Introduction The best goal of metal cutting is to maximize economic efficiency. There are a lot of variable parameters to achieve this goal, and a reasonable choice of cutting amount is particularly important. The economics of turning cylindrical cylinders of equal diameter have been studied, but trapezoidal parts of unequal diameters are often encountered in factories, and turning such parts can have two methods of selecting cutting speeds, ie constant speed method and constant. Cutting speed method. This paper analyzes the economics of the machining of stepped parts by these two methods and provides the basis for selecting cutting speeds for turning stepped parts. 1 Machining costs for turning stepped parts In the turning stepped parts, the machining of a cutting stroke at the i-th step is: ti=pDiLi/(1000fivi)=Li/Nif (1) where: i— - indicates the i-th step surface of the part; Di - the diameter of the i-th step surface (mm); Li - the axial length of the i-th step surface (mm); vi - the i-th step surface of the turning Cutting speed (m/min); f = feed rate (mm/r); Ni - Spindle speed (r/min) of the i-th step surface. For parts with m steps, the process cost per part is: C=pm/(1000f) m DiLi/vi+Mtvt+(MIct+Ci)/P ∑ i=1 (2) Where: M— Cost of the whole plant shared by the process per unit time (yuan/min); tvt-hours of auxiliary work in addition to tool change (min/piece); tct—tool change time (min); Ct—tool cost (yuan/ P)—The number of parts to be machined before each cutting edge of the tool reaches the tool's durability standard. 2 Constant spindle speed method Turning the machining cost of the stepped parts and the determination of the optimal cutting conditions The constant spindle speed method turns the stepped parts, that is, the spindle speed is unchanged during turning, and the cutting speed of each step is changed. of. Let the spindle speed be N, then the cutting speed of the i-th step surface is: vi=pDiN/1000 (3) For a step-like part with m steps, m ti/T=1/P ∑ i=1 (4 In the formula, T is the tool life. Then, 1/P=m ti/T=pxNx-1fy-1apz(m DixLi)/1000xCT ∑ ∑ i=1 i=1 (5) CN=M/(fN) m Li+Mtct+(Mtct+Ct)pxNx -1fy-1apz(m DixLi)/1000xCt ∑ ∑ i=1 i=1 (6) Similarly, the spindle speed that can export the lowest machining cost is: Nmin*C=[1000xCtM m Li/[(x-1)(Mtct) +Ct)pxfy] m DixLi]1/x ∑ ∑ i=1 i=1 (7)
Figure 1 Parts diagram
Fig. 2 Diameter ratio and processing cost
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