OBRABOTKAMETALLOV TECHNOLOGY Vol. 24 No. 3 2022 where M is the torque generated by the force Fr when the grinding wheel contacts the surface of the rail, Н·m; φc is the angle of rotation of the grinding wheel in relation to the calculated axis of rotation per time unit t, determined by the angular velocity ωc by the equation: . ñ ñt (18) Taking into account equations (15), (16) and (18), the dependence for determining the work of grinding wheels (17) will take the following form: for the HSG method: cos , A Q V t (19) for the STU method: . c Q eV A t R (20) Substituting equations (13), (14) and (19), (20) for the respective processing methods into equation (11) and solving it with respect to the grinding wheel speed Vc, we obtain: for the HSG method: cos , c Q V t m (21) for the STU method: 4 5 . c Q e V t mR (22) The obtained dependencies make it possible to take into account the force and kinematic components of the considered processes of passive rail grinding and to assess its effectiveness for a fi rst approximation. Results and its discussion The obtained dependencies (21) and (22) for the previously determined optimal values of α = 45° and e = 88.4 mm are calculated taking all other conditions remaining equal: the range of variation of pressing force Q from 100 to 1,000 N, m = 10 kg, λ = 1. The results of the calculations are shown in diagram in Fig. 11. The diagram (Fig. 11) shows that with the same pressing force of the grinding wheel to the rail Q, the effective operation speed according to the HSG method is 20 % higher than the speed that occurs with the STU method. For example, at Q = 450 N, the effective operation of the grinding wheel with the HSG method will be achieved at Vc = 31.8 m/s, and with the STU method at Vc = 25.5 m/s. Thus, it can be concluded that at equal values of Q, the performance of the HSG method is 20 % higher than that when using the STU method. It should be noted that in accordance with the kinematics of the processing process, at the same speed of the grinding train, the possible speed of the grinding wheel according to the STU method is almost 2 times higher than the speed of the wheel according to the HSG method. Thus, at a train speed of Vt = 100 km/h, the maximum possible grinding wheel speed for the HSG method is Vc = 19.6 m/s, and Vc = 36.3 m/s (Fig. 8) for the STU method. Therefore, the passive grinding technology implemented by the HSG method will initially be limited by the maximum achievable grinding wheel speed and the corresponding pressing force. In the graph (Fig. 11), the area of possible values of Vc and Q for the HSG method are shown in dark gray. In this case, using the STU method, both the rotating speed of the grinding wheel and the pressing force it exerts have a wider range of variation and, as a consequence, there is a greater possibility of increasing the removal of metal. The light gray area, shown on the diagram, is the range of possible values of Vc and Q for t he STU method. These areas are an example of a grinding train moving at a speed of 100 km/h. In general, the results of theoretical studies correlate with the obtained experimental data presented in [21, 22].
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