In traditional electricity generation plants,large powerful synchronous,induction,and direct current generators were used.With the proliferation of microgrids focused on electricity generation from renewable energy so...In traditional electricity generation plants,large powerful synchronous,induction,and direct current generators were used.With the proliferation of microgrids focused on electricity generation from renewable energy sources in today’s power grids,studies have been conducted on different types of generators.Instead of the traditional generator architecture,generators with brushless structures,particularly those utilizing magnets for excitation,have found broad applications.Fluxswitching generators(FSGs)are innovative types owing to their robust structure,active stator design,and high power density capabilities.However,designs have typically relied on rare-earth element magnets.Rare-earth magnets possess negative characteristics such as price uncertainty,the potential risk of scarcity in the future,and limited geographical production,leading to research on FSGs that do not depend on rare-earth magnets.This study comprehensively examines FSGs that do not use rare-earth element magnets.The study delves into the usage areas,operational mechanisms,structural diversities,and counterparts in the literature of these generators.展开更多
A dynamical dq model is proposed for a linear flux-switching permanent magnet(LFSPM) machine which is suitable for high-precision control applications.The operation principle of the prototype machine is analyzed usi...A dynamical dq model is proposed for a linear flux-switching permanent magnet(LFSPM) machine which is suitable for high-precision control applications.The operation principle of the prototype machine is analyzed using the finite element method(FEM),and the parameters,such as the back electromotive force(EMF) and the phase flux linkage,are calculated.The calculated and measured results reveal that the back EMF and the flux linkage are essentially sinusoidal,and the variation of the phase flux linkage profile of the LFSPM machine is similar to that of the linear surface permanent magnet(LSPM) machine.Based on this,a dynamical dq model and a simulation control model are proposed.The simulation results are compared with the test results obtained from a DSP-based control platform,which verifies that the model is correct and effective.Moreover,the model can be used for design optimization and control development.展开更多
A novel flux-switching permanent magnet linear motor(FSPMLM) is proposed for linear direct driving machine tools.First,the two-and three-dimensional topological configuration of the proposed motor is presented;the b...A novel flux-switching permanent magnet linear motor(FSPMLM) is proposed for linear direct driving machine tools.First,the two-and three-dimensional topological configuration of the proposed motor is presented;the basic operational principle of the FSPMLM is introduced;and the magnetic fields at the two typical conditions of no-load are analyzed.Secondly,the FSPMLM is analyzed by the two-dimensional finite element method(FEM) to investigate the static electromagnetic characteristics such as flux-linkage,back EMF(electromotive force) and inductance performances.The cogging forces of two kinds of FSPMLMs with different shaped cores are analyzed and compared,and the results show that the cogging force is significantly reduced by using the E-shaped cores.Additionally,based on the co-energy method,the thrust equation is derived and verified by the simulation results obtained by the FEM.Finally,an experimental prototype is used to test the characteristics under open circuit and load conditions.The simulation and experimental results indicate that the proposed motor has advantages of a sinusoidal back-EMF waveform,a small cogging effect and a high thrust density,and it is suitable for the application of linear direct driving machine tools.展开更多
Flux-switching permanent magnet(FSPM)machine is a kind of stator-typed permanent magnet machine,which is suitable for driving electric vehicles and hybrid electric vehicles because of their large power/torque density ...Flux-switching permanent magnet(FSPM)machine is a kind of stator-typed permanent magnet machine,which is suitable for driving electric vehicles and hybrid electric vehicles because of their large power/torque density and high efficiency.The axial field flux-switching permanent magnet machine(AFFSPMM)and radial field flux-switching permanent magnet machine(RFFSPMM)with H-typed iron cores are reached and compared in this paper.On the condition of the same outer diameters and total volumes,the electromagnetic performances of the two machines are analyzed and compared by the three-dimensional finite element method,including the air gap flux density,inductance,back electromotive force(EMF),electromagnetic torque and loss.The finite element results show that the copper loss of AFFSPMM is higher than that of RFFSPMM at the rated load,however,the total loss of AFFSPMM is lower than that of the RFFSPMM.Meanwhile,AFFSPMM has greater torque than RFFSPMM in the constant power range.The related experiments are done to validate the finite element results,which are basically consistent with experiment results.展开更多
This paper proposes a type of flux-switching permanent magnet(FSPM)motor,where the design concept of the hybrid permanent magnets(HPM)and the compound rotor are incorporated into the motor design.In such design,the pr...This paper proposes a type of flux-switching permanent magnet(FSPM)motor,where the design concept of the hybrid permanent magnets(HPM)and the compound rotor are incorporated into the motor design.In such design,the proposed motor can not only realize the significant reduction of NdFeB volume,but also artfully convert external magnetic flux leakage into the air-gap field to achieve competitive torque density and desirable PM usage efficiency.For extensive investigation,two topologies of the HPM are designed and analyzed for the proposed motor,which consist of the parallel-magnetic-hybrid(PMH)mode and serial-magnetic-hybrid(SMH)mode.To fully exploit the potential advantages of the proposed motor,a multi-objective optimization design is conducted,where the response surface method(RSM)and sequential non-linear programming(SNP)method are purposely utilized.After optimization,the electromagnetic performances of the motor with PMH mode and SMH mode are evaluated and compared by using finite element method(FEM),which include the back-EMF,cogging torque,output torque,and so on.Furthermore,the partial demagnetization of the ferrite PM is also investigated in the paper.Finally,the theoretical analysis and simulation study verify the effectiveness of the proposed motor and corresponding optimization design.展开更多
Permanent magnet flux-switching machine (PMFSM) is a relatively new structure. Available literatures mainly focused on its general design procedure and performance analysis. In this paper, Finite Element Method (FEM) ...Permanent magnet flux-switching machine (PMFSM) is a relatively new structure. Available literatures mainly focused on its general design procedure and performance analysis. In this paper, Finite Element Method (FEM) is taken to ana-lyze various design techniques to reduce the cogging torque in a prototype 12/10-pole PMFSM.展开更多
Electrically-excited flux-switching machines are advantageous in simple and reliable structure,good speed control performance,low cost,etc.,so they have arouse wide concerns from new energy field.However,they have muc...Electrically-excited flux-switching machines are advantageous in simple and reliable structure,good speed control performance,low cost,etc.,so they have arouse wide concerns from new energy field.However,they have much lower torque density/thrust density compared with the same type PM machines.To overcome this challenge,electromagnetic-thermal coupled analysis is carried out with respect to water-cooled electrically-excited flux-switching linear machines(EEFSLM).The simulation results indicate that the conventional fixed copper loss method(FCLM)is no longer suitable for high thrust density design,since it is unable to consider the strong coupling between the electromagnetic and thermal performance.Hence,a multi-step electromagnetic-thermal joint optimisation method is proposed,which first ensures the consistency between the electromagnetic and thermal modelling and then considers the effect of different field/armature coil sizes.By using the proposed joint optimisation method,it is found that the combination of relatively large size of field coil and relatively low field copper loss is favourable for achieving high thrust force for the current EEFSLM design.Moreover,the thrust force is raised by 13-15%compared with using the FCLM.The electromagnetic and thermal performance of the EEFSLM is validated by the prototype test.展开更多
In this paper,key dimensions of a co-axial dual-mechanical-port flux-switching permanent magnet(CADMP-FSPM)machine for fuel-based extended range electric vehicles(ER-EVs),including split ratio,stator/rotor pole arcs,r...In this paper,key dimensions of a co-axial dual-mechanical-port flux-switching permanent magnet(CADMP-FSPM)machine for fuel-based extended range electric vehicles(ER-EVs),including split ratio,stator/rotor pole arcs,rotor yoke thickness,etc.,are analyzed and optimized.Firstly,the topologies and operation principles of an exampled 3-phase CADMP-FSPM are introduced briefly,in which an inner-rotor FSPM machine with 12-stator-slots/10-rotor-poles for high-speed generation and an outer-rotor FSPM machine with 12-stator-slots/22-rotor-poles for low-speed motoring are assembled co-axially.Then,the relationship between the key dimensions and electromagnetic performance,particularly for electromagnetic torque(power),of the CADMP-FSPM machine is studied by 2D-finite element analysis(FEA).Further,the reasonable matches of split ratio,rotor/stator pole arcs and rotor yoke are determined and the original CADMP-FSPM machine is optimized correspondingly.Finally,the static characteristics,including no-load PM flux-linkage,electro-motive-force(EMF),winding inductances,cogging torques and electromagnetic torques,of the original and optimized machines are compared by 2D-FEA.The results verify that the optimized CADMP-FSPM machine can exhibit improved torque characteristics than the original one,i.e.,the torque ripples of the inner and outer machines can be reduced by 22.7%and 4.7%,respectively,and the average torque of the inner and outer machines can be increased by 0.43Nm and 2Nm,respectively.展开更多
This paper presents a comparative performance analysis of a new five-phase fault-tolerant flux-switching permanent-magnet(FT-FSPM)motor for high-reliability applications under the two most popular control schemes,name...This paper presents a comparative performance analysis of a new five-phase fault-tolerant flux-switching permanent-magnet(FT-FSPM)motor for high-reliability applications under the two most popular control schemes,namely,field-oriented control(FOC)and direct torque control(DTC)based on stator-flux orientation.Firstly,the new motor topology and structural characteristics are briefly presented.Secondly,the d-and q-axis for the FT-FSPM motor are defined,which is crucial to the mathematical model and control scheme,and the mathematical models are derived.Then,two control schemes,i.e.,FOC and DTC,and the main system are proposed.The operational principles of the two control schemes are presented,and space vector pulse width modulation(SVPWM)based on four neighboring vectors is adopted to reduce current harmonics and torque ripples.Finally,the simulated and experimental results are given,and performance analysis of the two control schemes are compared and discussed.The results reveal that FOC scheme has the sinusoidal phase current and low torque ripples,while the DTC scheme has fast dynamic response,verifying the effectiveness of the two proposed control schemes.This paper is a primary investigation for more possible improvements in the control schemes of the five-phase FS-FTPM motor.展开更多
Substantial efforts are currently underway around the world to develop environmentally friendly transportation,of which the development of electric vehicles plays a key role.Statorpermanent magnet(PM)machines have att...Substantial efforts are currently underway around the world to develop environmentally friendly transportation,of which the development of electric vehicles plays a key role.Statorpermanent magnet(PM)machines have attracted wide attention due to the robust rotor structure and comparable performance in terms of normal permanent magnet synchronous machines(PMSM)having magnets in the roto.In particular,the flux-switching machines feature a particular magnetic circuit configuration that favors Dy-free magnets in terms of demagnetization risk,and as a result,the cost of the motor can be reduced considerably.With focus on applications in electric vehicles(EVs)and hybrid electric vehicles(HEVs),this paper reviews the latest developments of PM flux switching machines,with particular emphasis on the novel machine topologies and control strategies.展开更多
In this paper,three advanced flux-switching(FS)machines,namely the radial-field flux-switching permanent-magnet(RF-FSPM)machine,the radial-field flux-switching DC-field(RF-FSDC)machine,and the axial-field FSDC(AF-FSDC...In this paper,three advanced flux-switching(FS)machines,namely the radial-field flux-switching permanent-magnet(RF-FSPM)machine,the radial-field flux-switching DC-field(RF-FSDC)machine,and the axial-field FSDC(AF-FSDC)machine are quantitatively compared.Upon the installation of the high-energy-density PM materials,the RF-FSPM machine can definitely provide the superior torque performances as compared to its magnetless counterparts.However,the PM machines suffer from two major fundamental problems,namely the high material costs,and the uncontrollable flux density.By utilizing the concept of axial-field structure,the AF-FSDC machine can offer comparable torque performance as the RF-FSPM machine.Hence,with the consideration of the cost-effectiveness and the control flexibility,the magnetless AF-FSDC machine has exhibited promising potential in various applications.展开更多
A novel topology of modular ferrite magnet fluxswitching linear motor(FMFSLM)use for track transport is presented in this paper,which enables more ferrite magnets to be inserted into the primary iron core.The motor ha...A novel topology of modular ferrite magnet fluxswitching linear motor(FMFSLM)use for track transport is presented in this paper,which enables more ferrite magnets to be inserted into the primary iron core.The motor has a significant low-cost advantage in long-distance linear drive.The proposed FMFSLM’s structure and working principle were introduced.Further,the thrust force expression of the motor was established.The thrust force components triggering thrust force ripple were investigated,and their expressions can be obtained according to the inductances’Fourier series expressions.Resultantly,the relationship between the harmonics of thrust force and that of self-and mutual inductances was revealed clearly.Based on the relationship,a skewed secondary should be practical to reduce the thrust force ripple.Thus,the effect of employing a skewed secondary to the proposed FMFSLM was investigated,and an optimized skewing span distance was determined.Finite element analysis(FEA)was conducted to validate the exactness of the theoretical analysis.The simulation results indicate that the strategy of suppressing thrust force ripple has a significant effect.Meanwhile,the motor maintains a good efficiency characteristic.The results of the prototype experiment are in good agreement with FEAs,which further verifies the proposed modular interior FMFSLM’s practicability.展开更多
文摘In traditional electricity generation plants,large powerful synchronous,induction,and direct current generators were used.With the proliferation of microgrids focused on electricity generation from renewable energy sources in today’s power grids,studies have been conducted on different types of generators.Instead of the traditional generator architecture,generators with brushless structures,particularly those utilizing magnets for excitation,have found broad applications.Fluxswitching generators(FSGs)are innovative types owing to their robust structure,active stator design,and high power density capabilities.However,designs have typically relied on rare-earth element magnets.Rare-earth magnets possess negative characteristics such as price uncertainty,the potential risk of scarcity in the future,and limited geographical production,leading to research on FSGs that do not depend on rare-earth magnets.This study comprehensively examines FSGs that do not use rare-earth element magnets.The study delves into the usage areas,operational mechanisms,structural diversities,and counterparts in the literature of these generators.
基金The National Natural Science Foundation of China (No.41076054)
文摘A dynamical dq model is proposed for a linear flux-switching permanent magnet(LFSPM) machine which is suitable for high-precision control applications.The operation principle of the prototype machine is analyzed using the finite element method(FEM),and the parameters,such as the back electromotive force(EMF) and the phase flux linkage,are calculated.The calculated and measured results reveal that the back EMF and the flux linkage are essentially sinusoidal,and the variation of the phase flux linkage profile of the LFSPM machine is similar to that of the linear surface permanent magnet(LSPM) machine.Based on this,a dynamical dq model and a simulation control model are proposed.The simulation results are compared with the test results obtained from a DSP-based control platform,which verifies that the model is correct and effective.Moreover,the model can be used for design optimization and control development.
文摘A novel flux-switching permanent magnet linear motor(FSPMLM) is proposed for linear direct driving machine tools.First,the two-and three-dimensional topological configuration of the proposed motor is presented;the basic operational principle of the FSPMLM is introduced;and the magnetic fields at the two typical conditions of no-load are analyzed.Secondly,the FSPMLM is analyzed by the two-dimensional finite element method(FEM) to investigate the static electromagnetic characteristics such as flux-linkage,back EMF(electromotive force) and inductance performances.The cogging forces of two kinds of FSPMLMs with different shaped cores are analyzed and compared,and the results show that the cogging force is significantly reduced by using the E-shaped cores.Additionally,based on the co-energy method,the thrust equation is derived and verified by the simulation results obtained by the FEM.Finally,an experimental prototype is used to test the characteristics under open circuit and load conditions.The simulation and experimental results indicate that the proposed motor has advantages of a sinusoidal back-EMF waveform,a small cogging effect and a high thrust density,and it is suitable for the application of linear direct driving machine tools.
基金supported by the National Natural Science Foundation of China(51507087)the Six Talents Summit Project of Jiangsu Province(XNYQC-017)the Science and Technology Planning Project of Nantong City(MS22019017 and JC2018145).
文摘Flux-switching permanent magnet(FSPM)machine is a kind of stator-typed permanent magnet machine,which is suitable for driving electric vehicles and hybrid electric vehicles because of their large power/torque density and high efficiency.The axial field flux-switching permanent magnet machine(AFFSPMM)and radial field flux-switching permanent magnet machine(RFFSPMM)with H-typed iron cores are reached and compared in this paper.On the condition of the same outer diameters and total volumes,the electromagnetic performances of the two machines are analyzed and compared by the three-dimensional finite element method,including the air gap flux density,inductance,back electromotive force(EMF),electromagnetic torque and loss.The finite element results show that the copper loss of AFFSPMM is higher than that of RFFSPMM at the rated load,however,the total loss of AFFSPMM is lower than that of the RFFSPMM.Meanwhile,AFFSPMM has greater torque than RFFSPMM in the constant power range.The related experiments are done to validate the finite element results,which are basically consistent with experiment results.
基金This work was supported in part by the Natural Science Foundation of China under Grant 51477069 and Grant 517in part by the Priority Academic Program Development of Jiangsu Higher Education Institutions.(Corresponding author:Xiaoyong Zhu)。
文摘This paper proposes a type of flux-switching permanent magnet(FSPM)motor,where the design concept of the hybrid permanent magnets(HPM)and the compound rotor are incorporated into the motor design.In such design,the proposed motor can not only realize the significant reduction of NdFeB volume,but also artfully convert external magnetic flux leakage into the air-gap field to achieve competitive torque density and desirable PM usage efficiency.For extensive investigation,two topologies of the HPM are designed and analyzed for the proposed motor,which consist of the parallel-magnetic-hybrid(PMH)mode and serial-magnetic-hybrid(SMH)mode.To fully exploit the potential advantages of the proposed motor,a multi-objective optimization design is conducted,where the response surface method(RSM)and sequential non-linear programming(SNP)method are purposely utilized.After optimization,the electromagnetic performances of the motor with PMH mode and SMH mode are evaluated and compared by using finite element method(FEM),which include the back-EMF,cogging torque,output torque,and so on.Furthermore,the partial demagnetization of the ferrite PM is also investigated in the paper.Finally,the theoretical analysis and simulation study verify the effectiveness of the proposed motor and corresponding optimization design.
文摘Permanent magnet flux-switching machine (PMFSM) is a relatively new structure. Available literatures mainly focused on its general design procedure and performance analysis. In this paper, Finite Element Method (FEM) is taken to ana-lyze various design techniques to reduce the cogging torque in a prototype 12/10-pole PMFSM.
基金supported in part by Zhejiang Provincial Natural Science Foundation of China under Grant LY21E070002 and LY17E070002。
文摘Electrically-excited flux-switching machines are advantageous in simple and reliable structure,good speed control performance,low cost,etc.,so they have arouse wide concerns from new energy field.However,they have much lower torque density/thrust density compared with the same type PM machines.To overcome this challenge,electromagnetic-thermal coupled analysis is carried out with respect to water-cooled electrically-excited flux-switching linear machines(EEFSLM).The simulation results indicate that the conventional fixed copper loss method(FCLM)is no longer suitable for high thrust density design,since it is unable to consider the strong coupling between the electromagnetic and thermal performance.Hence,a multi-step electromagnetic-thermal joint optimisation method is proposed,which first ensures the consistency between the electromagnetic and thermal modelling and then considers the effect of different field/armature coil sizes.By using the proposed joint optimisation method,it is found that the combination of relatively large size of field coil and relatively low field copper loss is favourable for achieving high thrust force for the current EEFSLM design.Moreover,the thrust force is raised by 13-15%compared with using the FCLM.The electromagnetic and thermal performance of the EEFSLM is validated by the prototype test.
基金This work was supported by The National Basic Research Program(973 Program)(2013CB035603).
文摘In this paper,key dimensions of a co-axial dual-mechanical-port flux-switching permanent magnet(CADMP-FSPM)machine for fuel-based extended range electric vehicles(ER-EVs),including split ratio,stator/rotor pole arcs,rotor yoke thickness,etc.,are analyzed and optimized.Firstly,the topologies and operation principles of an exampled 3-phase CADMP-FSPM are introduced briefly,in which an inner-rotor FSPM machine with 12-stator-slots/10-rotor-poles for high-speed generation and an outer-rotor FSPM machine with 12-stator-slots/22-rotor-poles for low-speed motoring are assembled co-axially.Then,the relationship between the key dimensions and electromagnetic performance,particularly for electromagnetic torque(power),of the CADMP-FSPM machine is studied by 2D-finite element analysis(FEA).Further,the reasonable matches of split ratio,rotor/stator pole arcs and rotor yoke are determined and the original CADMP-FSPM machine is optimized correspondingly.Finally,the static characteristics,including no-load PM flux-linkage,electro-motive-force(EMF),winding inductances,cogging torques and electromagnetic torques,of the original and optimized machines are compared by 2D-FEA.The results verify that the optimized CADMP-FSPM machine can exhibit improved torque characteristics than the original one,i.e.,the torque ripples of the inner and outer machines can be reduced by 22.7%and 4.7%,respectively,and the average torque of the inner and outer machines can be increased by 0.43Nm and 2Nm,respectively.
基金Supported by Key Research and Development Program of Jiangsu Province under Grant BE2018107,Natural Science Foundation of Jiangsu Province under Grant BK20171298Natural Science Foundation of Jiangsu Higher Education Institutions under Grant 18KJB470008.
文摘This paper presents a comparative performance analysis of a new five-phase fault-tolerant flux-switching permanent-magnet(FT-FSPM)motor for high-reliability applications under the two most popular control schemes,namely,field-oriented control(FOC)and direct torque control(DTC)based on stator-flux orientation.Firstly,the new motor topology and structural characteristics are briefly presented.Secondly,the d-and q-axis for the FT-FSPM motor are defined,which is crucial to the mathematical model and control scheme,and the mathematical models are derived.Then,two control schemes,i.e.,FOC and DTC,and the main system are proposed.The operational principles of the two control schemes are presented,and space vector pulse width modulation(SVPWM)based on four neighboring vectors is adopted to reduce current harmonics and torque ripples.Finally,the simulated and experimental results are given,and performance analysis of the two control schemes are compared and discussed.The results reveal that FOC scheme has the sinusoidal phase current and low torque ripples,while the DTC scheme has fast dynamic response,verifying the effectiveness of the two proposed control schemes.This paper is a primary investigation for more possible improvements in the control schemes of the five-phase FS-FTPM motor.
基金part by 973 Program of China(2013CB035603)NSFC(51137001,51322705).
文摘Substantial efforts are currently underway around the world to develop environmentally friendly transportation,of which the development of electric vehicles plays a key role.Statorpermanent magnet(PM)machines have attracted wide attention due to the robust rotor structure and comparable performance in terms of normal permanent magnet synchronous machines(PMSM)having magnets in the roto.In particular,the flux-switching machines feature a particular magnetic circuit configuration that favors Dy-free magnets in terms of demagnetization risk,and as a result,the cost of the motor can be reduced considerably.With focus on applications in electric vehicles(EVs)and hybrid electric vehicles(HEVs),this paper reviews the latest developments of PM flux switching machines,with particular emphasis on the novel machine topologies and control strategies.
基金Supported by a grant(Project No.17200614)the Hong Kong Research Grants Council,Hong Kong Special Administrative Region,China.
文摘In this paper,three advanced flux-switching(FS)machines,namely the radial-field flux-switching permanent-magnet(RF-FSPM)machine,the radial-field flux-switching DC-field(RF-FSDC)machine,and the axial-field FSDC(AF-FSDC)machine are quantitatively compared.Upon the installation of the high-energy-density PM materials,the RF-FSPM machine can definitely provide the superior torque performances as compared to its magnetless counterparts.However,the PM machines suffer from two major fundamental problems,namely the high material costs,and the uncontrollable flux density.By utilizing the concept of axial-field structure,the AF-FSDC machine can offer comparable torque performance as the RF-FSPM machine.Hence,with the consideration of the cost-effectiveness and the control flexibility,the magnetless AF-FSDC machine has exhibited promising potential in various applications.
基金supported by Shandong Provincial Natural Science Foundation under Grant ZR2020ME205.
文摘A novel topology of modular ferrite magnet fluxswitching linear motor(FMFSLM)use for track transport is presented in this paper,which enables more ferrite magnets to be inserted into the primary iron core.The motor has a significant low-cost advantage in long-distance linear drive.The proposed FMFSLM’s structure and working principle were introduced.Further,the thrust force expression of the motor was established.The thrust force components triggering thrust force ripple were investigated,and their expressions can be obtained according to the inductances’Fourier series expressions.Resultantly,the relationship between the harmonics of thrust force and that of self-and mutual inductances was revealed clearly.Based on the relationship,a skewed secondary should be practical to reduce the thrust force ripple.Thus,the effect of employing a skewed secondary to the proposed FMFSLM was investigated,and an optimized skewing span distance was determined.Finite element analysis(FEA)was conducted to validate the exactness of the theoretical analysis.The simulation results indicate that the strategy of suppressing thrust force ripple has a significant effect.Meanwhile,the motor maintains a good efficiency characteristic.The results of the prototype experiment are in good agreement with FEAs,which further verifies the proposed modular interior FMFSLM’s practicability.