To investigate the centering accuracy of the Cubic Press hammer during the operation of diamond synthesis equipment, the solving process of hammer centering accuracy under load was studied in detail on the basis of the static assembly deviation analysis of the press. First, a finite element analysis model of the press was constructed to calculate the structural deformation under load. Then, based on the least square fitting theory and small displacement torsor theory, a three-dimensional mathematical model of deformation deviation transmission of the press under load was established, and the possible error range of the intersection point between the axes of the bottom, left, and upper hinge beam piston hammers and the outer end face of the hammer was calculated. After that, by superimposing the static assembly error and the deformation deviation under load, the peak offset value that may occur in the centering axis of the hammer was obtained. Finally, the error variation range of the intersection point between the piston hammer axis and the hammer outer end face under different tolerance requirements was calculated. The study shows that in the static assembly, the error mainly originates from the machining and matching tolerances among the components, resulting in a relatively uniform and limited spatial variation of the hammer axis offset. Under load, however, the structural deformation and stress distribution of the press exhibit a nonlinear response, and the offset value increases significantly compared with the static state. This study establishes a three-dimensional transmission analysis model of pin-hinge beam-hammer error and determines the key component rings that exert significant influence on the centering accuracy of the hinge beam hammer assembly through tolerance sensitivity analysis, thereby providing a theoretical basis for the subsequent optimization of the press structure and the rational allocation of the machining accuracy of the hinge beam.