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53 Engineering a More Sustainable Future | ADI ( relative deformation ) of a design. Finite element methods ( FEM ) using ANSYS or similar programs can be used to simulate the modal response of structures, helping to optimize the design and reduce the number of sensor prototype iterations. Equation 1 is a simplification of the governing equation of modal analysis for a single degree of freedom system. The natural frequency is related to the mass matrix ( M ) and stiffness matrix ( K ) of the enclosure design. Equation 1 provides a simple intuitive way to evaluate a design. As you reduce the height of the sensor enclosure, the stiffness increases and the mass decreases, therefore the natural frequency increases. Also, as you increase the height of enclosure, the stiffness reduces and the mass increases, resulting in a lower natural frequency. Most designs have multiple degrees of freedom. Some designs have hundreds. Using the finite element method provides quick calculations for Equation 1, which would be very time consuming to do by hand. When simulating using ANSYS modal, both natural frequencies and mode participation factor ( MPF ) are output by the solver. The MPF is used to determine which natural frequencies are the most important for your design. A relatively high MPF means that a particular frequency may be a problem in your design. The examples shown in Table 3 illustrate that while a 500 Hz natural frequency is predicted in simulation for the x-axis, the mode is weakly excited, and is unlikely to be a problem. An 800 Hz strong mode is excited in the enclosure x-axis and will be a problem if the MEMS sensitive axis is orientated in the enclosure x-axis. However, this x-axis strong mode at 800 Hz is not of interest if the designer has a MEMS sensor PCB orientated to measure in the enclosure z-axis. Table 3. Natural Frequency ( Freq, Hz ) , Mode Participation Factor ( MPF ) , and Axis of Interest Modal Analysis for a 10BASE-T1L Sensor Prototype The article "How to Design a Good Vibration Sensor Enclosure Using Modal Analysis" 3 provides a detailed overview of modal analysis. While ANSYS is an efficient and sophisticated tool to analyze the modal response of structures, an understanding of the underlying equations will help in design. The underlying equations show that enclosure natural frequencies are influenced by both material choice and geometry. Cylindrical shapes with higher cross-sectional areas are better designed for higher rigidity and natural frequencies across all axes, compared to rectangular shapes. Rectangular shapes offer more options in sensor orientation and equipment attachment, compared to cylindrical shapes. Please refer to the article for examples and simulation results. The 10BASE-T1L sensor prototype is designed using a triaxial 1 kHz bandwidth MEMS sensor ( ADXL357 ) , and the design goal is to create an enclosure that supports greater than 1 kHz. A rectangular enclosure design was created, as shown in Figure 7, and simulated using ANSYS. Table 4 shows the simulation results, with natural frequencies and mode participation factors indicating a minimum of 6 kHz bandwidth across all three axes. The design uses M6 lugs on the x-axis surface ends. Using these attachment points will ensure a solid equipment attach and best modal performance. Table 4. Natural Frequency ( Freq, Hz ) , Mode Participation Factor ( MPF ) , and Axis of Interest for 10BASE-T1L Sensor Prototype 6 Figure 6. MEMS and mechanical enclosure frequency response design goal. Mode Freq, Hz Axis MPF MPF Comment 1 500 x 0.001 Weak mode 2 800 x 0.45 Strong mode 3 1500 y 0.6 Strong mode 4 3000 y 0.002 Weak mode 5 10,000 z 0.33 Strong mode Mode Freq, Hz Axis MPF 1 11663 x 0.287 2 6632 y 0.057 3 30,727 y 0.187 4 6080 z 0.370 Adobe Stock / Yingyaipumi – stock.adobe.com