstand occasional impact force;
ease of installation and removal, available space for installation, and so on.
It should be noted that, though in most single-shot hardening applications flux concentrators will improve efficiency, there are other cases where no improvement will be recorded, or efficiency may even drop. A detailed discussion regarding the subtleties of using magnetic flux concentrators is provided in [See References 1, 2.].
Sufficient rotation is critical when using any single-shot inductor design. As an example, Figure 3 shows the sketch of a single-shot induction hardening system.
Figure 3. Sketch of single-shot induction hardening of an axle shaft. Note: The right half of this induction system is computer-modeled in Fig. 4 [3].Taking advantage of symmetry, only the right side of such a system was modeled using finite-element analysis. Figure 4 shows the result of computer simulation of initial, interim, and final heating stages, taking into consideration the shaft rotation. Insufficient part rotation resulted in a non-uniform temperature distribution along the shaft perimeter (Figure 4, left). Proper shaft rotation results in a sufficiently uniform temperature pattern (Figure 4, right).
Figure 4. Results of numerical simulation of heating an axle shaft by using a single-shot inductor [3].There should be at least eight full rotations per heat cycle (preferably more than 12 rotations), depending on the size of the workpiece and the design specifics of the inductor, though, as always in life, there are some exceptions. Shorter heating times and narrower coil copper heating faces require faster rotation during the austenitization cycle.
An appropriate inductor design with a closely controlled and monitored rotation speed will produce a hardness pattern with minimum circumferential and longitudinal temperature deviations, which will result in sufficiently uniform hardness patterns (Figure 5, left four images). Failure to ensure proper rotation as well as the use of worn centers (lacking grabbing force resulting in slippage and excessive part wobbling) could lead to an unacceptable heat non-uniformity, severe local overheating, and even melting (Figure 5, right). Manufacturers of induction equipment such as Inductoheat have developed various proprietary tools, holders, fixtures, and monitoring devices to ensure proper rotation and high quality of single-shot hardened parts.
Figure 5. Inductor design with closely controlled rotation speed will produce a hardness pattern with minimum circumferential temperature deviations (left four images). Failure to ensure proper rotation speed as well as the use of worn centers (lacking grabbing force resulting in slippage) could lead to unacceptable heat non-uniformity and can even cause a localized melting (right image).
The next installment of this column, "Dr. Valery Rudnev on . . . ", will continue the discussion of design features of induction single-shot hardening systems.
Induction heat treaters know that proper coil design is crucial to increasing longevity, improving production quality, and cutting costs. Among the topics addressed in this paper about induction heat treat coil design and fabrication (presented by R. Goldstein, W. Stuehr, and M. Blackby at ASM International) are these:
The design and fabrication of induction heating coils over the years
The Variable of Flow and the Influence of Frequency
Control and Presentation
Structure, Quenching, and Cooling
The paper closes out with a case study using computer simulation to show typical temperature distributions in a single-shot induction hardening coil.
A good place to start whenever preparing parts for induction heat treating is the consideration of inductor design. The authors provide this list (an excerpt):
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Considerations for Inductor Design
Induction heat treating coils are available in many shapes and sizes and must perform a variety of tasks in a given induction heat treating application. Depending on the application, the induction coil design requirements include:
Meet heat treatment specifications in desired production rates
Be robust enough to tolerate manufacturing variations
Mount into the induction machine
Have electrical parameters that match the induction power supply
Deliver quench
Have a satisfactory lifetime
Have satisfactory efficiency
Be repeatable from inductor to inductor
In developing a new induction heat treating coil and process, the first question is whether the component will be produced on an existing system or if a new machine must be built. In many cases, the part producer’s desire is to develop new tooling for an existing machine with spare capacity. This reduces the degree of freedom and can make the induction coil design procedure more complicated because a less-than-optimal frequency or coil style will be necessitated to fit the existing machine (Ref 16).
To determine the ability to use existing equipment, it is necessary to make an analysis of the part to be heat treated. Part material, prior processing, geometry, production rate, and heat treatment specifications all play roles. The part material and prior processing determine what the minimum heat treatment temperature should be, along with how much time is allowed for cooling. The part geometry and heat treatment specifications indicate how much energy is required, what the preferred frequency ranges are, and what type of induction method (i.e., single shot, scanning) is best suited for the application. Finally, the production rate determines how much power and/or how many spindles or stations are required.
This article continues the ongoing discussion on Equipment Selection for Induction Hardening by Dr. Valery Rudnev, FASM, IFHTSE Fellow. Six previous installments in Dr. Rudnev’s series on equipment selection addressed selected aspects of scan hardening and continuous/progressive hardening systems. This post continues a discussion on equipment selection for induction hardening focusing on single-shot hardening systems.
The first part on equipment selection for continuous and progressive hardening is here. The second part in this series on equipment selection for single-shot hardening is here; the third part is here. To see the earlier articles in the Induction Hardening series at Heat TreatTodayas well as other news about Dr. Rudnev, click here. This installment continues a discussion on equipment selection for continuous and progressive hardening applications.
Why Single-Shot Hardening?
With the single-shot method, neither the workpiece (cylinder shaft, for example) nor the coil moves linearly relative to each other; the part typically rotates instead.¹ The entire region that is to be hardened is heated all at once rather than only a short distance, as is done with scan hardening.
With conventional scan hardening of cylindrical parts, induced eddy currents flow circumferentially. In contrast, a single-shot inductor induces eddy currents that primarily flow along the length of the part. An exception to this rule would be the half-moon regions (also called the crossover or bridge sections) of a single-shot inductor, where eddy current flow is circumferential.
Normally the single-shot method is better suited for hardening stepped parts where a relatively short (1.5–2 in. [38–50mm] long heated area is commonly minimum) or moderate length area is to be heat treated. This method is also better suited to cylindrical parts having axial symmetry and complex geometry including various diameters.
When scanning these types of parts, improper austenitization of certain areas may occur due to localized electromagnetic field distortion, for example. Insufficient quenching due to the deflection of quench flow not allowing it to properly impinge on the surface in various diameter regions may also occur. Both factors are considered undesirable and can cause low hardness, spotted hardness, or even cracking. For example, the use of scan hardening on stepped shafts with large shoulders, multiple and sizable diameter changes, and other geometrical irregularities and discontinuities (including fillets, flanges, undercuts, grooves, etc.) may produce severely non-uniform hardened patterns. In cases like this, a scan hardening inductor or progressive/continuous hardening system would be designed around the largest diameter that would have sufficient clearance for safe part processing.¹ However, variations in the shaft’s diameter, to a significant extent, will result in a corresponding substantial deviation in the workpiece-to-coil coupling in different sections of the shaft, potentially causing irregular austenization.
Besides that, sharp corners have a distinct tendency to overheat owing to the buildup of eddy currents, in particular when medium and high frequencies are used. The electromagnetic end and edge effects may also cause the shoulders to severely overheat while the smaller-diameter area near the shoulder (including undercuts and fillets) may have noticeable heat deficit. These factors may produce a hardness pattern that might grossly exceed the required minimum and maximum case depth range, making it unacceptable. Single-shot hardening is usually a better choice in such applications. As an example, Figure 1 shows some examples of components for which single-shot hardening would be a preferable method of heat treating.
Examples of components for which a single-shot hardening would be a preferable method of heat treating. (Courtesy of Inductoheat Inc., an Inductotherm Group company)
In some not so frequent cases, when hardening larger parts, there are advantages to the single-shot method over the scanning method, such as the reduction of shape/size distortion, enhanced metallurgical quality, and increased production rate.
Single-shot hardening may also be the preferred choice when shorter heat times/high production rates are desired. For example, in some applications, the time of heating for single-shot hardening can be as short as 2 s, though 4 to 8 s is more typical.
However, the single-shot method has some limitations as well. One of them is cost. Single-shot inductors are typically more expensive to fabricate compared to the coils used for scanning. This is because the single-shot inductor, to some degree, must follow the contour of the entire region required to be heated. Additionally, a single-shot inductor is usually able to harden only one specific part configuration, whereas a coil used for scanning may be able to harden a family of parts.
Besides that, in some case hardening applications using a scanning method, it is possible to apply certain pre-programmed pressure/force on a workpiece during heat treating. This allows distortion to be controlled. Single-shot hardening might also permit applying this technique but there might be some limitations.
Design Features of Single-Shot Inductors
Single-shot inductors are made of tubing, either 3-D printed or CNC-machined from solid copper to conform to the area of the part to be heated. This type of inductor requires the most care in fabrication because it usually has an intricate design and operates at high power densities, and the workpiece’s positioning is critical with respect to the coil copper profiling. Figure 2 shows several examples of induction heating of different components using single-shot inductors.
Several examples of induction heating of different components using single-shot inductors. (Courtesy of Inductoheat Inc., an Inductotherm Group company)
In order to provide the required temperature distribution before quenching, heat is sometimes applied in several short bursts (pulse heating) with a timed delay/soaking between them to allow for thermal conduction toward the areas that might be difficult to heat.
Single-shot inductors typically require higher power levels than used in scan hardening because the entire area of the workpiece that needs to be hardened is austenitized at once. This is the reason why single-shot hardening normally requires having a noticeably larger power supply compared to scan hardening, resulting in increased capital cost of power source. Additionally, the increased power usage and power densities combined with complex geometry can reduce the life of the inductor. For this reason, single-shot inductors often have shorter lives than scan inductors.
It is always important to keep in mind that, electrically speaking, the inductor is typically considered the weakest link in an induction system. For this reason, most single-shot inductors have separate coil-cooling and part-quenching circuits. The inductor will fail if power is increased to the point at which the water cannot adequately cool it. Additional cooling passages may be needed with high-power density, single-shot inductors. A high-pressure booster pump is also frequently required.
The next several installments of Dr. Valery Rudnev on . . . will continue the discussion on design features of single-shot inductors and equipment selection.
The parent company of a U.S.-based induction heating equipment manufacturer was selected to supply an induction heating system to an international fan manufacturer, replacing their aging heating system with a UNI HEAT system.
Elektror, headquartered in Ostfildern, Germany, purchased the induction heating system from EMAG eldec, the parent company of eldec LLC, a heating equipment supplier in Auburn Hills, Michigan. Elektror has two production sites in Waghäusel, Germany, and Chorzów, Poland, and creates industrial fans and side channel compressors. The Waghäusel site, which manufactures nearly 250 devices a day, purchased the UNI HEAT from EMAG eldec in hopes of achieving precise induction heating of motors for their fans.
Induction heating is used to manufacture the electric motors that drive Elektror’s fans and side channel compressors by combining the empty stator housing and the motor winding. To achieve this, the housing is first heated to a temperature of 280 to 300 degrees Celsius. This causes it to expand and allows for the motor winding to be inserted. Once they have cooled down, both components establish a form-fitting and solid bond. Although Elektror used the joining process previously, their former induction heating system was in need of improvement. For instance, it did not indicate the component’s actual temperature after heating, which led to extended throughput times when joining the empty stator housing and the motor winding. The company hoped to improve this process and make it more reliable.
Roland Sand, head of the production team at Elektror, found Emag Eldec with an Internet search for potential suppliers that would have the required expertise and proximity to Waghäusel to deliver timely service. His company then visited the EMAG eldec site in Dornstetten and discussed the project. “In the end,” he said, “it was EMAG eldec’s extensive experience with induction turn-key solutions that convinced us.”
Roland Sand (2nd from left) with colleagues at Elektror and a representative from EMAG eldec (Source: EMAG eldec).
The two companies collaborated on subsequent development of the UNI HEAT system. They worked out details regarding the control unit, safety, and the design of the new comprehensive solution, including a modified induction heating process. To ensure precise heating results, they set an induction rod to plunge into the hollow component rather than using a ring inductor, which enclosed the component from outside.
They implemented several steps to develop process reliability. First, the operator places the empty housing in the custom-fit workpiece carrier and pushes it inside the UNI HEAT. As soon as he closes the front door, the first mechanical processes are initiated in the machine; the component is lifted and encompasses the inductor when it reaches its processing position. The actual induction heating then only lasts 30 to 120 seconds depending on the size of the housing. When complete, a warning light signals to the operator that the component can be removed. The actual component temperature is continuously shown on the operator panel.
The operator then places the hot housing on a mold, which is ready at the cooling location. He pushes the motor winding from the top into the housing. The component is cool in approximately two minutes and then placed on a conveyor belt.
The machine undergoes many retooling processes, because Elektror produces a variety of motor sizes, and sometimes the batches change several times a day. The process is brief; the operator loosens two screws on the inductor mount, removes the inductor and attaches one of six different inductors for the various empty housings. The workpiece carrier is simply set down and can be changed easily in a few seconds. The program on the operator panel can be set in just a few clicks, which completes the process.
Dr. Mihails Scepanskis is the CEO and co-founder of CENOS LLC.
Induction heating is an efficient way to quickly heat electrically conductive metals with pinpoint accuracy. It starts very simply, with a coil of conductive material, however initial design and optimization of the process are very complicated—it's hard to predict power, frequency, and heating time to get necessary results.
Computer simulation for induction heating is a powerful tool that enables engineers to investigate or design a physical system and process using a virtual mathematical model, thus saving time and money on numerous physical design iterations.
Dr. Vadims Geza is the chief scientist at CENOS.
Induction heating computer simulation offers the most efficient means of developing customized and optimized solutions and is, therefore, a necessity—not a luxury—in the modern induction heating industry. In this article, Dr. Mihails Scepanskis and Dr. Vadims Geza, both of CENOS LLC, based in Riga, Latvia, list features and benefits, obstacles and solutions of induction heating; advantages and disadvantages of computer simulation vs physical testing; what should be taken into account when choosing the right simulation software.
How simulation software can help companies save time and money on induction coil and process design
About Induction Heating
Today induction heating is used in many industrial processes, such as heat treatment in metallurgy, crystal growth and zone refining used in the semiconductor industry, and to melt metals which require very high temperatures.
Where Is Induction Heating Used?
Automotive
Construction
Aerospace
Metallurgical Plants
Oil & Gas Component Manufacturing
Special Applications
NASA's experimental NTP fuel elements heated with induction (Photo: CENOS)
Features:
Heat generation occurs inside the part.
Heating is contactless—as a result, product warpage, distortion and reject rates are minimized.
This method can provide very high power densities.
Heating may be highly selective in the depth and along the surface.
Any processing atmosphere (air, protective gas, vacuum) can be applied.
Very high temperatures may be reached.
The general benefits of induction surface heat treatment are
Short heating times—production rates can be maximized.
Optimized consistency—induction heating eliminates the inconsistencies and quality issues associated with open flame, torch heating, and other methods.
Extended fixture life—induction heating delivers heat to very small areas of your part without heating any surrounding parts. This extends the life of the fixturing and mechanical setup.
Environmentally sound without burning fossil fuels—induction is a clean, non-polluting process. Improves working conditions for employees by eliminating smoke, waste heat, noxious emissions, and loud noise.
Effective energy consumption—this uniquely energy-efficient process converts up to 90% of the energy expended energy into useful heat; batch furnaces are generally only 45% energy-efficient. Requires no warm-up or cool-down cycle.
Flexible adaptation to the hardening tasks
Closed loop computerized process control and compatibility with overall process automation
Large gear heat treatment (Photo: CENOS)
Obstacles:
Initial design and optimization of the process is very complicated.
It is hard to predict power, frequency and heating time to get necessary results.
Unlike other heating methods, induction heating requires specific coil design for each workpiece, so it's not very economic unless you need to process multiple similar workpieces.
To design and calculate the induction heating process you can:
Do a rough analytical estimation, then proceed with countless design iterations in the lab.
Find a professional company that can do induction coil and process design for you, but keep in mind that you most likely will be charged for design hours spent in the lab.
Buy a sophisticated multi-physics simulation software and hire a trained simulation engineer/analyst or pay for engineer's training (usually takes 3 months).
Start using a simple, affordable, and induction heating-focused simulation software like CENOS Platform, which features online training and templates for a quick and easy start.
Induction Heating and Computer Simulation
What Is a Computer Simulation?
Nowadays, in various industries, manufacturers prefer using software simulations over physical testing. Computer simulation is a powerful tool that enables engineers and scientists to investigate or design a physical system and/or process using a virtual mathematical model, thus saving time and money on numerous physical design iterations.
The vast majority of modern computer simulation software packages utilize numerical methods (e.g. finite element method or “FEM”) to evaluate extremely complex physical systems—systems that are otherwise impossible to precisely analyze. By leveraging the power of modern computer hardware, simulation software can provide substantial improvements in the efficiency, reliability, and cost-effectiveness in design and development processes.
Computer Simulation in Induction Industry
First works on computer simulation of induction coils were made in the 1960s. Due to limited access to computers, their low memory, speed, and poor programming methods, the computer simulation did not receive significant industrial application until the 1980s.
Now computer simulation has become a practical tool for everyday use in the induction industry. It allows the user to design optimal systems, improve equipment performance, dramatically reduce development time and costs, and better understand the process dynamics, etc.
Though there are still difficulties in an accurate simulation of non-linear and different mutually coupled tasks, computer simulation is effectively used for the design of induction heating coils and problem solution.
The 10 cm gear hardening with one concentric inductor at 170 kHz and 1.9 kA over 120 ms
Benefits and Value of Induction Heating Computer Simulation
The use of induction heating computer simulation software can promote substantial improvements in the performance and cost-effectiveness of induction heating equipment, in addition to large reductions in the cost and time required to design and develop induction heating processes.
From a design perspective, computer simulation is valuable for a number of reasons, two of the most notable being:
The physics involved in utilizing electromagnetic induction as a deliberate and controlled source of heat generation is extensive and multi-faceted. Computer simulation provides a quantitative approach to designing and developing induction heating processes, allowing complex physical phenomena that cannot be physically observed and/or measured to be clearly visualized and quantified.
Because electromagnetic induction offers an extremely effective, economical, and versatile means of heating conductive materials, the scope of induction heating applications is very broad. This includes (but is not limited to):
Furthermore, each of these general applications includes countless different workpiece types, geometries, materials, and heating requirements. As a result, no “universal solution” exists in the design of induction heating equipment. Induction heating computer simulation offers the most efficient means of developing customized and optimized solutions and is, therefore, a necessity—not a luxury—in the modern induction heating industry.
Combining Simulation With Real World Tests for the Best Results
Example of simulation results (Photo: CENOS)
Inductor design is one of the most important aspects of the overall induction heating system. A well-designed inductor provides the proper heating pattern for your part and maximizes the efficiency of the power supply, while still allowing easy insertion and removal of the part. With the right design, it's possible to heat conductive materials of any size and form, or only the portion of material required.
Computer Simulation vs Experimental Method
Computer Simulation
Advantages
Can work for any geometry and operating conditions
Demonstrates the entire dynamics of the process
Leaves records for future
Limitless accuracy of calculations
Does not require special equipment
Less expensive and less time-consuming
Future improvements expected
Provides 3D process visualization for customers (pictures, video)
Limits and Disadvantages
Requires special software and databases
Not all the processes may be simulated (as of today)
Does not provide physical samples
Experimental Method
Advantages
May provide the most reliable results
Can show the performance of the whole system including unexpected effects and troubles
Does not require a material property database
Provides physical samples for properties validation
Limits and Disadvantages
May require expensive equipment
Does not provide a good understanding of the process
Difficult to transfer knowledge (to scale a company)
Case dependent accuracy
Limited access to production equipment (expensive)
Time-consuming—may cause production delay due to multiple design iterations.
Challenges in coil design
The induction coil, also known as an "inductor", is essential to induction heating. Single-turn, flexible, multi-turn cylindrical, left-turn, right-turn, rod-shaped, hair-pin, parallel, ear-shaped, tiny, big—whatever the coil shape and size—the right design maximizes the lifetime of the coil and ensures lowest energy consumption and best effects on work process and materials.
Many factors contribute to a coil’s effectiveness: the care taken to make it, the quality of the materials used, its shape, its maintenance, its correct matching with the power source, etc.
Here are just three of the many hurdles to be overcome in order to make safe and efficient coils:
Impedance matching
It is necessary to achieve the correct impedance matching between the coil and the power source in order to use the latter’s full power. The coil designer must also consider that coils need five to ten times as much reactive as active power.
Magnetic flux concentrators
Concentrators focus the current in the coil area facing the workpiece. Without concentrators, much of the magnetic flux may propagate around the coil. This flux could engulf adjacent conductive components. But when concentrated, the flux is restricted to precise areas of the workpiece.
Water flow and speed
It is generally important to achieve an adequate flow of cooling water through the coil. When high power density is expected in the inductor, the coil designer must consider the flow rate and the water’s velocity. This is because velocity significantly influences the heat transfer between inductor and coolant and therefore has a major impact on the longevity of the coil. A booster pump is sometimes needed to maintain the desired flow and velocity. Professional designers will also specify a purity level for the water in order to minimize coil corrosion.
Tools and Processes Necessary To Ensure Coil Longevity and Performance
Advanced induction coil design includes:
Detailed analysis of specifications, available equipment, and environment
Coil style and heating process selection (scanning, single-shot, static, etc.)
3D design programs and computer simulation for coil head optimization
Analysis of benefits of magnetic flux controllers application
Advanced manufacturing techniques, mandrels to achieve tight tolerances
Testing in a laboratory or industrial plant for performance and final dimensional check
Final corrections if required
Designing and making induction coils is technically challenging. Computer simulation helps tackle some of the challenges, limiting costs and maximizing effectiveness.
CENOS Platform's mission is to help companies switch from old and cumbersome experimental methods to a powerful computer simulation that is simple, affordable, and induction heating-focused. CENOS, combined with real-world trials, will yield the best results in a fast and cost-effective way.
How To Choose the Right Simulation Software
The induction heating market is small compared to other industrial sectors, and there are only a few specialized simulation packages on the market that can be used for induction process and coil design. Induction heating simulation involves a set of mutually coupled non-linear phenomena. Many induction applications are unique and may require different program modules. In addition to computer simulation software, an extensive material database is necessary for accurate results.
1D, 2D or 3D?
Majority of practical simulations now are being made in 1D or 2D approaches. But with 1D and 2D, the structure and geometry of real induction systems are often very simplified. In reality, a majority of induction systems are 3D. In addition, interference of induction device and source of power must be considered in many cases. That's why 3D will ensure less space for errors and a more thorough analysis.
Cloud vs Desktop
Working with cloud-based software requires uploading your data to the third party. Frequently induction heating equipment manufacturers are not allowed to share their customer CAD files with a third party due to NDA. Furthermore, while cloud computing may provide increased calculation speed, one should consider the time it takes for uploading the design files and downloading the result files.
Importance of training & support (time, costs)
There is a common opinion that simulation software requires a specially educated (and well paid) simulation engineer/analyst, usually hired only for one kind of task—simulation. This is definitely true for sophisticated multi-physics simulation packages, which might require 3 to 4 months of intense training because of a plethora of numerical aspects which should be taken into account in order to get reliable results in a simulation. However, CENOS 3D desktop software keeps focus solely on induction heating and tries to avoid any unnecessary functionality which might confuse an inexperienced user. By using CENOS-dedicated templates, a beginner can run his first induction simulation in just under 30 minutes and become a pro user with any 3D geometry after 2 weeks of training, guided by CENOS engineers.
Cost
Licensing software can cost $20,000 to $80,000 up front plus additional annual payments in 20% value of purchase price just for support and updates. And that's only for an induction heating module, whereas CENOS's annual license is $7,200 and requires no upfront investment. Alternatively, one could consider a “pay as you go” purchase model, paid by hours, but one must keep in mind that 3D calculations take time, which might make this particular subscription model cost inefficient.
Open Source software—a free alternative with some drawbacks
Open source is very cost efficient—open source tools like Elmer or GetDP are free to use. However, these tools might require a long training period (6 to 10 months); plus extra steps and routines required for everyday simulation will take up to 1,000 additional hours a year. Overall, open source tools are a solid choice because they are validated by the community but not focused on user experience.
Benefits:
Community. Open source solutions often have thriving communities around them, bound by a common drive to support and improve a solution and introduce new concepts and capabilities faster, better, and more effectively than internal teams working on proprietary solutions.
The power of the crowd. The collective power of a community of talented individuals working in concert delivers not only more ideas but quicker development and troubleshooting when issues arise.
Transparency. Open source code means just that—you get full visibility into the code base, as well as all discussions about how the community develops features and addresses bugs.
Reliability. Because there are more eyes on it, the reliability of open source code tends to be superior as well. Code is developed on online forums and guided by experts. The output tends to be extremely robust, tried, and tested. In fact, open source code now powers about 90% of the internet and is being rapidly adopted across major enterprises for this reason.
Better security. As with reliability, open source software's code is often more secure because it is much more thoroughly reviewed and vetted by the community.
Drawbacks:
Because there is no requirement to create a commercial product that will sell and generate money, open source software can tend to evolve more in line with developers’ wishes than the needs of the end user. For the same reason, they can be less “user-friendly” and not as easy to use because less attention is paid to developing the user interface.
There may also be less support available for when things go wrong – open source software tends to rely on its community of users to respond to and fix problems.
Because of the way it has been developed, open source software can require more technical know-how than commercial proprietary systems, so you may need to put twice as much time and effort into training employees to the level required to use it.
Many different open source solutions are not compatible with each other. Take for example GetDP - an open source finite element solver, its core algorithm library uses its native pre-processing and post-processing tool Gmsh, which frankly, compared to other solutions, is not the best in its class.
CENOS Makes Open Source User-Friendly and Easy To Use
CENOS Platform uses GetDP solver and offers integration with far more superior open source tools like SALOME for pre-processing and Paraview for post-processing, which by default are not compatible with GetDP.
“CENOS” stands for “Connecting ENgineering Open Source”, highlighting its new software approach: connecting the best of open source tools in one seamless user experience. CENOS platform technology enables affordable simulation available for small to midsize companies by connecting third-party open source algorithms GetDP, Salome, and Paraview, developed by strong academic communities involving world top research centers and universities like Sandia National Lab, Imperial College, KU Leuven, and others. The academic world has already built plenty of smart algorithms; there is no need to charge money for the scientific heritage. Use of free open source algorithms makes it possible for CENOS to be affordable for everyone.
The company has built a user-friendly interaction layer and interconnection between previously incompatible separate open source software algorithms. CENOS Platform consists of a user interface, special data optimization procedures including necessary data reformatting for inter-operational compliance ensuring data flow and control between different open source tools. This way CENOS lets engineers save up to 80% of design time by replacing physical prototyping with powerful simulation software which is affordable and easy to use.
About the Authors: Dr. Mihails Scepanskis is the CEO and co-founder of CENOS LLC, based in Riga, Latvia. Dr. Vadims Geza is the chief scientist at CENOS.
This article continues the ongoing discussion on Equipment Selection for Induction Hardening by Dr. Valery Rudnev, FASM, IFHTSE Fellow. Previously, Dr. Rudnev reviewed equipment selection for scan hardening in three parts. This first installment in a new sub-series addresses equipment selection for continuous and progressive hardening. The second part in this series on equipment selection for continuous and progressive hardening is here; the third part is here. To see the earlier articles in the Induction Hardening series at Heat Treat Today as well as other news about Dr. Rudnev, click here.
Introduction
The hardening of steels, cast irons, and P/M materials represent the most popular application of induction heat treatment. There are four primary methods for induction hardening [1]:
Scan hardening,
Continuous and progressive hardening,
Static hardening, and
Single-shot hardening.
These methods are related to the heating mode, essentials of inductor design, part geometry, and processing specifics. The previous three installments of this column, “Dr. Valery Rudnev on …”, discussed select subtleties associated with induction scan hardening. This article is devoted to continuous and progressive induction hardening techniques.
Continuous and Progressive Hardening
This method is commonly applied when heat treating elongated workpieces, such as bars, tubes, rods, wires, plates, beams, pins, and others. Long parts are more readily processed in a horizontal manner and heated as they progressively pass through multiple inductors. Inductors are positioned in-line or side by side. Each inductor may have a different design and power/frequency setting. This type of hardening is not limited to horizontally processed parts; vertical processing and arrangements at certain angles are also possible, if suitable.
There are also cases when a workpiece is statically heated to a certain temperature and then progressively moved to another heating position or static inductor for the next heating stage. These processes are referred to as progressive processing/heat treatment.
Induction practitioners sometimes consider continuous or progressive horizontal hardening systems as horizontal scanners. The difference is vague and it is a matter of terminology. Some heat treaters feel that it would be appropriate to differentiate these systems based on the number of inductors included in the induction machine design. Horizontal systems consisting of a single inductor are commonly referred to as horizontal scanners. In contrast, if a system consists of two or more heat treat inductors, then it might be referred to as a continuous or progressive heat treat system.
With the continuous hardening method, the workpiece is moved in continuous motion through a number of in-line inductors. Multiturn solenoid coils and, to lesser a degree, channel-style inductors and split-return inductors are most typically used in continuous heat treating lines. As an example, Figure 1 shows a side view of a horizontally arranged continuous induction system consisting of three in-line coils. Each coil consists of three turns.
Figure 1
As another example, Figure 2 shows a top view of a continuous heat treating line that comprises four in-line hardening coils and a spray quench device positioned after the last inductor. Workpieces (e.g., bars, shafts, rods, pins, etc.) are processed end-to-end through the inductors in a continuous motion.
Figure 2
Progressive multi-stage hardening is used when multiple workpieces are moved (via a pusher, indexing mechanism, robot, walking beam, etc.) through a number of coils. Therefore, the entire component or its portions are sequentially heated (in a progressive manner) at certain predetermined heating stages inside the in-line horizontal (being more typical) induction heater or a multi-position horizontal or vertical heater where coils are positioned side by side.
Continuous or progressive hardening methods are typically used for through hardening of elongated or moderate-length parts processing end to end and, to a lesser degree, for surface hardening. Outside diameters for case hardening (surface hardening) usually vary from 1/2 in. (12 mm) to 4 in. (100 mm). In through hardening applications of solid cylinders, the diameters may be as small as 1/8 in. (3 mm).
It is possible to recognize three heating stages in through hardening applications [1]:
Initial or magnetic stage,
Interim stage, and
Final heating stage.
Initial or magnetic stage. Temperatures anywhere within the workpiece are below the A2 critical temperature (Curie point); thus, the steel is ferromagnetic and the current penetration depth is typically quite small. Skin effect is fairly pronounced at this stage and the heat source distribution resembles a conventional exponential distribution. The maximum power density is located at the surface and sharply decreases toward subsurface and the core. Heat source generation is localized by the fine surface layer of the workpiece. This leads to a rapid increase in temperature at the surface with a minor change in the core. This stage is characterized by high electrical efficiency often reaching 90% or so.
Interim stage. During this stage, the austenized surface layer and near-surface area is heated above the A2 critical temperature; however, the internal region, having temperatures below the Curie point, retains its ferromagnetic properties. At this stage, the power density distribution along the radius has a unique non-exponential “wave-like” distribution, which is very different from the commonly assumed exponential distribution. The cause for this behavior has been explained in Ref.1.
Final heating stage. The thickness of the austenized surface layer that exhibits nonmagnetic properties becomes greater than the current penetration depth in hot steel at a given frequency, and the “wavelike” distribution disappears. The classical exponential power density distribution will then take place. As expected, heat source generation depth has increased dramatically compared to an initial stage resulting in a more in-depth heating effect. With time, the core temperature exceeds the Curie point and the entire cross section will be nonmagnetic.
In surface hardening applications, there are typically only the first two heating stages.
Depending on the application specifics, the same frequency may be used for various coils or process stages. In other cases, power levels and frequencies may vary at the different heating stages. The presence of above-described process stages makes a marked impact on a selection of process parameters and design of an induction system and will be discussed in the next installment of this column.
References
1. V. Rudnev, D. Loveless, R. Cook, Handbook of Induction Heating, 2nd Edition, CRC Press, 2017.
Dr. Valery Rudnev, FASM, IFHTSE Fellow, is the Director of Science & Technology, Inductoheat Inc., and a co-author of Handbook of Induction Heating (2nd ed.), along with Don Loveless and Raymond L. Cook. The Handbook of Induction Heating, 2nd ed., is published by CRC Press. For more information click here.
Modern rotary-wing aircraft propulsion systems rely on different types of gears to transmit power from the turbine engines to the rotors. The basic requirements of these gears are that they are high strength, sustain long life, meet weight considerations, and have a high working temperature and low noise and cost, among others.
Most importantly, these gears require a hard, wear-resistant surface with a ductile core.
Gas carburizing is the current heat treat method used to produce these aircraft quality gears, but this method of heat treatment is costly due to the large number of process steps, huge footprints, energy consumption, and environmental issues. Moreover, the final grinding of gear teeth to correct distortion produced during quenching reduces effective surface compressive stresses.
An investigation into low-cost alternatives for surface hardening aerospace spur gears was conducted where specimens of the selected gears were induction hardened using a patented process. Dimensional and microstructural analyses were conducted, and residual stress studies were performed. This article is a summary of the steps and observations of the case study that resulted from this investigation, which can be summarized this way:
The proposed induction process is a low-cost alternative to conventional gas carburization. In some applications, a 25% savings is estimated.
The first step to gear manufacturing demands a total understanding of aerospace gear requirements. As the gear transmits torque, the teeth are subjected to a combination of cyclic bending, contact stresses, and different degrees of sliding or contact behavior. It is, therefore, critical for a gear to have the proper case and core structure to withstand these loading conditions.
With every revolution, a cyclic bending load is applied, resulting in tensile stress at the root region of the gear. The core of the gear has to be soft to absorb impact load and prevent brittle failure. Due to high-speed contact between adjacent gear teeth, peak shear stresses generated at the surface act in the normal direction to the surface. Pitting, spalling, or case crushing types of failures can occur due to low residual stress or inadequate case depth.
For aircraft quality gears, typical surface hardness is around 58Rc to 60Rc. The case depth is in reference to 50Rc and is controlled by diametral pitch.
Carburization
Carburization hardening is the most widely used technique for surface hardening of aerospace quality gears. A brief introduction to carburization is necessary to understand the potential benefits of this process and how other surface transformation can improve on some of the drawbacks of this commonly used process.
After raw material is received, it is forged to achieve proper grain structure and core hardness. The alloy most commonly used is ASM 6260 (AISI 9310). This low carbon alloy steel exhibits high core toughness and ductility.
Parts are loaded in a furnace and heated to 1650ºF – 1750ºF in a carbon rich atmosphere, where approximately 1% carbon potential is maintained. The depth and level of carbon absorption depend on carbon potential, temperature, time inside the furnace, and the alloy content of the material. After the desired carbon gradient is achieved, the gears are cooled slowly. Then the parts are heated to austenitizing temperature and quenched.
The process depends on the size, geometry, dimension tolerances, and other gear requirements.
The heat treat cycles shown above are two commonly used carburization processes. The difference in post carburization steps depends on the alloy used and final product requirement.
The characteristic of carburization is the inherent distortion associated due to the difference in cooling rates between the thin web and thicker rim. Distortion can occur as a size growth, a change in involute profile, or the loss of crown in spur gears.
Case Hardening by Selective Heat Treatment
The number of process steps required to case carburize a gear can be significantly reduced only if the gear tooth surface areas are heat treated.
Processes for locally heating only the tooth surface include induction, flame, laser, and electron beam.
In order to use induction, steel with a minimum of 0.5% carbon must be used. Several different alloy steels were experimented with, such as AMS 6431, AlSl 6150, and AlSl 4350/4360/4370. These steels were selected due to their combination of toughness, temper resistance, hardenability, and strength. The hardened case is obtained by heating a specific volume of the tooth surface above the transformation temperature for that material. Rapid contour heating produced a case of martensitic structure around the profile-hardened area, resulting in high compressive residual stress at the surface at the root fillet. This compressive stress increases the tooth bending fatigue life, where tensile stress exists due to tooth bending.
Transformation hardening allows a significant reduction in process steps and associated fabrication costs, due to two different factors:
Since sufficient carbon is already present in the base material, copper masking, plating, stripping and carburization steps are eliminated.
In selective hardening, the area of the heated zone is limited to only the hardened sections, and distortion is minimal and predictable.
Surface hardening applications are generally controlled by three process parameters, namely frequency, power level, and time. In this respect, several different hardening processes have been used for gear hardening. The proposed method discussed in this presentation is known as Dual Pulse Induction Hardening (DPIH).
DPIH Process
The DPIH is a patented process (U.S. patent #4,639,279). The process uses single frequency for both the preheat and final heat cycles. Two different power levels are used. This allows the entire process to be performed in one setup, using a single solid-state power supply.
The DPIH process consists of the steps described below:
The heat treatment process steps for both the carburized and DPIH processes for the aircraft gear are compared below:
An 85% reduction in heat treat process steps occurs when the gear hardening method is changed from conventional gas carburization to DPIH.
Conclusion:
Comparison of the above data and the conventional carburization process to DPIH process.
Carburizing grade material has to be changed from low carbon to medium carbon steel for induction hardening. In both the processes, surface hardness achieved is comparable, but the characteristic of induction hardening is that the gear section maintains a constant hardness value from the surface up to the transition zone, where it rapidly drops to core hardness levels, unlike a more gradual decrease in hardness in case of carburized gears. Low distortion of induction hardening gear is also a major cost reducing factor.
Acknowledgment:
This work was performed at AGT, Division of General Motors.
Madhu Chatterjee is founder and president of AAT Metallurgical Services LLC in Michigan with extensive experience in advanced engineering, research and development, and process and product improvement. He is also one of the original dozen consultants that inaugurated Heat TreatToday’sHeat TreatConsultants resource page. You can learn more about Madhu Chatterjee here.
Look for more on aerospace heat treating in the upcoming special aerospace manufacturing edition of Heat TreatToday.
During the day-to-day operation of heat treat departments, many habits are formed and procedures followed that sometimes are done simply because that’s the way they’ve always been done. One of the great benefits of having a community of heat treaters is to challenge those habits and look at new ways of doing things. Heat TreatToday‘s 101 Heat TreatTips, tips and tricks that come from some of the industry’s foremost experts, were initially published in the FNA 2018 Special Print Edition, as a way to make the benefits of that community available to as many people as possible. This special edition is available in a digital format here.
In today’s Technical Tuesday, we continue an intermittent series of posts drawn from the 101 tips. The category for this post is Induction Heating, and today’s tips–#29, #73, and #83–are from Dr. Valery Rudnev, FASM, Fellow of IFHTSE, “Professor Induction”, Director of Science & Technology at Inductoheat Inc., an Inductotherm Group company. Dr. Rudnev is a regular contributor to Heat TreatToday.
Heat TreatTip #29
Induction Heating Non-Ferrous Metals & Alloys
Dr. Valery Rudnev, FASM, Fellow IFHTSE, Professor Induction, Director Science & Technology, Inductoheat Inc., an Inductotherm Group company
Steel components by far represent the majority of hot worked and heat-treated parts for which electromagnetic induction is used as a source of heat generation. At the same time, many other non-ferrous metals and alloys are also inductively heated for a number of commercial applications. Induction heating of low electrically resistive metals such as Al, Mg, Cu, and others typically require using lower electrical frequencies compared to carbon steels, cast irons, or high resistive non-magnetic metals (such as Ti or W, for example) and metallic alloys. The lower value of electrical resistivity results in smaller current penetration depth (depth of heat source generation), making it possible to apply much lower frequencies without facing the danger of eddy current cancellation.
Heat TreatTip #73
Induction Hardening Powder Metal
When induction hardening powder metallurgy (P/M) materials, it is good practice to have a minimum density of at least 7.0 g/cm3 (0.25 lb/in.3). This will help obtain consistent induction hardening results. When hardening surfaces that have cuts, shoulders, teeth, holes, splines, slots, sharp corners, and other geometrical discontinuities and stress risers, it is preferable to have a minimum density of 7.2 g/cm3 (0.26 lb/in.3). Low-density P/M parts are prone to cracking due to a penetration of the gases into the subsurface areas of the part through the interconnected pores. Interconnected pores contribute to decreased part strength and rigidity compared with wrought materials. In addition, the poor thermal conductivity of porous P/M parts encourages the development of localized hot spots and excessive thermal gradients and also requires the use of quenchants with intensified cooling rates to obtain the required hardness and case depths. This is so because an increase in pore fraction and a reduction in density negatively affect the hardenability of P/M materials compared to their wrought equivalents.
Heat TreatTip #83
Induction Hardening Cast Iron
Induction hardening of cast irons has many similarities with hardening of steels; at the same time, there are specific features that should be addressed. Unlike steels, different types of cast irons may have similar chemical composition but substantially different response to induction hardening. In steels, the carbon content is fixed by chemistry and, upon austenitization, cannot exceed this fixed value. In contrast, in cast irons, there is a “reserve” of carbon in the primary (eutectic) graphite particles. The presence of those graphite particles and the ability of carbon to diffuse into the matrix at temperatures of austenite phase can potentially cause the process variability, because it may produce a localized deviation in an amount of carbon dissolved in the austenitic matrix. This could affect the obtained hardness level and pattern upon quenching. Thus, among other factors, the success in induction hardening of cast irons and its repeatability is greatly affected by a potential variation of matrix carbon content in terms of prior microstructure. If, for some reason, cast iron does not respond to induction hardening in an expected way, then one of the first steps in determining the root cause for such behavior is to make sure that the cast iron has not only the proper chemical composition but matrix as well.
If you have any questions, feel free to contact the expert who submitted the Tip or contact Heat TreatToday directly. If you have a heat treat tip that you’d like to share, please send to the editor, and we’ll put it in the queue for our next Heat TreatTipsissue.
Induction heat treaters know that proper coil design is crucial to increasing longevity, improving production quality, and cutting costs. The authors of this paper on Coil Design Techniques (C. Yakey, V. Nemkov, R. Goldstein, J. Jackowski) draw on an extensive library of published case histories in induction coil design and performance evaluations and provide their own case study of an automotive CVJ stem hardening coil in order to demonstrate how the elimination of failure points and application of improved design guidelines can result in increased coil lifetimes, even in an inductor that in some circumstances can have a short lifetime.
An excerpt:
“The quality of an induction coil is a major determinant of the cost to produce induction heat treated components. Oftentimes, the difference between a well designed and manufactured inductor and a poor performing inductor is not readily apparent. However, a high-quality induction coil can lead to substantially lower component manufacturing costs and higher profitability for the induction heat treater.”
![Figure 2. Computer-modeled EMF distribution in the transverse cross-section of a bare inductor (left) compared to an inductor with U-shaped flux concentrator (right). Note: the scale of magnetic field intensity on both images is different [1].](https://www.heattreattoday.com/wp-content/uploads/2019/08/Rudnev-Part-2-Fig-2.jpg)
![Figure 3. Sketch of single-shot induction hardening of an axle shaft. Note: The right half of this induction system is computer-modeled in Fig. 4 [3].](https://www.heattreattoday.com/wp-content/uploads/2019/08/Rudnev-Part-2-Fig-3.jpg)
![Figure 4. Results of numerical simulation of heating an axle shaft by using a single-shot inductor [3].](https://www.heattreattoday.com/wp-content/uploads/2019/08/Rudnev-Part-2-Fig-4.jpg)
