Skip to main content
SpringerLink
Log in

Modal Control of Quasi-Static Linear Elastic Displacements of Precision Equipment

  • Published:
Russian Engineering Research Aims and scope

Abstract—

A new modal method for controlling the deformation of a linear elastic structure under conditions of quasi-static loading is proposed. The advantage of the new method is independent control of orthogonal modes, which increases the accuracy and speed of control. To illustrate the proposed method, compensation of the deformation error in a rotary table with a high tilt accuracy is considered.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. Diez, E., Leal-Muñoz, E., Perez, H., and Vizan, A., Dynamic analysis of a piezoelectric system to compensate for workpiece deformations in flexible milling, Mech. Syst. Signal Process., 2017, vol. 91, no. 7, pp. 278–294.

    Article  Google Scholar 

  2. Meirovitch, L., Dynamics and Control of Structures, New York: Wiley, 1990.

    MATH  Google Scholar 

  3. Belyaev, A.K., Kotov, V.N., Polyanskii, V.A., and Smirnova, N.A., Bimorph control in the problem of active suppression of oscillations, Vestn. S.-Peterb. Univ., Ser. 1: Mat., Mekh., Astron., 2014, no. 1, pp. 59–68.

  4. Minowa, K., Kumagai, T., and Ogawa, T., Active response control of arch structures using modal control method, J. Struct. Constr. Eng., 2013, vol. 78, no. 687, pp. 939–948.

    Article  Google Scholar 

  5. Hamelinck, R.F.M.M., Adaptive deformable mirror, based on electromagnetic actuators, PhD Thesis, Eindhoven: Tech. Univ. Eindhoven, 2010.

  6. Uhlmann, E., Saojia, M., and Peukerta, S., Utilization of thermal energy to compensate quasi-static deformations in modular machine tool frames, Procedia CIRP, 2016, vol. 40, pp. 1–6.

    Article  Google Scholar 

  7. Diez, E., Perez, H., Marquez, J., and Vizan, A., Feasibility study of in-process compensation of deformations in flexible milling, Int. J. Mach. Tools Manuf., 2015, vol. 94, pp. 1–14.

    Article  Google Scholar 

  8. Tikhonov, A.N. and Arsenin, A.Ya., Metody resheniya nekorrektnykh zadach (Solution of Incorrect Problems), Moscow: Nauka, 1986.

  9. Paterson, C., Munro, I., and Dainty, J.C., A low cost adaptive optics system using a membrane mirror, Opt. Express, 2000, vol. 6, pp. 175–185.

    Article  Google Scholar 

  10. Cho, M.K., Active optics performance study of the primary mirror of the Gemini Telescopes Project, Proc. SPIE, 1997, vol. 2871, pp. 272–290.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Samara State Technical University, Samara, Russia

    Ya. M. Klebanov, I. E. Adeyanov, A. I. Simakov & E. A. Soldusova

Authors
  1. Ya. M. Klebanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. E. Adeyanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. I. Simakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. A. Soldusova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. E. Adeyanov.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klebanov, Y.M., Adeyanov, I.E., Simakov, A.I. et al. Modal Control of Quasi-Static Linear Elastic Displacements of Precision Equipment. Russ. Engin. Res. 41, 392–397 (2021). https://doi.org/10.3103/S1068798X21050087

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068798X21050087

Keywords:

Search

Navigation