Analysis of anvil centering accuracy of cubic press based on small displacement torsor theory

Objectives: The diamond synthetic equipment in China is mainly the hinged cubic press (referred to as cubic press). With the acceleration of large-scale presses, the performance of cubic presses has greatly improved, but higher requirements have also been put forward for the assembly accuracy of these presses. In order to improve the centering accuracy of the top hammer of the cubic press, the assembly errors of the working cavity of the hinge beam for the cubic press are researched. Methods: Firstly, based on the small displacement torsor (SDT) theory, the assembly tolerance model of the hinge beam of the cubic press with different tolerance principles is established. Secondly, the space vector is used to represent the three-dimensional dimension chain. Based on the space vector ring superposition principle, the closed ring size and its variation calculation model representing the motion posture of the hinge beam piston top hammer is derived, and the possible error range of the intersection points between the bottom, the left, and the upper top hammer axes and their respective top hammer outer end faces are obtained. Finally, the cumulative closed-loop error FR obtained from the three-dimensional tolerance analysis of the single hinge beam piston top hammer posture is compared with the similar error X₁ obtained from the one-dimensional dimensional chain analysis. At the same time, the Plackett-Burman design (PBD) is used to screen out the variables that have a significant effect on the sealing ring of the top hammer posture of a single hinge beam piston. Results: (1) Through the calculation of the three-dimensional tolerance analysis method established by the cubic press, it is found that the possible errors of the axis of the top hammer of the left hinge beam are [−0.070, 0.095] in the X direction, [−0.655, 0.655] in the Y direction, and [−0.855, 1.035] in the Z direction. The possible errors of the axis of the top hammer of the bottom hinge beam are [−0.030, 0.055] in the X and Y directions, and [0.080, 0.100] in the Z direction. The possible errors of the axis of the top hammer of the upper hinge beam are [−0.111, 0.135] in the X direction, [−1.180, 1.155] in the Y direction, and [−1.820, 1.915] in the Z direction. (2) The dimensional variation error X₁ of the hydraulic cylinder axis of the left hinge beam in the Z direction is compared and calculated by using the one-dimensional dimensional chain. The variation error X₁ of the closed ring is [−1.000, 0.780] when the dimensional chain extreme value method is used for analysis, and the variation error X₁ of the closed ring is [−0.930, 0.410] when the Monte Carlo method is used for analysis. The calculated result of the Monte Carlo method is less than that of the extreme value method. This is because the calculation assumes that the tolerances of each part follow a normal distribution, which is more in line with the actual production situation and closer to the actual assembly error. (3) When the diameter of the pin adopts the principle of independence, the possible position error of the size of the hydraulic cylinder axis of the left hinge beam in the Z direction is [−1.005, 1.005]. When the diameter of the pin is marked by the inclusion principle, the position error changes to [−0.855, 0.980]. From the comparison of results, the use of different tolerance principles leads to different tolerance analysis results. (4) The Plackett-Burman design (PBD) is used to screen out four highly significant variables, namely, the parallelism tolerance corresponding to variable M₁, the dimensional tolerance corresponding to variable M₂, and the straightness tolerance corresponding to variables M₅ and M₇, which have a great impact on the precision of the hinge beam. Conclusions: Based on SDT theory, the three-dimensional tolerance analysis method under different tolerance principles is established for the cubic press, and the possible error variation ranges of the bottom, left and upper hinge beam top hammer axes are calculated respectively. By comparing the errors obtained by the three-dimensional analysis method with those obtained by the one-dimensional dimensional chain method, it is found that the former has a larger error range than the latter, which proves that the three-dimensional analysis model method used in this paper is superior to the one-dimensional tolerance analysis method. At the same time, when the pin diameter is marked with different tolerance principles, the axis error of the hinge beam hydraulic cylinder is calculated, and the error range corresponding to the inclusion principle is smaller than that corresponding to the independent principle. That is to say, when the inclusion principle is applied in the pin diameter marking, the position variation error of the hinge beam hydraulic cylinder axis can be ensured to be smaller, which is more in line with the high-precision requirements of the diamond cubic press. Finally, the four highly significant variables that have great influence on the precision of the hinge beam are selected, providing a theoretical basis for the reasonable distribution of the machining precision of the press hinge beam.