The Spur: A Short Film Screenplay
Among the friction models that describe the friction coefficient for gears in contact, emphasis should be given to i the DIN equation; ii the equation described in ISO ; iii the model proposed by Michaelis Winter and Michaelis, ; iv the Kelly expression, and v an equation for FZG gears proposed by Castro It is known from studies conducted by Honh that friction is also greatly influenced by the additive types present in the lubricants. Another important factor mentioned by Honh is related to the gears coating. Therefore, it can be stated that the proposed models may show some changes when working with gears coated with fortified lubricants.
Lubrication is aimed at introducing a low shear strength film, which ends up weakening the resistance of these joints, and thus reducing friction. In some cases, the lubricant may not fully prevent contact between the asperities, although it may reduce the severity of contact conditions. In other situations, the lubricant separates the surfaces completely, and joints with asperities are not formed.
Thus, to a greater or lesser extent, the use of lubricants will always reduce the wear rate, and this will be a direct function of this type of lubrication. There are basically three different lubrication regimes: hydrodynamic HD , elasto-hydrodynamic EHD and boundary lubrication.
In many cases, a mixed lubrication condition refers to the intermediate regime between EHD and boundary lubrication. The contact between the gear teeth surfaces is "non-conformal", i. Under these conditions, elasto-hydrodynamic EHD is the predominant lubrication regime. Whenever the oil film breaks, the lubrication regime turns into boundary lubrication, where almost the entire load is supported by the asperities Grubin, This parameter depends only on the minimum lubrication film thickness and surface roughness.
Under these conditions, some contact between the asperities will occur, and the wear will be greater than in conditions where a full fluid lubricant film is present Hutchings, The main objective of this work is monitoring changes in the contact conditions Hertzian pressures, specific film thickness and friction coefficient along the mesh while testing the contact fatigue of spur gears made from AISI hardened steel, with two different kinds of surface finishing: shaving and milling.
The material used in the manufacture of spur gears was the AISI steel. The schematic sequence of such treatments is shown in Fig. Figure 5 b shows the AISI steel microstructure resulting after the heat treatments that formed martensite with some retained austenite.
The final layer hardness was 40 HRc. The gears were dip lubricated with an oil volume of 1. After each test step the used oil was removed and replaced by new oil so that the debris generated in the previous step would not influence the pitting formation by indentation. The main properties of the lubricant are shown in Table 2. Figure 6 shows an overview of this equipment.
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By using the power recirculation principle, two pairs of gears can be tested at the same time. The load is imposed on the gears by applying torque on the shaft that the wheel is mounted on FZG loads k6 and k9. A twist on the wheel axis is achieved by applying an eccentric load, using a lever and dead weight. To produce accelerated wear on the flank of gear teeth, it is common to use gears with modified profile.
FZG type-C spur gears were used in the contact fatigue tests, and their characteristics are shown in Table 3. In this method, in addition to the geometrical characteristics of the gears, the loading forms for the running-in and pitting test stages are also presented. The loading stages are shown in Table 4.
Figure 7 shows the sequence of the methodology used in the contact fatigue experiments in gears. At the end of the tests, each gear four pairs was subjected to a 7.
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Macroscopic images were taken from the gear teeth flank, showing the condition before running-in and after each step of the fatigue tests, so that the damage evolution in the flanks with the loading cycles could be observed. These images were used to quantify the pitting area. This procedure was done for all damaged teeth of each gear. Figure 8 a shows an image of a pinion tooth flank where it is possible to identify two regions: 1 the effective contact area and 2 the lateral areas where there is no contact during mesh.
Areas with pitting damage identified in Fig. The ratio of the damaged area and the effective contact area reports the percentage of damage on each tooth at each step of pitting test. The total damage of all the gear teeth was divided by the total active area of all flanks and, in this paper, the resulting value is called average damage percentage.
Figure 9 shows an example of the damage evolution in a pinion tooth.
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To determine roughness of the gear teeth, measurements were made on the teeth flank in the axial direction parallel to the gear axis. Figure 10 shows the directions of roughness measurements. Five teeth of each pinion and wheel were selected randomly. Having the roughness values measured in these teeth, two different types of statistical analysis were performed after each fatigue test: average roughness around the flank see Table 5 and tooth roughness by region addendum, pitch diameter and deddendum. Table 5 shows that there was a clear roughness reduction after the running-in stage for both kinds of surface finishing milling and shaving.
In EHD conditions, the film variation as a function of local surface roughness is perhaps best characterized by a parameter proposed by Tallian In Eq. The parameters R q1 and R q2 are the root mean square RMS roughness values of each surface in contact pinion-wheel. Equation 2 , proposed by Dowson and Higginson , is used to determine the minimum film thickness. To calculate the friction coefficient on the contact path at each point of the flank of gear teeth, it was used the model proposed by Michaelis Castro and Seabra, , which is shown in Eq.
Along the contact path, several parameters may change on each point of the flank of gear teeth. Listed below are the equations for the evaluation of each parameter that changes along the contact path. In Eqs. This parameter represents the distance from the pitch point up to the contact point considered. To calculate the contact stress on the flank of teeth, the analytical solution proposed by Hertz Norton, was used.
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In this solution, the gear contact is analyzed as if the contact was between two cylinders, and is assumed that the radii of these two cylinders are equal to the curvature radius of the teeth in each point in contact. With these assumptions, the contact-patch half-width a is then found by Eq. A plot of the pressure distribution in the contact zone is depicted in Fig. The maximum contact pressure can be obtained by Eq.
Except to the pitch point, there is the possibility of sliding as well as rolling in all contact points. In the pitch point exists only rolling motion. The tangential sliding force friction force causes a significant effect on the stress when compared to the situation where there is only the pure rolling or static pressure. According to the contact geometry shown in Fig.
The total stresses on each cartesian plane is found superposing the components due to the normal and tangential loads, as shown in Eqs. The running-in stage aims at equalizing the contact area and stabilizing such parameters as the friction coefficient. Figure 12 shows the friction coefficient along all points of contact during meshing, based on the pinion diameter.
It can be observed that, during the running-in test, there is a drop in the friction coefficient for both milling and shave finishes. This fact is related to the reduction of surface roughness of the flank during the tests see Table 5. Figure 13 shows the roughness profile measured at the pitch-line region of a shaved gear, before and after the running-in stage. Both the roughness height R a reduction and the increased number of peaks R sm lead to the actual growth of the contact area and a local reduction of the stress situation on the surface.
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Similar results were shown by Cardoso et al. Figure 12 a shows that, along the contact path, the friction coefficient presents a decline in the region between the root and the top of the gear. This fact is due to the increased normal load, which is defined by the load sharing function. This load change can be clearly observed in Fig. It also identifies a similar behavior of the contact stresses distribution for the two test conditions. As presented by Krishnamurthy and Rao , the influence of the torque and the presence of high contact stresses in the deddendum region can be observed once again.