Full-factor matrix model of accuracy of dimensions performed on CNC multipurpose machines

OBRABOTKAMETALLOV Том 23 № 4 2021 TECHNOLOGY During the assessment of the adequacy of the theoretical full-factorial model of dimensional distortion after installing the workpiece to level the error in the position and shape of the workpiece, we pre-machine it to a certain size of 75 mm. This, in turn, ensures an equal distribution of the depth of cut during subse- quent machining. The initial machining is carried out with a small feed s and a depth of cut t . After that, by measuring its dimension with a micrometer, we note the result. To check the adequacy of the theoretical dependences, the theoretical and experimental values of the accuracy of the dimensions performed were compared. The analysis showed that these values are located quite close (for the cases indicated in the table and other cases, the difference does not exceed 10 %). All experiments were carried out with an estimate of the average value taking into account the distri- bution of results and its correspondence to the theoretical model according to the Student’s criterion. The required number of repetitions of experiments was determined by the Romanovsky criterion [28]. It should be noted that due to the fact that the depth of cut t , its change ∆ t , as well as the property of in- stability ω of the technological system are the cause of the appearance of a scattering fi eld of the performed dimension, special attention was paid to these factors during the veri fi cation of the developed models. Other factors in the models under consideration, depending on the cutting conditions, are involved in the models through the cutting force. The developed multi-factor matrix model, taking into account not only plane-parallel movements of technological subsystems, but also angular displacements around base points, forms the basis for a model of distortion of the performed dimensions in a double-carriage adjustment. The study of mathematical models for the formation of errors in the dimensions performed makes it possible to perform accuracy calculations for various machining conditions. These models take into ac- count the combined effect of a combination of factors – the characteristic of the rigidity of the subsystems of the technological system, the geometry of the cutting tools, the value of the bluntness of the tool, cutting conditions, etc. To check the operability of the models, variants were calculated with different initial data that determine the action of the formula, that is, for various variants, a study of machining accuracy was carried out. The performance of accuracy models of multi-tool double-carriage machining was tested using the in fl uence of technological factors and design dimensions of the adjustment on the value of the scattering fi eld of the diametrical size performed by the longitudinal carriage during multi-tool double-carriage machining. As an example, Figure 1 shows the effect of the diametric dimension performed on the longitudinal carriage dur- ing multi-tool double-carriage machining on the value of the scattering fi eld at its values t 1 = 1…6 mm, t 2 = 1…4 mm. Base variant: double-carriage machining – longitudinal and transversal carriage, cutting insert- CNMG 120408 P04 4225 CoroKey , workpiece – steel 45, tolerance grade – ITP 1 12, ITP 2 12, dimen- sions of the workpiece D = L = 74.9 mm, cutting speed V 1 = V 2 = 200 m/min, feed s 1 = s 2 = 0.24 mm/rev, ω ≈ 0.2, coordinates of connecting vectors of points O 0 and O 1 relative to the base points of application of forces 1 P and 2 : P X 0 = 74.9 mm, Y 0 = 37.45 mm, X 1 = 136 mm, Y 1 = 130 mm. Changes indicated for another option. 3 pivot (links) points are highlighted on the graphs: ● – t 1 = 2 mm, t 2 = 2 mm ▲ – t 1 = 3 mm, t 2 = 1 mm and ■ – t 1 = 1 mm, t 2 = 3 mm. In the base variant (Fig. 1, a ), for each control point, it is shown on which branch of the graph it is located. But in the variant (Fig. 1, b ), the sliding of these points relative to the base variant is shown on the corresponding form of labels (tags). From fi gure 1 it can be seen that, the nature of the ∆ w curves completely coincides with the embedded opinion for the opposite and non-opposite adjustments, that is, they have 3 branches (sleeves). In fi g. 1, b shows the effect on the error of the formed diametrical dimension on the longitudinal carriage during an increase of 12 times in comparison with the base version of the ratio of the length of the workpiece to the diameter. From this it can be seen that the error of the diametric dimension formed at this time on the longitudinal carriage changes at the base points from a decrease of –1,989 % to an increase of +376 %. In general, the carried out studies have shown that with an increase in the ratio of the length of the workpiece to the diameter in comparison with the base variant by 2 times, 3 times, 5 times, 10 times, the error of the formed diametrical dimension on the longitudinal carriage changes accordingly at the base points