Hertz pressure

Fig. 18. Adhesive contact of elastic spheres. pH(r) and pa(r) are the Hertz pressure and adhesive tension distributions, (a) JKR model uses a Griffith crack with a stress singularity at the edge of contact (r = a) (b) Maugis model uses a Dugdale crack with a constant tension aa in a < r < c [1111.

Fig. 40—Friction coefficient versus sliding speed [60]. Base oil PEG, Temperature 20°C, Maximum Hertz pressure 219 MPa.

N corresponding to the maximum Hertz pressure of 0.375 GPa. The height of asperities becomes smaller as a result of asperity deformation. Figure 34(e) gives the contact ratio curve as a function of load. 

Fig. 36—Contact ratio a versus average film thickness, combined surface roughness 17 nm, maximum Hertz pressure 0.293 GPa.

Fig. 38—Relation between contact ratio a and surface roughness, lubricant 13604, maximum Hertz pressure 0.292 GPa.

Figure 2.10. Hertz pressure distribution for frictionless contact.

It is necessary to find an appropriate form for the pressure distribution p so that Eq. (2.65) can be satisfied for any r provided that r is small compared to the radii of spheres. One such pressure distribution is the Hertz pressure distribution in which the pressure at any location within the contact area is represented, as illustrated in Fig. 2.10, by... 

Using the Hertz pressure distribution, an integration along the cord mn in Fig. 2.8(b) gives... 

Figure 6. EHD Traction of LCl Liquid Crystal at Various Maximum Hertz Pressures...

Figure 7. EHD Film thickness and traction of a common lubricating fluid at various maximum Hertz Pressures.

The first experiments are performed with the paraffinic base oil LI for maximum Hertz pressures from 0.2 to 2 GPa, two rolling speeds 0.8 and 2 m/s and slide/roll ratios from - 0.3 to + 0.3. Additional lateral sliding and spin are also considered. 

The elasCohydrodynamic point contact lubrication has been investigated for typical maximum Hertz pressures from 1 to 2 GPa and rolling speeds from 1 to 3 m/s near ambient temperature. In this range of operating conditions surface deformations at contact are important and Che lubric t is submitted high shear rates from 10 s o 10 s during short transit times from 10 s Co 10 s. 

The main problem is then to compute " g(t). Note that it is not equal to the shear relaxation time in the fluid element at equilibrium with the external Hertz pressure. 

In equation (5.29), a is the contact radius and P is the maximum stress applied, sometimes called the Hertz pressure. 

Figure 1. Adhesive contact of elastic spheres. Surface tractions comprise two terms Hertz pressure pi and adhesive tension pa- (a) JKR model has infinite...

Hertz pressure field perturbation caused by roughness for a lubricated contact, ... 

Analysing figure 11, which con ares experimental and numerical friction coefficients, it is clear that the influence of load (or maximum Hertz pressure) decreases when the rotational speed increases, particularly for high speeds. This tendency is very significant for the numerical values. 

As a comparison consider the sliding point contact results of Vergne, et al. [15]. Here the film thickness was calculated numerically over the entire contact assuming the constitutive equation (6) for various values of r . Their results for central film thickness are shown as the solid points in Figure 3. A simple Grubin style analysis for the same Hertz pressure, Ph, the same pressure-viscosity behavior, and the same reduced radius of curvature as reference [15]was... 

Fig. 3.22. Schematic illustration of the formation of longitudinal (1), lateral (2) and radial (4) cracks in the surrounding of a Hertz pressure half sphere (3) in glasses...

---