To Issue of Application of Method of Dynamic Mechanical Analysis (DMA) to Determine Viscoelastic Properties and Heat Generation in Rubber Elements of Solid Tires

  • E. E. RichterEmail author
  • A. V. Ignatova
  • A. V. Ponkin
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Solid tires are widely used for the undercarriage of track vehicles. Intense dynamic loading of solid tires in the process of operation leads to substantial self-heating and subsequent thermo-mechanical destruction. Reduction in the level of heat generation in rubber is connected with viscoelastic properties of materials. Most often, this task is solved by testing structurally similar samples or full-scale structures using unique stands and equipment. In this paper, we suggest a technique that allows to determine characteristics of rubber using the method of dynamic mechanical analysis (DMA). Rubber samples were tested in the temperature range from 25 to 60 °C and loading frequencies from 5 to 50 Hz. As a result of the carried experiments, we have obtained the dependences of the valid and imaginary moduli of elasticity of the material on the loading frequency and ambient temperature. On the basis of the obtained data, we have constructed the hysteresis loops, calculated the values of specific energy loss per loading cycle, and the power of the heat sources in rubber. The results have been compared with the data in the literature and they showed a good agreement, which enables to apply this methodology to estimate the intensity of heat generation in rubber elements of solid tires.


Rubber Viscoelastic DMA Frequency Temperature Loss modulus Specific energy 



The work was supported by Act 211 Government of the Russian Federation, contract No. 02.A03.21.0011.


  1. 1.
    Savosin VS, Bograchev ML (1981) Solid tires (construction, production, operation). Chemistry, Moscow (in Russian)Google Scholar
  2. 2.
    Riznikovsky MN, Lukomskaya AI (1968) Mechanical testing of caoutchouc and rubber. Chemistry, Moscow (in Russian)Google Scholar
  3. 3.
    Dyrda VI (1988) Strength and fracture of elastomeric structures under extreme conditions. Naukova Dumka, Kiev (in Russian)Google Scholar
  4. 4.
    Poturaev VN (1966) Rubber and rubber-metal parts of machines. Mechanical Engineering, Moscow (in Russian)Google Scholar
  5. 5.
    Avramov VP, Pankratov VP (1983) Mathematical modeling of the process of rolling of the track roller of a track vehicle along a caterpillar chain made of links. In: Collection of research papers: Theory of mechanisms and machines. KhPI Publishing House, Kharkov, pp 38–43 (in Russian)Google Scholar
  6. 6.
    Platonov VF (1973) Dynamics and reliability of caterpillar tracks. Mechanical Engineering, Moscow (in Russian)Google Scholar
  7. 7.
    Pisarenko GS (1962) Energy dissipation under mechanical vibrations. AS UkrSSR Publishing House, Kiev (in Russian)Google Scholar
  8. 8.
    Troshchenko VT (1978) Energy dissipation under vibrations of elastic systems. Naukova Dumka, Kiev (in Russian)Google Scholar
  9. 9.
    Lepetov VA, Yurtsev LN (1987) Calculation and design of rubber products: study guide for higher education institutions, 3rd edn. Chemistry, Leningrad (in Russian)Google Scholar
  10. 10.
    Ma S, Thio Y (2016) Dynamic mechanical properties of elastomeric nanoparticle composites. Macromol Res 24(10):915–923. Scholar
  11. 11.
    Lemos MF, Bohn MA (2016) DMA of polyester-based polyurethane elastomers for composite rocket propellants containing different energetic plasticizers. J Therm Anal Calorim, 1–6. Scholar
  12. 12.
    Datta J, Parcheta P (2017) A comparative study on selective properties of Kraft lignin-natural rubber composites containing different plasticizers. Iran Polym J 26:453–466. Scholar
  13. 13.
    Strizhak EA (2013) The role of caoutchouc polarity in formation of rubber hysteretic properties under harmonical dynamic stress. Omsk Sci Chem Technol Chemical Ind Bull 3(123):308–312 (in Russian)Google Scholar
  14. 14.
  15. 15.
    Veselov IV et al (1990) Study of volumetric and plane stress state of a solid tyre model using the method of “freezing”. Solid tires. Calculation, design, technology, testing, vol 26. CNIIT Eneftekhim Publishing House, Moscow, pp 41–52 (in Russian)Google Scholar
  16. 16.
    Semenov VK, Belkin AE, Veselov IV (2014) Experimental study of contact, rolling resistance and self-heating of a solid tire under running on a drum bench. Eng J Mech Eng 12:151–160 (in Russian)Google Scholar
  17. 17.
    Berezin IYa, Dneprovskiy OA, Richter EE, Shapovalov VV (1985) Taking account of the viscoelastic properties to calculate the thermal state of structures. In: Collection of research papers: Strength and dynamic characteristics of machines and structures. PPI Publishing House, Perm, pp 20–27 (in Russian)Google Scholar
  18. 18.
    Berezin IYa, Richter EE (2004) Thermal state and forecasting performance for elastomeric structures taking into account the criterion of thermomechanical destruction. SUSU Bull Ser Mech Eng 5(12):11–21 (in Russian)Google Scholar
  19. 19.
    Dneprovskiy OA et al (1983) Study of heating of rubber-metal joints of caterpillar tracks in operation. In: Gokhfeld DA (ed) Thematic collection of research papers Strength of machines and devices under variable loadings. ChPI Publishing House, Chelyabinsk, pp 23–29 (in Russian)Google Scholar
  20. 20.
    Vorobev EV et al (1990) Experimental determination of stresses and strains in modelling of a solid tire. Solid tires. Calculation, design, technology, testing, vol 26. CNIIT Eneftekhim, Moscow, pp 104–112 (in Russian)Google Scholar
  21. 21.
    Semenov VK, Belkin AE (2013) Experimental study of hysteretic properties of tread rubbers under cyclic loading conditions typical of automobile tires. News of higher educational institutions. Mech Eng 2:9–14 (in Russian)Google Scholar
  22. 22.
    Belkin AE, Semenov VK (2016) Theoretical and experimental analysis of the contact of a solid tyre with the chassis dynamometer. Proc RAS Solid Mech 3:71–82 (in Russian)Google Scholar
  23. 23.
    Zherebtsov AN et al (1990) Investigation of temperature distribution in a solid tire. Solid tires. Calculation, design, technology, testing, vol 26. CNIIT Eneftekhim, Moscow, pp 41–52 (in Russian)Google Scholar
  24. 24.
    Richter EE, Ignatov AV, Efremenko AV (2017) Comparative analysis of loading and the thermal state of solid tires with external and internal amortization. In: Radionov AA (ed) ICIE’2017: The 3nd international conference on industrial engineering, Chelyabinsk, May 2017. SUSU Publishing House, Chelyabinsk, pp 85–90 (in Russian)Google Scholar
  25. 25.
    Berezin IYa, Richter EE (2009) Energy criterion of destruction for analysis of endurance strength of structures with elastomers. SUSU Bull Ser Mech Eng 13(11):73–78 (in Russian)Google Scholar
  26. 26.
    Richter EE, Berezin IYa, Shapovalov VV (2011) The experiment-calculated method for analysis of thermal condition and performance of rubber-metal joints of tracks of high-speed caterpillar track vehicles. In: Proceedings of the 14th all-Russian scientific-practical conference “Actual problems of protection and security”, RARAS, St. Petersburg, 4–7 Apr 2011 (in Russian)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • E. E. Richter
    • 1
    Email author
  • A. V. Ignatova
    • 1
  • A. V. Ponkin
    • 1
  1. 1.South Ural State UniversityChelyabinskRussia

Personalised recommendations