Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments

Abstract

The Direct Linearization Method (DLM) for tolerance analysis of 3-D mechanical assemblies is presented. Vector assembly models are used, based on 3-D vector loops which represent the dimensional chains that produce tolerance stackup in an assembly.Tolerance analysis procedures are formulated for both open and closed loop assembly models. The method generalizes assembly variation models to include small kinematic adjustments between mating parts.Open vector loops describe critical assembly features. Closed vector loops describe kinematic constraints for an assembly. They result in a set of algebraic equations which are implicit functions of the resultant assembly dimensions. A general linearization procedure is outlined, by which the variation of assembly parameters may be estimated explicitly by matrix algebra.Solutions to an over-determined system or a system having more equations than unknowns are included. A detailed example is presented to demonstrate the procedures of applying the DLM to a 3-D mechanical assembly.

To model bolted parts for tolerance analysis using variational model

“…Considering the 2D case and that the two plates have small thickness, the relative location deviation of the second plate as regards to the first plate, due to the tolerances and the clearance among the bolts and the two coupled holes, may be characterized by three contributors ∆x, ∆y and ∆ respectively along the X-axis, along the Y-axis and around the Z-axis (see Figure 2). These relative location deviations are also named as small kinematic adjustments [9] and they are the parameters of the proposed assembly model. These are the parameters needed to build the homogeneous transformation matrix that permits to pass from the local Datum Reference Frame (DRF) of the first component, to the local DRF of the second component [9] in order to build the stack-up functions of the assembly.…”

“…These relative location deviations are also named as small kinematic adjustments [9] and they are the parameters of the proposed assembly model. These are the parameters needed to build the homogeneous transformation matrix that permits to pass from the local Datum Reference Frame (DRF) of the first component, to the local DRF of the second component [9] in order to build the stack-up functions of the assembly. Assuming the simplified hypothesis that each surface keeps its nominal shape, i.e.…”

Taxonomy of models for tolerance analysis in assembling

“…The vector loop model uses vectors to represent relevant dimensions in an assembly (Chase et al 1995, Chase et al 1996, Chase et al 1997 To better understand the vector loop model, the basic steps for applying it to a tolerance analysis problem are provided below (Gao et al 1998, Chase 1999, Faerber 1999, Nigam and Turner 1995.…”

“…References Vector loop (Chase et al 1995, Chase et al 1996, Chase et al 1997, Gao et al 1998, Chase 1999, Faerber 1999, Nigam and Turner 1995.…”

A New Approach in Tolerance Analysis

“…Bu yöntemde, analizi yapılacak mekaniksel montajlarda vektör bağlama oluşturularak, montaj grubunda birbiriyle ilişkili olduğu düşünülen montaj parçaları arasında iletişime göre belirlenen vektör halkaları bir döngü ile kapatılarak matrisler elde edilmektedir. Elde edilen bu matrisler ile hassasiyet hesaplanmaktadır (7). Fakat yapılan hesaplamalar ve iletişimli montaj parçaların tespiti işlem karmaşıklığı ve zorluğunu beraberinde getirmektedir.…”