Comparison of Novel Identification Method of Suspension Force Parameters and the Conventional Identification Method in Bearingless Motors

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1 Comparson of Novel Identfcaton ethod of Suspenson orce Parameters and the Conventonal Identfcaton ethod n Bearngless otors Yuma Otsu, Kouk Nakaya, Kmo Hjkata and Yasuhro Tanaka Department of echancal Systems Engneerng, Tokyo Cty Unversty, Japan Abstract At load operaton, bearngless motors are became unstable by nterference of the motor flux. Therefore, t s necessary to decouplng compensaton parameters for stable magnetc levtaton. Conventonally, perform the parameter dentfcaton test of suspenson force by attachng a specal jg to bearngless motors. However, conventonal method restrcted n the shape of the rotor. The novel dentfcaton method wthout usng jg s proposed [1]. In ths paper, we demonstrate the utlty of the novel method by comparson wth the conventonal method. Index Terms Bearngless motors, agnetc levtaton, Parameters dentfcaton I. INTRODUCTION Bearngless motors that have the two wndngs of the electrc motor and suspenson n the stator s an electromagnetc devce that combnes an electrc-machne and magnetc bearngs. Ths motor can solve varous problems caused by mechancal contact as wth magnetc bearngs. urther, bearngless motor can be mnaturzed than the case of provdng ndvdually magnetc bearng because tself have a functon of the magnetc barng. In addton, t s possble to mprove the crtcal speed of the motor by shortng the shaft. Therefore, bearngless motor s possble to acheve both hgh speed and hgh torque. In the bearngless motors, the electromagnetc force s generated by the nteracton of exctaton flux of motor wndngs and suspenson flux of suspenson wndngs as the suspenson force. Ths electromagnetc force that generated by exctaton flux and suspenson flux s called the suspenson force. The bearngless motors use the suspenson force for magnetc suspenson. However, the other force that generated by the nteracton of the torque flux of motor wndngs that use for generatng torque and the suspenson flux of suspenson wndngs s generated at the tme of load operaton. Ths force that s called the nterference force s not requred for suspenson. Therefore, stable magnetc levtaton at the tme of load operaton s need to estmate the suspenson force parameters that are factors of the suspenson force aganst the current and be decouplng control. When performng decouplng control, t s necessary to obtan the ampltude of the suspenson force and the argument that s defned as the angle between the suspenson force command and actually the suspenson force. The ampltude of the suspenson force s compensated by the PID controller of sngle axs sde control systems. On the one hand, t s dffcult to compensate for the argument n sngle axs sde control systems. Because the argument s generated n the nteracton between the axes. In ths study, we focused on the argument. Conventonally dentfcaton methods are two. One s the method to dentfy the parameters usng the fnte element analyss, another s the method to dentfy the parameters usng specal jg [2]-[3]. In addton, the novel dentfcaton method wthout usng jg s proposed. In ths paper, we demonstrate the utlty of the novel method by comparson wth the conventonal method. II. PRINCIPLE O RADIAL ORCE GENERATION AND OCCURRING INTERERENCE AT LOAD OPERATION A. Radal force generaton g. 1 shows the prncple of generatng suspenson force for the synchronous reluctance type bearngless motors. g. 1 shows the fxed coordnate n the case of the rotatonal angle s 0 deg. The rotor s excted by the d- axs wndng wre N of 4-pole electrc motor. Therefore, the exctaton magnetc flux s generated as g. 1. In ths case, contrastng electromagnetc force s generated n the gap porton. In addton, overlayng the suspenson flux generated by the 2-pole of the suspenson wndng n order to control the electromagnetc force. Then, the dfference occurs n the magnetc flux densty at the argap of the upper and lower rotor, radal force s generated downward as shown n g. 1. Ths radal force generated by the nterference of the exctaton flux and suspenson flux s defned as the suspenson force. B. Interference at load operaton At the tme of load operaton, the torque s generated by the exctaton flux and the torque flux that s generated by the q-axs wndng wre N of 4-pole electrc motor n g.2. At ths tme, radal force that occurs g. 1 Radal force generaton

2 perpendcular to the suspenson force s generated by nterference torque flux and suspenson flux s2d. Ths radal force generated by the nterference of the torque flux and suspenson flux s defned as the nterference force. or that reason, at the tme of load operaton, the suspenson force and nterference force are generated. Therefore, as show n g.3, the resultant force of suspenson force and nterference force s determnate the radal force. In addton, the resultant force has the angle from drecton of the suspenson force. Ths angle that s called the argument s defned as the angle between the suspenson force and resultant force. In addton, counterclockwse from drecton of the suspenson force s postve. -axs and -axs are dong an ndependent suspenson control. Thus, t s necessary to compensate the nterference. Because the mutual nterference of the radal force between the axes hnder stable magnetc levtaton. g. 2 Occurrng nterference force III. PRINCIPLE O IDENTIICATION O RADIAL ORCE PARAETERS O BEARINGLESS OTORS A. Radal force parameters In ths secton, we descrbe the relatonshp between the suspenson force parameters and the argument. The suspenson force parameters are the constants of radal force that represent the relatonshp between the current and the suspenson force when gven arbtrary the wndng current value. rst, n a-axs and b-axs of the fxed coordnate, the radal force that s exerted on the rotor s expressed by the followng equaton. m m 4d 4q cos sn 2 sn2 2 cos2 s s In the eq. (1), and s the Partal dfferental value of mutual nductance that s generated by the motor wndngs and the suspenson wndng. Then, and are the motor wndng current, s2a and s2 are -axs and -axs suspenson wndng current. In ths study, we use rotatng coordnate n the control system of the suspenson. In addton, the suspenson wndng s controlled by convertng to DC current on the - rotatng coordnate. At ths tme, the relatonshp between the suspenson current s2a, s2 on the fxed coordnates and the suspenson current s2, s2 on the rotatng coordnates are obtaned as follows. 2 cos2 sn2 s s2 (2) s2 sn 2 cos 2 s2 s2 shows the ampltude of the fundamental component of the -axs suspenson current. And s2 shows the ampltude of the fundamental component of the -axs suspenson current. In addton, by substtutng the eq. (2) to eq. (1), the relatonshp between the radal force, on the fxed coordnates and the suspenson current s2, s2 on the rotatng coordnates are obtaned as follows. s2 (3) s2 2 2 (1) g. 3 resultant radal force and the argument If we consder the case of the -axs suspenson current s2 gve zero and the -axs suspenson current s2 gve arbtrary value. The argument generated at ths tme can be determned by eq. (4). m q tan tan (4) Therefore, n order to calculate the argument, t s necessary to seek and n advance. As the method of obtanng and, there are the method that s dentfy the parameters usng the fnte element analyss, and the method that s dentfy the parameters usng specal jg. B. Calculaton of radal force parameters by usng fnte element analyss results The radal force generated by arbtrary wndng current can computed by the fnte element analyss. In addton, and are calculated from the radal force and current. or example, the case of applyng the exctaton current, the torque current and the -axs suspenson current s2 to the bearngless motor, the suspenson force and nterference force are generated. At ths tme, and can be calculated as

3 shown n eq. (5) and eq. (6) from eq. (3). s2 and that are calculated by ths method are ncorporated tentatvely controlled n case of the frst suspenson control. However, t s dffcult to consder modelng errors caused when creatng actual, there s the case where the control becomes unstable. Accordngly, and requres the dentfcaton method usng the testng machne.[4] C. The conventonal dentfcaton method of radal force parameters wth usng specal jgs The conventonal dentfcaton method usng the testng machne measures the suspenson current generated by applyng load n the radal drecton. In ths method, performng the test n a state of magnetc levtaton wth usng the provsonal value and obtaned by the fnte element analyss. If to gve the load n the -axs drecton, the suspenson force command value that becomes par the load s calculated. In addton, the nterference force n the b-axs drecton s generated by the suspenson current, s calculated. At ths tme, these values that are the suspenson current, the suspenson force command value and and provsonal value and obtaned from fnte element analyss substtute the followng equaton, t s possble to obtan the and of testng machne. 2 2 In ths method, t s possble to obtan fnte element analyss more accurate and, because t consders actual fabrcaton error. However, t s necessary to create the jg for applyng the load to the shaft for each motor. Also, t s consdered to mpossble dependng on the shape of the motor. Therefore, to solve these problems, we propose the smple suspenson force parameters dentfcaton method that s not requre the specal jg wth usng testng machne. s2 2 2 (5) (6) (7) (8) IV. THE NOVEL IDENTIICATION ETHOD O RADIAL ORCE PARAETERS g. 4 shows the suspenson control system of synchronous reluctance type bearngless motor. The radal dsplacement and of the shaft are detected by the gap sensor that s dsposed n stator. These axes dsplacement are feedback to the PID controller, the suspenson force command value are calculated. Then, thnk about the argument. In eq. (3), f we consder the case of the -axs suspenson current s2 gve zero and the -axs suspenson current s2 gve arbtrary value. At ths tme, n eq. (3), the suspenson force and the nterference force are generated by the - axs suspenson current. In addton, f the suspenson systems have the dsplacement feedback control of the a- axs drecton, the a-axs suspenson current s generated so as to cancel the nterference force. Therefore, the a- axs radal force s zero. Accordngly, t obtans the equaton below from the eq. (3). s 2 s 2 Therefore, from eq. (4) and eq. (9), the argument can be expressed by the followng equaton. 1 1 s2 tan tan (10) s2 rom eq. (10), the argument can be calculated wth usng the rato of suspenson current s2 and s2. Ths research has been compensated for by the use of the argument. V. ARGUENT IDENTIICATION TEST A. Identfcaton of argument of radal force In the suspenson force parameter novel dentfcaton method measurng the -axs suspenson force current s2 that generated for cancel the generated nterference force by changng the -axs suspenson force current s2. It s appled to the calculaton to compensate for the argument of the measured current value by substtutng the eq. (10). Indcate the status of the testng machne of conductng the dentfcaton test to propose n g. 5. When dentfyng the parameters, one of the unt s used as the dentfcaton test machne, another unt s used as the load for generatng torque. Consder the case of measurng the suspenson force parameters of Unt1 sde. Unt2 sde used as the load s dong the normal control. In the Unt1 sde used as testng machne, the z1-axal 0 (9) g. 4 Suspenson control system of bearngless motor

4 Argument [deg] Argument [deg] drecton and the a1-axal drecton are mantaned n the center poston by the dsplacement feedback control. The -axs drecton s not performed the dsplacement feedback control. Thus, t s possble to gve the arbtrary -axs suspenson current. At ths tme, the dentfcaton test s performed n the state of the shaft s touchng down n the 1-axs drecton. The novel dentfcaton method s not usng specal jg, because t performs the measurement gvng arbtrary current from the controller. Therefore, no matter of the shape of the bearngless motor, ths method can be dentfed the argument generated n load operaton. The novel method s only possble to determne the argument from the rate of secton that are the suspenson force and nterference force n eq. (3). Accordngly, although t s possble to compensate the argument generated n load operaton, t s mpossble to dentfy the ampltude tself of the nterference force as n the conventonal dentfcaton method. B. Result of argument dentfcaton test In the exctaton current s 16.6 A (80% of the rated current), the suspenson current s2 and s2 were measured on the condton that the torque current command value s changed to 20 A from -20 A n steps of 2 A. In addton, the argument s calculated wth eq. (10) usng s2 and s2. g. 6 shows the relatonshp between the argument and the torque current. In addton, g. 6 show the results that are obtaned by the fnte element analyss and the method of usng specal jg n order to compare. In the case of fnte element analyss, nte element analyss Usng specal jg Novel method Torque current 1 [A] (a) Unt1 sde -10 nte element analyss Usng specal jg Novel method Torque current 2 [A] (b) Unt2 sde g. 6 Relatonshp between the torque current and the argument of radal force n 80 % of rated exctaton current g.5 Condton of suspenson control system of Bearngless motor on argument dentfcaton the radal force was calculated by usng the electromagnetc feld analyss software JAG of JSOL Corporaton on the condton that the suspenson current s flowng the rated current. Analyss was used the cylndrcal slde mesh n two dmensons. The number of elements s about , and the number of nodes s about Substtute the radal force and the suspenson current n eq. (5) and eq. (6), t obtaned the suspenson coeffcent = H/m and = H/m. Also, the parameter of method usng specal jg was measured by added the load of 2 kgf to radal drecton n the exctaton current of 16.6 A. Substtute the motor current and the suspenson current n eq. (7) and eq. (8), t obtaned the suspenson coeffcent =0.415 H/m and =0.064 H/m n Unt1 and =0.446 H/m and =0.065 H/m n Unt2. urther, the argument n the condtons of each motor current s calculated by substtutng these values n eq. (10). In g.6, at tme of gvng the torque current 20 A, the argument calculated by the novel method s dfferent about up to 5 deg as compared wth the argument calculated by the fnte element analyss. On the other hand, the novel method s almost the same when comparng the dentfcaton method usng jg. or ths reason, t s dffcult to model of the testng machne n the fnte element analyss, the magnetc flux dstrbuton s consdered to change by non-unformty of the manufacturng error or wndng. Therefore, when performng the argument compensaton by fnte element analyss, t s consdered that the suspenson control become unstable dependng on the motor current. Thus, the argument that s determned by the novel dentfcaton method s consdered to be necessary. VI. ARGUENT COPENSATING TEST A. Argument compensaton In g. 4, the suspenson force s modulated to the current command value s2 and s2 usng eq. (11). Eq. (11) s obtaned by solvng the eq. (3) that s the relaton of the suspenson force and the suspenson current, -1 s expressed by eq. (12). s2 s 2 1 (11)

5 (12) The current command value s2 and s2 are current components for generatng the suspenson force on each of the axes drecton n the fxed coordnate. When performng the calculaton of the voltage command value by the PI control, the suspenson current command value s2 and s2 are converted the suspenson current to the - axs component and the -axs component n the fxed coordnates, because t performs the comparson. If the suspenson current s2 and s2 are consdered to follow the suspenson current command value s2 and s2, the suspenson force and become equal the suspenson command value and from eq. (3) and eq. (11). Therefore, t s possble to the decouplng control, because the nterference force s counteracted by -1. In the conventonal suspenson force control, by usng prevously and that are calculated the dentfcaton method of usng specal jg or the fnte element method, t performs to decouplng control. On the other hand, the suspenson control n ths study calculates the suspenson force by usng and that are obtaned by fnte element analyss. Thereafter, to compensate by adjustng the phase of the command value usng the coordnate transformaton matrx C as shown n eq. (13). C cos sn sn cos (13) Ths transformaton compensates only the dfferences of drecton of the suspenson force by usng the argument calculated by the fnte element analyss and the novel dentfcaton method. Then, the suspenson force s decoupled by eq. (11) and eq. (12) wth usng the suspenson coeffcent and obtaned n fnte element analyss, the ampltude of suspenson force. Thus, the ampltude of the suspenson force s compensated by the parameter of fnte element analyss, the drecton of the suspenson force s compensated by the parameter of novel dentfcaton method. Therefore, by performng the decouplng control usng the argument calculated by the novel dentfcaton method, t s consdered to become the stable magnetc levtaton n load operaton. However, t s possble to reduce the shaft vbraton because t can compensate for the argument. B. Acceleraton test The accelerated test was performed by usng the parameters determned n each dentfcaton method n order to nvestgate the effect of the dfference n the argument durng hgh-speed drvng. The accelerated test s performed n condton that occurs the largest dfference n each dentfcaton method gvng the exctaton current of 16.6 A and the torque current of 20 A. The rotaton speed s accelerated up to mn -1, the vbraton characterstcs compensated by the argument obtaned n each dentfcaton method were compared how to changed. The results of the accelerated test at the tme of the exctaton current 16.6 A s shown n g. 7. The ar gap between the rotor shaft and the touchdown bearng s about 130 m. In g.7, the shaft vbraton around 8000 mn -1 after startng the load operaton s ncreased about 100 m n usng the fnte element analyss parameter. On the other hand, although the shaft vbraton n the same manner around 8000 mn -1 n the method usng specal jg and the novel method s ncreased, the shaft vbraton s smaller than the case of usng the fnte element analyss parameter. C. Load varaton test In order to nvestgate the effect of load fluctuaton gven to the suspenson control, the load fluctuaton test by usng the parameters determned n each dentfcaton method was performed. The load fluctuaton test s performed by gvng the exctaton current of 16.6 A and the arbtrary torque current command value 1 n (a) nte element analyss (b) Usng specal jg g. 7 Acceleraton test at 80 % of rated exctaton current (c) Novel method

6 Unt1 sde at the constant speed mn -1. The vbraton characterstcs compensated by the argument obtaned n each dentfcaton method were compared how to changed. The results of the load fluctuaton at the tme of the exctaton current 16.6 A s shown n g. 8. In g. 8, the shaft vbraton over the torque current 15 A s ncreased n usng the fnte element analyss parameter. The shaft vbraton was not occurred n the cases of usng the parameter of novel method and the parameter of method usng specal jg. In addton, there s no salent dfference n shaft vbraton usng the parameter of novel method and the parameter of usng specal jg. Accordngly, n the compensaton usng the fnte element analyss parameter, t s consdered that the operatng range s lmted. In contrast, by the compensaton usng the parameter of novel method can be performed the magnetc levtaton. Ths compensaton effect s comparable to compensaton n the case of usng the parameter of method usng specal jg. VII. CONCLUSIONS In ths paper we compared the novel dentfcaton method and the conventonal method of suspenson force parameters. A result of obtanng the argument n the novel method, t was about the same as the dentfcaton method of usng specal jg. In contrast, at tme of maxmum load, the argument of the novel method s dfferent about 5 deg as compared wth the argument calculated by the fnte element analyss. To nvestgate the effect of the dfference of the argument on the shaft support control at the tme of load operaton, the shaft vbraton at the tme of maxmum acceleraton and load varaton was measured. As a result, the shaft vbraton n case of compensaton by usng the argument determned by the novel method and the parameter of fnte element analyss are more decrease than the case of performng the compensaton only by the fnte element analyss. Addtonally, t was confrmed that equvalent compensaton effect to the case of compensatng the suspenson force parameter obtaned by the method of usng specal jg. Therefore, by applyng the proposed method to the bearngless motor that can only be used the fnte element analyss parameters, t s possble to obtan easly compensaton effect equvalent to that of the method of usng specal jg wthout usng a jg. REERENCES [1] Nozomu Ando, asahro Nakao; Kmo Hjkata, Yasuhro Tanaka, A proposal of a novel dentfcaton method of radal force parameters for bearngless motors, Electrcal achnes and Systems (ICES), th Internatonal Conference on, Oct. 2014, pp [2] C.choka, T.Sakamoto, O.Ichkawa, A.Chba, T,ukao, A Decouplng Control ethod of Reluctance-Type Bearngless otors Consderng agnetc Saturaton, IEEE Transactons on Industry Applcatons, Vol.32-No.5 (1996), pp [3] asahde Ooshma, Akra Chba, Tadash ukao, Satoru yazawa, ukuzo Nakamura, Identfcaton ethods of Radal orce Parameters for Salent-pole Permanent agnet Synchronous Bearngless otors, IEEJ Trans. IA, Vol.124, No.8 (2004), pp [4] J.Asama, D.Kanehara, T.Owa, A.Chba, Development of a Compact Centrfugal Pump Wth a Two-Axs Actvely Postoned Consequent-Pole Bearngless otor, IEEE Transactons on Industry Applcatons, Vol.50-No.1 (2014), pp (a) nte element analyss (b) Usng specal jg g. 8 Load varaton test at 80 % of rated exctaton current (c) Novel method

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