A Mathematical Model for Layout Design of Linear Induction Motors
Keywords:
designing, mathematical model, main dimensions, electromagnetic loads, linear induction motor
Abstract
The designing of induction motors is considered as a two-stage process of synthesizing an electromechanical system. At the first stage, the device layout is designed, during which the electric motor main dimensions and electromagnetic loads are determined based on empirical data. At the second stage, the device detailed design is developed. The models and methods applied at the stages of layout and detailed designing of rotating and linear induction motors (LIM) differ radically from each other. The following requirements are imposed on the LIM design models. First, the LIM model should allow the designer to calculate the intensity and spatial distribution pattern of the electromagnetic field and secondary current for each speed value. Second, the LIM model should be able not only to link the main dimensions with electromagnetic loads, but also explicitly produce the numerical indicators of electric motor energy efficiency and thermal load. A design model is proposed that satisfies the above-mentioned requirements and describes the LIM electromechanical, energy and thermal states. The model input parameters are the main dimensions and electromagnetic loads of the device. The controlled parameters are the electromagnetic force, efficiency and temperature of the inductor winding. The system layout is designed by evaluating the values of controlled parameters with variations of input parameters in technically feasible ranges.
The article presents the results of designing a LIM according to the proposed model with an electromagnetic force of up to 1000 N, motion speed up to 12 m/s, working stroke up to 2.16 m, and efficiency up to 46%. The results of the thermal calculation testify that the electric motor can operate in short-term and intermittent modes. The results of calculating the performance of an electric motor with the same dimensions and a reduced current density in the inductor winding are also presented. An electric motor with insulation class F and natural air cooling develops an electromagnetic force of up to 116 N and can operate continuously over the entire speed range.
References
1. Копылов И.П. Электрические машины. М.: Высшая школа, 2004.
2. Иванов-Смоленский А.В. Электрические машины. Т. 1. М.: Изд-во МЭИ, 2004.
3. Иванов-Смоленский А.В. Электрические машины. М.: Издат. дом МЭИ, 2006.
4. Беспалов В.Я., Котеленец Н.Ф. Электрические машины. М.: Академия, 2006.
5. Копылов И.П. и др. Проектирование электрических машин. М.: Альянс, 2016.
6. Гольдберг О.Д., Макаров Л.Н., Хелемская С.П. Инженерное проектирование электрических машин. М.: Издат. дом. «Бастет», 2016.
7. Справочник по электрическим машинам / Под общ. ред. И.П. Копылова, Б.К. Клокова. Т. 1. М.: Энергоатомиздат, 1988.
8. Справочник по электрическим машинам / Под общ. ред. И.П. Копылова, Б.К. Клокова. Т. 2. М.: Энергоатомиздат, 1989.
9. Электротехнический справочник. Т. 4. Использование электрической энергии / Под общ. ред. В.Г. Герасимова и др. М.: Изд-во МЭИ, 2004.
10. Кацман М.М. Справочник по электрическим машинам. М.: Академия, 2005.
11. Кобелев А.С., Макаров Л.Н. Интегрированная среда для повседневного поискового проектирования электрических машин // Электромеханика, электротехнологии, электротехнические материалы и компоненты: Труды XVII Междунар. конф., М.: Знак, 2018. С. 139—141.
12. Makarov L.N., Denisov V.N., Kurilin S.P. Designing and Modeling a Linear Electric Motor for Vibration-technology Machines // Russian Electrical Engineering. 2017. V. 88. No. 3. Pp. 166—169.
13. Вольдек А.И. Индукционные магнитогидродинамические машины с жидкометаллическим рабочим телом. Л.: Энергия, 1970.
14. Ямамура С. Теория линейных асинхронных двигателей. Л.: Энергоатомиздат, 1983.
15. Sarapulov F.N., Frizen V.E., Shvydkiy E.L., Smol’yanov I.A. Mathematical Modeling of a Linear-induction Motor Based on Detailed Equivalent Circuits // Russian Electrical Engineering. 2018. V. 89. No. 4. Pp. 270—274.
16. Yu S.O., Sarapulov F.N., Tomashevsky D.N. Mathematical Modeling of Electromechanical Characteristics of Linear Electromagnetic and Induction-dynamic Motors // IOP Conf. Series: Materials Sci. and Eng. 2020. V. 950. Iss. 1. P. 012020.
17. Smolyanov I., Sarapulov F., Tarasov F. Calculation of Linear Induction Motor Features by Detailed Equivalent Circuit Method Taking Into Account Non-linear Electromagnetic and Thermal Properties // Computers and Mathematics with Appl. 2019. V. 78. Iss. 9. Pp. 3187—3199.
18. Sarapulov F.N., Goman V., Trekin G.E. Temperature Calculation for Linear Induction Motor in Transport Application with Multiphysics Approach // IOP Conf. Series: Materials Sci. and Eng. 2020. V. 966. Iss. 1. P. 012105.
19. Сарапулов Ф.Н., Смольянов И.А. Исследование тягового линейного асинхронного двигателя конвейерного поезда // Известия высш. учеб. заведений. Серия «Электромеханика». 2019. Т. 62. № 1. С. 39—43.
20. Smolyanov I., Shmakov E., Gasheva D. Research of Linear Induction Motor as Part of Driver by Detailed Equivalent Circuit // Proc. Intern. Russian Automation Conf. Sochi, 2019. Pp. 1—6.
21. Чапаев В.С., Волков С.В., Мартяшин А.А. Основные математические соотношения для исследования распределения магнитного поля в линейном асинхронном двигателе с управляющим слоем // Надежность и качество: Труды Междунар. симпозиума. Пенза: Изд-во ПГУ, 2016. Т. 1. С. 153—155.
22. Kazraji S.M., Sharifyan M.B.B. A Predictive Control Model for an Induction Motor Linear Drive // Proc. 43rd IEEE Industrial Electronics Soc. Annual Conf. 2017. Pp. 3736—3739.
23. Creppe R.C., Ulson J.A.C., Rodrigues J.F. Influence of Design Parameters on Linear Induction Motor End Effect // IEEE Trans. Energy Conversion. 2008. V. 23. No. 2. Pp. 358—362.
24. Merlin Mary N.J., Ganguly C., Kowsalya M. Mathematical Modelling of Linear Induction Motor with and Without Considering End Effects Using Different Reference Frames // Proc. IEEE I Intern. Conf. Power Electronics, Intelligent Control and Energy Systems. 2016. Pp. 1—5.
25. Cho H., Liu Y., Kim K.A. Short-primary Linear Induction Motor Modeling with End Effects for Electric Transportation Systems // Proc. Intern. Symp. Computer, Consumer and Control. 2018. Pp. 338—341.
26. Kurilin S.P., Dli M.I., Sokolov A.M. Linear Induction Motors for Non-ferrous Metallurgy // Non-ferrous Metals. 2021. No. 1. Pp. 67—73.
27. Курилин С.П., Рубин Ю.Б., Дли М.И., Денисов В.Н. Модели и методы проектирования линейных электродвигателей для цветной металлургии // Цветные металлы. 2021. № 11. С. 83—90.
---
Для цитирования: Курилин С.П. Математическая модель для компоновочного проектирования линейных асинхронных электродвигателей // Вестник МЭИ. 2023. № 3. С. 11—20. DOI: 10.24160/1993-6982-2023-3-11-20
---
Работа выполнена при поддержке: Российского научного фонда (грант № 22-61-00096)
#
1. Kopylov I.P. Elektricheskie Mashiny. M.: Vysshaya Shkola, 2004. (in Russian).
2. Ivanov-Smolenskiy A.V. Elektricheskie Mashiny. T. 1. M.: Izd-vo MEI, 2004. (in Russian).
3. Ivanov-Smolenskiy A.V. Elektricheskie Mashiny. M.: Izdat. Dom MEI, 2006. (in Russian).
4. Bespalov V.Ya., Kotelenets N.F. Elektricheskie Mashiny. M.: Akademiya, 2006. (in Russian).
5. Kopylov I.P. i dr. Proektirovanie Elektricheskikh Mashin. M.: Al'yans, 2016. (in Russian).
6. Gol'dberg O.D., Makarov L.N., Khelemskaya S.P. Inzhenernoe Proektirovanie Elektricheskikh Mashin. M.: Izdat. Dom. «Bastet», 2016. (in Russian).
7. Spravochnik po Elektricheskim Mashinam. Pod Obshch. Red. I.P. Kopylova, B.K. Klokova. T. 1. M.: Energoatomizdat, 1988. (in Russian).
8. Spravochnik po Elektricheskim Mashinam. Pod Obshch. Red. I.P. Kopylova, B.K. Klokova. T. 2. M.: Energoatomizdat, 1989. (in Russian).
9. Elektrotekhnicheskiy Spravochnik. T. 4. Ispol'zovanie Elektricheskoy Energii. Pod Obshch. Red. V.G. Gerasimova i dr. M.: Izd-vo MEI, 2004. (in Russian).
10. Katsman M.M. Spravochnik po Elektricheskim Mashinam. M.: Akademiya, 2005. (in Russian).
11. Kobelev A.S., Makarov L.N. Integrirovannaya Sreda dlya Povsednevnogo Poiskovogo Proektirovaniya Elektricheskikh Mashin. Elektromekhanika, Elektrotekhnologii, Elektrotekhnicheskie Materialy i Komponenty: Trudy XVII Mezhdunar. Konf., M.: Znak, 2018:139—141. (in Russian).
12. Makarov L.N., Denisov V.N., Kurilin S.P. Designing and Modeling a Linear Electric Motor for Vibration-technology Machines. Russian Electrical Engineering. 2017;88;3:166—169.
13. Vol'dek A.I. Induktsionnye Magnitogidrodinamicheskie Mashiny s Zhidkometallicheskim Rabochim Telom. L.: Energiya, 1970. (in Russian).
14. Yamamura S. Teoriya Lineynykh Asinkhronnykh Dvigateley. L.: Energoatomizdat, 1983. (in Russian).
15. Sarapulov F.N., Frizen V.E., Shvydkiy E.L., Smol’yanov I.A. Mathematical Modeling of a Linear-induction Motor Based on Detailed Equivalent Circuits. Russian Electrical Engineering. 2018;89;4:270—274.
16. Yu S.O., Sarapulov F.N., Tomashevsky D.N. Mathematical Modeling of Electromechanical Characteristics of Linear Electromagnetic and Induction-dynamic Motors. IOP Conf. Series: Materials Sci. and Eng. 2020;950;1:012020.
17. Smolyanov I., Sarapulov F., Tarasov F. Calculation of Linear Induction Motor Features by Detailed Equivalent Circuit Method Taking Into Account Non-linear Electromagnetic and Thermal Properties. Computers and Mathematics with Appl. 2019;78;9:3187—3199.
18. Sarapulov F.N., Goman V., Trekin G.E. Temperature Calculation for Linear Induction Motor in Transport Application with Multiphysics Approach. IOP Conf. Series: Materials Sci. and Eng. 2020;966;1:012105.
19. Sarapulov F.N., Smol'yanov I.A. Issledovanie Tyagovogo Lineynogo Asinkhronnogo Dvigatelya Konveyernogo Poezda. Izvestiya Vyssh. Ucheb. Zavedeniy. Seriya «Elektromekhanika». 2019;62;1:39—43. (in Russian).
20. Smolyanov I., Shmakov E., Gasheva D. Research of Linear Induction Motor as Part of Driver by Detailed Equivalent Circuit. Proc. Intern. Russian Automation Conf. Sochi, 2019:1—6.
21. CHapaev V.S., Volkov S.V., Martyashin A.A. Osnovnye Matematicheskie Sootnosheniya dlya Issledovaniya Raspredeleniya Magnitnogo Polya v Lineynom Asinkhronnom Dvigatele s Upravlyayushchim Sloem. Nadezhnost' i Kachestvo: Trudy Mezhdunar. Simpoziuma. Penza: Izd-vo PGU, 2016l1:153—155. (in Russian).
22. Kazraji S.M., Sharifyan M.B.B. A Predictive Control Model for an Induction Motor Linear Drive. Proc. 43rd IEEE Industrial Electronics Soc. Annual Conf. 2017:3736—3739.
23. Creppe R.C., Ulson J.A.C., Rodrigues J.F. Influence of Design Parameters on Linear Induction Motor End Effect. IEEE Trans. Energy Conversion. 2008;23;2:358—362.
24. Merlin Mary N.J., Ganguly C., Kowsalya M. Mathematical Modelling of Linear Induction Motor with and Without Considering End Effects Using Different Reference Frames. Proc. IEEE I Intern. Conf. Power Electronics, Intelligent Control and Energy Systems. 2016:1—5.
25. Cho H., Liu Y., Kim K.A. Short-primary Linear Induction Motor Modeling with End Effects for Electric Transportation Systems. Proc. Intern. Symp. Computer, Consumer and Control. 2018:338—341.
26. Kurilin S.P., Dli M.I., Sokolov A.M. Linear Induction Motors for Non-ferrous Metallurgy. Non-ferrous Metals. 2021;1:67—73.
27. Kurilin S.P., Rubin Yu.B., Dli M.I., Denisov V.N. Modeli i Metody Proektirovaniya Lineynykh Elektrodvigateley dlya Tsvetnoy Metallurgii. Tsvetnye Metally. 2021;11:83—90. (in Russian).
---
For citation: Kurilin S.P. A Mathematical Model for Layout Design of Linear Induction Motors. Bulletin of MPEI. 2023;3:11—20. (in Russian). DOI: 10.24160/1993-6982-2023-3-11-20
---
The work is executed at support: Russian Science Foundation (Grant No. 22-61-00096)
2. Иванов-Смоленский А.В. Электрические машины. Т. 1. М.: Изд-во МЭИ, 2004.
3. Иванов-Смоленский А.В. Электрические машины. М.: Издат. дом МЭИ, 2006.
4. Беспалов В.Я., Котеленец Н.Ф. Электрические машины. М.: Академия, 2006.
5. Копылов И.П. и др. Проектирование электрических машин. М.: Альянс, 2016.
6. Гольдберг О.Д., Макаров Л.Н., Хелемская С.П. Инженерное проектирование электрических машин. М.: Издат. дом. «Бастет», 2016.
7. Справочник по электрическим машинам / Под общ. ред. И.П. Копылова, Б.К. Клокова. Т. 1. М.: Энергоатомиздат, 1988.
8. Справочник по электрическим машинам / Под общ. ред. И.П. Копылова, Б.К. Клокова. Т. 2. М.: Энергоатомиздат, 1989.
9. Электротехнический справочник. Т. 4. Использование электрической энергии / Под общ. ред. В.Г. Герасимова и др. М.: Изд-во МЭИ, 2004.
10. Кацман М.М. Справочник по электрическим машинам. М.: Академия, 2005.
11. Кобелев А.С., Макаров Л.Н. Интегрированная среда для повседневного поискового проектирования электрических машин // Электромеханика, электротехнологии, электротехнические материалы и компоненты: Труды XVII Междунар. конф., М.: Знак, 2018. С. 139—141.
12. Makarov L.N., Denisov V.N., Kurilin S.P. Designing and Modeling a Linear Electric Motor for Vibration-technology Machines // Russian Electrical Engineering. 2017. V. 88. No. 3. Pp. 166—169.
13. Вольдек А.И. Индукционные магнитогидродинамические машины с жидкометаллическим рабочим телом. Л.: Энергия, 1970.
14. Ямамура С. Теория линейных асинхронных двигателей. Л.: Энергоатомиздат, 1983.
15. Sarapulov F.N., Frizen V.E., Shvydkiy E.L., Smol’yanov I.A. Mathematical Modeling of a Linear-induction Motor Based on Detailed Equivalent Circuits // Russian Electrical Engineering. 2018. V. 89. No. 4. Pp. 270—274.
16. Yu S.O., Sarapulov F.N., Tomashevsky D.N. Mathematical Modeling of Electromechanical Characteristics of Linear Electromagnetic and Induction-dynamic Motors // IOP Conf. Series: Materials Sci. and Eng. 2020. V. 950. Iss. 1. P. 012020.
17. Smolyanov I., Sarapulov F., Tarasov F. Calculation of Linear Induction Motor Features by Detailed Equivalent Circuit Method Taking Into Account Non-linear Electromagnetic and Thermal Properties // Computers and Mathematics with Appl. 2019. V. 78. Iss. 9. Pp. 3187—3199.
18. Sarapulov F.N., Goman V., Trekin G.E. Temperature Calculation for Linear Induction Motor in Transport Application with Multiphysics Approach // IOP Conf. Series: Materials Sci. and Eng. 2020. V. 966. Iss. 1. P. 012105.
19. Сарапулов Ф.Н., Смольянов И.А. Исследование тягового линейного асинхронного двигателя конвейерного поезда // Известия высш. учеб. заведений. Серия «Электромеханика». 2019. Т. 62. № 1. С. 39—43.
20. Smolyanov I., Shmakov E., Gasheva D. Research of Linear Induction Motor as Part of Driver by Detailed Equivalent Circuit // Proc. Intern. Russian Automation Conf. Sochi, 2019. Pp. 1—6.
21. Чапаев В.С., Волков С.В., Мартяшин А.А. Основные математические соотношения для исследования распределения магнитного поля в линейном асинхронном двигателе с управляющим слоем // Надежность и качество: Труды Междунар. симпозиума. Пенза: Изд-во ПГУ, 2016. Т. 1. С. 153—155.
22. Kazraji S.M., Sharifyan M.B.B. A Predictive Control Model for an Induction Motor Linear Drive // Proc. 43rd IEEE Industrial Electronics Soc. Annual Conf. 2017. Pp. 3736—3739.
23. Creppe R.C., Ulson J.A.C., Rodrigues J.F. Influence of Design Parameters on Linear Induction Motor End Effect // IEEE Trans. Energy Conversion. 2008. V. 23. No. 2. Pp. 358—362.
24. Merlin Mary N.J., Ganguly C., Kowsalya M. Mathematical Modelling of Linear Induction Motor with and Without Considering End Effects Using Different Reference Frames // Proc. IEEE I Intern. Conf. Power Electronics, Intelligent Control and Energy Systems. 2016. Pp. 1—5.
25. Cho H., Liu Y., Kim K.A. Short-primary Linear Induction Motor Modeling with End Effects for Electric Transportation Systems // Proc. Intern. Symp. Computer, Consumer and Control. 2018. Pp. 338—341.
26. Kurilin S.P., Dli M.I., Sokolov A.M. Linear Induction Motors for Non-ferrous Metallurgy // Non-ferrous Metals. 2021. No. 1. Pp. 67—73.
27. Курилин С.П., Рубин Ю.Б., Дли М.И., Денисов В.Н. Модели и методы проектирования линейных электродвигателей для цветной металлургии // Цветные металлы. 2021. № 11. С. 83—90.
---
Для цитирования: Курилин С.П. Математическая модель для компоновочного проектирования линейных асинхронных электродвигателей // Вестник МЭИ. 2023. № 3. С. 11—20. DOI: 10.24160/1993-6982-2023-3-11-20
---
Работа выполнена при поддержке: Российского научного фонда (грант № 22-61-00096)
#
1. Kopylov I.P. Elektricheskie Mashiny. M.: Vysshaya Shkola, 2004. (in Russian).
2. Ivanov-Smolenskiy A.V. Elektricheskie Mashiny. T. 1. M.: Izd-vo MEI, 2004. (in Russian).
3. Ivanov-Smolenskiy A.V. Elektricheskie Mashiny. M.: Izdat. Dom MEI, 2006. (in Russian).
4. Bespalov V.Ya., Kotelenets N.F. Elektricheskie Mashiny. M.: Akademiya, 2006. (in Russian).
5. Kopylov I.P. i dr. Proektirovanie Elektricheskikh Mashin. M.: Al'yans, 2016. (in Russian).
6. Gol'dberg O.D., Makarov L.N., Khelemskaya S.P. Inzhenernoe Proektirovanie Elektricheskikh Mashin. M.: Izdat. Dom. «Bastet», 2016. (in Russian).
7. Spravochnik po Elektricheskim Mashinam. Pod Obshch. Red. I.P. Kopylova, B.K. Klokova. T. 1. M.: Energoatomizdat, 1988. (in Russian).
8. Spravochnik po Elektricheskim Mashinam. Pod Obshch. Red. I.P. Kopylova, B.K. Klokova. T. 2. M.: Energoatomizdat, 1989. (in Russian).
9. Elektrotekhnicheskiy Spravochnik. T. 4. Ispol'zovanie Elektricheskoy Energii. Pod Obshch. Red. V.G. Gerasimova i dr. M.: Izd-vo MEI, 2004. (in Russian).
10. Katsman M.M. Spravochnik po Elektricheskim Mashinam. M.: Akademiya, 2005. (in Russian).
11. Kobelev A.S., Makarov L.N. Integrirovannaya Sreda dlya Povsednevnogo Poiskovogo Proektirovaniya Elektricheskikh Mashin. Elektromekhanika, Elektrotekhnologii, Elektrotekhnicheskie Materialy i Komponenty: Trudy XVII Mezhdunar. Konf., M.: Znak, 2018:139—141. (in Russian).
12. Makarov L.N., Denisov V.N., Kurilin S.P. Designing and Modeling a Linear Electric Motor for Vibration-technology Machines. Russian Electrical Engineering. 2017;88;3:166—169.
13. Vol'dek A.I. Induktsionnye Magnitogidrodinamicheskie Mashiny s Zhidkometallicheskim Rabochim Telom. L.: Energiya, 1970. (in Russian).
14. Yamamura S. Teoriya Lineynykh Asinkhronnykh Dvigateley. L.: Energoatomizdat, 1983. (in Russian).
15. Sarapulov F.N., Frizen V.E., Shvydkiy E.L., Smol’yanov I.A. Mathematical Modeling of a Linear-induction Motor Based on Detailed Equivalent Circuits. Russian Electrical Engineering. 2018;89;4:270—274.
16. Yu S.O., Sarapulov F.N., Tomashevsky D.N. Mathematical Modeling of Electromechanical Characteristics of Linear Electromagnetic and Induction-dynamic Motors. IOP Conf. Series: Materials Sci. and Eng. 2020;950;1:012020.
17. Smolyanov I., Sarapulov F., Tarasov F. Calculation of Linear Induction Motor Features by Detailed Equivalent Circuit Method Taking Into Account Non-linear Electromagnetic and Thermal Properties. Computers and Mathematics with Appl. 2019;78;9:3187—3199.
18. Sarapulov F.N., Goman V., Trekin G.E. Temperature Calculation for Linear Induction Motor in Transport Application with Multiphysics Approach. IOP Conf. Series: Materials Sci. and Eng. 2020;966;1:012105.
19. Sarapulov F.N., Smol'yanov I.A. Issledovanie Tyagovogo Lineynogo Asinkhronnogo Dvigatelya Konveyernogo Poezda. Izvestiya Vyssh. Ucheb. Zavedeniy. Seriya «Elektromekhanika». 2019;62;1:39—43. (in Russian).
20. Smolyanov I., Shmakov E., Gasheva D. Research of Linear Induction Motor as Part of Driver by Detailed Equivalent Circuit. Proc. Intern. Russian Automation Conf. Sochi, 2019:1—6.
21. CHapaev V.S., Volkov S.V., Martyashin A.A. Osnovnye Matematicheskie Sootnosheniya dlya Issledovaniya Raspredeleniya Magnitnogo Polya v Lineynom Asinkhronnom Dvigatele s Upravlyayushchim Sloem. Nadezhnost' i Kachestvo: Trudy Mezhdunar. Simpoziuma. Penza: Izd-vo PGU, 2016l1:153—155. (in Russian).
22. Kazraji S.M., Sharifyan M.B.B. A Predictive Control Model for an Induction Motor Linear Drive. Proc. 43rd IEEE Industrial Electronics Soc. Annual Conf. 2017:3736—3739.
23. Creppe R.C., Ulson J.A.C., Rodrigues J.F. Influence of Design Parameters on Linear Induction Motor End Effect. IEEE Trans. Energy Conversion. 2008;23;2:358—362.
24. Merlin Mary N.J., Ganguly C., Kowsalya M. Mathematical Modelling of Linear Induction Motor with and Without Considering End Effects Using Different Reference Frames. Proc. IEEE I Intern. Conf. Power Electronics, Intelligent Control and Energy Systems. 2016:1—5.
25. Cho H., Liu Y., Kim K.A. Short-primary Linear Induction Motor Modeling with End Effects for Electric Transportation Systems. Proc. Intern. Symp. Computer, Consumer and Control. 2018:338—341.
26. Kurilin S.P., Dli M.I., Sokolov A.M. Linear Induction Motors for Non-ferrous Metallurgy. Non-ferrous Metals. 2021;1:67—73.
27. Kurilin S.P., Rubin Yu.B., Dli M.I., Denisov V.N. Modeli i Metody Proektirovaniya Lineynykh Elektrodvigateley dlya Tsvetnoy Metallurgii. Tsvetnye Metally. 2021;11:83—90. (in Russian).
---
For citation: Kurilin S.P. A Mathematical Model for Layout Design of Linear Induction Motors. Bulletin of MPEI. 2023;3:11—20. (in Russian). DOI: 10.24160/1993-6982-2023-3-11-20
---
The work is executed at support: Russian Science Foundation (Grant No. 22-61-00096)
Published
2023-02-14
Section
Electrical Complexes and Systems (2.4.2)
