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Thermal design guidelines for solid-state lighting applications using LEDs

Here are six critical steps necessary to developing a successful, cost-effective thermal design for an LED application. Two families of LED applications have been used to illustrate many of the design choices that are open to the thermal designer to satisfy these application issues.

By Henry F. and Peter A. Villaume, Villaume Associates -- EDN, 9/11/2009

Adequate thermal designs are the pacing item in achieving successful SSfL applications using LEDs. The lighting marketplace is extremely cost-sensitive as well as very concerned with reliable long life (50,000 to 100,000 operating hours; note, there are a total of 8,766 hours in a year). A thermal design that meets these requirements is passive—that is, it has no fans of any type nor other subcomponents with any failure modes. This thermal design depends upon maximizing the available natural convection air-flow rate with the minimum amount of material and cost.

Define the LED thermal requirements

LEDs have very quickly risen to prominence as a light source because they are very efficient (lumens/watt) and they have the potential of very long life compared with other light sources. The fine print here is that these advantages are only available when strict conditions of thermal management are met. These are defined in the LED suppliers' data sheets and usually require some interpretation/clarification.

The application requirements define the lumens required and the color temperature required. From this the data sheets will show the power required to drive the LED array. The total power is then the sum of the number of LEDs times the forward voltage times the current as charted to achieve the light output desired. An LED light source also needs a specific power supply, which adds to the power needs by an approximate 20% value that must be provided for in the area of the light or base or someplace nearby. This total power is a generous/conservative estimate by including the amount of energy that goes out as light. Since this is generally much less than 10%, we can ignore this adjustment at this early stage of design. A conservative early estimate for the LED driver supply is about 20% of the total LED power to make sure that nothing is overlooked.

In the data sheet will be a range of conditions (driving power and ambient temperature conditions) with an operating-life estimate. This will need to be compared with the chosen operating point and compared to see if there is a compromise or adjustment in operating temperature to achieve the desired life for the application. During the design cycle these values will probably be revisited a couple of times to satisfy the evolving electrical and optical sides of the project. Be prepared for redos as things will change during the stages of a developing design.

Define realistic boundary conditions

The definition of these application requirements specifies indirectly the size, cost, and complexity of the thermal solution required to produce the necessary thermal results. Be very realistic, therefore, in setting all-encompassing requirements. Examine the impact of minor adjustments—that is, run sensitivity studies—on the impact of thermal-defining boundary conditions.

The altitude range for most applications is overlooked. Altitude is important. In essence, you are defining the expected minimum density for the surrounding air to accomplish the convective cooling required. A good compromise for all-over service is to use a specification of 8,000 (a correction factor of 0.86, or 14% less effective than air at sea level). Figure 1 shows typical correction factors. The impact of altitudes other than specified on LED maximum case/junction temperatures can be directly calculated with any spreadsheet thermal-analysis program (see Table 1).

Lighting applications are almost always dependant upon natural convection developed air-flow rates because of the cost, noise, reliability, and life limitations associated with fans. Natural convection air flow is optimal at 75 lfm (linear feet per minute), and goes down from there. This is an extremely low energy process so that extreme mechanical design care must be taken to facilitate as great a natural convection air-flow rate as possible. A reasonable design starting point is 50 lfm, as it is roughly in the center of the range of natural convection air-flow rates (see Table 2). The effective air-flow rate is the most significant factor in determining the heat transfer for an application.

Heat transfer occurs because there is a temperature differential between the ambient conditions (temperature and altitude) and the maximum case temperature of the LED chip. Do not, therefore, set the allowed maximum ambient temperature higher than necessary. Military applications typically have ambient temperatures like 55°C (131°F) to 70°C (158°F). A specified limit of 50°C (122°F) might be a more practical limit and take the short-term and infrequent excursions above the 50°C as low short-term and infrequent probabilities. As the temperature gradient left for the convective heat transfer decreases below 25°C, the heat-sink size becomes much larger, heavier, and more costly. While heat-sink designs can be done for convective gradients as low as 12°C, they are not generally cost-effective.

Click here to see the thermal results for Application 1, "Extruded wedge LED SSL."

Click here to see the thermal results for Application 2, "Conductive plastic over aluminum cup insert for an LED Edison socket bulb."

Minimize conductive path

LED applications differ from others in the electronics field by the fact that most optical and cosmetic design considerations require an indirect conductive path for the heat to flow from the heat source (the LEDs) to the convective fin/pin surface area. The typical CPU in a computer is close-coupled in a vertical stack to the heat sink directly above the CPU. The conductive path is minimal and usually contains just one significant interface. This is the major difference with LED applications; that is, there is generally a significant conductive temperature gradient component to the thermal solution.

We have an LED reading light application with more than a 1-in. conductive post to feed the heat to the center of the convective pin fin heat-sink base. In order to consider low-cost injection molding, our first consideration was to use a thermally conductive plastic material (thermal conductivity equal to 20W/m°K; about 100 times the thermal conductivity of most plastics). This resulting conductive gradient was too large to consider. We then considered the impact on reducing this conductive gradient by over-molding a machined aluminum insert with a higher thermal conductivity (210W/m°K). After the initial conductive loss from the LED junction to the package as defined by the LED vendor, we calculated the conductive loss in the post, spreading across the base and finally up into the pin array. This compromise allowed the post/base conductive loss to be reduced to an acceptable level and allowed a molded-part thermal solution.

The conductive temperature gradient can be approximated using the following equation:

Q = k × A × ΔT/L

shuffled to get

ΔT = Q × L/k × A.

Approximating the cross-sectional area (A) of the conductive path and the heat-flow length from area center to center (L), we can greatly simplify and speed up the arithmetic. For example, the area center plane in the base to the pin set is half of the pin height plus half of the base thickness for the last leg of the conductive path. This equation can be simplified to the following when a very common set of dimensions is used (k in W/m°K and heat in W, metric; and all others are in inches):

ΔT = 39.4 × Q × L/k × A

for each leg of the conductive path.

With this step completed we can proceed to the next step in selecting a budgeted value for the convective and conductive portions of this solution.

Budget conductive and convective needs

There are three methods of heat transfer, specifically radiation, convection, and conduction.We can now deal with the radiation component by specifying a high-emissivity surface finish that will not compromise any of the cosmetic requirements of the application.

Conservatively, we can use the calculated value for the conductive temperature gradient to get the allowable temperature gradient for the convective heat-transfer component from the following relationship:

Tmaxcase – Tmaxambient@design altitude – ΔT cond. = ΔT conv.

To minimize the size, weight, and complexity of the convective heat transfer, we are looking for this value to be at least 25°C. If this is not the case it may be necessary to go back and reduce the conductive temperature gradient by reducing the path length and/or altering the material to improve the thermal conductivity of the legs of the conductive path.

Match cost targets with production processes

The two most common economical processes for the production of heat sinks are aluminum extrusions and the plastic injection molding of net finished fin surface shapes in thermally conductive plastics. We have selected two LED applications, one based on an aluminum extrusion and the second using an injection-molded aluminum-insert plastic design. The requirements of these two applications have been made as close to the same as possible except for the conductive temperature gradient.

There are sketches for each as well as several spreadsheet thermal analyses presented in a graphical form to show the solution. These solutions have been shown in relationship to the other design parameters. The key here is that these solutions were all done on the computer in just a few minutes, allowing the examination of a wide range of design variables very quickly that meet the boundary conditions of the two applications. All of these variables were effectively evaluated without having to resort to the construction of elaborate computer models or the fabrication and testing of prototype hardware.

In reviewing the initial plots for application number 1, we could see that a modest increase in extrusion size would allow an open application without the adding of a set of radial folded fins on the 45° flat face. This would be a great deal less expensive even with the added material in the extruded wedge design. It also offer a modest increase in the internal space available for the driver board that will be required. If the under-cabinet arrangement required the wedge to be placed against the back wall, thus obstructing the development of a natural convection air-flow path on the back side, then the radial folded fins could be added to the open side of the basic wedge shape and thereby meet the thermal requirements of the LEDs. Future light modules that would require an LED closer than every two inches could also be dealt with in a similar manner—that is, adding fin surfaces would add to the now-required increase in convective fin surface area with a minimum of added hardware.

Test to verify design performance

The most critical feature in the success of an LED design is that the design natural convection air-flow rate assumption is met in the real-life application. Natural convection is an extremely low energy process and as such it is extremely sensitive to the basic heat-sink design requirement that the convective fin/pin surfaces be aerodynamic in shape, design, and orientation. Convectively heated buoyant air wants to float vertically upward. This means that all of the surfaces need to be smooth and finned surfaces want to be as vertical as possible. Please note that all of the finned surfaces in the two example designs are essentially vertical.

The effectiveness of the two fin designs, as demonstrated in the pressure drop calculator on the thermal-analysis table, have pressure drops in the range of 0.08 in. of water. This is an approximate general-purpose calculator based on the pressure drop between two parallel plates. At this point it will be necessary to demonstrate the actual real-life natural convection air-flow rate. This is normally accomplished with a shielded thermocouple/thermocouple pair with an open port of about ¼ in. to get a map of the developed air-flow rate across the outlet air side of the heat sink. Fan-style air-flow meters are not as satisfactory as they average the air-flow rate over an area somewhat greater than the diameter of the fan-blade set. Natural convection air-flow rates are at the very low end of their typical scale range. Pay particular attention to the regular calibration of this essential instrument.

The second and equally critical parameter is to understand the temperature profile across the entire heat sink, particularly an application that has such a critical element as a long and critical conductive path. Multiple thermocouples are necessary to develop the type of temperature map that is useful in critiquing the thermal effects of any heat-sink design. The more thermocouples the better the thermal map, but the greater the opportunity for shielding and conductive errors. The laboratory and operator time-dictated solution to this problem is to utilize an IR (infrared) thermal-imaging camera as shown in Figure 2. This was the performance of a multiple-LED light bulb that was fabricated copper with folded fins wrapped around the driver board housing. This picture quickly told us that we could go to full extruded fins in aluminum and have a much less expensive design with almost a 40% increase in fin surface area that weighed considerably less than the initial copper design.

The IR thermal image of an LED-light-bulb heat sink fabricated from all copper components graphically shows the temperature distribution throughout. The copper fins are 0.01 in. thick. They show nearly complete thermal spreading throughout the fins. (The color gradient is minimal.) This suggests that we can substitute an extruded aluminum shape as the extruded shape will have the thicker fins necessary to have the same effective spreading as the copper parts. The extrusion process requires the thicker cross sections that will effectively compensate for the difference in thermal conductivities between the copper and the aluminum. The potential cost savings are substantial—75%.

Conclusion

Thermal management must be considered an essential part of an adequate design process for SSL-LED lighting applications. Without this input, the full potential for energy savings and long life will probably not be realized.

We have presented a six-step methodology that applies to two widely divergent LED applications to illustrate the flexibility of a simple spreadsheet thermal-analysis software package. This software is very quick, intuitive, and easily followed by any skilled mechanical designer. Model solutions can be developed and presented in minutes and hours rather than days and weeks. Elapsed time during a product-development cycle is always a critical element in the successful completion of a program.

The least expensive thermal solution is always the one required by the marketplace. This solution is usually the one that has been designed in from the start of the program. A solution that has been "patched on" afterwards like the hump on a camel is seldom the most cost-effective or desirable solution.

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