18 November, 2019

Complex design decisions require powerful tools. Electronics are increasingly pushed towards applications which require smaller, lighter electronics packaging. As a result, engineers are pressured to optimize cooling solutions to reduce weight, size and power consumption.

Designing a heatsink solution for in-line components presents a unique challenge. The pair of components' temperature response is coupled such that reducing the temperature of the front component can increase the temperature of the second. As a result, an engineer must be careful not to over or under-design the heatsinks.

An example of such a design can be seen below, in which three fans supply airflow to two identical in-line heatsinks. In a typical situation one might manually adjust the properties of these heatsinks and run simulations to confirm that they meet the design requirements. However, a more powerful approach is to utilize the 6SigmaET Optimization tool to find the optimal solution within the design space.

*Figure 1. Screenshot of Baseline Model*

**Design of Experiments (DOE)**

The first step is to define the design space by choosing the input parameters and selecting the minimum and maximum values for each. In this case, we want the two heatsinks to be identical and centered on the components with a height no greater than 25 mm. In 6SigmaET, input parameters can be grouped by type so that the heatsink parameters are kept identical for all DOE cases. The dimensional parameters of the heatsinks are shown in Table 1 along with their design range.

*Table 1. Design Parameters and value boundaries.*

6SigmaET intelligently distributes the parameters across the range for the selected number of design scenarios using an Optimal Space Filling Algorithm to effectively capture the design space. For this study, 50 simulations are considered and added to a Parameterize, Analyze, Compare (PAC) Matrix. Running these simulations may be a relatively large time investment depending on the complexity of the model, but 6SigmaET’s powerful optimization capabilities mean that this single data set gives the user tremendous ability to explore the design space. It is important to note, however, that to achieve a true optimum, you need to feed the optimization algorithm with as much data as possible.

*Figure 2. 6SigmaET’s DOE functionality distributes the input parameters across the design space*

*Figure 3. Outputs of the simulation set*

**Sensitivity Analysis**

Conducting a sensitivity analysis is an excellent way to inform design choices. Understanding which parameters have the most significant impact on a component’s temperature response is simple with 6SigmaET. The surface plot allows an engineer to easily evaluate the sensitivity of parameters and explore the design space. By adjusting the axes and sliders, any combination of parameters can be evaluated. This is a quick way to select the best off-the-shelf part for your application. In this case, we can see that the fin height has a much larger effect on the U2 junction temperature than the number of fins. By adjusting the sliders, it can also be seen that increasing the base width and depth also decreases the U2 Junction Temperature.

*Figure 4. Surface Plot allows for exploration of the design space*

**Optimization**

When faced with complex design decisions, a cost function can be defined to weigh the importance of various parameters in the design. 6SigmaET allows the user to define a cost function using an extensive library of operators and functions. Once this function is defined, it can be minimized or maximized based on the simulated scenarios to achieve the desired optimization outcome. For this example, we want to minimize the Junction temperature without significantly increasing the weight of the heatsinks. Conveniently, the heatsink weight (in grams) and the Junction Temperatures (°C) are of the same order of magnitude. This means that simply adding the four output variables and minimizing the total will optimize the heatsink design to reduce the Junction Temperature without a significant increase in the weight.

*Figure 5. Cost Function *

In the Optimize Window, 6SigmaET minimizes the cost function by way of a multidimensional response surface and displays the existing best scenario from the 50 simulations as well as the projected optimum configuration based on the available simulation data. This optimized case can be added as a scenario in the PAC Matrix to be simulated and reviewed. Notably, if the optimized design doesn’t meet the desired outcomes, the cost function can be quickly adjusted and a new projected optimum generated. This allows for quick iteration to determine the best possible outcome within the solution space.

*Figure 6. Optimization window gives the projected optimal solution within bounds*

Figure 7 shows the (a) baseline heat sink and (b) optimized heat sink based on the Optimization tool. By utilizing 6SigmaET’s Optimization tool, the U1 Junction Temperature was reduced by 14% and the U2 Junction Temperature was reduced by 31%. Furthermore, the total weight of the heatsink was reduced by 6%.

*Figure 7. (a) Baseline Heat Sink Model (b) Optimized Heat Sink Model*

**Conclusion**

6SigmaET’s Optimization feature gives the user powerful tools to analyze their designs for sensitive design parameters and optimize their designs according to precise cost functions. Without this tool, many individual simulations would be required to achieve the desired performance and it would still not be optimal. With increasing pressure to minimize weight, maximize performance and reduce power consumption, the design engineer needs the 6SigmaET optimization tool in their thermal simulation toolkit.

Learn more about new and updated features in 6SigmaET Release 14 here.

*Blog written by: Joseph Warner, Applications Engineer*