多直升机空气动力学：六轴飞行器上的特征推力
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Overview
资料来源：普拉申·夏尔马和埃拉·阿特金斯，密歇根大学航空航天工程系，安阿伯，密歇根州
多直升机正在成为各种爱好和商业应用的流行。它们通常可作为四轴飞行器（四个推进器）、六轴飞行器（六个推进器）和八轴飞行器（八个推进器）配置。在这里，我们描述了一个实验过程来描述多直升机的性能。测试了提供推进单元冗余的模块化小型六轴器平台。使用测功机和不同的螺旋桨和输入命令确定单个静态电机推力。然后，此静态推力表示为电机 RPM 的函数，其中转速由电机功率和控制输入确定。然后，六轴飞行器安装在5’x 7’低速再循环风洞的称重传感器测试台上，其空气动力学提升和阻力部件在飞行过程中以不同的运动信号、自由流动速度和攻击角度进行特征。
六轴飞行器之所以被选中用于这项研究，是因为它能够适应电机（推进单元）故障，如《克洛蒂耶1号》所报道的。除了推进系统的冗余外，安全飞行也需要选择高可靠性部件，特别是对于任务人口过剩的地区。在《安帕地斯2》中，作者讨论了多轴飞行器部件的最佳选择，如电机、叶片、电池和电子速度控制器。贝尔沙斯基3号也进行了类似的研究，该研究的重点是正确选择螺旋桨系统，以满足任务要求。除了部件的冗余和可靠性外，了解车辆性能对于确保遵守飞行包络限制和选择最有效的设计也至关重要。
Principles
Procedure
Results
Dynamometer Tests
In Figures 5-6, the plots illustrate the variation of thrust and torque, respectively, with increasing motor RPM. From these plots, the minimum motor RPM required for the multicopter to hover can be determined. A plot showing data from multiple propellers can be obtained from Sharma12. Further, the quadratic relations between thrust vs. RPM and moment vs. RPM can be clearly observed, which are described in Equations (1) and (2). Using this quadratic relationship, we can then determine the 
and 
coefficients for the 6040 propeller, which are as follows:
Figure 7 shows that an increase in RPM corresponding with an increase in electrical power consumption results in decreased motor efficiency. Similar experiments can be conducted for different propellers to obtain motor efficiency for the motor-propeller pair. The results from such experiments are useful during vehicle design to determine the optimal motor-propeller pair to be used on the multicopter. These decisions are based on the desired mission parameters, such as the duration and speed of the flight.
Since there is no direct RPM sensor feedback on the low-cost hexacopter, we estimate RPM by fitting a surface across RPM, electrical power, and throttle (PWM) command. This surface fit is used to estimate RPM as a function of electrical power and PWM value. Based on data collected from the dynamometer, the surface fit is shown in Figure 8, with the corresponding equation:
where 
is the motor PWM (throttle) setting normalized by the mean bias value 1550 
with a standard deviation of 201.9 
, while 
is normalized by bias 71.11 W with a standard deviation of 55.75 W.
After analyzing the dynamometer data, a second dataset was collected for validation and provided as an input to 
function. The results are then plotted in a time series of RPM variation, as seen in Figure 9 and Figure 10. These plots confirm that the fit estimates RPM to within 95% bounds of the actual RPM, as shown in Figure 9.
Wind Tunnel Results
Experiments in the wind tunnel were conducted following the test matrix in Table 1. To reduce complexity, a zero yaw (sideslip) angle condition was maintained at all times. This is consistent with most flight profiles in which cameras and other sensors are mounted with a preferred forward-facing orientation. The variation of drag and lift are plotted against different pitch angles of the hexacopter and are shown in Figures 11 and 12, respectively. Both plots show that increasing the throttle command results in a significant increase in lift (motor thrust) force. Similarly, an increase in wind tunnel speed results in a significant increase in the drag force acting on hexacopter. These trends are consistent with Equation (7).
A static thrust model only requires dynamometer testing. However, to gain an accurate estimate of dynamic thrust and drag, wind tunnel experiments with FT load cell sensing were required. With collected data, we can develop a lookup table of and and drag coefficients 
,
as a function of pitch angle and free stream airspeed to enable accurate hexacopter FT modeling.
Figure 1. Reference world and body coordinate frames. Please click here to view a larger version of this figure.
Figure 2. Multicopter load cell test stand. Please click here to view a larger version of this figure.
Figure 3. Wind tunnel data acquisition (DAQ) system diagram. Please click here to view a larger version of this figure.
Figure 4. Dynamometer setup. Please click here to view a larger version of this figure.
Figure 5. Relationship between motor thrust and RPM. Please click here to view a larger version of this figure.
Figure 6. Relationship between motor torque and RPM. Please click here to view a larger version of this figure.
Figure 7. Overall motor efficiency vs. RPM. Please click here to view a larger version of this figure.
Figure 8. Surface fit over throttle (PWM), electrical power, and RPM. Please click here to view a larger version of this figure.
Figure 9. Validation of 
with RPM measured directly from the dynamometer. Please click here to view a larger version of this figure.
Figure 10. Validation of estimated thrust data with measured thrust data. Please click here to view a larger version of this figure.
Figure 11. Load cell lift and drag forces for different pitch angles and throttle commands given constant wind speed of 5 m/s. Please click here to view a larger version of this figure.
Figure 12. Load cell lift and drag forces for different pitch angles and throttle commands given constant wind speed of 8.47 m/s. Please click here to view a larger version of this figure.
Table 1. Wind tunnel test matrix
| Wind Tunnel Test Matrix | |||
| Wind Speed (m/s) | Pitch Angle (°) | Yaw Angle(°) | Throttle Command (ms) |
| 2.2 | 30 to -30 | 0 | 0 and 1300 to 1700 |
| 4.5 | 30 to -30 | 0 | 0 and 1300 to 1700 |
| 6.7 | 30 to -30 | 0 | 0 and 1300 to 1700 |
| 8.9 | 30 to -30 | 0 | 0 and 1300 to 1700 |
Table 2. Parts list
| Parts List for Hexacopter | |||||
| Sr No | Part No | Description | Img | Link | Qty |
| 1 | SKU: 571000027-0 | HobbyKing™ Totem Q450 Hexacopter Kit |  |
https://hobbyking.com/en_us/hobbykingtm-totem-q450-hexacopter-kit.html | 1 |
| 2 | SKU: 571000064-0 | OpenPilot CC3D Revolution (Revo) 32bit F4 Based Flight Controller w/Integrated 433Mhz OPLink |  |
https://hobbyking.com/en_us/openpilot-cc3d-revolution-revo-32bit-flight-controller-w-integrated-433mhz-oplink.html | 1 |
| 3 | SKU: 571000065-0 | Openpilot OPLink Mini Ground Station 433 MHz |  |
https://hobbyking.com/en_us/openpilot-oplink-mini-ground-station-433-mhz.html | 1 |
| 4 | SKU: 9536000003-0 | Multistar Elite 2204-2300KV 3-4s 4 pack (2/CCW 2/CW) |  |
https://hobbyking.com/en_us/multistar-elite-2204-2300kv-set-of-4-cw-ccw-2-ccw-2-cw.html | 2 |
| 5 | SKU: 9192000131-0 | Afro 20A Muti-Rotor ESC (SimonK Firmware) |  |
https://hobbyking.com/en_us/afro-esc-20amp-multi-rotor-motor-speed-controller-simonk-firmware.html | 8 |
| 6 | SKU: T2200.3S.30 | Turnigy 2200mAh 3S 30C Lipo Pack |  |
https://hobbyking.com/en_us/turnigy-2200mah-3s-30c-lipo-pack.html | 1 |
| 7 | SKU: 9171000144 | Hobby King Octocopter Power Distribution Board |  |
https://hobbyking.com/en_us/hobby-king-octocopter-power-distribution-board.html | 1 |
| 8 | SKU: 426000022-0 | King KongMultirotor Prop 6×4 CW/CCW |  |
https://hobbyking.com/en_us/kingkong-multirotor-propeller-6×4-cw-ccw-black-20pcs.html | 1 |
| 8 | SKU: 329000304-0 | Gemfan Propeller 5×3 Black (CW/CCW) (2pcs) |  |
https://hobbyking.com/en_us/gemfan-propeller-5×3-black-cw-ccw-2pcs.html | 10 |
| 9 | – | Spektrum DX6 Transmitter System MD2 with AR610 Receiver |  |
https://www.amazon.com/Spektrum-Transmitter-System-AR610-Receiver/dp/B01B9DYOWG/ref=sr_1_2?ie=UTF8&qid=1494000219&sr=8-2&keywords=spektrum+dx6 | 1 |
| 10 | 709-RSP-1600-12 | Switching Power Supplies 1500W 12V 125A |  |
https://www.mouser.com/ProductDetail/Mean-Well/RSP-1600-12/?qs=%2fha2pyFadujYDPrAgY3T1JlGoR5AZMKL7jhmRydJUc1Z44%252bNekUvbQ%3d%3d | 1 |
| Parts List for DAQ | |||||
| Sr No | Part No | Description | Img | Link | Qty |
| 1 | ATHM800-256ALP Rev F | Athena II PC /104 SBC |  |
http://www.diamondsystems.com/products/athenaii | 1 |
| 2 | SI-145-5 | Mini 45 Force /Torque Sensor |  |
http://www.ati-ia.com/products/ft/ft_models.aspx?id=Mini45 | 1 |
| 3 | – | Hobbypower Airspeed Sensor MPXV7002DP Differential Pressure |  |
https://www.amazon.com/Hobbypower-Airspeed-MPXV7002DP-Differential-controller/dp/B00WSFWO36/ref=pd_day0_21_2?_encoding=UTF8&pd_rd_i=B00WSFWO36&pd_rd_r=8KRZ03PR2XAJ1HXD4BKS&pd_rd_w=M1tek&pd_rd_wg=LVHjU&psc=1&refRID=8KRZ03PR2XAJ1HXD4BKS | 1 |
| Parts List for Dynamometer | |||||
| Sr No | Part No | Description | Img | Link | Qty |
| 1 | Series-1580 | RC Benchmark Dynamometer |  |
https://www.rcbenchmark.com/dynamometer-series-1580/ | 1 |
Applications and Summary
Here we describe a protocol to characterize the aerodynamic forces acting on a hexacopter. This protocol can be applied to other multirotor configurations directly. Proper characterization of aerodynamic forces is needed to improve control design, understand flight envelope limits, and estimate local wind fields as in Xiang13. The presented protocol for determining motor RPM based on power consumption and throttle command has direct applications to estimate RPM and thrust when low-cost electronic speed controllers (ESCs) without RPM sensing are used. Finally, the application of advanced control techniques, such as in model predictive control for trajectory tracking, require knowledge of vehicle aerodynamics and thrust forces, as described in Kamel14.
References
- Clothier, R.A., and Walker, R.A., “Safety Risk Management of Unmanned Aircraft Systems,” Handbook of Unmanned Aerial Vehicles, Springer, 2015, pp. 2229–2275.
- Ampatis, C., and Papadopoulos, E., “Parametric Design and Optimization of Multi-rotor Aerial Vehicles,” Applications of Mathematics and Informatics in Science and Engineering, Springer, 2014, pp. 1–25.
- Bershadsky, D., Haviland, S., and Johnson, E. N., “Electric Multirotor UAV Propulsion System Sizing for Performance Prediction and Design Optimization,” 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf., 2016.
- Bangura, M., Melega, M., Naldi, R., and Mahony, R., “Aerodynamics of Rotor Blades for Quadrotors,” arXiv preprint arXiv:1601.00733, 2016
- Ducard, G., and Minh-Duc Hua. "Discussion and Practical Aspects on Control Allocation for a Multi-rotor Helicopter." Conf. on Unmanned Aerial Vehicle in Geomatics, 2011.
- Powers C., Mellinger D., Kumar V. “Quadrotor Kinematics and Dynamics” In: Handbook of Unmanned Aerial Vehicles. Springer, 2015
- McClamroch, N. Harris. “Steady Aircraft Flight and Performance.” Princeton University Press, 2011.
- Quan, Q., “Introduction to Multicopter Design and Control”, Springer Singapore, 2017.
- LibrePilot, https://www.librepilot.org/site/index.html
- Foster, J. and Hartman, D., “High-Fidelity Multi-Rotor Unmanned Aircraft System Simulation Development for Trajectory Prediction under Off-Nominal Flight Dynamics,” Proc. Air Transportation Integration & Operations (ATIO) Conference, AIAA, 2017.
- Russell, Carl R., et al. "Wind Tunnel and Hover Performance Test Results for Multicopter UAS Vehicles," 2016.
- Sharma, P. and Atkins, E., “An Experimental Investigation of Tractor and Pusher Hexacopter Performance,” Proc. AIAA Aviation Conference, AIAA, June 2018. (to appear)
- Xiang, X., et al. "Wind Field Estimation through Autonomous Quadcopter Avionics." 35th AIAA/IEEE Digital Avionics Systems Conference (DASC), IEEE, 2016.
- Kamel, M., et al. "Model Predictive Control for Trajectory Tracking of Unmanned Aerial Vehicles using Robot Operating System." Robot Operating System (ROS). Springer, Cham, 2017, 3-39.
Transcript
Multicopters are small aerial vehicles with multiple rotors, as opposed to traditional helicopters with one main rotor. A traditional helicopter rotor has variable pitch, which enables the pilot to control lift and steering. However, multicopters rely on fixed pitch rotors. Some rotate clockwise, and some rotate counterclockwise. Flight is controlled by varying the speed of one or more rotors. For example, in this hexacopter, all of the propellers operate at the same speed. This produces the same thrust for it to hover.
Like fixed wing aircraft, hexacopter attitude is described about three axes: the pitch axis, the roll axis, and the yaw axis. The hexacopter can be controlled about the pitch axis by increasing the speed of the propellers on one side of the pitch axis and decreasing the speeds of the ones on the other side. This creates a thrust differential between the two sides. If thrust is increased in the rear propellers and decreased in the forward propellers, the hexacopter pitches forward.
Similarly, the hexacopter can be controlled about the roll axis in the same way. This causes side-to-side movement. This is done by increasing the speed of the propellers on one side and decreasing the speed of the propellers on the other side.
Yaw control, which changes the heading angle, is achieved by balancing the clockwise propeller rotational torques with the counterclockwise propeller rotational torques. By spinning the counterclockwise propellers faster than the clockwise propellers, the opposite net reaction induces a clockwise rotation about the yaw axis.
We can calculate the thrust and torque of each propeller unit using the equations shown. where T is the thrust generated, CT is the thrust coefficient, tau is the torque, CQ is the torque coefficient, and omega is the rotational speed in RPM. Both the electrical power input and the mechanical power output can be calculated using the following equations. The electrical and mechanical power are then used to determine the efficiency of the propeller motor. The two coefficients, along with the electrical and mechanical power, are calculated using data acquired from experiments.
In this lab, we will demonstrate how to calculate aerodynamic and thrust forces on a hexacopter using a load cell mounted on a test stand. Then, we will characterize and analyze lift and drag over a range of air speeds using a wind tunnel.
To begin this experiment, we’ll use a dynamometer to measure and calculate parameters of one propeller. First, obtain a dynamometer with an onboard data acquisition system. Run the graphical user interface provided with the dynamometer system. Mount the motor on the dynamometer test stand and connect all device wires. Then, calibrate the system by following the onscreen instructions, using weights and the known lever arm when prompted.
Once calibration is complete, attach the propeller in a ‘puller’ configuration. Before running the experiments, make sure the dynamometer is firmly secured to the workbench using C-clamps, and that it is placed behind a plexiglass protection wall.
Now connect the battery to the dynamometer. Run the step input program, which powers the DC motors using a pulsed signal. The program will record the measured thrust, torque, motor RPM, motor current, and pulse with modulation throttle command.
For this part of the experiment, we will measure thrust from the hexacopter using a load cell outside of the wind tunnel to avoid disturbances from the wind tunnel walls.
First, fasten the hexacopter onto the load cell test stand using mounting screws. Then, open the data acquisition system and run the load cell strain gauge bias program to remove all of the bias load cell values. Connect the hexacopter flight controller to the computer using a micro USB cable, and connect the power supply to the hexacopter.
Then, open the ground controller station program. Under the configuration tab, link all motors by clicking the tick mark on the right side. Move the output channel slider to the desired throttle command at 1,300 microseconds. Let the system stabilize for a few seconds and then run the program to collect data from the load cell.
When the program is complete, stop the motors by moving the output channel sliders to the left on the ground controller station. Repeat the test with throttle commands of 1,500 and 1,700 microseconds. Then stop the motors, and transfer all of the data to a flash drive to use as a baseline for the wind tunnel measurements in the next test.
For the next part of the experiment, we will conduct the same test, except it will be done inside of the wind tunnel with airflow. To begin, mount the hexacopter on the load cell test stand. Then, connect the load cell to the data acquisition computer, and connect the hexacopter to the ground control station. Secure the test stand to the base of the wind tunnel using C-clamps, making sure that the hexacopter is free of the wind tunnel walls, floor, and ceiling to minimize free stream flow disturbances.
Then, mount two pitot tubes inside of the wind tunnel using industrial tape, making sure to place them a few feet away from the hexacopter to sample the undisturbed airflow. Now, set the pitch angle of the hexacopter to 0° by adjusting the hinge joint of the test stand. Then, close the wind tunnel.
Connect the pitot tube sensors to the data acquisition system. Next, run the bias program to establish the load cell voltage biases. Then, initialize the wind tunnel and set the wind speed to about 430 ft/min, or 2. 2 m/s. Once the free stream flow speed settles to the desired value, collect the baseline lift and drag readings from the load cell with the hexacopter motors off.
Now, turn the hexacopter motors on by initializing the throttle command to 1,300 microseconds. Let the air speed in the wind tunnel settle and then collect the readings from the load cell and from the pitot tubes. Then, repeat the test again for the three throttle command settings at varied hexacopter pitch angles and wind tunnel air speeds. To reduce complexity, a zero-yaw angle was maintained at all times.
Now let’s interpret the results. First, plot the thrust versus RPM and torque versus RPM data collected from the dynamometer experiment.
Here, we show the data for one motor. The plots illustrate that an increase in motor RPM results in an increase in torque and thrust. Now, fit a quadratic curve to the data in the form of the following equations. Using the quadratic relation, we can then determine the thrust coefficient, CT, and the torque coefficient, CQ.
Next, plot input motor RPM, electrical power, and throttle command on a 3-D plot. Since there is no direct RPM sensor feedback on our hexacopter, we have fit a polynomial surface to the data to obtain the actual RPM as a function of electrical power and throttle command.
Now that we’ve looked at the dynamometer results, let’s take a look at the wind tunnel experiments conducted using the parameters listed here. The variation of drag and lift are plotted against the different pitch angles tested. Both plots show that increasing the throttle command results in significant increase in lift, or motor thrust, as well as an increase in drag. An increase in wind tunnel air speed does not significantly increase lift. However, higher air speed did result in a significant increase in the drag force acting on the hexacopter.
In summary, we learned how aerodynamic forces control the flight of multicopters. We then tested a hexacopter in a wind tunnel and analyzed the lift and drag forces produced over a range of air speeds.