Ge Liu 2021a - Revision history

Rimni: /* 5.2 Dynamic characteristics of TRMG equivalent model */

2021-10-21T13:53:43Z

‎5.2 Dynamic characteristics of TRMG equivalent model

Rimni at 13:49, 21 October 2021

2021-10-21T13:49:59Z

Rimni at 13:30, 21 October 2021

2021-10-21T13:30:59Z

Rimni at 13:30, 21 October 2021

2021-10-21T13:30:36Z

Rimni at 13:30, 21 October 2021

2021-10-21T13:30:16Z

Rimni at 13:29, 21 October 2021

2021-10-21T13:29:55Z

Rimni at 10:38, 21 October 2021

2021-10-21T10:38:35Z

Rimni at 10:26, 21 October 2021

2021-10-21T10:26:26Z

Rimni at 10:24, 21 October 2021

2021-10-21T10:24:16Z

Rimni at 14:33, 20 October 2021

2021-10-20T14:33:11Z

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 From [[#img-4|Figure 4]], the electromagnetic torque and output speed of low-speed permanent magnet ring change regularly with time, finally converging to  <math display="inline">67\mbox{r/}min</math>, around  <math display="inline">124\mbox{N}\cdot \mbox{m}</math>, and  <math display="inline">M_{max}=130\mbox{N}\cdot \mbox{m}</math>, meeting the design requirements. The ratio of input to output of speed and torque is about 22/23, which meets the transmission ratio design requirements in Equation (14).
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 <!--<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Draft_Dongning_226371700-image84.png|centre|thumb|728x728px|<span style="text-align: center; font-size: 75%;"> Figure 8. Speed and Torque characteristic curve Start </span>with starting point V]]<span style="text-align: center; font-size: 75%;"> </span></div>-->
-From [[#img-8|Figure 8]], it can be seen that from moment 0, the electromagnetic torque of low-speed permanent magnet ring shows periodic changes and starts to decrease gradually from equal to the load torque. The speed accelerates reversely from 0. This is because: when <math display="inline">\alpha \in [{\beta }_3,{\beta }_4]</math>, the electromagnetic torque of the low-speed permanent magnet ring is less than the load torque, and the torque difference gradually increases with α increasing, which makes the low-speed permanent magnet ring reverse speed up rotation. After TRMG enters negative electromagnetic torque period, TRMG accelerates reverse rotates under the action of load torque and negative electromagnetic torque, which eventually leads to start-up failure.
+From [[#img-8|Figure 8]], it can be seen that from moment 0, the electromagnetic torque of low-speed permanent magnet ring shows periodic changes and starts to decrease gradually from equal to the load torque. The speed accelerates reversely from 0. This is because: when <math display="inline">\alpha \in [{\beta }_3,{\beta }_4]</math>, the electromagnetic torque of the low-speed permanent magnet ring is less than the load torque, and the torque difference gradually increases with <math display="inline">\alpha</math> increasing, which makes the low-speed permanent magnet ring reverse speed up rotation. After TRMG enters negative electromagnetic torque period, TRMG accelerates reverse rotates under the action of load torque and negative electromagnetic torque, which eventually leads to start-up failure.
 == 6. Conclusions ==

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 [[#img-8|Figure 8]] shows the speed and torque characteristic curve with starting point V.
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 According to the changed model transmission ratio, the input speed of ring plate permanent magnet ring is  <math display="inline">70\mbox{r/}min</math>, and the load torque of low-speed permanent magnet ring is  <math display="inline">124\mbox{N}\cdot \mbox{m}</math>. The dynamic characteristic curve of changed model is shown in [[#img-4|Figure 4]].
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 | colspan="1" style="padding:10px;"| '''Figure 5'''. Speed and Torque characteristic curve Start with starting point P
 |}-->
 === 5.3 TRMG start-up characteristic analysis ===

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 Among the 5 types mentioned above, (1) is the motion mode of TRMG, and (2)~(5) are the motion mode of TRMG after fixing different TRMG components. For (1), (2), (3) and (4), there are rotation movement around the eccentric axis, so Ansys Maxwell cannot be used for dynamic simulation. For the motion mode (5), the ring plate and the low-speed permanent magnet ring both move around their own shafts in a fixed axis, which can be accurately simulated dynamically. Therefore, we finally changed TRMG into model (5). If the dynamic characteristics of model (5) meet the design requirements of transmission ratio and torque density after modification, the dynamic characteristics of TRMG can also meet the same requirements under the same structural size, rated power and rated load conditions of the model. The mechanism diagram of TRMG and its changed model (5) is shown in [[#img-3|Figure 3]].
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 In Equation (2),  <math>M_{max}</math> is the static maximum torque. [[#img-2|Figure 2]] shows the relationship between  <math>M_{out}</math> and <math display="inline">\beta </math>.
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 == References ==
-[2] Kang Y.F., Luan J.Y., Tian Y., Zheng H.Q. Cao J.H., Application of the Order Tracking Analysis in Gear Wearing. Journal of Vibration and Shock. 25(4):112-113+118+180,2006.
+<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
-[3] Jing L.B., Zhang Y., Huang Z., Chen J.L. Development Course and Research Question of Magnetic Gear. Journal of Mechanical Transmission. 43(1):165-170,2019.
+[1] Chen X.F., LI J.M., Cheng H., Li B., He Z.J. Research and application of condition monitoring and fault diagnosis technology in wind turbines. Journal of Mechanical Engineering, 47(9):45-52, 2011.
-[4] Atallah K., Rens J., Mezani S. Howe D., A novel “pseudo” direct-drive brushless permanent magnet machine. IEEE Transactions on Magnetics. 44(11): 4349-4352, 2008.
+[2] Kang Y.F., Luan J.Y., Tian Y., Zheng H.Q., Cao J.H. Application of the order tracking analysis in gear wearing. Journal of Vibration and Shock, 25(4):112-113+118+180, 2006.
-[5] Rens J., Atallah K., Calverley S.D., Howe D. A novel magnetic harmonic gear. IEEE Transactions on Industry Applications, 46(1): 206-212,2010.
+[3] Jing L.B., Zhang Y., Huang Z., Chen J.L. Development course and research question ofmMagnetic gear. Journal of Mechanical Transmission, 43(1):165-170, 2019.
-[6] Jorgensen F., Andersen T., Rasmussen P. The Cycloid Permanent Magnetic Gear. IEEE Transactions on Industry Applications. 6(44): 1659-1665,2008.
+[4] Atallah K., Rens J., Mezani S., Howe D. A novel “pseudo” direct-drive brushless permanent magnet machine. IEEE Transactions on Magnetics, 44(11):4349-4352, 2008.
-[7] Rens J., Clark R., Calverley S., Howe D. Design, analysis and realization of a novel magnetic harmonic gear. IEEE Transactions on Industry Applications. 46(1): 206-212,2009.
+[5] Rens J., Atallah K., Calverley S.D., Howe D. A novel magnetic harmonic gear. IEEE Transactions on Industry Applications, 46(1):206-212, 2010.
-[8] Davey K., Hutson T., Mcdonald L., Hutson G. The design and construction of cycloidal magnetic gears. Inernational Conference on Electrical Machines, 2008.
+[6] Jorgensen F., Andersen T., Rasmussen P. The cycloid permanent magnetic gear. IEEE Transactions on Industry Applications, 6(44):1659-1665, 2008.
-[9] Huang H., Qu R., Bird J. Performance of Halbach Cycloidal Magnetic Gears with Respect to Torque Density and Gear Ratio. 2019 IEEE International Electric Machines & Drives Conference (IEMDC). 2019: 1977-1984.
+[7] Rens J., Clark R., Calverley S., Howe D. Design, analysis and realization of a novel magnetic harmonic gear. IEEE Transactions on Industry Applications, 46(1):206-212, 2009.
-[10] Hao W.N., Zhou J. The Cycloid Magnetic Gear Based on Halbach Array. Journal of Mechanical Strength. 39(1):226-229,2017.
+[8] Davey K., Hutson T., Mcdonald L., Hutson G. The design and construction of cycloidal magnetic gears. 2017 International Conference on Electrical Machines and Drives Conference (IEMDC), pp. 1-6, 2017.
-[11] Wu S.Z., He W.D., Zhang Y.H. Analysis of Force and Contact Characteristics of Rotating Arm Bearings for RV Transmissions Mechanism. Journal of South China University of Technology (Natural Science Edition). 48(6):25-33,2020.
+[9] Huang H., Qu R., Bird J. Performance of Halbach cycloidal magnetic gears with respect to torque density and gear ratio. 2019 IEEE International Electric Machines & Drives Conference (IEMDC), pp. 1977-1984, 2019.
-[12] Zhao D.L., Dang W.J., Sun W.P., Guo P.C. Influence of unbalanced magnetic pull on rub-impact rotor-bearing system. Journal of Huazhong University of Science and Technology(Natural Science Edition). 47(10):34-39,2019.
+[10] Hao W.N., Zhou J. The cycloid magnetic gear based on Halbach array. Journal of Mechanical Strength, 39(1):226-229, 2017.
-[13] Jian L., Chau K.T. Analytical calculation of magnetic field distribution in coaxial magnetic gears. Progress In Electromagnetics Research. 92: 1-16,2009.
+[11] Wu S.Z., He W.D., Zhang Y.H. Analysis of force and contact characteristics of rotating arm bearings for RV transmissions mechanism. Journal of South China University of Technology (Natural Science Edition), 48(6):25-33, 2020.
-[14] Lubin T., Mezani S., Rezzoug A. Analytical computation of the magnetic field distribution in a magnetic gear. IEEE Transactions on magnetics. 46(7): 2611-2621,2010.
+[12] Zhao D.L., Dang W.J., Sun W.P., Guo P.C. Influence of unbalanced magnetic pull on rub-impact rotor-bearing system. Journal of Huazhong University of Science and Technology (Natural Science Edition),  47(10):34-39, 2019.
-[15] Deng Z., Nas I., Dapino M.J. Torque Analysis in Coaxial Magnetic Gears Considering Nonlinear Magnetic Properties and Spatial Harmonics. IEEE Transactions on Magnetics. PP(2): 1-11,2019.
+[13] Jian L., Chau K.T. Analytical calculation of magnetic field distribution in coaxial magnetic gears. Progress In Electromagnetics Research, 92:1-16, 2009.

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 == 6. Conclusions ==
 (1) Based on structure mechanism of mechanical ring-plate drive mechanism, TRMG magnetic structure is proposed, and the operation mechanism and changed model of the model are elaborated. The dynamic verification model by finite element software shows that the simulation results are equivalent to the theoretical design output, which proves the established model is correct.
-(2) Through the analysis of the starting position, it can be seen that  <math display="inline">\left[{\beta }_1,{\beta }_2\right]</math> interval in Figure2 is the optimal starting interval of TRMG, and point Q is the optimal starting point.
+(2) Through the analysis of the starting position, it can be seen that  <math display="inline">\left[{\beta }_1,{\beta }_2\right]</math> interval in [[#img-2|Figure 2]]  is the optimal starting interval of TRMG, and point Q is the optimal starting point.
 (3) If TRMG can be started successfully, the deceleration interval  <math display="inline">\Delta \mbox{PSQ}</math> of low-speed permanent magnet ring should be minimized. and increase acceleration interval  <math display="inline">\Delta \mbox{QUV}</math> to achieve synchronous speed of coupled magnetic field.

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 [[#img-7|Figure 7]] shows the speed and torque characteristic curve with starting point U.
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+<div id='img-7'></div>
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
 |style="padding:10px;"| [[File:Draft_Dongning_226371700-image81.png|730x730px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 7'''. Speed and Torque characteristic curve Start with starting point U
-|}
+|}-->
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 [[#img-8|Figure 8]] shows the speed and torque characteristic curve with starting point V.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Draft_Dongning_226371700-image84.png|centre|thumb|728x728px|<span style="text-align: center; font-size: 75%;"> Figure 8. Speed and Torque characteristic curve Start </span>with starting point V]]<span style="text-align: center; font-size: 75%;"> </span></div>
+<div id='img-7'></div>
 From [[#img-8|Figure 8]], it can be seen that from moment 0, the electromagnetic torque of low-speed permanent magnet ring shows periodic changes and starts to decrease gradually from equal to the load torque. The speed accelerates reversely from 0. This is because: when <math display="inline">\alpha \in [{\beta }_3,{\beta }_4]</math>, the electromagnetic torque of the low-speed permanent magnet ring is less than the load torque, and the torque difference gradually increases with α increasing, which makes the low-speed permanent magnet ring reverse speed up rotation. After TRMG enters negative electromagnetic torque period, TRMG accelerates reverse rotates under the action of load torque and negative electromagnetic torque, which eventually leads to start-up failure.

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 | colspan="1" style="padding:10px;"| '''Figure 5'''. Speed and torque characteristic curve start with starting point P
 |}
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 <div id='img-6'></div>
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"|  [[File:Draft_Dongning_226371700-image79.png|719x719px|]]
+|style="padding:10px;"| [[File:Ge_Liu_2021a_4084_Figure6a.png]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding:10px;"| '''Figure 6'''. Speed and Torque characteristic curve Start with starting point Q
+| colspan="1" style="padding:10px;"| '''Figure 6'''. Speed and torque characteristic curve start with starting point Q
 |}
 From [[#img-6|Figure 6]], it can be seen that from moment 0, the low-speed permanent magnet ring gradually increases and periodically changes from electromagnetic torque equal to load torque, and the speed gradually increases from 0 and stabilizes gradually after vibration. TRMG starts smoothly. This is because: when  <math display="inline">\alpha \in [{\beta }_1,{\beta }_3]</math>, the forward electromagnetic torque impulse of the low-speed permanent magnet ring is greater than the load torque from moment 0, and the deceleration area  <math display="inline">\Delta \mbox{PSQ}</math> is avoided. So that the speed of the low-speed permanent magnet ring reaches synchronous speed of rotating magnetic field smoothly, and the speed and torque curve gradually converge.