OBRABOTKAMETALLOV Vol. 24 No. 3 2022 TECHNOLOGY 2 , R e (10) with an assumed grinding wheel radius R = 125 mm and e = 88.4 mm. The obtained optimal values of α and e are constant and unalterable, regardless of the values of Q and λ. Looking at the kinematic analysis, we can compare the rotation speed of the grinding wheels for the obtained optimal values α and e (Fig. 8). For example, at a value of α = 45° and a rail grinding train speed of 100 km/h, the grinding wheel speed for the HSG method will be 19.6 m/s. For the STU method, conditions being equal, at a value of e = 88.4 mm the speed of the grinding wheel will be 39.3 m/s, which indicates the potential of the STU method in terms of greater effi ciency of machining. The kinematic and force analyzes of the considered grinding methods performed separately does not allow to fully evaluate the effi ciency of machining processes. In order to compare the results obtained, it is needed to determine the rotation speed of the grinding wheel as a function of the force effect on the abrasive tool. To do this, the law of variation of kinetic energy is used. If the limit is set so that the initial kinetic energy is equal to zero, in other words, the motion begins from a state of rest, then the equation will be as follows: 0 1 , k n k T T A (11) where T is the kinetic energy of the considered system, J; T0 is the initial kinetic energy of the considered system, J; Ak is the work of the k-th force affecting the grinding wheel, J. In general, the kinetic energy for the cases under consideration will be calculated using the formula: 2 2 2 2 , c c mV J T (12) where ωc is the angular velocity the grinding wheel rotation, rad/s; J is the grinding wheel moment of inertia, kg·m2. Omitting the determination of the moments of inertia and angular velocity of grinding wheels, formula (12) will take the following form for the grinding methods under consideration: for the HSG method: 2, c T mV (13) for the STU method: 2 5 4 , c T mV (14) where m is the mass of the grinding wheel in kilograms. From the diagrams (Fig. 9) it can be seen that the work is performed only by the torque of the grinding wheels, which is determined by the following equations: for the HSG method: cos , r M F R Q R (15) for the STU method: . r M F R Q e (16) Thus, the work of the torque of the grinding wheel for both methods will be determined by the equation: , c A M (17)
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