PSI - Issue 81

Igor Stoiko et al. / Procedia Structural Integrity 81 (2026) 447–454

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operations as the final stage to achieve the necessary precision and stability throughout the entire technological process. Resolving this problem and its theoretical substantiation enables the practical achievement of required accuracy under batch and mass production conditions. As mentioned above, the part design precludes the creation of coaxial technological center holes along the geometric axis of rotation, which would enable part locating in the centers of turning and grinding machines. Traditional locating of a straight part in coaxial centers eliminates five degrees of freedom in space – three at the headstock center and two at the tailstock center. To eliminate the sixth degree of freedom, conventional technology employs a special drive dog on the headstock side. The essence of locating with three center holes lies in using two centers offset from the machine's geometric axis of rotation and lying in the same plane with it, instead of a single axial center hole intended for the headstock center. Three locating schemes for turning and grinding operations using three center holes have been technologically developed: - using a parallel-offset center 1, angular center 2 and axial center 3 (Fig. 2, a); - using two perpendicularly offset centers 1 and 2 and an axial center 3 (Fig. 2, b); - using two centers positioned in the part's plane of symmetry, 1 and 2 and an axial center 3 (Fig. 2, c).

Fig. 2. Methods for locating curved axes using three center holes: a – using parallel-offset, angular and axial centers; b – using two perpendicularly offset and axial centers; c – using two centers in the plane of symmetry and axial center.

In all three cases, assuming ideal positioning of center holes in the part and centers in the corresponding tooling, the primary datum is center 1, which eliminates three degrees of freedom for the part in space. Axial center 3 eliminates two additional degrees of freedom. Center 2 is adjustable and eliminates the sixth degree of freedom for the part. In the first locating method for turning and grinding operations, in addition to two face center holes, a third center hole is employed, offset from the geometric axis of rotation and executed in a technological protrusion specifically provided in the workpiece (Fig. 2, a). To machine both ends of the axis, four center holes must be created in the workpiece. Machining of one side is performed using centers 1-2-3, while the other side uses centers 4-3-2. The second method of locating using three center holes involves positioning two center holes in a plane perpendicular to the machine tool's axis of rotation during machining (Fig. 2, b). This requires creating six center holes in the workpiece prior to turning. Three center holes 1-2-3 are utilized for machining one side of the part and three holes 4-5-6 for the other. The third method involves locating using three center holes, two of which are positioned in the axis plane of symmetry (Fig. 2, c). This utilizes four center holes in the workpiece. The advantage of this method is that a single fixed center 1 is used for machining both ends of the part. Part machining is performed sequentially using center holes 1-2-3 and 1-2-4. The specified locating methods are characterized from the standpoint of cutting force action on the datum centers, which is of great importance for ensuring rigidity of the entire system and reliability of the technological tooling. If in the first case the resultant cutting force is directed almost directly at the primary datum center, then in the other two cases it has a shearing component directed relative to the center. Reality introduces its corrections into all three locating schemes. This is associated with the technological accuracy of both center hole execution and corresponding tooling for securing parts in turning and grinding equipment. Under ideal positioning of center holes in the workpiece and centers in the corresponding technological tooling, centers 2 and 3 eliminate two and one degrees of freedom, respectively. However, in practical use, errors in center hole execution and tooling with offset centers can redistribute the degrees of freedom between these centers. Specifically, instead of two degrees of freedom at center 2 and one at center 3, there may be one degree of freedom at center 2 and two at center 3. This involves the principle of locating indeterminacy in three center holes, which ultimately affects the accuracy of executing the angle of intersection of geometric axes in the part during the machining process. Consideration of this locating moment for part machining using three center holes ultimately determines the achievable accuracy of the angle of intersection of geometric axes in the part. Unlike locating in coaxial centers, where center coaxiality is ensured by the equipment, offset centers are executed in the technological tooling and offset from the part's axis of rotation. This introduces a whole range of errors in both part locating and ensuring design quality indicators. The primary causes of errors in these locating schemes are: - displacement of the primary datum center from its nominal position; - error in executing the angle of intersection of geometric axes in the technological fixture;