Generalized definition and application of tolerance

Tolerance with upper deviation less than lower deviation is defined as virtual tolerance; the dimension between two extreme values required with tolerance (virtual tolerance) is expressed by a set. The changed characteristics of the set range when the tolerance value is continuously reduced from positive to negative are explored. The nature of virtual tolerance is that the absolute value of virtual tolerance is the error compensation amount, and the dimension between two extreme values is the error compensation range. On the basis of the concept of positive and negative number, the theory of dimensional homogeneity, the existing conditions of the general formula of the dimensional chain, the accuracy of the calculation results of tolerance, and so on, the concept of virtual tolerance and its relationship of unity of opposites with tolerance are proposed. Based on the concept of virtual tolerance, analysis and calculation processes of various assembly dimensional chains are unified, and general formulation of calculating the range of false waste is established, and the method of determining the range of false waste by using probabilistic method in machining process is deduced.