OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 2 2 inertia of the masses depend on the angle of rotation of the driver (drive shaft), and the drive has an asynchronous electric motor (see diagram shown in Fig. 1). The development of the mathematical model was carried out by means of the Mathcad software product with the direct use of the computer-aided design system Compass 3D. Fig. 1. Kinematic diagram and mathematical model of the kneader design that includes an epicyclic gearing The nature of the change in the process load acting on the working shafts of the device was presented earlier in [25]. This paper presents only the values and nature of the reduced moments of these forces to the main shaft of the device. In our case, it is presented, consisting of two components: ( ) 24 12 cos(2 / 16 ) c M ; and the moment of the driving forces is represented by a parabola 2 d d M A B dt , where 2 2 0 m m M A ; 2 0 2 2 0 m m M B . The maximum values of the total moment of the useful resistance and the moment of inertia amounted to 46 N·m, the minimum amounted to 22 N·m and depend on the rotation angle of the kneading shafts blades. The device operating peculiarities are described in detail in [24–27]. This paper presents a mathematical model of the device, with the following values introduced: the rotor moment of inertia is designed as JEM; the drive pulley moment of inertia is designed as J1; the driven pulley moment of inertia is designed as J2; gears moments of inertia are designed as J3, J4, J5, J6, J8, J9, J10, J11; that of carrier is J7. The shafts that translate motion from the motor to the working shafts are designated as a, b, c, d, e, f. It is proposed to determine the equation of machine motion using the Lagrange equation of the second kind, which in this instance will have the following form: 2 2 2 1 2 d c d d dJ J M M dt dt d , (1) where J is the reduced moment of inertia; φ is the generalized coordinates of the system; Мd is driving moment; Mc is the moment of resistance. The drive moment is determined by 2 m d m m M M , (2) where J is the reduced moment of inertia; σ is the slip corresponding to the value of Мd; σm is the slip corresponding to the value of Мm; Мm is the maximum (overturning moment).
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