# Preliminary Finite Element Analysis and Flight Simulations of a Modular Drone Built through Fused Filament Fabrication

^{*}

## Abstract

**:**

## 1. Introduction

- the UPenn Piccolissimo drone [15], the smallest flying vehicle designed by the University of Pennsylvania; it features a single propeller, but a spinning body, which has been produced in 3D printable polymer;
- the X VEIN drone [16], an open-source project developed for disaster response. It features a lattice structure, which results from a topologic optimization and takes advantage of the additive strategy for its evolutive shape;
- the Tundra-M drone [17], a quadcopter whose central body and arms are produced via Selective Laser Sintering (SLS); this gave the opportunity to iterative optimize its geometry looking for extreme flight conditions scenarios;
- the Iris+ drone [18], whose frame parts can be printed via Fused Filament Fabrication (FFF) and assembled by the final users, together with the electronics provided by the designing company;
- the Skeleton X-14 drone [19], a quadcopter with an FFF-printable single-piece body, home built by the final user, whose peculiar design allows a partial view of the interior components.

## 2. Design of a Modular Drone

- S3A-C: Single motor // 3 Arms Configuration,
- S4A-C: Single motor // 4 Arms Configuration,
- S6A-C: Single motor // 6 Arms Configuration,
- S8A-C: Single motor // 8 Arms Configuration.

#### 2.1. Design Requirements

- all configurations work with the same avionics, electronics, propulsion system, and battery,
- the control unit is designed to identify and manage all the setups,
- the battery is adequately sized for all the configurations.

Remotely piloted aircraft system (RPAS) specialized operations with remotely piloted aircraft (RPA) with an operating take-off mass of less than or equal to 2 kg are to be considered non-critical in any operative scenario, providing that the RPA design criteria and manufacturing techniques result in harmless features that shall be verified in advance by ENAC or by an organization recognized by ENAC.

#### 2.2. Definition of the Components

- propellers,
- DC brushless motors,
- electronic speed controls (ESC),
- Li-Po battery,
- control unit,
- frame.

#### 2.2.1. Propeller Design

- trust constant, ${T}_{c}$, which adjusts the percentage of absorbed power converted into thrust. An efficient propeller would see ${T}_{c}=1$, by converting all the absorbed power into trust; in practice, this value is less than 1.
- power constant, ${P}_{c}$, which adjusts the absorbed power to ideal conditions. A propeller with very narrow blades would see ${P}_{c}=1$; in practice, this value is higher than 1.
- pitch, p, its actual effect on thrust is non-linear. An increase in pitch increases the generated thrust but also makes the propeller absorb more power. Above a critical angle, near the propeller stall, the thrusts curve flattens.

#### 2.2.2. Motor Design

- all-up-weight,
- propeller diameter,
- number of propeller blades,
- propeller pitch,
- battery-rated voltage,
- frame size,
- number of rotors.

- rpm/voltage, which represents the number of revolutions per minute at which the engine rotates without propeller per Volt;
- minimum motor power;
- minimum Electronic Speed Controller (ESC) size, expressed in A.

#### 2.2.3. Electronic Speed Controller Design

## 3. Design of the Frame Components

#### 3.1. Design Requirements

- Direction 1, i.e., the one of filaments deposition, defined in the building platform;
- Direction 2, it is normal to the filaments and still defined in the building platform;
- Direction 3, which is normal to both the filaments and the building platform.

- a coherent definition of the characterization tests setup;
- experimental validation of the predictive capabilities through the mechanical properties defined.

#### 3.2. Components of the Frame

#### 3.2.1. Main Core Elements

#### 3.2.2. Arms

#### 3.2.3. Domes and Landing Gears

- the geometry of the elements,
- the polymeric material,
- the actual setup (e.g., the arm number).

## 4. UAV Virtual Testings

#### 4.1. Model Setup

#### Flight Environment

#### 4.2. Analysis Results

- frame: it is that already discussed in Table 7 considering the structural elements of the UAV;
- drive: it considers the motors, the ESCs, the electrical wires, and the control unit;
- battery: it is constant across all the configuration as they consider the same battery;
- all-up: it defines the take-off weight of the UAV without any additional payload;
- additional payload: it evaluates the payload weight that can be carried, considering the 2000 g limit previously discussed;
- max payload: it represents the maximum additional load that such configuration would sustain.

- load: it defines the discharge rate of the battery, defined as its capacity divided by the discharge time in hours; lower values indicate that the discharge is faster;
- voltage: it is the calculated battery voltage at the highest current flow.

- the minimum flight time assumes maximum throttle for all the flight long;
- the mixed flight time considers an intermediate scenario between the full throttle and the hovering;
- the hover flight time relies on the hovering plan only.

- the current draw of each motor, referred to as current;
- the voltage each motor is subject to;
- the Revolutions Per Minute (RPM);
- the absorbed (electrical) and the generated power (mechanical), together with the efficiency (that is, the ratio between the two);
- the estimated temperature of the motor;
- the power-to-weight ratio, which compares electrical power to the all-up-weight.

- 1.2–1.5: indoor flight, no wind;
- 1.5–1.9: gentle flying under the light wind, good maneuverability;
- 1.9–3.0: heavy wind, excellent maneuverability;
- 3.0–5.0: acrobatic, racing.

- the highest tilt angle the multicopter would sustain in hovering;
- the highest forward speed of the considered setup at full throttle and maximum tilt angle;
- the maximum flight range;
- the maximum climb rate.

## 5. FEM Modeling of the Arm Assembly

#### 5.1. Model Setup

#### 5.1.1. Boundary Conditions

#### 5.1.2. Mesh and Properties Definition

- A 2D orthotropic material for a single layer, defined through the in-plane elastic coefficients of Table 5. The $5\times 5$ stiffness matrix has been traced back to the $3\times 3$ stiffness matrix with appropriate penalties over the shear moduli ${G}_{23}$ and ${G}_{13}$. The layers have been laid up with their real raster angle and thickness, thus defining a laminated composite. This model defined the mechanical behavior of the lower and upper surfaces.
- A 2D isotropic constitutive model, defined through the in-plane direction 1 elastic coefficient of Table 5. For consistency with the previous model and to keep the kinematics unaltered, the isotropic coefficients have been supplied in a 2D orthotropic model. It defines the mechanical properties of the lateral surfaces.

#### 5.2. Analysis Results

- the hollow section is aimed to house the avionics; its horizontal and vertical surfaces guarantee waterproofing in the case of a water landing,
- reducing the stiffness of the arm would result in an increased deflection under the same load, which would modify the application line of the thrust,
- decreasing the wall thickness would reduce the impact resistance of the frame.

## 6. Conclusions and Future Developments

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**Graphic rendering of the PoliDrone UAV in the S4A-C configuration: four arms with a single motor/propeller each.

**Figure 2.**Graphical representation of the setups considered in the design phase. The elements in these figures are not in scale. (

**a**) S3A-C. (

**b**) S4A-C. (

**c**) S6A-C. (

**d**) S8A-C.

**Figure 3.**Material reference system of a layer featuring linear infill. All the filaments are parallel to direction 1, which lies on the building platform together with direction 2. 3 is the out-of-plane direction, orthogonal to the building platform.

**Figure 4.**Comparison between unidirectional laminae, stacked into a laminate, and FFF layers, piled into a component with a linear infill.

**Figure 6.**Graphic rendering of the arm assembly. The support is colored in gray; the upper and the lower elements are those in red.

**Figure 8.**Components of the arm: preview of the 3D-printing strategy via FFF. (

**a**) Arm elements, top view. (

**b**) Support, top view. (

**c**) Arm elements, side view. (

**d**) Support, side view..

**Figure 11.**FE model, model setup: surrogate shell representation of the arm assembly for FE analysis.

**Figure 13.**FE model, model setup: convergence analysis of the total strain energy vs. the global edge length.

**Figure 15.**Transverse displacement map (X direction), superimposed on the arm deformed shape. The results are expressed in mm.

**Figure 16.**Axial component (Y direction) of the stress tensor map, superimposed on the arm deformed shape. The results are expressed in MPa. (

**a**) Top view. (

**b**) Bottom view.

**Figure 17.**Transverse components of the stress tensor map, superimposed on the arm deformed shape. The results are expressed in MPa. (

**a**) X component. (

**b**) Z component.

**Figure 20.**Von Mises stresses distribution in the lateral surfaces of the support (

**left**) and of the arm (

**right**).

**Table 1.**Design of a modular drone: datasheet of the Aeronaut propellers defined per each configuration.

Setup | Manufacturer | Model | Dia | Pitch | ${\mathit{T}}_{\mathit{c}}$ | ${\mathit{P}}_{\mathit{c}}$ |
---|---|---|---|---|---|---|

S3A-C → | Aeronaut | CamCarbon | ${13}^{\prime}$ | ${5}^{\prime}$ | $1.07$ | $0.99$ |

S4A-C → | ${13}^{\prime}$ | ${5}^{\prime}$ | $1.07$ | $0.99$ | ||

S6A-C → | ${11}^{\prime}$ | ${4.5}^{\prime}$ | $1.07$ | $0.99$ | ||

S8A-C → | ${8}^{\prime}$ | ${4.5}^{\prime}$ | $1.07$ | $0.99$ |

Motor Wizard | |||||
---|---|---|---|---|---|

Input parameters | S3A-C | S4A-C | S6A-C | S8A-C | |

all-up weight | 2000 g | 2000 g | 2000 g | 2000 g | |

n${}^{\circ}$ of rotors | 3—flat | 4—flat | 6—flat | 8—flat | |

frame size | 580 mm | 580 mm | 580 mm | 580 mm | |

battery-rated voltage | $11.1$ V | $11.1$ V | $11.1$ V | $11.1$ V | |

propeller diameter | ${13}^{\prime}$ | ${13}^{\prime}$ | ${11}^{\prime}$ | ${8}^{\prime}$ | |

propeller pitch | ${5}^{\prime}$ | ${5}^{\prime}$ | ${4.5}^{\prime}$ | ${4.5}^{\prime}$ | |

propeller blades | 2 | 2 | 2 | 2 | |

Calculated optimal design ranges | |||||

rpm/voltage [rpm/V] | → | 790–1150 | 680–1000 | 740–1070 | 1090–1580 |

min. motor power [W] | → | 415–725 | 270–475 | 175–305 | 155–275 |

min ESC size [A] | → | 45–75 | 30–50 | 20–35 | 20–30 |

NeuMotors Model 1230/5Y | |
---|---|

rpm/voltage | 987 KV |

body length | 33 mm |

weight | 35 g |

idle current | $0.5$ A @ 10 V |

max cont. power | 250 W |

resistance | $0.225$$\Omega $ |

torque constant | $9.698$ mNm/A |

KISS 18A ESC | |
---|---|

input voltage | 2–4 S |

max continuous amperage | 18 A |

peak amperage | 30 A |

width | 12 mm |

length | 23 mm |

weight | 2 g |

**Table 5.**Comparison between the experimental mechanical properties under the hypothesis of orthotropy and those declared by the manufacturer, assuming that PLA keeps isotropic behavior even after FFF processing.

PLA Mechanical Properties | |||||||
---|---|---|---|---|---|---|---|

Experimental (ORT) | Datasheet (ISO) | ||||||

${E}_{11}$ | 3008 | MPa | [31] | E | 3950 | MPa | [50] |

${E}_{22}$ | 2876 | MPa | [31] | − | − | − | |

${E}_{33}$ | 2894 | MPa | [47] | − | − | − | |

${\nu}_{12}$ | $0.286$ | − | [31] | $\nu $ | $0.3$ | − | [50] |

${G}_{12}$ | 1227 | MPa | [31] | G | 1182 | MPa | [50] |

${\sigma}_{11}^{max}$ | $56.4$ | MPa | [31] | ${\sigma}^{max}$ | $60.0$ | MPa | [50] |

${\sigma}_{22}^{max}$ | $48.0$ | MPa | [31] | − | − | − | |

${\sigma}_{33}^{max}$ | $17.5$ | MPa | [47] | − | − | − | |

${\sigma}_{11}^{pro}$ | $54.0$ | MPa | [31] | − | − | − | |

${\sigma}_{22}^{pro}$ | $46.2$ | MPa | [31] | − | − | − | |

${\sigma}_{33}^{pro}$ | $13.1$ | MPa | [47] | − | − | − | |

${\tau}_{12}^{max}$ | $30.6$ | MPa | [31] | − | − | − |

1st layer height | $0.20$ | mm |

Gen. layer height | $0.10$ | mm |

Nozzle diameter | $0.40$ | mm |

Extrusion width | $0.50$ | mm |

Infill percentage | $100\%$ | - |

1st layer extrusion temp. | 190 | ${}^{\circ}$C |

Extrusion temperature | 200 | ${}^{\circ}$C |

Bed temperature | 30 | ${}^{\circ}$C |

Extrusion multiplier | $1.05$ | - |

Default speed | 3000 | mm/min |

Retraction distance | 3 | mm |

Individual Weights | Bill of Materials | ||||
---|---|---|---|---|---|

Description | Weight [g] | S3A-C | S4A-C | S6A-C | S8A-C |

Upper plate | $108.2$ | 1 | 1 | 1 | 1 |

Bottom plate | $77.7$ | 1 | 1 | 1 | 1 |

Upper arm element | $16.0$ | 3 | 4 | 6 | 8 |

Bottom arm element | $20.3$ | 3 | 4 | 6 | 8 |

Arm support | $23.6$ | 3 | 4 | 6 | 8 |

Upper dome | $72.5$ | 1 | 1 | 1 | 1 |

Bottom dome | $87.0$ | 1 | 1 | 1 | 1 |

Landing gear | $49.8$ | 2 | 2 | 2 | 2 |

Overall structure weight → | 625 g | 684 g | 804 g | 924 g |

Field Elevation | Air Temperature | Pressure |
---|---|---|

254 m ASL | $14.8$${}^{\circ}$C | $987.1$ hPa |

PoliDrone Multicopter—Preliminary Design | |||||
---|---|---|---|---|---|

S3A-C | S4A-C | S6A-C | S8A-C | ||

Weights | Frame | 625 g | 684 g | 804 g | 924 g |

Drive | 161 g | 201 g | 280 g | 359 g | |

Battery | 426 g | 426 g | 426 g | 426 g | |

ALL-UP | 1212 g | 1311 g | 1510 g | 1709 g | |

Add. Payload | 788 g | 689 g | 490 g | 291 g | |

Max. Payload | 1212 g | 1756 g | 2102 g | 912 g |

**Table 10.**Preliminary design of PoliDrone multicopter: battery performance estimations. Calculations are based on a 6000 mAh, 11.1 V battery used up to 90%.

PoliDrone Multicopter—Preliminary Design | |||||
---|---|---|---|---|---|

S3A-C | S4A-C | S6A-C | S8A-C | ||

Battery | Load | $9.68$ C | $12.58$ C | $13.23$ C | $8.44$ C |

Voltage | $10.44$ V | $10.24$ V | $10.19$ V | $10.52$ V | |

Min. flight time | $5.6$ min | $4.3$ min | $4.1$ min | $6.4$ min | |

Mixed flight time | $14.2$ min | $14.0$ min | $13.7$ min | $12.6$ min | |

Hovering flight time | $19.7$ min | $20.9$ min | $20.6$ min | $16.0$ min |

**Table 11.**Preliminary design of PoliDrone multicopter: single-motor performance estimations. Calculations are based on a 6000 mAh, 11.1 V battery used up to 90%.

PoliDrone Multicopter—Preliminary Design | |||||
---|---|---|---|---|---|

S3A-C | S4A-C | S6A-C | S8A-C | ||

@ optimum | Current | $4.80$ A | $4.77$ A | $4.72$ A | $4.67$ A |

Tension | $10.92$ V | $10.86$ V | $10.76$ V | $10.66$ V | |

RPM | 9664 | 9617 | 9526 | 9436 | |

Electrical power | $52.3$ W | $51.8$ W | $50.8$ W | $49.7$ W | |

Mechanical power | $42.1$ W | $41.7$ W | $40.8$ W | $40.0$ W | |

Efficiency | $80.4$% | $80.4$% | $80.4$% | $80.4$% | |

@ maximum | Current | $19.37$ A | $18.86$ A | $13.23$ A | $6.33$ A |

Tension | $10.36$ V | $10.16$ V | $10.14$ V | $10.50$ V | |

RPM | 5740 | 5663 | 6945 | 8894 | |

Electrical power | $200.6$ W | $191.7$ W | $134.2$ W | $66.5$ | |

Mechanical power | $110.7$ W | $106.3$ | $90.5$ W | $52.9$ | |

Power to weight | $496.5$ W/kg | $585.0$ W/kg | $533.2$ W/kg | $311.1$ W/kg | |

Efficiency | $55.1$% | $55.4$% | $67.4$% | $79.6$% | |

Est. temperature | 50 ${}^{\circ}$ | 48 ${}^{\circ}$ | 32 ${}^{\circ}$ | 20 ${}^{\circ}$ | |

@ hovering | Current | $5.48$ A | $3.87$ A | $2.62$ A | $2.52$ A |

Tension | $10.89$ V | $10.91$ V | $10.91$ V | $10.86$ V | |

RPM | 3482 | 3136 | 3760 | 5891 | |

Electrical power | $59.7$ W | $42.2$ W | $28.6$ W | $27.4$ W | |

Mechanical power | $34.7$ W | $25.3$ W | $20.1$ W | $21.7$ W | |

Power to weight | $150.5$ W/kg | $131.0$ W/kg | $115.5$ W/kg | $131.1$ W/kg | |

Efficiency | $58.1$% | $60.0$% | $70.5$% | $79.0$% | |

Est. temperature | 25 ${}^{\circ}$ | 22 ${}^{\circ}$ | 18 ${}^{\circ}$ | 17 ${}^{\circ}$ |

**Table 12.**Preliminary design of PoliDrone multicopter: motors performance estimations. Calculations are based on a 6000 mAh, 11.1 V battery used up to 90%.

PoliDrone Multicopter–Preliminary Design | |||||
---|---|---|---|---|---|

S3A-C | S4A-C | S6A-C | S8A-C | ||

Trust-to-weight | 2.2:1 | 2.7:1 | 2.8:1 | 1.8:1 | |

@ Hover | Current | $16.44$ A | $15.47$ A | $15.70$ A | $20.19$ A |

P(in) | $182.5$ W | $171.7$ W | $174.3$ W | $224.1$ W | |

P(out) | $104.0$ W | $101.3$ W | $120.8$ W | $173.2$ W | |

Efficiency | $57.0$% | $59.0$% | $69.3$% | $77.3$% | |

@ Max | Current | $58.10$ A | $75.45$ A | $79.40$ A | $50.66$ A |

P(in) | $644.9$ W | $837.5$ W | $881.4$ W | $562.3$ W | |

P(out) | $332.0$ W | $425.2$ W | $542.8$ W | $423.5$ W | |

Efficiency | $51.5$% | $50.8$% | $61.6$% | $75.3$% |

**Table 13.**Preliminary design of PoliDrone multicopter: flight performance estimations. Calculations are based on a 6000 mAh, 11.1 V battery used up to 90%.

PoliDrone Multicopter—Preliminary Design | |||||
---|---|---|---|---|---|

S3A-C | S4A-C | S6A-C | S8A-C | ||

Efficiency | Max tilt | 58 ${}^{\circ}$ | 65 ${}^{\circ}$ | 65 ${}^{\circ}$ | 49 ${}^{\circ}$ |

Max speed | 47 km/h | 49 km/h | 53 km/h | 50 km/h | |

Est range | 3458 m | 3373 m | 3554 m | 3906 m | |

Climb rate | $5.2$ m/s | $6.0$ m/s | $6.8$ m/s | $5.5$ m/s |

**Table 14.**Mesh convergence through gradually smaller element dimensions, expressed in terms of Global Edge Length.

GEL | Nodes No. | Elements No. | Total Strain Energy | ${\mathit{u}}_{\mathit{tip}}$ |
---|---|---|---|---|

mm | [${10}^{-3}\mathit{J}$] | [mm] | ||

10 | 3229 | 2741 | $9.126$ | $-1.0$ |

$7.5$ | 3489 | 2978 | $5.342$ | $-1.0$ |

6 | 3618 | 3086 | $5.330$ | $-1.0$ |

5 | 3801 | 3269 | $4.922$ | $-1.0$ |

4 | 4324 | 3769 | $4.995$ | $-1.0$ |

3 | 5277 | 4725 | $4.869$ | $-1.0$ |

2 | 8215 | 7662 | $4.809$ | $-1.0$ |

1 | 23,297 | 22,639 | $4.787$ | $-1.0$ |

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## Share and Cite

**MDPI and ACS Style**

Brischetto, S.; Torre, R.
Preliminary Finite Element Analysis and Flight Simulations of a Modular Drone Built through Fused Filament Fabrication. *J. Compos. Sci.* **2021**, *5*, 293.
https://doi.org/10.3390/jcs5110293

**AMA Style**

Brischetto S, Torre R.
Preliminary Finite Element Analysis and Flight Simulations of a Modular Drone Built through Fused Filament Fabrication. *Journal of Composites Science*. 2021; 5(11):293.
https://doi.org/10.3390/jcs5110293

**Chicago/Turabian Style**

Brischetto, Salvatore, and Roberto Torre.
2021. "Preliminary Finite Element Analysis and Flight Simulations of a Modular Drone Built through Fused Filament Fabrication" *Journal of Composites Science* 5, no. 11: 293.
https://doi.org/10.3390/jcs5110293