Viscoelastic Properties Of Rubber Research Articles

Determination of the stress-strain state of structures made of viscoelastic fibrous composite materials based on the stiffness matrix of a spatio-temporal finite element

Abstract. Increase in spheres of composite materials application leads to the need to improve the methods of composite structures calculation, increase their efficiency and adequacy to real processes. The use of fibrous composite materials creates difficulties in determining the stress-strain state of the structure due to the different physical and mechanical properties of the material components. As a rule, a fibrous composite consists of two components: a matrix and a fiber. The matrix ensures the material monolithicity fixing the shape of the product and the relative position of the reinforcing fibers. The fibers absorb the main stresses that occur during operation, and provide rigidity and strength of the composite. The combination of the matrix and fiber properties allows creating special types of composites to be used in various equipment. The use of rubber as a matrix gives the structure viscoelastic properties, which can be seen in the deformation creeping and stress relaxation in the material, which complicates the calculation of the stress-strain state of the whole structure greatly. The paper proposes an approach that is the development of a moment scheme of finite elements in the form of the displacements method based on the Lagrange principle. Using this approach, a special space-time finite element has been developed that takes into account the viscoelastic properties of the material matrix and the fiber elastic properties. The proposed numerical approach allows obtaining a solution to the problems of viscoelasticity of composite materials mechanics in three-dimensional model. Using the applications package created on the basis of this approach, the calculation of the stress-strain state of a single-cavity pneumatic cylinder with a rubber cord shell has been done. The influence of the reinforcement scheme and rubber viscoelastic properties on the parameters of the pneumatic cylinder deformation has been analyzed. In particular, it becomes possible to adjust the structure stiffness properties by changing the orientation, type and concentration of fibers, as well as the type of matrix and other material characteristics. Keywords: fibrous composite material, viscoelasticity, space-time finite element.

Present problems of vibration isolation in heavy mining machines at long-term cyclic loads

Abstract. An integrated approach was used, including the construction of a mathematical model and the results of lengthy industrial tests of heavy mining machines with rubber elastic bonds. The issues of vibration isolation of heavy machines operating in extreme conditions, i.e. with prolonged cyclic loads and the influence of an external aggressive environment inherent in mining and processing enterprises. As an example, we con-sider vortex mixers with a vibration isolation system containing rubber elements. During long-term operation, the mass of the mixer does not remain constant; its increase is associated with the sticking of the initial product on the moving parts of the ma-chine. The location of such machines in the sinter factory at + 10.4 m, as well as the change in time of rotational symmetry of the drum rotation imposes certain requirements on the vibration isolation system: the system must be "soft" and stable in time, i.e. during 9-10 years of operation, its stiffness and dissipative parameters should not go beyond the permissible values. In order to reduce the aging effect, type 2959 rubber based on natural caoutchouc with a reinforced protective group was used, while the instability of the main mechanical parameters was taken into account in the developed theory of vibration isolation of machines. On the basis of the developed simulation model and the Boltzmann-Volterra integral relations with kernels of relaxation and aftereffect, an equation was worked out, which made it possible to take into account the rubber viscoelastic properties in full volume; in this equation, stiffness operator of elastic suspension in the machine is written by using fractional exponential function of the Yu. Rabotnov's type; on the basis of the mathematical model, the basic parameters of the machine under the study were calculated; in particular, for the vortex mixer, the time dependences of amplitude of the mixer housing vibrations and coefficient of vibration isolation efficiency were calculated with taking into account aging of elastic link material in the ma-chines; the calculation results were compared with the results of industrial tests of the vortex mixer operation lasting for 16 years. The theory and method for calculating vibration isolation systems with rubber elastic links for heavy mining machines were developed with taking into account material structure changes due to the effects of aging. The paper considers an example of calculating the mixer vibration isolation system taking into account rubber aging; the magnitude of the change in time of the main mechanical parameters was obtained experimentally over 16 years. This made it possible to determine temporary changes in the amplitude of oscillations of the mixer body and the coefficient of efficiency of the vibration isolation system. It was shown that the mixer vibration isolation system remained effective for 9-10 years, after which the mechanical characteristics of the rubber went beyond the permissible values and the system lost its functional pur-pose, and the amplitude of the mixer body exceeded the existing sanitary standards.

Present problems of vibration isolation in heavy mining machines at long-term cyclic loads

On the basis of the developed simulation model and the Boltzmann-Volterra integral relations with kernels of relaxation and aftereffect, an equation was worked out, which made it possible to take into account the rubber viscoelastic properties in full volume; in this equation, stiffness operator of elastic suspension in the machine is written by using fractional exponential function of the Yu. Rabotnov’s type; on the basis of the mathematical model, the basic parameters of the machine under the study were calculated; in particular, for the vortex mixer, the time dependences of amplitude of the mixer housing vibrations and coefficient of vibration isolation efficiency were calculated with taking into account aging of elastic link material in the machines; the calculation results were compared with the results of industrial tests of the vortex mixer operation lasting for 16 years. The theory and method for calculating vibration isolation systems with rubber elastic links for heavy mining machines were developed with taking into account material structure changes due to the effects of aging.

Multiobjective Trajectory Optimization and Adaptive Backstepping Control for Rubber Unstacking Robot Based on RFWNN Method

Multiobjective trajectory optimization and adaptive backstepping control method based on recursive fuzzy wavelet neural network (RFWNN) are proposed to solve the problem of dynamic modeling uncertainties and strong external disturbance of the rubber unstacking robot during recycling process. First, according to the rubber viscoelastic properties, the Hunt-Crossley nonlinear model is used to construct the robot dynamics model. Then, combined with the dynamic model and the recycling process characteristics, the multiobjective trajectory optimization of the rubber unstacking robot is carried out for the operational efficiency, the running trajectory smoothness, and the energy consumption. Based on the trajectory optimization results, the adaptive backstepping control method based on RFWNN is adopted. The RFWNN method is applied in the main controller to cope with time-varying uncertainties of the robot dynamic system. Simultaneously, an adaptive robust control law is developed to eliminate inevitable approximation errors and unknown disturbances and relax the requirement for prior knowledge of the controlled system. Finally, the validity of the proposed control strategy is verified by experiment.

Estimation of Energy Loss in Conveyor Systems due to Idler Indentation

This paper applies viscoelasticity and Winkler foundation assumptions to the analysis of the energy loss in conveyor systems caused by idler-indentation into the rubber cover of the belt. The analysis yields a simple algebraic model that relates the indentation energy loss to various critical parameters of a conveyor system. Such properties include rubber viscoelastic properties characterized by G′ and G′′, transportation rate, speed, idler spacing, and belt width. Analysis shows that this model is more accurate and more informative than other prevailing models. This model will be useful for the design and optimization of energy consumption in conveyor systems.

Rubber friction on rough and smooth surfaces

Some rigorous contact mechanics is used in a dynamic stiffness approach to generate a new theory for hysteresis sliding friction on some ideal peak shapes. These were the two- and three-dimensional projections: cylinder, wedge, sphere and cone, configured singly or as a periodic array. The theory is then extended for a ‘single roughness order’ i.e. identical peaks arranged with a randomly distributed envelope. A simple algebraic expression is obtained that is closely linked to the rubber complex modulus, with friction bandwidths extending over several decades. Several other secondary effects are introduced: multiple roughness orders, adhesion, stick-slip behaviour, friction magnification from either moments or atmospheric pressure, as these influence the observed friction bandwidth and amplitude. The sliding friction theory and secondary effects are compared to the measurements of Grosch [K.A. Grosch, The relation between the friction and the visco-elastic properties of rubber, Proc. Roy. Soc. Lond. A 274 (1963) 21–39] and Barquins et al. [M. Barquins, A.D. Roberts, Rubber friction variation with rate and temperature: some new observations, J. Phys. D: Appl. Phys. 19 (1986) 547–563], and are able to account for the friction amplitude and bandwidth for both gum and carbon loaded rubbers.

Three-dimensional modeling of tires

Modeling the stress-strain state of pneumatic tires in the conditions of steady-state and transient rolling is of interest for mechanics of composites and computational mechanics and important from the applied point of view. Mechanical models of various levels of complexity can be used for numerical modeling. In quite a few papers, the corresponding models are derived from the theory of orthotropic shells [1]. However, more thorough and accurate studies of the stress-strain state can be carried out on the basis of three-dimensional models based on the elasticity or viscoelasticity equations. As far as Russian authors are concerned, this approach has first been suggested and implemented in [2]. Another, combined approach uses both the shell theory and the three-dimensional equations of elasticity theory [3, 4]. This approach is reasonable, because the tire structure includes both volumes filled with rubber and thin layers of the rubber cord. The rubber cord layers can be considered as a composite whose structural components possess very different properties. Also, it is quite admissible to consider the rubber cord as a structure periodic in the horizontal projection. Note that the mathematical theory of periodic composites has been developed in [5]. Owing to strong anisotropy and inhomogeneity of the material, large shape distortions of the tire, and, in some cases, its large deformations, viscoelastic properties of rubber play an important role, so that the mechanic model of the tire turns out to be quite complex. The large property differences between various structural components make the matrix of the resulting system of linear equations ill-conditioned, which complicates its numerical solution [6].

Numerical Analysis of Sliding Friction Behaviour of Rubber

A study has been made of asperity interaction of unlubricated steel/rubber sliding pair. The aim is to study the effect of the internal friction (hysteresis) of rubber on the friction force. In the two-dimensional finite element analysis, asperities are modeled by cylinders and both the interfacial adhesion and the friction at steel-rubber interface are neglected. Rate-dependent material behavior of rubber is described, as a first approximation, by a three-parameter Zener-model. It is found that the viscoelastic properties of rubber have a strong influence on the hysteresis component of friction. Distribution of energy loss generated over a cycle of contact in the rubber asperity is also studied. It is concluded that the energy dissipation is most intensive at a certain depth below the rubber surface.

A potential biodegradable rubber—Viscoelastic properties of a soybean oil‐based composite

AbstractScientists are more and more interested in biodegradable materials owing to their environmental advantage. We investigated viscoelastic properties of a newly developed biomaterial made from epoxidized soybean oil (ESO). ESO cross‐linked by triethylene glycol diamine exhibited viscoelastic solid properties. The storage modulus (G′) was 2×104 Pa over four frequency decades. The phase angles were 14–18°. Stress relaxation measurements showed that there was no relaxation up to 500 s. From the plateau modulus we estimated that the M.W. of this cross‐linked soybean oil was on the order of 105. The composites of cross‐linked ESO with three different fibers had 50 times higher elasticity (G′) than those without fiber. Phase shifts were the same as those of cross‐linked oil without fibers, but the linear range of rheological properties was much narrower than that of the material without fibers. All these results indicated that this new biopolymer made from soybean oil exhibited strong viscoelastic solid properties similar to synthetic rubbers. These rheological properties implied that this biomaterial has high potential to replace some of the synthetic rubber and/or plastics.

The relation between the friction and visco-elastic properties of rubber : K. A. Grosch, (The Natural Rubber Producers' Research Association, Welwyn Garden City, Herts.) Proc. Roy. Soc., A 274 (1963) 21–39. (See also p. 375.)

The relation between the friction and visco-elastic properties of rubber : K. A. Grosch, (The Natural Rubber Producers' Research Association, Welwyn Garden City, Herts.) Proc. Roy. Soc., A 274 (1963) 21–39. (See also p. 375.)

Visco-Elastic Properties and the Friction of Solids: Relation between the Friction and Visco-elastic Properties of Rubber

Visco-Elastic Properties and the Friction of Solids: Relation between the Friction and Visco-elastic Properties of Rubber

Stress-Strain Testing of Rubber at High Rates of Elongation

Abstract It is well known that the properties of rubbery materials depend upon the speed or rate at which they are tested or used. A considerable body of work has shown that the dynamic properties of rubber change with the time scale of the test and, in particular, at very short times or at very fast rates, the properties approach those of plastics, i.e., high modulus and low elongation. These dynamic properties are measured by oscillation methods, usually at small strains. In contrast to this class of information, where the material is rarely strained to failure, one can also strain rubbers unidirectionally to failure at strain rates that correspond to the high frequencies of dynamic measurements. In linear extension experiments, as the rate of stretching increases tensile strength rises, elongation drops, apparent modulus increases, and relaxation losses may go up or down depending upon the particular rubber and the time scale of the phenomenon that is being investigated. Extrapolating the change in tensile strength with rate of testing suggests that tensile strength as we know it should change drastically when measured at very high rates of speed. That is, since the viscoelastic properties of rubber are time dependent, and also dependent upon the speed at which they are tested, the tensile properties of rubbers measured at room conditions with the ordinary Scott or Instron machines probably do not have the same values as at the speeds and frequencies that might be encountered in such situations as tire wear. Hence, we should like to measure the properties of rubbers at very high rates of speed, presumably comparable to those encountered in tire tread wear, in order to find out how much properties do change as the speed of test is increased. In order to measure stress-strain properties at rates of elongation comparable to those we believe exist in tire tread usage, we had to develop a small high speed tensile machine. The purpose of this paper is to describe that machine and some results obtained with it.

An Investigation of the Visco-elastic Properties of Rubber

Abstract An account is given of an investigation of the visco-elastic properties of rubber by means of observations on the damping of forced longitudinal vibrations. An attempt is made to determine the visco-elastic limits for rubber, as well as the normal visco-elastic constant τ and the coefficient of normal viscosity E′. The analysis of the experiment predicts the form of the photographic record of the damped vibrations, and gives an expression for τ in terms of the period of vibration and the logarithmic decrement of the amplitude per vibration. Two series of experiments are described in detail. In the first series, where catapult elastic was used, the experimental results are susceptible of detailed analysis. They agree with those predicted by the theory of visco-elasticity when the rate of strain does not exceed 0.1 per second. This is the upper visco-elastic limit. The lower visco-elastic limit for the rate of strain was not reached, so it must be less than 0.017 per second. The value obtained for τ is 28.7×10−4 seconds, and the corresponding value of E′ is 3.42×104 in c.g.s. units. In the second series of experiments pure black rubber was used, and a wider range of frequency of vibration and rate of strain was obtained. Also experiments were carried out at different mean tensions. The experimental results show signs of some unknown disturbance and are difficult to analyze. They suggest 6×10−4 seconds as a probable value Ä , and 0.78×104, for pure black rubber, with a rate of strain 0.1 per second as a probable upper visco-elastic limit (at a mean tension of 150 grams weight). The value of Ä at 300 grams mean tension does not differ significantly from that at 150 grams.