Mechanics, Materials Science & Engineering, September 2016
ISSN 2412-5954
Prediction of Rubber Element Useful Life under the Long-Term Cyclic Loads Dyrda V.I.1, Loginova A.A.2, Shevchenko V.G.3
1 M.S. Polyakov Institute of Geotechnical Mechanics, NAS of Ukraine, Professor, Doctor of Technical Sciences (D. Sc.) 2
National Mining University, Doctoral Student
3 M.S. Polyakov Institute of Geotechnical Mechanics, NAS of Ukraine, Senior Researcher, Doctor of Technical Sciences (D.Sc.) DOI 10.13140/RG.2.2.25883.46884
Keywords: rubber element useful life, failure of vibroinsulators, cyclic loads.
ABSTRACT. Problems associated with the change of physical and mechanical properties and structure of resilient rubber elements of the VR type under long-term cyclic loads are considered integrally. A general algorithm was developed for predicting useful life for the resilient rubber elements, which is based interrelated equations of equilibrium and simultaneousness of deformations for determining deflected mode of vibroinsulators; equations of local useful life; equations of heat conductivity for determining temperature field in rubber mass; criterion equation of destruction, which connects parameters of the system destruction with hours of system service till its failure.
on: the the the
The algorithm for predicting useful life for the elements of the VR type takes into account changes of the element physical and mechanical properties.
The resilient rubber elements of the VR type [1] are considered, general view of which is shown on the fig. 1. Mainly, in the process of exploitation, the VR vibroinsulators experience cyclic compressive deformation [2, 6-7]. Algorithm for predicting useful life of the VR elements. A procedure for predicting useful life assumes a necessity to solve interrelated equations of equilibrium and simultaneousness of deformations for determining deflected mode of the vibroinsulators; equations of local useful life; equations of heat conductivity for determining temperature field in the rubber mass; criterion equation of fracture, which connects parameters Fig. 1. is Vibration insulator of the VR type. of the system fracture with hours of the system service till its failure. equations of equilibrium
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Mechanics, Materials Science & Engineering, September 2016
where
ISSN 2412-5954
is the Laplace operator; is a displacement vector; is the Poisson's ratio.
The boundary conditions are as follows: in the lower boundary of the rubber mass; in the upper boundary of the rubber mass; where ur, uz are the radial and axial displacements, accordingly; equation of stationary heat conductivity ,
(2)
where k is a heat conductivity; D
is a cycle average dissipative function expressed as:
(3)
where z, , r, rz are components of deformation tensor calculated by displacements ur, uz in the formulas of elasticity theory:
where
is a dynamic modulus of elasticity; is a the energy dissipation factor.
The boundary conditions in the assumed convective heat exchange with the environment on the vibroinsulator surface are as follows:
on the lateral surface; on the supporting surfaces; in initial moment of time
where
is ambient temperature.
This scheme of calculation is based on the energy fracture criterion, which is justified in [1, 3]. MMSE Journal. Open Access www.mmse.xyz
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(4)
Mechanics, Materials Science & Engineering, September 2016
ISSN 2412-5954
Change of rubber properties in the process of long-term cyclic loading. Such changes can be caused by time and environment influence: heat, oils, acids, solar radiation. Sometimes, exactly they become the key reason of the system failure, as the system parameters can exceed the tolerable values. The fig. 2 and fig. 3 show experimental time dependences between dynamic modulus of elasticity and dissipation factor. As it is stated in the [4], the dynamic modulus of elasticity is changed by the exponential law; and functional dependence E(t) can be expressed as: (6) where Ed1
is an initial value of the dynamic modulus of elasticity;
Ed2 is the modulus final value. In the considered vibroinsulator: Ed1 = 47,8 MPa; Ed2 = 82 MPa, velocity constant k = 1,1 10-4 h-1 [3].
Fig. 2. Time dependence of dynamic module of compression. Functional dependence (t) is practically linear [4]
(7)
where
is an initial value of coefficient of power adsorption ; k
is a velocity constant.
In the considered vibroinsulator:
0
= 0,31; k = 0,083 10-8
-1
[3].
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Mechanics, Materials Science & Engineering, September 2016
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Prediction of the element useful life with taking into account change-in-time of the rubber mechanical properties. Analytical expressions are of the form [1,3]:
(8)
Fig. 3. is Time dependence of the dissipation factor. where
,
(9)
is hours till vibroinsulator failure (destruction of central area of the rubber); is number of cycles till the vibroinsulator failure; is an absolute value of the complex modulus of elasticity; is relative deformation of the vibroinsulator; is a maximum (critical) value of energy density, which destructs the rubber; is an energy dissipation factor;
is a coefficient, which shows which part of the energy dissipating in the rubber is used for heat buildup; is a function, which characterizes distribution of the stress field and deformation field in the loaded vibroinsulator. In the case under the consideration, the VR vibroinsulator loading is characterized by stationary temperature field caused by dissipative self-heating, and parameter , in the first approaching, can be assumed as independent from the loading conditions and temperature of external environment; this parameter can be also assumed as permanent by rubber volume [1,3]. With these assumptions, it is possible to write down the criterion equation (9) for the central area of the vibroinsulator in more simplified form:
(10)
where is a coefficient, which characterizes those part of the energy, which is directly used for destructing the rubber structure, for averagely filled rubber of the A-1 grade (soot of 220 grade, raw rubber of the SKI-3 grade) = 0,6 [3]. Or, if to take into account:
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Mechanics, Materials Science & Engineering, September 2016
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(11)
we can get: (12)
where is a critical (tolerable) value of the energy density, which dissipates in the vibroinsulator under the loads. If parameters and of the rubber depend on time of the vibroinsulator loading, the expression (12) can be rewritten in the following way
(13)
Or
.
(14)
If to take into account the evolutional equations (6) and (7) for the dynamic modulus of elasticity Ed(t) and energy dissipation factor (t), the expression (14) will be of the form:
(15)
As values of the last two members of the equation (15) are too small, we can ignore them and get the following equation:
(16)
Experimental data and analysis of the equation (16) show that changing of the energy dissipation factor is the key aspect impacting on the vibroinsulator useful life.
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Summary. Comparison of the calculation data with experimental data, which have been received in process of long-term exploitation of the RV rubber vibroinsulators, shows their satisfactory matching. References [1] Dyrda V.I. (1988) The strength and the destruction of elastomeric structures in extreme conditions, Kiev, 239 p. [2] Loginova A.A., Dyrda V.I. and Shevchenko V.G. (2015) Study parameters anti-vibration mounts under cyclic loading. Geo126, Pp. 249-259. [3] Bulat A.F., Dyrda V.I., Zviagilskiy E.L. and Kobets A.S. (2012) Applied mechanics of elastichereditary environments, Vol. 2. Metody calculation elastomeric parts, Kiev, 616 p. [4] Loginova A.A., Dyrda V.I. and Shevchenko V.G. (2015) Calculation of vibration isolation systems of mining machines in view of the aging, GeoVol. 125, Pp. 249-259. [5] Massimo Viscardi, Maurizio Arena (2016), Experimental Characterization of Innovative Viscoelastic Foams, Mechanics, Materials Science & Engineering Journal, Vol.4, Magnolithe GmbH, Austria , DOI: 10.13140/RG.2.1.5150.6325 [6] A. Touache, S. Thibaud, J. Chambert, P. Picart (2016), Characterization and Thermo Elasto Viscoplastic Modelling of Cunip Copper Alloy in Blanking Process, Mechanics, Materials Science & Engineering Journal, Vol.3, Magnolithe GmbH, Austria , DOI: 10.13140/RG.2.1.3289.0645 [7] Qian Li, Jian-cai Zhao, Bo Zhao (2009), Fatigue life prediction of a rubber mount based on test of material properties and finite element analysis, Engineering Failure Analysis, Volume 16, Issue 7, DOI: 10.1016/j.engfailanal.2009.03.008 Cite the paper Dyrda V.I., Loginova A.A. & Shevchenko V.G (2016). Prediction of Rubber Element Useful Life under the Long-Term Cyclic Loads. Mechanics, Materials Science & Engineering Vol.6, doi: 10.13140/RG.2.2.25883.46884
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