During our recent webinar with COMSOL on thermal-structure interaction modeling, we at AltaSim Technologies demonstrated modeling of a MEMS energy harvester that scavenges waste heat. Examples of sources for waste heat range from microprocessor chips, to internal combustion engines, to chemical processing plants. If the waste heat generated from these cases could be used to generate additional energy, then overall energy consumption could be reduced. Estimates from CANMET Energy Technology Centre indicate that worldwide, waste heat exceeds 1 TJ annually.

The device modeled in the webinar consists of bimetallic cantilevered beam subjected to a thermal cycle. The beam tip contacts a hot surface and heat conducts into the bimetallic beam. As the beam heats up, the difference in coefficient of thermal expansion between the two metals generates a bending moment that causes the beam to deflect. Once the beam has lost contact with the heating surface, the beam begins to cool and return to the undeformed shape. The beam will eventually contact the heating surface and continue the deformation cycle. This bimetallic strip can be used with a range of materials that convert mechanical energy to electrical current, including piezoelectric, pyroelectric, and ferroelectric materials. Applying these materials to the bimetallic strip produces electrical energy with each mechanical cycle. Maximizing the energy per cycle then becomes the design goal.

COMSOL Multiphysics provides the modeling environment needed to consider each aspect of the design. During the webinar, we demonstrated how to develop a model of the heat transfer and mechanical deformation of the MEMS energy harvesting device. The model included both mechanical and thermal contact. The thermal contact released in COMSOL 4.3b represents a key feature for modeling the device accurately. As the mechanical force increases between the cantilever and hot surface during cooling, the heat transfer becomes more efficient. The coupling of the mechanical and thermal contact within COMSOL Multiphysics provides the most accurate solution of this design.

*If you missed the webinar, you can catch a clip about modeling the MEMS energy harvester in the Video Center.*

Modeling of the conversion between mechanical and electrical energy was not demonstrated in the webinar since the focus was on thermo-mechanical analysis. COMSOL Multiphysics provides the ability to model piezoelectric, pyroelectric, and ferroelectric materials. With the addition of these physics, the model would provide a direct calculation of the device efficiency for converting waste heat to electricity.

Kyle C. Koppenhoefer, Ph.D., has 20+ years of experience working with computational analysis. Together with Jeffrey Crompton, he started AltaSim Technologies, LLC eleven years ago to assist in new product design through the application of advanced computational tools. To facilitate this goal, AltaSim Technologies became a founding member of the COMSOL Certified Consulting program, and continues to be a leader in providing COMSOL services to those interested in receiving the benefits of modeling with COMSOL Multiphysics. In addition to guest blogging for COMSOL, AltaSim Technologies also blogs about multiphysics modeling on their own website.

As part of our efforts to assist COMSOL users in performing high-quality analysis, we recently used our bi-monthly email to remind users to include twelve degrees of freedom per wavelength when meshing wave problems. This article builds on our previous advice. Wave-type problems develop in a variety of analyses that include acoustics, electromagnetics, and structural vibrations. Thus, this mesh refinement issue touches many different industries.

Wave propagation problems require twelve degrees of freedom per wavelength to accurately represent the wave. This requirement develops from the error associated with approximating a sine wave with a polynomial. Twelve degrees of freedom provide a solution with less than 1% deviation from the approximated sine wave. These degrees of freedom may be obtained by using linear, quadratic, or cubic elements with fewer elements needed for the higher order elements.

To determine a proper mesh size, the analyst must know the wavelength of the problem that they are attempting to solve. The wavelength is the ratio of the wave speed to the frequency. For radio frequency problems, wave speed is inversely proportional to the refractive index of the media. For the case of mechanical wave propagation in solids and gases, wavelength depends on the density and bulk modulus of the material.

In problems with inhomogeneous media, the analyst should account for changes in wavelength within the solution domain. For example, speed of sound in the atmosphere depends on elevation. Thus, the mesh density should change with elevation.

A mesh refinement study provides valuable information and confidence in solution accuracy. Thus, solve the problem using multiple mesh densities to determine how the solution changes with increasing degrees of freedom. A demonstration of how to set up a simple wave propagation problem and the effects of the number of degrees of freedom on the solution can be found on the AltaSim Technologies Blog.

*Wave propagating from pulsing sphere.*

Kyle C. Koppenhoefer, Ph.D., has more than twenty years of experience working with computational analysis. He and Jeffrey Crompton started AltaSim Technologies, LLC eleven years ago to assist in the design of new products through the application of advanced computational tools. To facilitate this goal, AltaSim Technologies became a founding member of the COMSOL Certified Consulting program, and continues to be a leader in providing COMSOL services to people interested in receiving the benefits of modeling with COMSOL Multiphysics. AltaSim Technologies maintains a blog on their website, which provides their thoughts on multiphysics modeling. |

Engineers typically design products based on known applied stresses and the yield strength of the material of construction. Traditional design calculations coupled with conservative factors of product safety, provide designs with a low likelihood of fracture. Consequently engineered products do not typically fracture due to a single-cycle overload as long as the loads experienced during use are maintained within design specifications. However, engineers may overlook the damaging effects of stresses that are well below the yield strength of the material. If these stresses are applied cyclically they can produce microscopic damage to the material. This damage accumulates over thousands, or even millions of cycles, prior to producing a catastrophic fracture.

Engineers who design products that experience fatigue failure may have calculated the correct applied stress but did not consider the effects of cyclic loading. In other cases, operation may introduce a cyclic load that was not considered in the initial design. Biomedical products represent one area where unexpected loads may occur due to the complex nature of the loadings that develop within the human body. The Bjork-Shiley convexo-concave heart valve (pictured below) offers an example of a medical product that developed unexpected loads on the outlet strut. Since heart valves experience millions of cycles, small loads can produce fatigue fractures that lead to negative outcomes for the patient.

*Bjork-Shiley convexo-concave heart valve*

When designing products that experience millions of loading cycles, engineers must have a full understanding of the effect of these complex loads on the performance of their products. Computational analysis (e.g., structural finite element and computational fluid dynamics) can provide engineers with the tools necessary to better understand the nature of the stresses in their products. For designs where a fluid and structure interact, multiphysics computational tools can provide more accurate analysis of the stresses developed and therefore greater fidelity in assessing the influence of loading. Using these tools engineers can better assess the influence of product loading and thus develop better and safer products.

Kyle C. Koppenhoefer, Ph.D., has over twenty years of experience working with fatigue design. He and Jeffrey Crompton started AltaSim Technologies, LLC ten years ago to assist in the design of new products through the application of advanced computational tools. To facilitate this goal, AltaSim Technologies became a founding member of the Certified COMSOL Consulting program.