IROS2019国际学术会议论文集 0416

Motor propeller Matching of Aerial Propulsion Systems for Direct Aerial aquatic Operation Yu Herng Tan and Ben M Chen Department of Electrical Computer Engineering National University of Singapore Singapore Abstract Electric aerial propulsion systems are commonly used for many small scale unmanned aerial vehicles UAVs providing a light and powerful method of generating thrust In the emerging area of aerial aquatic vehicles most existing prototypes rely on such systems to propel themselves in both air and water As the density of water is three orders of magnitude larger than that of air a spinning aerodynamic body in the medium will experience signifi cantly higher torque at the same speed This results in aerial propulsion systems to be heavily mismatched underwater as the required torque is higher than the drive torque that a typical aerial motor can provide Here an in depth investigation of such off design operation is conducted Based on numerical simulation we identify the feasible operating range of such systems and present an evaluation framework that identifi es a motor propeller combination from a component database that maximises underwater performance while ensuring aerial thrust requirements are met I INTRODUCTION Aerial aquatic robots are an emerging type of multimodal vehicles Similar to the concept of amphibious vehicles and land air hybrids aerial aquatic vehicles expand the range of operation and application possibilities of mobile robots by being able to operate in two mediums The uniqueness of aerial aquatic vehicles as compared to other multimodal ones is the fact that it can also benefi t from the properties of the surrounding fl uid The high density of water results in a signifi cant buoyancy force on any submerged vehicle This phenomenon when calibrated to offset weight greatly reduces the energy required for the vehicle to hover or hold position in 3D space In air the low density of the medium results in signifi cantly lower drag forces making high speed travel more effi cient However it is exactly because of these widely varying properties that designing a vehicle to operate in both mediums becomes extremely challenging with the most fundamental problem being locomotion and propulsion methods Being fl uid mediums both air and water require the vehicle to navigate in 3D space as opposed to terrestrial motion whereby one plane is defi ned by the land terrain This requirement has been separately solved by different vehicle designs in each medium ranging from fi xed wing planes to multirotors in air to boats and submersibles in water While aerial aquatic vehicles can borrow from these existing solutions the challenge of choosing a propulsion system that can operate effectively in both mediums remains The most common and cost effi cient thrusters used in fl uid mediums are typically motor driven rotors or propellers As such the thrust produced is dependent on the change in mass fl ow rate of the fl uid caused by momentum imparted on the fl uid by the thruster This implies that the density of the medium is a key parameter that affects the rotational speed and torque of the thruster The implications can be observed in common aerial propeller designs which are long and slender and spin at high speeds as opposed to aquatic propellers which have broad wide blades driven by high torque motors or engines at low speeds due to the needs of operating in a much denser medium In existing aerial aquatic vehicles several solutions avoid the problem of aerial aquatic propulsion by limiting the aquatic portion of the vehicle s mission profi le to be either passive or restricted to the water surface These include the prototype presented in 1 which uses water bodies as a landing surface and does not submerge its propeller for underwater propulsion Other prototypes such as submersible launched unmanned aerial vehicles UAVs engage the use of external shells or propulsion devices to move underwater before shedding them in the transition to aerial operation All these examples however are limited in their aerial aquatic mobility as they are not fully functional multimodal designs Achieving aerial aquatic mobility that can effectively move both within and between mediums is the ultimate goal for this design concept Despite the challenges there are already several existing prototypes that demonstrate the possibility of this concept ranging from multirotor 2 3 to fi xed wing 4 7 platforms These prototypes commonly use a single set of aerial propulsion systems in both air and water for simplicity and to avoid the weight penalty of having to carry a second unused propulsion system at any one point in the mission profi le Using a typical underwater propulsion system is not feasible in air as the small blade area and low rotational speeds cannot generate suffi cient thrust in a low density medium to produce the required lift for fl ight Hence aerial aquatic vehicles that use a single propulsion system uses their regular aerial propulsion system underwater In the examples above this consists of common electric brushless outrunner motors with fi xed pitch aerial propellers The trade off for doing so is having to run the propulsor at very low effi ciencies as a result 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE1963 of the torque mismatch between the propulsion system and the medium The intuitive method of running at low speeds underwater has been adopted in most of the above prototypes to make such confi gurations feasible though the performance of doing so has rarely been evaluated Although experimental studies of running aerial propellers underwater were conducted in 4 and 8 both evaluated the performance using only a single motor and did not consider the full effect of motor propeller matching Here we propose a strategy to fi nd an optimal confi guration of motor propeller matching for aerial aquatic usage based on a database of available electric motors and propellers and given constraints We fi rst look into the mathematical model of a motor propeller system and use simulation results to identify the optimal operating range of a given aerial propulsion system underwater Next we propose an evaluation framework that takes a more balanced view of aerial aquatic operation in the process of motor propeller selection The results determine the suitability of different motor and propeller combinations based on their characteristic properties and the implementation feasibility is also considered by selecting different limiting constraints for different systems An example is shown to demonstrate how the best motor propeller combination can be selected from an existing component database based on performance parameters in both air and water II MOTOR PROPELLERMATCHING Running aerial motor propeller systems underwater directly will inevitably lead to low effi ciencies due to the torque mismatch of the system and the environment Although sep arate propulsion systems or additional gearing as proposed in 9 can be used the preferred method of many aerial aquatic designs is still to use the same set of aerial motors and propellers underwater directly to avoid additional weight penalties As such it is worthwhile to investigate the properties and behaviour of such systems in the off design regime and reconsider the selection of aerial motor propeller systems so that they are better suited for aerial aquatic usage In order to do so we fi rst discuss the fundamentals of a typical aerial propulsion system consisting of a brushless outrunner motor and a fi xed pitch propeller and how choosing components with different parameters can affect performance A Propeller properties The thrust T and torque Q produced by a spinning propeller can be modelled as T kT 2D4 1 Q kQ 2D5 2 where is the fl uid density is the rotational speed and D is the propeller diameter kTand kQare the thrust and torque coeffi cients respectively and are dependent on geo metric properties such as the blade area and pitch Here the propellers will be defi ned generally by a manufacturer make and follow the standard labelling convention using its basic defi ning dimensions diameter Diand pitch pi which are 00 511 522 533 5 RPM 104 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Torque Nm V spec 1304 T MOTOR F20II 2800KV T MOTOR F40PROII 2400KV T MOTOR F40PROII 2600KV Multistar 2206 2150KV Multistar 2814 700KV Multistar Elite 2312 960KV Fig 1 The fi rst order models of various motors at 11 1 V written as Di pi where the values are in inches and pi is the forward distance travelled for every rotation in a solid medium The propeller effi ciency P is given by p Tv Q 3 where v is the forward speed This is equivalent to the ratio of output power produced by the propeller to the input power generated by the motor shaft B First order model of motor The motor can be described as a fi rst order model Q V KV 1 R I0 1 KV 4 where Q is the shaft torque V is the voltage applied KV is the characteristic revolutions per minute RPM per volt R is the internal resistance and I0is the no load current of the motor KV R and I0are the motor characteristic values that can either be obtained experimentally or given by the manufacturer This model defi nes the motor characteristic curve on the torque speed plot and hence the equilibrium operating speed with a given propeller The fi rst order models of a range of different small scale motors at 11 1 V are shown in Figure 1 Bigger motors that are able to spin larger propellers more effi ciently appear on the plot as capable of generating higher torques at the same speed compared to smaller motors Conversely smaller motors are able to spin at higher RPMs shown as gentler slopes that extend further in the RPM range The motor effi ciency M is defi ned as the ratio of motor power output to electrical input which is M Q IV 5 where I is the current draw of the motor 1964 C Torque balance As the motor and propeller operate as a single combined system the operating point of the system is determined by the torque equilibrium between the two components This is the point whereby the torque acting on the propeller by the surrounding fl uid is the same as the shaft torque generated by the motor Mathematically it is represented by the point where Equation 2 and 4 meet on the torque speed plot To analyse the performance of a motor propeller system we use the open source program QPROP 10 to simulate the operation in given conditions In these simulations the fl uid properties can be separately defi ned which allows the same system to be simulated in both air and water The motor and propeller to be tested are modelled as two input fi les for the program The propeller is defi ned by the chords and twists of sections along the blade as well as the aerodynamic lift and drag coeffi cients of these sections The motor input fi le uses the motor characteristic values to build a fi rst order model as described above At a given vehicle velocity QPROP can simulate a motor propeller system by sweeping across a given RPM range or voltage range Due to the characteristics of the system operation at each RPM point will correspond to a particular applied voltage Hence the specifi cation of RPM range or voltage range has similar meaning and is chosen according to the operational range that is to be investigated By plotting the found propeller curve which is dependent on the environmental fl uid characteristics together with the motor torque curve which is dependent on the applied volt age the equilibrium operational point can be found The RPM value of this point will correspond with the set voltage input This process can be used to investigate the aerial performance of a motor propeller system and verify its suitability Results from 9 have shown that the simulations using QPROP provide high fi delity to physical experiments Each motor and propeller has its own design operating point where its respective effi ciencies peak Ideally the system has to be well matched meaning that the torque equilibrium speed is near the design operating point of both the motor and propeller This can be identifi ed by observing the effi ciency curves The overall effi ciency of the system is given by P M 6 hence the peak values of the two effi ciency curves need to be relatively close and the equilibrium operating point of the system is near the maximum of the overall effi ciency in order to achieve a well matched system that can operate effi ciently III AERIAL AQUATICOPERATIONANALYSIS To evaluate the performance of a chosen motor propeller combination under aerial aquatic operation we will study the simulation results of such systems in the two mediums sepa rately As this is a practical feasibility study all models used are based on commercially available off the shelf components with manufacturer given data The use of actual component parameters are important as the results and fi ndings from TABLE I PERFORMANCE OF AMULTISTAR2206 2150KV GWS 6 3SYSTEM AT 11 1 VIN AIR AND WATER AirWater RPM208472052 Thrust N 7 4156 39 Torque Nm 0 06370 4832 Motor Effi ciency0 83220 0843 Current A 15 03109 49 Electrical Power W 1671231 the proposed evaluation method can be directly implemented into physical prototypes In this section an example of the procedure is presented using a Multistar 2206 2150KV motor and GWS 6 3 propeller with a 3 cell 11 1 V LiPo battery We fi rst simulate the motor propeller system to operate at on design points i e normal aerial operation where the operating point is determined by the equilibrium of the mo tor and propeller torque curves as described above Here we will consider the static thrust case where the vehicle velocity is zero This is a relevant and important operating point for a system such as a multirotor where the vehicle is stationary even though the rotors are rotating at a non zero speed i e hovering The performance characteristics including the thrust torque motor effi ciency voltage and current of the specifi ed motor propeller combination obtained from the simulation process described above is shown in Table I If the same procedure is repeated with the fl uid character istics of water the results can be similarly obtained although this operating condition is likely to be physically infeasible As seen in the comparison of the results in Table I the same motor propeller system generates a much higher thrust at a signifi cantly lower RPM when underwater due to the higher density of the medium The design concern however is the high current draw and low motor effi ciency which is the result of operating at off design conditions This has several implications on the physical system the electronic speed controller ESC used to control the motor has to be able to deliver the continuous current required and the motor has to be able to dissipate the corresponding power generated The maximum power that the motor can dissipate is given by the manufacturer as the power rating In the case above the power of the system simulated is more than three times over the power rating of 320 W indicating that running the system as such is likely to cause damage to the motor Furthermore considering the motor size and the aerial current draw the current draw underwater will be severely over the limits of a typical ESC chosen to match the motor for aerial fl ight Instead of simulating the motor propeller system to operate at the equilibrium point of the nominal voltage of the battery a more realistic way of operating such propulsion systems underwater is to run them at very low speeds and hence voltage Instead of setting a fi xed voltage input a voltage input range can be given to generate the corresponding speed and 1965 50010001500 RPM 0 0 05 0 1 0 15 0 2 Efficiency Motor Efficiency Optimal Efficiency Power Limit ESC Current Limit 50010001500 RPM 0 0 1 0 2 0 3 0 4 0 5 Specific thrust N W Specific Thrust Maximum Specific Thrust Power Limit ESC Current Limit Static Performance water 50010001500 RPM 0 5 10 15 20 25 30 Thrust N Thrust Optimal Efficiency Maximum Specific Thrust Power Limit ESC Current Limit Fig 2 The effi ciency specifi c thrust and thrust curves when the system is run at low speeds underwater TABLE II PERFORMANCE OF AMULTISTAR2206 2150KV GWS 6 3SYSTEM IN WATER AT MAXIMUM SPECIFIC THRUST AND LIMITING CONDITIONS Max Specifi c Thrust ESC Current Limit Power Limit RPThrust N 0 31818 2726 210 Torque Nm 0 00610 17440 2408 Voltage V 0 2674 3015 813 Current A 2 0639 9654 92 Electrical Power W 0 55171 90319 96 Motor Effi ciency0 18010 12430 1106 Specifi c Thrust N W 0 57680 10630 0821 performance results By limiting the range of this input voltage to a low value 0 to 3 V we can closer examine the motor effi ciency curves of such systems underwater As the static thrust case is considered here the overall effi ciency will be zero by defi nition because v 0 implies P 0 according to Equation 3 Instead the specifi c thrust T defi ned as thrust generated per unit of electrical power can be used as an effective effi ciency parameter The speed corresponding to the peak of the specifi c thrust curve as shown in Figure 2 should be the lower limit of the system s underwater operating range since running at speeds lower than this point yield both lower absolute and specifi c thrust As shown in Figure 2 the maximum achievable motor effi ciency is 0 2085 Though this is signifi cantly lower than 0 8322 in aerial operation it is still more than two times greater than running at the nominal voltage of the battery On the same graph the power limit line is also shown which is the operating speed that corresponds with the maximum power rating of the motor The performance results of running at these points are shown in Table II Running the system at the motor power limit results in a current draw of 54 92 A In order to safely run the system the ESC has to be rated 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