Computational Design of Innovative Mechanical Vibration Energy Harvesters with Piezoelectric Materials

Transcription

1 Computational Design of Innovative Mechanical Vibration Energy Harvesters with Piezoelectric Materials Shikui Chen Computational Modeling, Analysis and Design Optimization Laboratory (CMADOL) Department of Mechanical Engineering Stony Brook University

2 Outline 1. Research Background Introduction; 2. Topology Optimization: State of the Art; 3. Formulations for An Energy Harvester Design Problem; 4. Numerical Examples; 5. Conclusion & Future Work.

3 Macro Scale Energy Harvesting around Us Windmills Watermills Wind Turbines Micro Scale Solar cell Bioenergy Harvester Vibration energy Harvester

4 Research Objective How to find a design which can harvest energy efficiently? To develop a unified computational topology optimization framework allowing easy and rapid design of efficient smart energy harvesters with piezoelectric material.

5 Topology Optimization What is Topology Optimization? A technique for optimum material distribution in a given design domain. Topology Why do topology optimization? Able to achieve the optimal design without depending on designers a priori knowledge. More powerful than shape and size optimization. Shape Size

6 Computational Topology Optimization: Applications from Micro World to Macro World Aircraft Structure Design (Boeing, 2004) Micro Structure of Composite Material MEMS Design Light Vehicle Frame Design Light (Mercedes-Benz, Vehicle Frame 2008) Design (Mercedes-Benz, 2008)

7 Topology Optimization: Chronological Review r E = E 0 r p Homogenization (Bendsoe & Kikuchi, 1988) SIMP (Rozvany, Zhou and Birker, 1992) Level Set Methods (Wang 2003, Allaire 2004 ) Ground Structure Method before 1980s

8 Dynamic Geometric Model: Level Set Methods ( x) = 0 ( x) 0 ( x) 0 x \ ( x) = 0 x ( x) 0 x D \ Hamilton-Jacobi Equation ( x) = 0 ( x) 0 D V ( ) 0 n x = t ( x) 0 ( x) 0 Implicit representation Benefits Precise representation of boundaries Simultaneous shape and topology opt. No chess-board patterns

9 Level Set Model for Multimaterial Representation Color Level Set Reconciled Level Set Wang & Wang Color level sets: a multi-phase method for structural topology optimization with multiple materials, Computer Methods in Applied Mechanics & Engineering, 193, , One level set function for each material Use Merriaman-Bence-Osher operator (MBO) to reconcile the level set functions = max 1 1/2 1/2 i i i j j Shikui Chen, Stefano Gonella, Wei Chen and Wing Kam Liu A Level-Set Approach for Optimal Design of Smart Energy Harvesters, Computer Methods in Applied Mechanics and Engineering, Volume 199, Issues 37 40, 1 August 2010, Pages ,

10 Example: Level-Set Based Topology Optimization of A Micro Gripper f in 1 2 f out f out Chen, S., Chen, W., and Lee, S., 2010, "Level set based robust shape and topology optimization under random field uncertainties," Structural and Multidisciplinary Optimization, 41(4), pp

11 Piezoelectric Effects What is piezoelectric? Materials that experience a change in their internal electric fields in response to applied mechanical force are said to be piezoelectric. e.g., Quartz SiO2, A piezoelectric material develops an internal electric field when AlPO4, Tourmaline, and compressed or stretched (from Zinc oxide ZnO et. al. Wikipedia). Source:

12 Piezoelectrical Constitutive Relations Stress vector Elastic coefficient matrix - T= C ε e E T D= e ε PE Piezoelectric coupling matrix T T T T T r d = ds uu ε C ε ε e E u t Electric displacement T T T d = 0 ε e E E P E Dielectric Strain vector coefficient matrix t Electric field

13 Formulations for An Energy Harvester Design Problem Minimize J (, ) = T WM 0 WE,, t,, t T Sub. to physics governing equations: T T T T T r d = ds uu ε C ε ε e E u t t T T T d = 0 ε e E E P E dt WM is the mechanical energy WE,, t (= kinetic energy + elastic energy); WM,, t is the instant energy WE is the electric energy. conversion efficiency ~ 13 ~

14 Example 1 2D Piezoelectric Energy Harvester The -31 mode Boundary Condition (Operation mode -31) Efficiency is ~10%

15 Example 2 One-Material Cylindrical Energy Harvester Boundary Condition (Operation mode -33) Optimization Process

16 Example 2 One-material Cylindrical Energy Harvester Design Efficiency Voltage Working State of the Design

17 Example 2 Optimal Results at Different Frequencies When frequency, volume, efficiency Frequency (HZ)

18 Example 3 Multi-Material Cylindrical Energy Harvesters Red represents piezoelectric material; Green represents aluminum. Boundary Condition (Operation mode -33) Efficiency is 16%

19 Example 3: Optimization Curve A B B A

20 Conclusion and Future Work Implemented level-set based TO for multiphysics energy harvesting problems; Reconciled level set (RLS) method for multimaterial representation; Future Work: Apply the methodology to designing other multiphysics energy harvesters; Multifunctional and multi-material structures; Pair TO with multi-material additive manufacturing to enable design of innovative energy harvesters.

21 Thanks!