PSI - Issue 81

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

450

- - error in center hole positioning in the part; error in center hole depth at the primary datum center; - error in offsetting the center plane from the axis of rotation.

Different methods of locating curved axes (CA) require specific approaches to determining locating errors, where various factors differently influence the result of achieving appropriate part accuracy parameters and, in many cases, necessitate experimental investigation. Theoretical substantiation of the achievable accuracy in obtaining the angle of intersection of geometric axes for different locating methods under conditions of indeterminacy will enable recommending one method or another for achieving appropriate manufacturing accuracy, particularly in batch production processes. 3. Results and discussion 3.1 Achievable accuracy of the angle of intersection of geometric axes during locating using parallel-offset, angular and axial centers The locating scheme for a curved axis using parallel-offset, angular and axial centers and the emergence of locating errors is presented in Fig. 3. Center hole 1 is offset relative to the part's axis of rotation I-I by distance a , center hole 2 is positioned on the part's axis of rotation, while center hole 3 is positioned at angle γ to the axis of rotation.

Fig. 3. Locating scheme using parallel-offset, angular and axial centers: a – locating scheme; b – dependence of locating error on center hole diameter; c – dependence of locating error on center hole offset

In this case, the part's axis of rotation I-I does not coincide with the part installation axis II-II and intersects with it at an angle. It can be stated that the machining surfaces are each positioned with its own eccentricity E relative to the part installation axis, which increases with proximity to the parallel-offset center. Depending on the angular error with which the part is installed on the primary datum center 2, the locating error for individual machining surfaces will vary. From the figure, it is evident that the eccentricity of surface positioning relative to the datum axis II-II at distance b from the primary datum center equals ( ) a E L b L = − . (1) Offsetting the center plane from the axis of rotation by angle β induces locating error εᵢ , calculated according to the relationship ( ) sin cos sin cos . i a X E L b L  = =  = −   (2) Angles β and ψ depend on the following factors: a) centering errors (both due to center hole offset and due to the conical center hole diameter), b) fixture execution accuracy. The influence of centering error on angles β and ψ results from the misalignment of the angular center axis with the angular center hole axis, both in the case of angular center offset error (Fig. 3, b) and center hole diameter error (Fig. 3, c). For center hole diameter error ΔD , the center hole axis D 0 will not coincide with the center axis D С along the contact line and the cutting force will press the part against the lateral surface of the center, producing axis offset Δ′ , which equals sin . 2tg 2 D   =   (3) Displacement of datum center 2 from its geometric position, analogous to the corresponding center hole offset, produces part and machine tool axis offset by magnitudes Δ″ b and Δ‴ b . Displacement of angular center 1 in the fixture, similar to angular center hole offset in the part, produces machine tool and part axis offset by magnitudes Δ″ k and Δ‴ k , respectively. Zha et al. (2023) in the process of investigating machining and locating errors, notes that the distribution of individual errors is subordinated to the general distribution of eccentricity (Rayleigh's law) when the random variable is a radius vector for a two-