OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 5 2 3 Results and discussion At the first stage of the synthesis, an analysis of the operating conditions of the same type of machine tools is carried out and the area of its rational use is established, i.e. the limits Xmin and Xmax of the variation of the parameter X are assigned. The number of members of the series m and the main parameters of the equipment Xmax i are to be determined. Initially, the minimum size of the interval is assigned and the value of its increment d is chosen. In practice, to ensure the required accuracy, the most preferred values are amin = 1.26 with increment d = 1.12. In turn, it should be noted that in real design conditions, other options are also acceptable. The presented parameters are interconnected by the following relation 2 ( )/2 min , z z z D a − = d (6) where z is the number of intervals of the random variable X; max min D X X = is the range of variation of the random variable X. Taking the logarithm of the indicated expression and solving it with respect to z, one finds the number of members of the parameter-oriented series 2 m z = − . (7) Then set the values of the denominators of the series for each of its members min ϕ = d , (8) where i k m i = − . Analyzing the obtained results, it can be stated that with an increase in the serial number of a member of the series, the value of ϕ decreases, while finding the main parameter of the equipment will be carried out according to the equation ( ) 2 /2 max max , i i i k k k i m X X − = φ d (9) where ϕm is the minimum value of the variable denominator of the series. The values of the base (average) i a and total Di ranges of variation of the X value of each of the members of the parameter-oriented series will be calculated according to the following dependencies 1 min i k i a a + = d and 3 ( ) i i D a = . Using the data obtained, the boundary lines of the size ranges are plotted on the graph (Fig. 8), after which you can proceed directly to the construction of the parameter-oriented series. To do this, from point A, corresponding to the upper boundary of the main subrange of the first member of the series, a horizontal line is drawn until it intersects at point B with the line defining the lower boundary of the subrange. The abscissa of point B specifies the main parameter of the second member of the series. Then the upper limit of the main subrange of the second member of the series (point C) is found and the process is repeated. Fig. 8. A promising parameter-oriented series of vertical milling machines with a cross table, upgraded to the level of hybrid technological equipment
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