[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content

Advertisement

Springer Nature Link
Log in

Optimization Techniques for Cogging Torque Reduction and Thermal Characterization in Brushless DC Motor

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Electrical Engineering Aims and scope Submit manuscript

Abstract

This paper presents soft computing-based optimization techniques for the cogging torque reduction and thermal characterization by finite element analysis in a permanent magnet brushless DC motor (BLDC). Stator and rotor structure of BLDC motor are optimized to reduce the cogging torque, noise, and vibration by using the design parameters namely: length of magnet, length of air gap and opening in the stator slot which are selected by performing variance-based sensitivity analysis. The proposed method is suitable in the preliminary design phase of the motor to determine the optimal structure to improve the efficiency. The comparison of results obtained using firefly algorithm , ant colony optimization algorithm and Bat algorithm indicate that Firefly-based optimization algorithm is capable of giving improved design parameter output. Cogging torque is created due to the interaction of magnets in the rotor and the stator slot of the motor. Thorough thermal analysis is also conceded out to investigate the thermal characteristics at dissimilar portions of the motor namely: stator core, stator slot, rotor core and permanent magnet at different operating environments in the continuous operation mode. Thermal investigation is required for the various high speed e-vehicle applications. The usefulness of the designed machine simulation is compared with the results obtained from hardware analysis. The outcomes attained from software simulation studies are validated through experimental hardware setup.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

  • Bora TC, Dos Santos Coelho L, Lebensztajn L (2012) Bat-inspired optimization approach for the brushless DC wheel motor problem. IEEE Trans Magn 48(2):947–950

    Article  Google Scholar 

  • Bramerdorfer G, Zăvoianu AC (2017) Surrogate-based multi- objective optimization of electrical machine designs facilitating tolerance analysis. IEEE Trans Magn 53(8):1–11

    Article  Google Scholar 

  • Cassimere BN, Sudhoff SD (2009) Population-based design of surface-mounted permanent magnet synchronous machines. IEEE Trans Energy Convers 24(2):338–346

    Article  Google Scholar 

  • Chakkarapani K, Thangavelu T, Dharmalingam K, Thandavarayan P (2019) Multiobjective design optimization and analysis of magnetic flux distribution for slotless permanent magnet brushless DC motor using evolutionary algorithms. J Magn Magn Mater 476:524–537

    Article  Google Scholar 

  • Chakkarapani K, Thangavelu T, Dharmalingam K (2020) Thermal analysis of BLDC motor using multiobjective optimization. Int Trans Electr Energy Syst 30(10):1–18

    Article  Google Scholar 

  • dos Santos CL, Barbosa LZ, Lebensztajn L (2010) Multi objective particle swarm approach for the design of a brushless DC wheel motor. IEEE Trans Magn 46(8):2994–2997

    Article  Google Scholar 

  • Ebrahim EA (2012) Ant-colony optimization control of brushless-DC motor driving a hybrid electric-Bike and fed from photovoltaic generator. In: IEEE conference on evolutionary computation (CEC), pp 4221–4228

  • Kamal C, Thyagarajan T, Selvakumari M, Kalpana D (2017), Cogging torque minimization in brushless DC motor using PSO and GA based optimization. In: IEEE proceedings of international conference on trends in industrial measurement and control

  • Khelifa M, Mordjaoui M, Medoued A (2017) An inverse problem methodology for design and optimization of an interior permanent magnetic BLDC motor. Int J Hydrogen Energy 42:17733–17740

    Article  Google Scholar 

  • Kim D-W, Kang B, Choi KK, Kim D-H (2016) A comparative study on probabilistic optimization methods for electromagnetic design’. IEEE Trans Magn 52(3):7201304–7201307

    Article  Google Scholar 

  • Pillay P, Krishnan R (1988) Modelling of permanent magnet motor drives. IEEE Trans Ind Electron 35(4):537–541

    Article  Google Scholar 

  • Pillay P, Krishnan R (1991) Application characteristics of permanent magnet synchronous and brushless DC motors for servo drives. IEEE Trans Ind Appl 27(5):986–996

    Article  Google Scholar 

  • Pontnuru D, Alice Mary K, Sai Babu Ch (2019) Experimental implementation of flower pollination algorithm for speed controller of a BLDC motor. Ain Shams Eng J 10(3):287–295

    Article  Google Scholar 

  • Rastgou A, Moshtagh J (2016) Application of firefly algorithm for multi-stage transmission expansion planning with adequacy-security considerations in deregulated environments. J Appl Soft Comput 1:373–389

    Article  Google Scholar 

  • Shabanian A, Tousiwas AA, Pourmandi M, Khormali A, Ataei A (2015) Optimization of brushless direct current motor design using an intelligent technique. ISA Trans 57:311–321

    Article  Google Scholar 

  • Srinivas KN, Arumugam R (2005a) Analysis and characterization of switched reluctance motors: Part I- dynamic, static and frequency spectrum analyses. IEEE Trans Magn 41(4):1306–1320

    Article  Google Scholar 

  • Srinivas KN, Arumugam R (2005b) Analysis and characterization of switched reluctance motors: Part II- flow thermal and vibration analyses. IEEE Trans Magn 41(4):1321–1332

    Article  Google Scholar 

  • Umadevi N, Balaji M, Kamaraj V, Padmanaban A (2014) Data interpolation and design optimization of brushless DC motor using generalized regression neural network’. J Electr Eng Technol 9:742–748

    Google Scholar 

  • Zhu ZQ, Howe D (2000) Influence of design parameters on cogging torque in permanent magnet machines. IEEE Trans Energy Convers 15(4):407–412

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by UGC-SAP-DRS-I. Department of Instrumentation Engineering, MIT campus, Anna University.

Author information

Authors and Affiliations

  1. Sri Venkateswara College of Engineering, Chennai, India

    C. Kamal

  2. MIT Campus, Anna University, Chennai, India

    T. Thyagarajan & D. Kalpana

Authors
  1. C. Kamal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Thyagarajan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Kalpana
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Kamal.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Appendix

Appendix

To predict the open-circuit magneto static field of electric motors, analytical magnetic circuit approach is needed. The magnetic flux \(\Phi_{m}\) is the flux actually linking with the magnet, which is equal to the summation of air gap flux and leakage flux. The leakage flux is an essential quantity for predicting the average flux density in the air gap. The magnetic circuit analysis takes the leakage flux into account.

The assumptions for magnetic modeling are as follows:

  1. (1)

    The magnetic field intensity in the stator winding is negligible.

  2. (2)

    Infinite permeability in stator and rotor core.

  3. (3)

    There is no magnetic saturation in the steel region.

Let,

\(\Phi_{r}\) as the flux source in weber,

\(\Phi_{g}\) as the air gap flux in weber,

\(\Phi_{m}\) as the flux leaving the magnet in weber,

\(\Phi_{{{\text{mm}}}}\) as the magnet to magnet leakage flux in weber,

\(\Phi_{{{\text{mr}}}}\) as the magnet to rotor leakage flux in weber,

\(R_{r}\) as the reluctance of the rotor in AT/weber,

\(R_{s}\) as the reluctance of the stator back irons in AT/weber,

\(R_{g}\) as the reluctance of the air gap in AT/weber,

\(R_{{{\text{mo}}}}\) as the reluctance of the magnet in AT/weber,

\(R_{{{\text{mm}}}}\) as the reluctance from magnet to magnet, and.

\(R_{{{\text{mr}}}}\) as the reluctance from magnet to rotor in AT/weber.

Based on assumption 1 listed above, the values of \(R_{s}\) and \(R_{r}\) can be ignored. The \(R_{m}\) can be expressed as given in Eq. (2).

$$R_{m} = \frac{{R_{{{\text{mo}}}} }}{1 + 2\eta + 4\lambda }$$
(2)

where

$$\eta = R_{{{\text{mo}}}} /R_{{{\text{mr}}}}$$
(3)

and

$$\lambda = R_{{{\text{mo}}}} /R_{{{\text{mm}}}}$$
(4)

Also, the air gap flux is expressed as given in Eq. (5)

$$\Phi_{g} = \frac{{R_{m} \Phi_{r} }}{{R_{m} + R_{g} }} = \frac{{R_{{{\text{mo}}}} }}{{R_{{{\text{mo}}}} + R_{g} \left( {1 + 2\eta + 4\lambda } \right)}}\Phi_{r}$$
(5)

The flux leaving the magnet is expressed as given in Eq. (6)

$$\Phi_{m} = \frac{{R_{{{\text{mo}}}} + R_{g} \left( {2\eta + 4\lambda } \right)}}{{R_{{{\text{mo}}}} + R_{g} \left( {1 + 2\eta + 4\lambda } \right)}}\Phi_{r}$$
(6)

In addition, the flux source of the magnet \(\Phi_{r}\) can be written as given in Eq. (7)

$$\Phi_{r} = A_{m} B_{r}$$
(7)

where \(A_{m}\) is the flux passing area and.

\(B_{r }\) represents the residential flux density of the magnet.

Based on Eqs. (5)–(7), the average flux densities within the air gap and the magnet can be obtained as follows.

$$B_{{g,{\text{ave}}}} = \frac{{A_{m} /A_{g} }}{{1 + \left( {R_{g} /R_{{{\text{mo}}}} } \right)\left( {1 + 2\eta + 4\lambda } \right)}}B_{r}$$
(8)

and

$$B_{m} = \frac{{1 + \left( {R_{g} /R_{{{\text{mo}}}} } \right)\left( {2\eta + 4\lambda } \right)}}{{1 + \left( {R_{g} /R_{{{\text{mo}}}} } \right)\left( {1 + 2\eta + 4\lambda } \right)}} .$$
(9)

where \(A_{m} /A_{g}\) is the ratio of the magnetic flux passing area of the magnet to that of the air gap.

Based on geometric and magnetic relationships, the following expressions are obtained:

$$A_{m} = \tau_{m} L$$
(10)
$$A_{g} = \left( {\tau_{m} + \tau_{f} } \right)L$$
(11)
$$R_{{{\text{mo}}}} = \frac{{l_{m} }}{{\mu_{o} \mu_{r} A_{m} }}$$
(12)
$$R_{g} = \frac{{g_{e} }}{{\mu_{o} \left( {\tau_{m} + 2g_{e} } \right)L}}$$
(13)
$$g_{e} = k_{c} g$$
(14)

where \(L\) is the stack length of the stator in mm, \(\tau_{m}\) is the magnet width in mm, \(\tau_{f}\) is the length of the two adjacent magnets, \(l_{m}\) is the magnet height in mm, \(\mu_{o}\) is the permeability of free space, \(\mu_{r}\) is the relative permeability of the magnet, \(g\) is the air gap length in mm, \(g_{e}\) is the effective air gap length in mm, and \(k_{c}\) is the carter’s co-efficient. In particular, the fringing effect is taken into consideration by adding the length 2 \(g_{e}\) to \(\tau_{m}\) for calculating \(R_{g}\) as expressed in Eq. (13).

The magnet-to-rotor as well as magnet-to-magnet reluctances can be further obtained by calculating their permeances using corresponding circular-arc and straight-line permanence models. Since, the reluctances are reciprocal to the permeance, thus can be represented as given in Eqs. (2–16).

$$R_{{{\text{mr}}}} = \frac{1}{{P_{{{\text{mr}}}} }}$$
(15)
$$R_{{{\text{mm}}}} = \frac{1}{{P_{{{\text{mm}}}} }}$$
(16)

The fringing permeance \(P_{{{\text{mr}}}}\) is an infinite sum of differential width permeances, each of length \(l_{m} + \pi x\), i.e.

$$P_{{{\text{mr}}}} = \sum \frac{{\mu_{o} {\text{d}}A}}{l} = \sum \frac{{\mu_{o} L}}{{l_{m} + \pi x}}{\text{d}}x$$
(17)

After simplification, the \(P_{{{\text{mr}}}}\) can be expressed as given in Eq. (17).

$$P_{mr} = \frac{{\mu_{o} L}}{\pi }\ln \left[ {1 + \frac{{\pi \min \left( {g_{e} ,\tau_{f} /2} \right)}}{{l_{m} }}} \right]$$
(18)

where \({\text{d}}A = L{\text{d}}x\) is the cross-sectional area of each differential permeance.

\(P_{{{\text{mm}}}}\) can be expressed as given in Eq. (19).

$$P_{{{\text{mm}}}} = \frac{{\mu_{0} L}}{\pi }\ln \left( {1 + \frac{{\pi g_{e} }}{{\tau_{f} }}} \right)$$
(19)

Based on Eqs. (10), (12), (15), (18) and (19), Eqs. (3) and (4) can be rewritten as given in Eqs. (20 and 21).

$$\eta = \frac{{l_{m} }}{{\mu_{r} \pi \tau_{m} }}\ln \left( {1 + \frac{{\pi \min \left( {g_{e} ,\tau_{f} /2} \right)}}{{l_{m} }}} \right)$$
(20)
$$\lambda = \frac{{l_{m} }}{{\mu_{r} \pi \tau_{m} }}\ln \left( {1 + \frac{{\pi g_{e} }}{{\tau_{f} }}} \right)$$
(21)

The magnetic flux density can be expressed as given in Eq. (22).

$$B_{g,ave} = \frac{{B_{r} }}{{1 + \frac{{\tau_{f} }}{{\tau_{m} }} + \mu_{r} \frac{{g_{e} }}{{l_{m} }}\frac{{\tau_{m} + \tau_{f} }}{{\tau_{m} + 2g_{e} }}\left( {1 + 2\eta + 4\lambda } \right)}}$$
(22)

and

$$B_{m} = \frac{{\left( {1 + \frac{{2g_{e} }}{{\tau_{m} }}} \right)\frac{1}{{\mu_{r} }}\frac{{l_{m} }}{{g_{e} }} + 2\eta + 4\lambda }}{{\left( {1 + \frac{{2g_{e} }}{{\tau_{m} }}} \right)\frac{1}{{\mu_{r} }}\frac{{l_{m} }}{{g_{e} }} + 1 + 2\eta + 4\lambda }}B_{r}$$
(23)

The leakage coefficient (\(f_{{{\text{LKG}}}}\)) is defined as the ratio of air gap flux to magnet flux and it is analytically expressed as given in Eq. (24).

$$f_{{{\text{LKG}}}} = \frac{{\Phi_{g} }}{{\Phi_{m} }} = \frac{1}{{1 + \frac{{\mu_{r} g_{e} \tau_{m} }}{{l_{m} \left( {\tau_{m} + 2g_{e} } \right)}}\left( {2\eta + 4\lambda } \right) }}$$
(24)

The average electromagnetic torque is expresses as given in Eq. (25).

$$T_{{{\text{ave}}}} = mk_{l} k_{w} N_{{{\text{tol}}}} B_{{g,{\text{ave}}}} R_{{{\text{ro}}}} Li_{{\text{ph }}}$$
(25)

where \(k_{w}\) is the winding factor, \(N_{{{\text{tol}}}}\) is the total conductors per phase, \(R_{{{\text{ro}}}}\) is the outside rotor radius in meter, \(m\) is the phases of conduction, \(k_{l }\) is the correction factor due to losses, \(i_{{{\text{ph}}}}\) is the phase current in amperes.

The cogging torque equation is expressed as given in Eq. (26)

$$T_{{{\text{cog}}}} = \left( {\frac{{{\text{d}}\omega_{\alpha } }}{{{\text{d}}\omega_{\theta } }}} \right)$$
(26)

where

$$\omega_{\alpha } = \frac{1}{{2\mu_{0} }}\int {B^{2} \left( \theta \right){\text{d}}V}$$
(27)
$$\begin{aligned} B\left( \theta \right) = & \;\;\mathop \sum \limits_{n = 1,3,5, \ldots }^{\infty } \frac{{2B_{r} \beta }}{{\mu_{r1} }} \times \frac{{\sin \left( {n\pi \beta /2} \right)}}{{\left( {n\pi \beta /2} \right)}} \\ & \;\; \times \frac{np}{{\left( {np} \right)^{2} - 1}}\left[ {\left( {\frac{{r_{g} }}{{r_{s} }}} \right)^{np - 1} \left( {\frac{{r_{r} }}{{r_{s} }}} \right)^{np + 1} + \left( {\frac{{r_{r} }}{{r_{g} }}} \right)^{np + 1} } \right] \\ & \;\; \times \left\{ {\frac{{\left( {np - 1} \right) + 2\left( {{\raise0.7ex\hbox{${r_{y} }$} \!\mathord{\left/ {\vphantom {{r_{y} } {r_{r} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${r_{r} }$}}} \right)^{np + 1} - \left( {np + 1} \right)\left( {{\raise0.7ex\hbox{${r_{y} }$} \!\mathord{\left/ {\vphantom {{r_{y} } {r_{r} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${r_{r} }$}}} \right)^{{2{\text{np}}}} }}{{\left( {{\raise0.7ex\hbox{${\left( {\mu_{r1} + 1} \right)}$} \!\mathord{\left/ {\vphantom {{\left( {\mu_{r1} + 1} \right)} {\left( {\mu_{r1} } \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {\mu_{r1} } \right)}$}}} \right)\left[ {1 - \left( {r_{y} /r_{s} } \right)^{{2{\text{np}}}} } \right] - \left( {\left( {\mu_{r1} - 1} \right)/\mu_{r1} } \right)\left[ {\left( {r_{r} /r_{s} } \right)^{{2{\text{np}}}} - \left( {r_{y} /r_{r} } \right)^{{2{\text{np}}}} } \right]}}} \right\} \\ \end{aligned}$$
(28)

\(\begin{gathered} np \ne 1 \hfill \\ r_{s} = r_{r} + l_{g} + l_{w} \hfill \\ r_{y} = r_{r} - l_{m} \hfill \\ r_{g} = r_{r} + l_{g} \hfill \\ \end{gathered}\)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kamal, C., Thyagarajan, T. & Kalpana, D. Optimization Techniques for Cogging Torque Reduction and Thermal Characterization in Brushless DC Motor. Iran J Sci Technol Trans Electr Eng 48, 889–909 (2024). https://doi.org/10.1007/s40998-024-00699-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40998-024-00699-w

Keywords