PSI - Issue 81

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

452

The calculation scheme is shown in Fig. 6. In this case, the locating error εᵢ depends on the centering error of holes Δ c and the error in offsetting the perpendicular center axis from the rotation axis (tooling manufacturing error) Δ dev .

Fig. 5. Locating of curved axis using two perpendicularly offset and axial centers.

Fig. 6. Calculation scheme for determining the locating error of a curved axis using two perpendicularly offset and axial centers.



/2tg , 2

The centering error for center angle β equals:

and for the standard center angle β=60° :

 =

C D



0,87 .

 =

= 

2 0,5774 D 

(12)

C

D

Errors Δc and Δ dev lie in perpendicular planes, therefore:

2 2 . i C dev  =  + (13) Machine tool equipment design and manufacturing practice confirms that error Δ dev lies within the range Δ dev =±(0.1...0.15) mm. Using equation (13), the maximum magnitude of locating error for the surface positioned in the plane of perpendicular centers is obtained. The locating error magnitude for an individual part surface is proportional to the distance of its placement from the axial center, meaning: (14) The locating error according to formula (14) is maximum. During the process development, centering and tooling manufacturing can be corrected to actual errors. The ratio of locating error εᵢ to length L equals the tangent of half the angle that determines angular error Δ γ , since during machining on one fixture, the total angular error Δγ is obtained for both shaft ends with repeated locating: tg / , 2 i L   = arctg . 2 i L    = Therefore, the error in the angle of intersection of geometric axes for a curved axis when locating using two perpendicularly offset and axial centers equals: 2 0,76 0,02 2arctg 2arctg . D i L L     +     =  =  (15) Angular error Δγ additionally accounts for the accuracy of axis centering in the rotary indexing fixture or machining center. 3.3 Achievable part accuracy for locating using two centers positioned in the plane of symmetry and an axial center The third locating scheme for CA using three center holes is the scheme shown in Fig. 7. Its characteristic feature is that two center holes are positioned in the CA plane of symmetry; both axis ends are machined in a constant rigid center 2 using centers 2 3-4 or 2-1-4. In this locating scheme, four center holes must be prepared for part machining. To determine the locating error with a minor assumption related to the change in center axis inclination, it is also advisable to 2 0,76 0,02.  + i D b L  =