Simulation Methods for Rubber Antivibration Systems

The following sections are included:

• Preface
• Contents

In engineering design and applications, stiffness from load-deflection curves is the first requirement for anti-vibration systems. The stiffness is normally obtained through a quasi-static analysis. In some cases, dynamic response can also be calculated using the quasi-static method if the inertial and damping forces can be reasonably ignored. Several cases are demonstrated for quasi-static simulations and experiments on ant-vibration springs.

In Chapter 1, we described the essential requirement for the rubber anti-vibration systems, that is, the stiffness. In many applications, the durability of the products is also required. Fatigue failure of an anti-vibration system is assessed by either visual crack observation or stiffness change. There are several methods for rubber fatigue assessment, especially the fatigue resistance of the components. In this chapter, fatigue requirement is described…

In current industrial design and applications, the most important design parameters for rubber components, that is, the stiffness and the fatigue requirements, are the main specifications and only referenced to the loading part of the loading–unloading history. In Chapter 1, we described the classic hyperelastic method to simulate the loading portion of rubber components. It is well known that the loading path and unloading path are substantially different. When a rubber component is loaded from its virgin state, residual strain is produced in addition to the stress softening during unloading. This phenomenon is referred to as the Mullins effect. Simulation on the full Mullins effect will be described in Chapter 4. During a service period, the residual strain from loading–unloading cycles can usually be ignored. Under this condition, only stress softening needs to be considered, known as the idealised Mullins effect. Hence, the simulation of loading–unloading procedure is much less complex than that with the residual strain. There are several methods available to simulate this idealised Mullins effect. The Ogden–Roxburgh model (Ogden and Roxburgh, 1999a, b) has been used for calculation of the idealised Mullins effect and included in some commercial software. Viscoelastic approaches can also be used to obtain the response. Readers are invited to study these approaches in the references listed or in literature. However, for the evaluation of the unloading response, it is necessary to use a data-fitting procedure to find suitable values for the calculation in each case. Due to the complexity of the stress–strain response with large deformations, non-linearity and softening, parameters of rubber models for the Mullins effect are difficult to include measurable physical properties…

Rubber-like materials show a substantial change in their mechanical properties during loading–unloading procedures, especially in the first few cycles after a moulding procedure. This stress-softening phenomenon with accumulated residual strain is referred to as the Mullins effect (or full Mullins effect). Several approaches have been suggested to simulate this effect. However, there are limited studies in the literature that consider this effect in the application and design of anti-vibration systems. There is neither a well-defined approach to model the Mullins effect during the design process nor a suitable criterion to evaluate the effect on polymer components. Typical practice in industry is to load and unload polymer products three times to remove the residual strain of the Mullins effect before starting a product test for a load–deflection measurement…

A solid rubber component can be simplified into an element with stiffness and damping if the main interest is for a whole system instead of individual rubber-metal bonded component. This simplification is essential for engineering structures, like rail vehicles. For a dynamic simulation on a behaviour of a solid rubber structure, the viscoelastic approach has received intensive attention over many years. Kelvin–Voigt, Maxwell, fractional Kelvin–Voigt models, and their modified versions have been investigated. On the other hand, the Rayleigh damping has been widely used in structure dynamics involving linear and non-linear materials, including impact simulation on composite materials. In industrial applications, for example, the Rayleigh damping is employed for rail vehicle dynamic evaluations and fatigue assessments in which a part of rubber anti-vibration suspensions is simulated as damping elements…

Heat generation (self-heating) due to dynamic loading has been a major concern for rubber component manufacturers over many years and temperature specifications in the environment are usually required. In addition, it is very difficult to monitor the inside temperature while the component is in service and in tests. In situations where a large rubber spring is involved, it is important to know an appropriate dynamic frequency range and time duration both in service environment and in a laboratory test in order to control the inside temperature within a reasonable range. Since a typical fatigue test usually requires over 1 million repeated loading cycles, it is necessary to arrange an accelerated fatigue test to meet the industrial requirement. There is predefined allowable temperature requirement in accelerated durability tests for engineering applications. To avoid an early failure of the component caused by the temperature rise, current industrial practice is to monitor the component surface temperature in accelerated durability tests. A typical value 45°C on the surface is normally acceptable to the rubber component. This criterion has been used successfully for many engineering applications. However, unexpected early failures from heat generation (self-heating) during accelerated durability tests and in service have been observed even the surface temperature is well-controlled. It has attracted attention in industry to investigate this traditional criterion…

Rubber material is an excellent option for anti-vibration components in industry with a long-term service. However, its time-dependent behaviour is an undesirable issue in engineering applications. When a constant load is applied to a rubber spring, the deflection increases with time, this is known as creep. On the other hand, when a constant deformation is held on a rubber spring, the stress generated gradually decreases with time. This phenomenon is known as stress relaxation. Both creep and relaxation are the phenomenon of the time-dependent response. Therefore, in this chapter, the method for creep and relaxation can be exchangeable. The time-dependent effect is one of the critical factors when considering engineering design and applications on anti-vibration systems. For example, an important requirement of rail vehicle design is to control rubber anti-vibration components not to exceed its structural limitation due to the creep effect and to avoid early failure over its service life required…

In addition to traditional pure rubber materials, fluid can be added into specially designed chambers of components for anti-vibration enhancement. With fluid in the same rubber anti-vibration components, there should be more anti-vibration effect in engineering applications. Rail vehicle suspensions, for instance, are subjected by various dynamic events generated from track irregularities. A better ride performance can be achieved by introducing rubber hydro components. An accurate evaluation on dynamic impact response for rubber-metal hydro components has been very challenging in industry over many years, especially using three-dimensional solid dynamic simulation…

The following sections are included:

• Bibliography
• Index