TL;DR: In this paper, a dimension chain determination method based on mapping software is presented, which belongs to the technical field of machining and assembling and can effectively improve the calculation efficiency and stabilize product quality.
Abstract: The invention provides a dimension chain determination method based on mapping software and belongs to the technical field of machining and assembling. The method comprises the steps that all working procedure graphs of a part are drawn and dimensioned in the mapping software, a closed ring, to be calculated, of a certain working procedure is determined, all composition ring bodies of the closed ring are obtained, and the dimension and the tolerance of the closed ring are determined, so that determination of a dimension chain is completed. When the mapping software is utilized for calculating the process dimension chain, a nominal value of the closed ring is obtained through measurement, tolerance calculation of the closed ring is not prone to go wrong, the composition ring bodies are determined by means of rules, it is unnecessary to judge whether the composition ring bodies are increased ring bodies or decreased ring bodies, and the method is simple and reliable, and can effectively improve calculation efficiency; meanwhile, calculation of the dimension chain and the process design can be carried out and adjusted at the same time, and by analyzing the dimension of all the composition ring bodies of the dimension chain, the key dimension is found out to be controlled and improved preferably, which is beneficial for stabilizing product quality and improving guarantee abilities of working procedures; time for the process design is saved.
TL;DR: In this article, a design method of computer assistant tolerance statistics based on mixed convolution algorithm is proposed, where a dimension chain is provided with n composition rings, the function relation between the dimension Z of a closed ring and the dimension Xi of the composition ring is set as a design function which is analyzed into a linear part and a nonlinear part, the nonlinear parts is linearized and a high-level remainder is omitted to transform the design function into linear function.
Abstract: The invention relates to a design method of computer assistant tolerance statistics based on mixed convolution algorithm. A dimension chain is provided with n composition rings, the function relation between the dimension Z of a closed ring and the dimension Xi of the composition ring is set as a design function which is analyzed into a linear part and a nonlinear part, the nonlinear part is linearized and a high-level remainder is omitted to transform the design function into a linear function, i.e., a mixed convolution method comprising a resolution convolution and a numerical convolution can be used for determining the distribution of the dimension Z of the closed ring, and the calculation results can be corrected by the adoption of a closed ring correction method or a composition ring correction method. The design method promotes the existing tolerance statistics method to the calculation of the dimension chain of the composition ring and the closed ring with different distributions, is applicable to the mixed convolution algorithm that is effective for various linear and nonlinear problems, and has relatively rapid calculation speed and relatively high calculation precision.
TL;DR: In this paper, the authors considered equations containing self-compositions of the unknown function, and the imbedding of the composition ring of these equations into skew fields was considered.
Abstract: In earlier papers the author studied some classes of equations with Carlitz derivatives for $\mathbb F_q$-linear functions, which are the natural function field counterparts of linear ordinary differential equations. Here we consider equations containing self-compositions $u\circ u\circ ... \circ u$ of the unknown function. As an algebraic background, imbeddings of the composition ring of $\mathbb F_q$-linear holomorphic functions into skew fields are considered.
TL;DR: In this paper, the authors introduce the notion of n-ary composition hyperring and study the connections with composition hyperrings, and show that strong multi-endomorphisms of hyperrings can determine the nary composition structure of a hyperring.
Abstract: Based on the concepts of composition ring and composition hyperring, in this note, we introduce the notion of n-ary composition hyperring and study the connections with composition hyperrings. Moreover, we show that special strong multiendomorphisms of hyperrings can determine the n-ary composition structure of a such hyperring and also a subclass of n-ary composition hyperrings. Finally, the three isomorphism theorems are studied in the framework of n-ary composition hyperrings.
TL;DR: In this article, a self-sealing combined type piston ring of the utility model can achieve the sealing effect of preventing the axial and the radial leakage of high pressure gas under the circumstance of different positioning devices, play the functions of saving energy sources, increasing power, reducing noise, and depositing carbon, save the cost, and simultaneously prolong the service life of the piston ring.
Abstract: The utility model discloses a self-sealing combined type piston ring, and comprises an upper composition ring and a lower composition ring with end opening positions being in radial lapping opening forms. The radial width of the inner edge lapping parts and the outer edge lapping parts of the upper composition ring and the lower composition ring is different, and the lapping direction of the lapping opening of the upper composition ring is opposite to the lapping direction of the lapping opening of the lower composition ring. The self-sealing combined type piston ring of the utility model can achieve the sealing effect of preventing the axial and the radial leakage of high pressure gas under the circumstance of different positioning devices, play the functions of saving energy sources, increasing power, reducing noise, and depositing carbon, save the cost, and simultaneously prolong the service life of the piston ring.