Design of a Drive-Mechanism for a Flapping Wing Micro Air Vehicle Satyandra K. Gupta Mechanical Engineering Department and Institute for Systems Research University of Maryland, College Park Students: Arvind Ananthanarayanan, Wojciech Bejgerowski, and Dominik Mueller Sponsors: ARO MURI and NSF

Motivation Attributes of fixed wing flight ─ High forward speeds required for generating lift ─ Low maneuverability ─ Difficult to operate in confined spaces Attributes of rotary wing flight ─ Low forward speeds and hovering possible ─ High frequency leads to noisy operation Attributes of flapping wing flight ─ Low frequency flapping leads to quiet flight ─ Low forward speeds lead to high maneuverability ─ Ability to use in surveillance operations

Design Goals Drive mechanism to convert rotary motion to flapping wing motion Include symmetry to ensure stability and minimize vibration Constraints ─ Transmit torque of 0.66 N-mm ─ Support wings of total area 260 cm2 ─ Flap wings at more than 10 Hz ─ Achieve flapping range between -12.5° and +52.5° Performance metrics ─ Weight ─ Cost ─ Power transmission efficiency Flapping range Requirement of low weight electronics demands high transmission efficiency Drive Mechanism Motor Wing Flapping range required to generate the right amount of thrust and lift demands highly synchronized drive mechanism Our exploratory experiments indicated that the drive mechanisms must weigh less than 1.5 g

Design Concept Compliant members used in mechanism to minimize power losses Molded mechanism frame used to minimize weight 2-stage gear reduction used to transmit motor torque Compliant Frame Rocker Crank Wing Supports Flexural Member Rocker Crank Motor with Pinion Gears DESIGN CONCEPT ACTUAL MECHANISM DESIGN

Problem Formulation Primary Objective: Minimize weight Secondary Objective: Minimize number of mold pieces Constraints: ─ Structure shape should be such that forces acting do not induce excessive stresses ─ Structure shape should satisfy molding constraints  Mold machinability  Demoldability of part ─ Weld-lines should be placed in low stress areas of the structure shape

Decomposing the Problem Objective function –Minimize weight Constraints –Stresses should not be excessive –Mold machinability Decision Variable –Structure shape and dimensions Objective function –Minimize mold pieces Constraints –Demoldability Decision Variable –Non-critical connector shapes –Parting lines Constraints –Mold filling –Demoldability –Location of weld-lines Decision Variable –Number of gates –Sacrificial shape elements Mechanism concept Final molded mechanism Shape Synthesis: Optimization problem Mold Piece Design: Optimization problem Gate Placement: Constraint satisfaction problem

Decomposing the Problem Objective function –Minimize weight Constraints –Stresses should not be excessive –Mold machinability Decision Variable –Structure shape and dimensions Mechanism concept Final molded mechanism Shape Synthesis: Optimization problem Objective function –Minimize mold pieces Constraints –Demoldability Decision Variable –Non-critical connector shapes –Parting lines Mold Piece Design: Optimization problem Constraints –Mold filling –Demoldability –Location of weld-lines Decision Variable –Number of gates –Sacrificial shape elements Gate Placement: Constraint satisfaction problem

Overview of Approach Elaborate Mechanism Shape Parametric Model 3D Model Mechanism shape analyzed ─ Forces at different points of the mechanism computed ─ Shape altered to allow for low deflection forces on structure Forces input into FE model to find stresses ─ Mechanism dimensions computed based on allowable stresses ─ Moldability constraints need to be met while selecting dimensions Mechanical Concept Molding Rules Design Requirements Parametric Optimization Moldability Constraints Stress Constraints

Kinematic Representation and Modeling Force estimated using MSC-ADAMS k rot Ω F applied Downstroke Wing Action k rot Ω F applied k rot F applied Torsion spring stiffnessk rot 0.7N-mm/deg Motion appliedΩ21387rpm Wing force resulting from flapping actionF applied 0.19N DC BA i1i1 i2i2 g b f e d c a E Upstroke Wing Action

Measurement of Forces Generated by Flapping Linear motion using a rigid linear MAV is mounted in a clamp fixed to the end of the linear air bearing COOPER LFS270 load cell with a 250 g capacity and g resolution is used for the measurement MAV Clamp Load Cell Air Bearing Vertical Setup Horizontal Setup MAV Clamp Load Cell Air Bearing

Shape Elaboration In-Plane Constraints for the Wing Supports Two-Point Support for the Gearing Axis Rounded Fillets around the Sleeve Crash Impact Protection Shape selection: ─ Bi-planar body-frame

Finite Element Analysis (Pro/Mechanica) and Optimization Maximum induced stresses at one time instant High Stress Concentration Area Large Displacement Areas Undesired Weld-line locations FE structural analysis conducted on the body frame using force estimates from ADAMS Large displacement and high stress concentration areas identified Feature sizes based on maximum allowable stresses

Shape Synthesis Result: Optimized 3-D Model b t Width = 16 mm Length = 41.7 mm Motor Support Diameter = 7mm Flexural Members for Compliant Mechanism x y z b = 0.89 mm t = 1.52 mm Final dimensions

Decomposing the Problem Objective function –Minimize mold pieces Constraints –Demoldability Decision Variable –Non-critical connector shapes –Parting lines Mechanism concept Final molded mechanism Mold Piece Design: Optimization problem Objective function –Minimize weight Constraints –Stresses should not be excessive –Mold machinability Decision Variable –Structure shape and dimensions Constraints –Mold filling –Demoldability –Location of weld-lines Decision Variable –Number of gates –Sacrificial shape elements Shape Synthesis: Optimization problem Gate Placement: Constraint satisfaction problem

Overview of Approach Part Model & Parting Lines Part Model Parting Line Optimization Modified Part Model Perform FEA-based Parametric Optimization Part Model & Parting Lines Add Sacrificial Shape Elements Change Connector Shape No Yes No Is it possible to change connector shapes? Demoldability or Excessive Flash Problems? Yes

Changing Connector Shape to Reduce Mold Pieces Consider different polygonal and circular shapes for non-critical connector shapes For each shape, determine the total number of mold pieces (used MoldGuru a software developed by my students) ─ identify candidate parting directions ─ compute the mold piece regions for each direction Select the connector shape that minimizes the mold pieces Triangular shape element

Mold Piece Optimization Result: Optimized Mold Pieces Side Mold Cores Top Mold Piece 3 Piece Middle Layer Assembly Bottom Mold Piece Step 3b: Removal of middle layer piece Step 3a: Removal of middle layer pieces Step 1: Removal of top and bottom layer of mold pieces post injection Step 2: Removal of cores Injection molded body frame Mold Piece Design: ─ five pieces ─ five side-cores

Decomposing the Problem Constraints –Mold filling –Demoldability –Location of weld-lines Decision Variable –Number of gates –Sacrificial shape elements Mechanism concept Final molded mechanism Gate Placement: Constraint satisfaction problem Objective function –Minimize weight Constraints –Stresses should not be excessive –Mold machinability Decision Variable –Structure shape and dimensions Objective function –Minimize mold pieces Constraints –Demoldability Decision Variable –Non-critical connector shapes –Parting lines Shape Synthesis: Optimization problem Mold Piece Design: Optimization problem

Overview of Approach Identified allowable gate locations ─ Low stress areas from FE analysis ─ Permissible location for flash Filling simulations conducted in Moldflow Plastics Insight for different number of gates and sacrificial shape elements Part Model Insert Gate Move gates Add Sacrificial Shape Elements Insert additional Gate Simulate Flow Yes No Yes No Yes No Yes Gate addition necessary? Gate move possible? Cavity fills? Weld-lines at acceptable locations? Final Mold Design

Filling Analysis Single gated mold leads to asymmetric filling ─ Causes warpage in molded body frame Gate location Gate locations (a) Single gate mold(b) Two gate mold

Appearance of Weld-lines Weld-lines appear in critical areas due to use of two gated mold Third gate introduced to move weld line to non-critical area Gate locations Undesirable weld-line location Weld-line moved to desired location (a) Two gate mold(b) Three gate mold Weld-lines still present in other critical areas Weld-lines

Introduction of Sacrificial Shape Elements Sacrificial shape elements added to: ─ Absorb Weld-lines from the critical areas ─ Absorb flash from the critical areas ─ Provide for better material flow within the cavity ─ Ensure that the part is sticking to only one mold piece during demolding Features sheared off and removed after molding completed Sacrificial element 1 absorbs weld lines Sacrificial element 2 ensures part sticks to one mold piece

Gate Placement Results: Gate Locations Sacrificial shape element 1 Sacrificial shape element 2 Location of Weld-lines Location of the Gates Gate 1 Gate 2 Gate 3 Resulting gate placement:Sacrificial shape elements: Sacrificial shape element 1: ─ completely eliminated the weld-line on the top of the compliant members ─ provided a better melt flow between the cavities ─ ensured safe demolding Sacrificial shape element 2: ─ eliminated the weld-line around the hole

Molded Mechanism Frame Top View Side View In-Plane Constraints for the Wing Supports Two-Point Support for the Gearing Axis Rounded Fillets around the Sleeve Crash Impact Protection In-mold fabricated Body-frame:Bi-planar Design:

Assembly of MAV Mechanism Integration into MAV

“Small Bird” Overall Weight12.9 g Payload Capability2.5 g Flapping Frequency12.1 Hz Wing Area260.0 cm 2 Wing Span34.3 cm Flight Duration5 min Flight Velocity4.4 m/s

“Big Bird” Overall Weight35.0 g Payload Capability12.0 g Flapping Frequency4.5 Hz Wing Area691.7 cm 2 Wing Span57.2 cm Flight Duration7 min Flight Velocity3.75 m/s

“Big Bird with Vision” We have build a version of big bird that flies with a miniature video camera ─ Camera, transmitter, and battery weigh 10.0g ─ Total weight is 45.0g

“Big Bird” with Folding Wing Weight: 36.9 g Wing Span: 57.2 cm Flapping Frequency: 4.5 Hz Pay Load Capability: 10.0 g

Summary Concurrent optimization of shape satisfying functionality and moldability constraints using multi-piece multi-gate mold design ─ Weight ─ Cost ─ High transmission efficiency drive mechanism developed to convert rotary motion to flapping wing motion Tools used ─ ADAMS ─ Pro/Mechanica ─ MoldGuru ─ MoldFlow ─ Pro/Manufacturing We had to rely on physical tests to estimate aerodynamic forces Designed and developed successfully flying flapping wing MAV