OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 1 2025 Fig. 2. Cam mechanism of the homogenizer The results of this study indicated that simple harmonic motion law is the most suitable one, as its maximum velocity values were 25 % and 30 % lower than those of double harmonic and cycloidal motion laws, respectively. The analytical expression for simple harmonic motion law is given by: max ( ) 1 cos , 2 S s φ φ = ⋅ − π ⋅ β (1) The kinematic characteristics for simple harmonic motion law were calculated using the Mathcad software package, with the listing shown in Fig. 3. a(φ) := ( ) 1 1 1 2 1 2 3 1 2 1 2 3 3 1 2 3 cos 0 1 1 1 0 1 2 0 360 deg, k if if k if if π φ ⋅ ⋅ π ⋅ ≤ φ ≤ φ φ φ φ ≤ φ ≤ φ + φ φ − φ + φ ⋅ − ⋅ φ + φ ≤ φ ≤ φ + φ + φ φ φ + φ + φ ≤ φ ≤ (2) The speed is defined as: v(φ) = ( ) ( ) 1 1 1 3 1 2 3 sin 0 0 0 360 deg, k if if k if 1 1 1 2 1 1 2 1 2 1 2 1 2 3 3 π π ⋅ φ − ⋅ ⋅ ≤ φ ≤ φ φ φ φ ≤ φ ≤ φ + φ φ − φ + φ ⋅ φ − φ + φ ⋅ 1 − φ + φ ≤ φ ≤ φ + φ + φ φ φ + φ + φ ≤ φ ≤ if (3) Fig. 3. Listing of a program for determining kinematic characteristics Displacement was calculated as the integral function of the velocities, using Equation (3): ( ) ( ) . 0 s v d φ ϕ = φ ⋅ φ ∫ (4) The torque acting on the first cam was determined using a program developed within the mathematical software package. The program listing is shown in Fig. 4.
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