Friction case studies

In this chapter, we discuss how to perform meaningful tribological simulations by avoiding the potential pitfalls that were mentioned above. In the next section, some theoretical aspects of friction between solids will be explained. Then an overview of algorithms that have been used in the simulation of tribological phenomena is provided. Selected case studies will be presented in the last section. 

For a specific resin, the shear stress at the interface depends on the temperature of the interface, pressure, and the sliding velocity, it also depends on resin type, additives and additive levels, and the rheological properties of the resin. Stresses at the interface and the coefficients of friction for numerous resins have been published previously from two sources, and the data can be found in the references [15-31]. Additional stress data are provided in Appendix A4 and in several of the case studies in Chapter 12. 

The case study. The hydrolytic stability, oxidation stability, thermal stability, friction and wear characteristics of both borate and carbonate RMs of sulfonate, salicylate and phenate are shown in Table 3.7 (Inoue, 1993). 

The case study. The composition of the surface tribofilms formed by ZDDP and of carbonate-phenate RMs in a cam and tappet friction apparatus were examined using a combination of surface analysis techniques. Adding carbonate-phenate RMs to ZDDP resulted in partial replacement of zinc by the detergent metal and loss of the higher molecular weight phosphates in favor of ortho- and... 

The Case Study. Comparison of laboratory test, sequence VIA and vehicle aging tests of the SAE 5W-20 engine oil modified by MoDTC additive, [Mo] = 700 ppm. Used oil samples were analyzed for the following properties MoDTC (%) left, antioxidant (%) left, ZDDP (%) left, and friction- reduction effectiveness. The case study includes a description of ... 

Hip joint replacements are the most common type of joint replacements, with 300 000 operations in the USA in 2000. The aim of this case study is to highlight the wear resistance and low friction properties of UHMWPE, to discuss the effects of sterilisation on the properties of plastics, and the effects of wear debris in the body. The order of presentation is that followed by the polymer, through fabrication, sterilisation, implantation and wear, to the reactions caused by wear debris. 

The case studied is characterized by a constant mass flow rate supplied to the channel entrance. All the results concerning pressure loss are on one line, which means the same variation law. Equation 2 gives the pressure loss scaling law numerically. It is also possible from Fig. 9 to extract the criterion for the transition from steady to unsteady. This law provides an equivalent friction factor for the two-phase flow ... 

Effort represented. In this Formal Graph (Graph 4.5), the presence of the force— the effort in translational mechanics—merely acts as a reminder that such a pole may become a mixed pole when friction occurs, thus converting kinetic energy into heat. In this case, the frictional force is connected to the velocity by an operator of resistance, not shown in this graph that features a fundamental pole (see case study AlO Motion with Friction ). 

The movement of a body that is slowed down by friction due to resistance of the medimn is a topic belonging to mechanics of the point as well as to fluid mechanics. Here, the case study will be treated in the frame of translational mechanics. In the Formal Graph theory, this system is modeled with the help of a mixed pole, because two constitutive properties of the system are required, an inductance (representing the inertial mass) and a conductance (representing the friction process). The case without friction has been treated in case study A1 Moving Body. ... 

Although incorporated in the poles and the dipole, the forces are not connected in this graph because they do not participate in the dynamics of the system. If friction (due to a viscous medium) were present for relating forces to velocities (see case study AlO Motion with Friction in Chapter 4), it would have been necessary to connect the pole forces to the dipole force. The dipole would enter the category of mixed dipoles, being of the inductive-conductive type instead of the fundamental type. 

In the scheme in the case study abstract is shown the momentum exchange that occurs through the interface and the forces due to the friction, that each layer exerts on the other in a parallel direction to the interface. The variables with a subscript belong to the poles and those without (here the force F) belong to the dipole. 

Conductive Property The friction resistance is the operator linking the velocity to the force (see the case study AlO Motion with Friction in Chapter 4). 

However, there are processes featured by a conductance that are not considered as involving transport, such as mechanical friction or chemical reaction. They are seen as nonlocalized processes and therefore no influence of space is awaited in their modeling. Although some systems show a close similarity between reaction and transport, as in the case of a chain reaction behaving as a transport from site to site or vice versa. This point has been discussed in case study E5 Diffusion through Layers in Chapter 8 devoted to multipoles. 

The other relationships modeling this system are the same as in the case of a moving body through an ideal medium without friction (see case study Cl Colliding Bodies in Chapter 6). Newton s second law of motion is decomposed in the definition of the inductive force (see case study FI Accelerated Motion in Chapter 9). 

This relationship is a generalization of Newton s law of viscosity already studied in case study G4 in Chapter 10. The dynamic viscosity is the spatially reduced form of the friction coefficient kf defined as a mechanical resistance at the global level. It consequently dissipates energy in the same manner as conductivity. 

The system depicted in this case study consists of a mobile mass M attached to a spring and laid on a horizontal support (for avoiding influence of gravity). The contact between the mass and the support is not ideal and creates friction when the mass moves, represented by an operator k/. The spring is featured by an elastance (spring constant ) ke and has its other end fixed to the support. 

The Formal Graph in the case study abstract provides the model of this system in the general case of nonlinear operators, which is a frequent case, at least for the friction and the elastance operators. The velocity is common to all dipoles and the three forces corresponding to the three constitutive properties are summed onto a null node because the system is isolated from any external influence. 

Generality of the conduction modei. As explained in case study All Reactive Chemical Species in Chapter 4, the classical approach in kinetics is based on the transition state theory (Laidler and King 1998). The Formal Graph approach is based on a simpler theory of conduction which is much more general as it works in all energy varieties. For instance, the same theory is able to model electrons and holes in a p-n junction (Shockley diode) as well as molecules or enzymes involved in chemical or electrochemical reactions. Mechanical friction or viscous fluids may also be modeled with this transverse approach. 

Poles or dipoles The state variables used in this case study are all relative to poles when the piston is at rest (static equilibrium). On the contrary, when the piston is asked to convert energy, by a displacement made at a given velocity (variable or not), it is necessary to complete the model for making two dipoles between the interior and the exterior of the piston for each of the two energy varieties. (Supplanentary conductive dipoles may be required if mechanical friction occurs or viscous fluids are used.) Recall that it is only by using dipoles that the time may be taken into account. 

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