GROUP 10 GAURAV POKHARKAR NIKHIL SONAWANE PREETI VAIDYA Design optimization of Quadcopter

Motivation Quadcopter’s have become popular in recent years in some areas like- Aerial surveillance Disaster aid and rescue operations Crop survey Applications will increase as it is an attractive alternative to other bigger unmanned aerial vehicles.

Subsystems classification for optimization-  Frame design optimization  Propulsion system optimization  Component placement and system integration

Methodology Assume target size and weight Set up design model, design variables, parameters Estimate variables iteratively and find optimal solution

Subsystem 1: Design of Arms Cross-section of the arm Solidworks structural optimization toolbox was used to estimate the basic dimensions of the arm

Optimization Problem Hollow circular tube was selected as the cross section of the arms as it has largest inertia for the same weight/area also it is symmetric My main aim was to reduce cost and weight of the arms To evaluate the cost following assumptions were made: Objective function = 0.25 *(Machining cost * Amount of Machining required + Cost for precision drilling of the hole + Cost of Raw material * Amount of raw material) +0.75*(Weight of the rod) Assumptions: Arms to be made of aluminum The arms acted as cantilever beam Thrust force acted on the arms due to motor at the end of the arms Rough estimate of the weight of the quadcopter 3 kg Hence the thrust force was estimated to be bout 1.5 kg on one arm Constraints: Tensile stress due to bending moment is less than the tensile strength of the material Natural frequency of the arms should not be equal to the frequency of motor to avoid resonance The thickness of the rod should be minimum of 3 mm from manufacturing point of view

Optimization Problem Objective function: min 0.25*((0.5*pi*ID^2*L/4)+(0.5*L/ID)+(pi*OD ^2*L/4))+0.75*(pi*(OD^2-ID^2)*L/4) Variables- OD, ID Constraints: OD-ID>=3 mm Stress due to bending σ=M*y/I <= 120 N/mm^2 Frequency of motors ~ rps First five natural frequencies >= 190 Hz For Aluminum: E = 6.9e10 N/mm^2 Density = 2700 Kg/m^3 Tensile Strength = 276 MPa Design Strength = 120 Mpa Length ~ 200 mm

Using GRG Algorithm Length300mm OD mm ID mm Modes1st Mode2nd Mode3rd Mode4th Mode5th Mode Frequency Weight Kg

Subsystem 2: Propulsion system optimization Objective function: Optimize efficiency of propeller for given payload capacity (3 kg) and aerofoil type (assumed similar to NACA 4415) Variables: Effect of variation in Diameter and angle of attack was to be analyzed Constraints: Thrust minimum >= 1.5 kg Diameter < (arm length*2)=300*2 mm Ct > 0

Design Model: Blade Element Theory

Equations : Blade Element theory

Design Model Algorithm Initial guess on inflow factors a,b Solve for elemental thrust ΔT, torque ΔQ Solve for alpha, Cl, Cd Solve for ΔT, ΔQ in terms of Cl and Cd Update a, b. Calculate final Thrust, Torque

Optimization problem

Fmincon solution Problems faced initially: Efficiency should increase till α <= 16° beyond which it should decrease for any given D ( as turbulence and drag increases exponentially with alpha). But, it kept hitting the upper bound. Modified the drag co-efficient equation after which solution converged to D = inch, α = 13.6° This solution satisfies the constraints. Thrust obtained at this combination is 1.9 kg and efficiency= 58.4%.

Motor and Battery Selection Based on the optimized propeller dimensions (12 x 5 inch) the motor and battery selected are- Motor: BLDC motor Outrunner 550 Plus 1470 KV Battery: Li-Po battery 3S4P at 11V

Subsystem 3: Component placement Plays a major role in quadcopter stabilization during flight and take off. The components are placed in such a way so that the moment generated by their weights are minimum about the center of the quadcopter and they must not overlap. The various components which are to be placed on the quadcopter frame are as follows- 1. Camera 2. Battery 3. Antenna 4. Receiver 5. 4 × ESC’s ( Electronic Speed Controller) 6. Flight control circuit

Assumptions The components are isotropic The components are treated as cuboids Aerodynamic drag is neglected. Weights of each components and Dimensions of each components ComponentWeight ( gms)Length (mm)Breadth(mm)Height(mm) Camera Battery Antenna+ Receiver Esc Flight control circuit

Optimization problem Objective function Minimize Mx =∑(Weight*Xcg) My=∑(Weight*Ycg) Variables- X,Y coordinates of all components Constraints- 1. All components are placed in xy plane. 2. The components must not overlap with each other in x or y direction. 3. Position of components must be closer to cg of quadcopter. 4. The camera is placed in the first quadrant so that it does not have interference in visibility due to propeller blades. 5. The upper and lower bounds on the values are 140mm and -140 mm, it depends on the circular disk to be mounted on the frame.

Issues faced Trying to optimize the problem by placing the components as close as possible to the center. Objective was to minimize the area within which the components can be placed. Variables and constraints being the same. This gives the feasible region for Placing the components but gives Highly unbalanced moment and thus such closed packing of components although being closest cannot satisfy moment minimization.

The optimal solution of the above problem along with obtained upper and lower bounds is considered as an initial point to the moment balance problem as all the constraints are already satisfied and iterations were performed accordingly. For UB=[96] and LB=[-96] f= e+08 ( highly infeasible !!!)

Final results- Xopt was found with UB=[140], LB=[-140] f= e-06 ( finally !!!)

System Integration The main aim of system integration is to avoid sub- optimization of sub-systems and lead to overall optimization. Famous example of sub-optimization is “The surgery was successful but the patient died.”

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