Friction force moment

FIGURE 17.9 Changes in friction force moment (A/x) as a function of load (N) for 0.5 wt% solutions of lauryl alcohols. 

The test at a constant load makes it possible to measure the changes in the friction force moment (M ) as a function of friction time. Hence, the coefficient of friction (p) was calculated from the equation... 

Antiseizure properties were determined according to the methodology presented in the previous section. Changes in the friction force moment (Mj) as a function of increasing load (P) form the basis for the determination of individual quantities. As an example, this dependence for 0.5 wt% solutions of lauryl alcohols is shown in fig. 17.9. 

The individual curves represent 0.5 wt% solutions of alcohols of various oxyeth-ylation degrees. Studies were also carried out for water, which represents a reference system. The course of changes observed is relatively complicated, but it is possible to notice three intervals that differ in the rate of increase in the friction force moment. A slight increase can be observed at low loads, a moderate one at intermediate loads, and a rapid one ending with seizure at the friction force moment 10 N-m. Three quantities will be used to assess antiseizure properties scuffing load (P,), maximum seizure load (P ), and the limiting pressure of seizure (p. Seizure tests were carried out in the presence of oxyethylated lauryl alcohol solutions at concentrations of 0.1, 0.5, 1, 4, and 10 wt%, and for cetyl, oleyl, and stearyl alcohols at concentrations of 0.1,1, and 10 wt%. 

The scuffing load is the lowest load at which there occurs a pronounced increase in the friction force moment, which indicates breaking of a lubricant film. The value of scuffing load for water (200 N) is several times lower than that for oxyethylated alcohol solutions, which exceeds 1000 N. The highest value was observed for a 1 wt% solution of C12H25EO23 (ca. 1500 N). High antiseizure efficiency of compounds can be observed even at the lowest concentrations (0.1 wt%). The dependence of... 

Seizure load is the highest value of the pressure at which the friction force moment exceeds 10 N m. In the four-ball machine used in the experiments, the loads range from zero to 7200 N. Several of the solutions tested reached the maximum load value without undergoing seizure. The 7200-N value is nearly two times higher than the seizure load for water (3700 N). The dependence of seizure load on concentration and type of compound is presented in fig. 17.12. 

The tests were carried out at a constant load of 2 kN, which is relatively small and corresponds to a moderate increase in the friction force moment (fig. 17.9). Examples of changes in the coefficient of friction as a function of time are given in fig. 17.16. 

In this approach, a body is thrown up and then it falls along the same path. Observations are made in passing two fixed positions during the movement up and down, Fig. 3.2b. Of course, inside the cylinder where the movement takes place, there is always some air, but this approach allows us to reduce its influence better than in the previous method. This is related to the fact that the resistance of air is the same during motion in the different directions. However, in one case the friction force and field g have the same direction, while in the second case they are opposite to each other. In the symmetrical approach we measure moments when a mass passes the upper and lower stations. The point 0 is origin that corresponds to the highest position of the body where... 

It can be shown that relations between measured lateral forces (half width of friction loop W = (Mu-Md)/2) and the friction loop offsets (A (Mu + Md)/2) for sloped and flat surfaces at a given load (2.7-2.10) can be used to calculate the friction force calibration factor a [nN/V]. M denotes the torsion moment involved, the subscripts u and d denote uphill and downhill scan directions, and the subscripts. v and/denote sloped and flat surfaces, respectively. 

Suppose for a moment that k > k. In this case there is a unique static solution for every x in Eq. (19), irrespective of the value of xq . When the upper sohd is moved at a constant (small) velocity vq relative to the substrate, each atom is always close to its unique equilibrium position. This equilibrium position moves with a velocity that is of the order of tiq- Hence the friction force is of the order of myvQ, and consequently Fk vanishes linearly with vq as vo tends to zero. The situation becomes different for k < k. Atoms with more than one stable equilibrium position will now pop from one stable position to another one when... 

To generate the trajectories that result from stochastic equations of motion (14.39) and (14.40) one needs to be able to properly address the stochastic input. For Eqs (14.39) and (14.40) we have to move the particle Linder the influence of the potential T(.v), the friction force—yvm and a time-dependent random force R(t). The latter is obtained by generating a Gaussian random variable at each time step. Algorithms for generating realizations of such variables are available in the applied mathematics or numerical methods hterature. The needed input for these algorithms are the two moments, (2J) and In our case (7 ) = 0, and (cf. Eq. (8.19)) = liiiyk/jT/At. where Ai is the time interval... 

This produces high bending moments and hence a relatively greater acceleration of the fibre after junction failure. The opportunity for the secondary junction formation is then reduced since the kinetic frictional force will decrease rapidly with velocity. There is some analogy to the dwell time effect in autoadhesion. 

Then we investigated the effect of surface roughness on the transportation. It was found that higher surface roughness is more effective in transporting the loaded gel because frictional force increases and the moment of force of the rotational motion increases. 

Considering that the number of split chemical bonds, in the time interval dt, is proportional to /-y f - representing the friction force that acts on the chain at a certain moment, t y - chemical... 

When the engine works at constant speed, the net moment that acts any of pulleys A-C and B-D is equal to zero. Neglecting the friction forces, it can be written ... 

Depending on the specific design of the joints at any moment we could obtain the friction forces as a function of the link position, velocities and accelerations, in other words to solve the first problem of dynamics... 

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