Increasing Inductor Lifetime by Predicting Coil Copper Temperatures Paper

ASM International Conference, September 2007, Detroit

Increasing Inductor Lifetime by Predicting Coil Copper Temperatures

R. Goldstein, V. Nemkov Fluxtrol Inc., Auburn Hills, MI, USA

Abstract

In recent years, there has been a significant increase in the

customer demands for improved induction coil lifetime. This

has led to several publications in recent years by induction

tooling manufacturers [1-4]. The main conclusion in these

papers is that besides mechanical crashes the cause of most

induction coil failures is localized overheating of the coil

copper due to insufficient cooling.

What is lacking from these publications is any way to

determine what is sufficient cooling. In this paper, a scientific

method for determining local copper temperatures will be

presented. This will include evaluations of heat transfer

coefficients for different sections of a multi-component

inductor, dependence of heat transfer coefficient on water

pressure and water passage cross-section, non-uniform power

density distributions in various 2-D cross-sections and the

resulting temperature distribution in the copper winding. The

effects of duty cycle on optimal design will also be

considered.

This method may be incorporated into the standard coil design

and development process, which can be used to prevent costly

tooling lifetime issues during the early stages of a production

run or avoid the purchase and use of unnecessary oversized or

booster pumps. It can also be used as a basis for more

advanced future studies into temperature distributions and

stresses within the induction coil itself, which lead to failure.

Introduction

Like most industrial processes, tooling failure is a leading

cause of induction heating machine downtime. This leads to

many challenges in today’s manufacturing environment. In

most cases, this downtime is unplanned for and results in

significant costs to ensure on-time delivery of parts to a

customer.

Induction heat treating tooling failures can be broken into

three main classes:

Mechanical Damage

Thermal Degradation

Electrical Break

Electrical breaks may be caused by different factors:

insufficient insulation between the coil turns, insulation

wearing, magnetic chips attracted to the conductors etc. This

failure mode may be prevented by proper design and

maintenance of the coil [3].

Mechanical damage may be caused by inaccurate coil setup

resulting in the part impact, by incorrect machine operation,

by the electromagnetic forces and by the thermal distortion of

the coil components. These factors can damage the coil

instantaneously, breaking the coil integrity or causing water

leakage or they can change the coil dimensions gradually. For

example, coil copper may be out of specifications due to

creeping, which can result in loss of the heat pattern. In many

cases, mechanical failure is preventable with the proper

precautions and maintenance on the machine.

Failures due to thermal degradation are more challenging to

resolve. Thermal degradation is caused by local or total

overheating of the coil head due to eddy-current losses in the

copper, magnetic losses in the flux concentrator and by heat

transfer from the hot surface of the part by convection and

radiation. Overheating can result in copper cracking or

deformation as well as the concentrator material degradation.

Copper cracking happens usually in hardening coils with a

short cycle due to thermal stresses, while a gradual coil

deformation is more typical for continuous processes. Thermal

effects can strongly increase the effects of electromagnetic

forces and accelerate the electrical insulation aging.

Copper overheating is the leading cause of failure in heavy-

loaded hardening inductors and the present article is focused

mainly on this mode of failure. For consistently manufactured

inductors, copper cracks occur in nearly the same place on an

inductor each time in a certain range of parts produced. There

are several approaches to increase the coil life: provide

additional cooling, reduce the density of heat sources or

change the coil design completely.

Additional cooling is provided by either increasing the water

flow rate, by adjustment of the water pocket or introduction of

additional cooling circuits. Water flow rate is the first step

and it will be increased until the pump output limit is reached.

Inductor manufacturers generally have internal guidelines

related to best practices for water pocket and cooling circuit

design, which have been developed over the years. Once

these standard options have been exhausted, the next step is to

replace the existing pump with a larger one or introduce a

booster pump to the system.

Sometimes on very high power density coils, a limit is

reached; where even with the best cooling circuit design and

very large pumps coil lifetime is still unsatisfactory. At this

point, it is necessary to try to minimize the localized power

density in the weak point of the inductor. This is oftentimes

challenging in complex inductors, as changing this section

may have some effect on the heat pattern in this area of the

part, as well as in the rest of the part.

The response to thermal degradation failures of inductors are

based upon practical experience and in many cases will

require several iterations to resolve. There is significant cost

associated with these each of these tests (prototype coils,

additional pumps, machine downtime, test parts, met lab time,

etc.), none of which were budgeted for.

A more scientific method, which would reduce the number of

iterations and optimize equipment purchases is of great value.

Furthermore, if this method is used up front in the coil

development, it can avoid troubleshooting due to insufficient

coil lifetime occurring during the early stages of production.

Computer simulation is a natural tool for analyzing all of these

factors (fluid dynamics, heat transfer, electromagnetic,

thermal, stresses and structural transformations) that go into

inductor failure by thermal degradation. However, there is no

one program on the market with strong 3-D coupling of all of

these phenomena at this time.

At the same time, there are simulation tools and analytical

formulae available now for tackling the problem in steps. The

following sections describe such a methodology currently

being used at Fluxtrol Inc. for predicting copper temperatures.

This method is viewed as a good first approach to the problem

and a basis for further improvements with future software

improvements. A case story is shown to demonstrate

representative results.

Technical Description

The current approach used by Fluxtrol Inc. is an iterative 7

step approach:

1. Electromagnetic + Thermal simulation to

optimize part heating and coil parameters

2. Coil Engineering using CAD program

3. Analytical hydraulic calculations for the coil

cooling circuit

4. Calculation of localized heat transfer coefficients

in high power density areas of the inductor

5. Electromagnetic + Thermal simulation of coil

component heating

6. If elevated component temperatures exist, return

to step 2 to improve cooling circuit

7. If elevated component temperature exist, return

to step 1 to improve induction coil geometry

from a cooling perspective with minimal

sacrifice in part heating or coil parameters

.

Computer simulation for optimization of the induction coil

based upon the part heating and coil parameters should be

done first. If the coil designed on this criterion will have

satisfactory lifetime, it will lead to the minimum cost

production.

In the coil engineering stage, the busswork, leads and

complete inductor cooling circuit should be layed out. This is

essential for the hydraulic calculations. The water cooling

circuit can be broken down into several components. Pressure

drops in every component of the circuit along with the

additional pressure drop due to directional or flow passage

geometry change should be calculated. These numbers will

give a flow rate and localized water velocities based upon the

pump pressure.

Using the water velocities and tubing cross-sections, it is

possible to calculate Reynolds, Prandtl and Nusselt numbers

for all of the different heating areas of the inductor. Heat

transfer coefficients are calculated from the respective Nusselt

numbers with equation 1.

ά = Nu k / De Equation 1

ά – heat transfer coefficient

Nu – Nusselt Number

k – thermal conductivity

De – Equivalent diameter

Using an Excel spreadsheet, it is possible make a good

approximation for the hydraulic and heat transfer coefficient

calculations. Both the hydraulic values and heat transfer

coefficients are dependent upon the bulk temperature of the

cooling water in that section of the inductor. It is possible to

incorporate in this spreadsheet the power dissipated in the

different sections of the inductor along with simple

calorimetric calculations for local water temperature.

Using the base data derived from the first four steps, we now

have all the required information to simulate the inductor

temperatures. An electromagnetic plus thermal simulation

program should be used for these calculations.

In many cases, the procedure will only be five steps and

further improvement will not be required. All inductor

temperatures will be acceptable and no further modification

will be required.

In very heavy loaded applications, there will be a need to have

an iterative process to resolve elevated temperatures in local

areas of the inductor. The first step for this should be to return

coil engineering and see if there is a way to improve the

cooling circuit to improve the areas of the inductor with high

temperature.

After updating the cooling circuit, the hydraulic and heat

transfer coefficient calculations should be remade. Then

simulation for the inductor temperature should be repeated.

If unacceptably high temperatures still exist in the same

components of the inductor, then it is necessary to return to

the first step, computer simulation for induction coil design.

Changes will need to be made to the coil copper profile and it

will be necessary to find a compromise between inductor

performance and coil component heating. After coming up

with a new design, the rest of the above steps need to be made.

This method should be repeated until satisfactory temperatures

are reached in all components of the induction coil. To

demonstrate this method, the case of a seam annealing coil

after arc welding of heavy wall tube is considered.

Case Story – Seam Annealing

In the tube and pipe industry, heavy walled tubes are

commonly arc welded. The arc welding process changes the

structure of the material in the seam area and this is oftentimes

restored using a local annealing process (seam annealing).

Induction heating is the preferred method for seam annealing

after welding.

Figures 1 and 2 shows parts of a coil drawing for seam

annealing after spiral welding of large diameter tubes used in

the oil and gas industry. Figure 1 shows the cross-section in

the heating area. There is a recess in the middle of the

inductor to allow room for the bead that is formed during the

welding process. Figure 2 shows the top view of the inductor.

In this projection, the inductor is shown as flat, but on this side

view (not shown) it is arced to follow the contour of the pipe.

Figure 1: Cross-section of induction coil for spiral welded

tube seam annealing

Figure 2: Top view of induction coil for spiral welded tube

seam annealing

For the case story, we can consider heating of a large diameter

pipe with ¼” wall thickness. The arclength of the “active”

area (does not include the cross-overs or leads area) of the

winding is 32.5”. The process is continuous with a feed rate

of the pipe is 7.4” / second. Frequency used for simulation is

1 kHz. Two different types of magnetic flux controller,

laminations and Fluxtrol A will be considered. Flux 2D

electromagnetic plus thermal program will be used for all

heating simulation.

Comparison will be made with the same maximum weld seam

temperature of 1200 C (± 20 C) exiting the inductor and

desired equalized annealing temperature of 1000 – 1050 C

shortly after exiting the inductor. This area of high

temperature should extend beyond both sides of the weld

bead.

The first step in the procedure is electromagnetic and thermal

simulation of the heating process. The coil is long and can be

considered as a 2-D, plane parallel system. Due to symmettry,

it is only necessary to simulate half of the induction coil.

Figure 3 shows the temperature of the pipe at the exit of the

induction coil for a coil with laminations (left) and 3 seconds

after exiting the coil (right). The inductor power required was

600 kW. The coil current was 18.8 kA in the main leg, 9.4 kA

on each of the return legs.

Figure 3: Temperature distribution for the induction coil with

laminations at the exit of the seam annealing coil(left) and 3

seconds later (right)

To compare the performance of laminations to Fluxtrol A,

we’ll change the magnetic flux controller properties and the

coil current required to reach the same temperature in the

Color Shade ResultsQuantity : Temperature Deg. Celsius Time (s.) : 4.4 Phase (Deg): 0Scale / Color42.3855 / 115.03716115.03716 / 187.6888187.6888 / 260.34045260.34045 / 332.99213332.99213 / 405.6438405.6438 / 478.29541478.29541 / 550.94708550.94708 / 623.59875623.59875 / 696.25043696.25043 / 768.90204768.90204 / 841.55371841.55371 / 914.20538914.20538 / 986.85699986.85699 / 1.05951E31.05951E3 / 1.13216E31.13216E3 / 1.20481E3

Color Shade ResultsQuantity : Temperature Deg. Celsius Time (s.) : 7.599999 Phase (Deg): 0Scale / Color45.1254 / 108.46457108.46457 / 171.80374171.80374 / 235.14291235.14291 / 298.48209298.48209 / 361.82126361.82126 / 425.16043425.16043 / 488.49957488.49957 / 551.83881551.83881 / 615.17792615.17792 / 678.51715678.51715 / 741.85626741.85626 / 805.1955805.1955 / 868.53461868.53461 / 931.87384931.87384 / 995.21295995.21295 / 1.05855E3

same amount of time. Figure 4 shows the temperature of the

pipe at the exit of the induction coil for a coil with Fluxtrol A

(left) and 3 seconds after exiting the coil (right). The

distribution is nearly identical. The inductor power required

was the same as for laminations, 600 kW. The coil current

was slightly higher, 20 kA in the main leg, 10 kA on each of

the return legs.

Figure 4: Temperature distribution for the induction coil with

Fluxtrol A at the exit of the seam annealing coil(left) and 3

seconds later (right)

After simulation of the part heating, the next step is the coil

engineering. We are using a real inductor where the drawings

are already completed, so it is not necessary in this case.

The next step is the hydraulic calculations. The magnetic flux

controller will have no effect on the hydraulic calculations.

There are 2 water inlets and 4 outlets on the inductor. Since

there are 2 separate water channels in the main leg, we can

consider the inductor as having 4 separate water circuits on

this inductor for the hydraulic calculations.

If we have 30 psi applied each of the 4 water circuits, the total

water flow rate should be around 23.2 gpm total or 5.8 gpm

per circuit. This calculation takes into account the pressure

drop in the inlet hose, the buss tubing, the bending areas and

the two active legs.

After the hydraulic calculations, we can derive the local heat

transfer coefficients. The areas of interest are the main

heating leg and the return leg. In the main water pocket, the

water velocity is 12 ft/sec and in the return leg the velocity is

close to 19 ft/sec. Putting the losses in the inductor sections

into the spreadsheet yields a temperature rise in the bulk water

of around 13º F (7º C), which does not have a significant

impact on heat transfer coefficients. Therefore, the heat

transfer coefficients for the main leg and return leg should be

14,000 and 22,500 W/m2K respectively.

To simulate the localized inductor temperatures, it is necessary

to consider the inductor construction for calculation of the

localized inductor loading. The power calculated in both

cases is the same. It is necessary to recalculate for the space

factor considering space unusable around the leads area, cross-

overs and copper keepers. This will not have an effect on the

total power, only on the required coil current.

For laminations, there needs to be a 1/8” copper keeper every

4”. Also, there should be at least a ¼” gap between the

laminate stack and the leads or the cross-overs to prevent

overheating from the 3-D magnetic fields. This means that the

effective length of the inductor is about 0.89 times ideal. To

achieve the results calculated above, it is necessary to increase

the coil current 5.7%.

For Fluxtrol A, copper keepers are not required. There is still

a ¾” wide busswork. The concentrator can come within

around 1/16” of an inch due to the better performance in 3-D

magnetic fields. This means the effective length of the

inductor is over 0.99 times ideal. Therefore, it is only

necessary to increase the coil current by 0.4%.

After recalculation, the current in the coil with laminations is

1% lower than the coil with Fluxtrol A. This is a much

smaller difference than 6% from the ideal inductors.

Therefore, a current of 19.9 kA will be used for the coil with

laminations and 20.1 kA for the coil with Fluxtrol A.

Besides current recalculation, it is also necessary to include

losses in the concentrators and heat transfer between the

copper and concentrator. Losses in the concentrator should be

calculated based upon flux density values from simulation of

the part heating and fed into the thermal block as a constant

power source in Flux 2D. The process is continuous, so

simulation should be run until steady state temperatures are

achieved in all components.

Figure 5: Steady state temperature distribution in the

induction coil with laminations- T scale 20 – 250 C

Figure 5 shows the temperature distribution after 2000

seconds for the coil with laminations. At this point, the

inductor is definitely at steady state. The maximum

temperature in the copper is 322º F (161º C). This is in the

corner of the main leg. The temperature in the lower half of

the laminations is nearly identical. This is due to poor heat

transfer between the laminations and the copper due to

uncertain thermal contact and low conductivity filling resins.

The temperature in the return leg is significantly lower due to

Color Shade ResultsQuantity : Temperature Deg. Celsius Time (s.) : 0.002E6 Phase (Deg): 0Scale / Color20 / 34.37534.375 / 48.7548.75 / 63.12563.125 / 77.577.5 / 91.87591.875 / 106.25106.25 / 120.625120.625 / 135135 / 149.375149.375 / 163.75163.75 / 178.125178.125 / 192.5192.5 / 206.875206.875 / 221.25221.25 / 235.625235.625 / 250

Color Shade ResultsQuantity : Temperature Deg. Celsius Time (s.) : 4.4 Phase (Deg): 0Scale / Color41.60269 / 113.62705113.62705 / 185.65143185.65143 / 257.67578257.67578 / 329.70013329.70013 / 401.72449401.72449 / 473.74884473.74884 / 545.77325545.77325 / 617.79761617.79761 / 689.82196689.82196 / 761.84631761.84631 / 833.87067833.87067 / 905.89502905.89502 / 977.91937977.91937 / 1.04994E31.04994E3 / 1.12197E31.12197E3 / 1.19399E3

Color Shade ResultsQuantity : Temperature Deg. Celsius Time (s.) : 7.599999 Phase (Deg): 0Scale / Color44.25912 / 106.98604106.98604 / 169.71295169.71295 / 232.43987232.43987 / 295.16675295.16675 / 357.89368357.89368 / 420.62061420.62061 / 483.34753483.34753 / 546.0744546.0744 / 608.80133608.80133 / 671.52826671.52826 / 734.25513734.25513 / 796.98206796.98206 / 859.70898859.70898 / 922.43591922.43591 / 985.16284985.16284 / 1.04789E3

lower losses, higher heat transfer coefficients and shorter

distance to the water cooling.

Figure 6 shows the temperature distribution in the coil with

Fluxtrol A after 2000 seconds. Steady state was definitely

achieved. The maximum temperature in the copper is slightly

lower, 311º F (155º C) compared to the coil with laminations.

The maximum temperature is again in the corner of the main

leg. The overall temperature of the Fluxtrol A is significantly

lower than the laminations due to good thermal contact with

the copper for heat extraction due to exact material dimensions

and the use of high thermal conductivity epoxies (Duralco

4525) [5]. As before, the temperature of the return leg is

significantly lower than those of the main leg.


induction coil with Fluxtrol A- T scale 20 to 250 C

Based upon these temperatures, it is the opinion of the authors

that both the inductor with laminations or Fluxtrol A would

have good lifetime and no further optimization would be

required.

For the sake of study, let’s consider the case of 50% higher

power in the inductor for both cases. Coil current would be

increased 22% for both cases and the losses in the

concentrator would increase by 50%. Heat transfer

coefficients used will remain the same.


seconds for the coil with laminations. The maximum



the laminations is nearly identical and there is even a small

spike on the outer corner. The temperature on the return leg is

relatively low.


induction coil with laminations with 50% higher power- T

scale 20 – 250 C


seconds for the coil with Fluxtrol A. The maximum



the Fluxtrol A is lower than in the copper, but still elevated.

There is no peak at the outer corner.


induction coil with Fluxtrol A with 50% higher power- T scale

20 – 250 C

Figure 9 shows the temperature evolution over time for the the

coil with laminations and with Fluxtrol A in two critical areas

of the induction coil, the copper corner and the center of the

bottom of the concentrator pole for a continuous heating

process.




Coil Heating Data

0

25

50

75

100

125

150

175

200

225

250

0 200 400 600 800 1000

Time (seconds)

Tem

pera

ture

(C

)

Cu Corner,

Fluxtrol A,

HP

Fluxtrol A

bottom, HP

Cu Corner,

Laminations,

HP

Laminations

Bottom, HP

Figure 9: Temperature evlolution in critical areas of the

induction coil with laminations and with Fluxtrol A for

continuous heating

When 50% higher power is used, both of these cases could be

considered to be in the critical temperature range for thermal

degradation. The copper temperature is around 33º F (18º C)

less for the coil with Fluxtrol A. The temperature on the

bottom of the Fluxtrol A is around 74º F (41º C) lower than on

laminations. The difference in overall temperature of the

concentrator is even greater. The lower temperatures present

on the coil with Fluxtrol A should lead to extended coil

lifetime.

The above considerations are for a continuous heating process.

From the above data we can make some short evaluations of

what we could expect during an intermittent heating process,

like single shot hardening. Figure 10 shows the heating

dynamics in the first 10 seconds of heating.

Coil Heating Data

0

25

50

75

100

125

150

175

200

225

250

0 2 4 6 8 10

Time (seconds)

Tem

pera

ture

(C

)

Cu Corner,

Fluxtrol A,

HP

Fluxtrol A

bottom, HP

Cu Corner,

Laminations,

HP

Laminations

Bottom, HP

Figure 10: Temperature evlolution in critical areas of the

induction coil with laminations and with Fluxtrol A for

intermittent heating with 10 second on-time

As we could expect, all temperatures are lower than for the

case of steady state. It is interesting to note though, that the

difference between the copper temperatures is much higher

than in the case of a continuous process. The temperature of

the copper in the coil with laminations is 72º F (40º C) higher

than for the coil with Fluxtrol A. This will have a dramatic

effect on the coil lifetime.

The temperature of the concentrators in this case is much

lower than for continuous and can be considered as well in the

safe range. This is only for one heating cycle. Further

analysis will be made in a future paper of the effect of cycling

on the coil temperatures and include running an intermittent

process to steady state.

One thing to note though, is that due to the shape of the curves

it is absolutely clear that the main source of heating in the

concentrator is conduction from the high temperature copper.

Therefore, the concentrator temperatures should be lower than

the high temperature corner of the copper. From this, it can

stated that keeping the coil copper cool will enhance not only

the lifetime of the copper, but the magnetic flux controller

also.

Conclusions

Improving induction coil lifetime in heavy loaded applications

is an area of growing importance. Coil lifetime can be

compromised by mechanical damage, electrical breaks and

thermal degradation. Problems related to mechanical damage

or electrical break can almost always be solved with the

proper maintenance procedures and machine design.

Induction coil failures due to thermal degradation are more

complicated. Reducing the induction coil component

temperatures has a dramatic effect on the coil lifetime in these

cases. Practical methods for increasing the coil lifetime

include raising water pressure and changes to the water circuit

in the inductor. These adjustments are commonly made

empirically based upon the experience of the induction coil

designer.

A more scientific method of predicting induction coil

temperatures is described. The method is based upon an

iterative approach using a combination of computer

simulation, good engineering practices and analytical

calculations. This method can be used for improvement to

existing design or in the process of new induction coil

development.

A case story for continuous seam annealing of heavy walled

tube is presented to demonstrate representative results. In this

case story, the effect of magnetic flux controller type on coil

temperatures is evaluated. Two types of magnetic flux

controller were considered: Fluxtrol A and laminations.

The induction coil with Fluxtrol A had lower overall

temperatures, both in the copper and magnetic flux controller,

than the one with laminations. This should lead to the coil

with Fluxtrol A lasting longer before thermal degradation

occurs than the one with laminations in a continuous

operation.

A quick evaluation was made for the case of a short heating

time with this inductor. For a shorter cycle, the difference

between the copper temperatures was much more pronounced.

Further study is required for determining the intermittent

cycling characteristics to lead to the steady state conditions.

It was clear from the temperature evolution curves that for this

case the main source of heating in the concentrators was

conduction from the high temperature copper corners.

Therefore, lowering the copper temperature will also lower the

concentrator temperature.

This paper sets a foundation for the study of induction coil

heating and further improves the state of the art in induction

coil design process. The method described here may be

applied to any induction coil. Future studies on different

induction heating applications using this method will lead to

further improvements in induction coil lifetime.

References

1. Pfaffman, G.D., (July 2006) Advancements in

Induction Heating Tooling Technology, J. Heat

Treating Progress

2. Stuehr, W.I. and Lynch, D.C., (Jan-Feb. 2006), How

to Improve Inductor Life, J. Heat Treating Progress

3. Haimbaugh, R.E., (2001), Practical Induction Heat

Treating, ASM Int.,

4. Rudnev, V.I., Loveless, D.L., Cook, R.L., Black,

M.R., (2003), Handbook of Induction Heating, NY,

Marcel Dekker

5. Nemkov, V.S., (2006), Resource Guide for Induction

Heating, CD-R, Fluxtrol Inc., MI

Increasing Inductor Lifetime by Predicting Coil Copper Temperatures Paper

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