Study Paper: Precision Design
1. Based on the 2D tolerance analysis techniques [1,2], we can determine the spatial variations of kinematic dimensions. In particular, we can use the sensitivity OTJaTT analysis [1,2] to identify key component dimensions in any design. This will allow us to focus on the key dimensions that affect the assembly dimensions u. The newtechnique can guide us to a new domain where we can improve our design to achieve high product quality without significant increase in cost. It is a new kind of design optimization, where we can achieve an optimal balance between product quality and production cost.
(1) Select a suitable design, where m=6 or greater and nv=2 or greater, for 2D precision analysis. Provide assembly drawing and also component drawings for your design and determine x. Describe your design (See the example below) and the assembly dimensions u. Also determine n, n, nv, vector chain L, Ix, Iu, Lilφ/Σφ table, Φ, Φk, Φ, Ik, It, n, m, q, total number of unknowns for nν.
(2) Discuss each of assembly dimensions, u, i=1,2,,mtq, and explain how quality or performance of your design is affected if ui, i=1,2,...,m+q, is changed.
(3) Identify the key component dimensions [1,2] to demonstrate the usefulness and applicability of the lecture contents [1,2]. Determine H, ua-n,. Фa-n, Ax, Δu, ΔH each A element, A, each B element, B, T, table, To, Tuo, u, Ф, oTuaToT. Based on x, give a list of key dimensions. Also, based on To for making x, determine the total manufacturing cost Cmo [3] for making x.
Consider two approaches:
(a) The precision of each key component dimension is increased by 30%, which is the new approach, based on the common approach of To. For the new approach the total manufacturing cost Cm(a) [3] for making x is to be examined. Based on To, give T(a). Also, base on T(a), determine Tu(a).
(b) The precision of every component dimension x is increased by 30%, which is the traditional approach, based on the common approach of To. For this approach, the total manufacturing cost Cm(b) [3] for making x is to be examined Based on To, give T(b). Also, base on Tb), determine Tu(b).
Now compare the two approaches, (a) and (b), in terms of assembly's precision or quality, specifically, in terms of Tu, and in terms of total manufacturing cost Cm [3] for x.
(4) Determine the total manufacturing cost increase ACma/b), ACm(a/b)=Cm(a/b) - Cmo, and the kinematic spatial error reduction ATu(a/b), ATu(ab)- Tuo-Tu(ab). Study the precision improvement per unit cost increase ATula/ACma). and ATub/ACm(b)
(5) Give your recommendation on choice of precision design approach, based on your analysis, when upgrading product quality.
The work in (6) is optional:
(6) Based on the 2D tolerance analysis techniques together with the sensitivity aTJaTT analysis technique [1,2], a nice precision design work can be done as in (1)-(5). In addition, a new kind, one step further, of good design work can also be done. This is precision based design optimization: Consider several designs under a particular set of design specifications, try to conduct the 2D sensitivity analysis and compare the elements in Tu/aTT and select the best design among the several available designs.
Example:
For your reference, an example of design for 2D tolerance analysis is the optical lens assembly (Fig. 1). The precision assembly includes two spherical lenses, a retainer, and a housing design. The assembly is symmetrical about the axis (Fig. 1), so only the upper half is illustrated. For simplicity, the section view hatchings for the retainer and the housing are omitted (Fig. 1). The assembly is also called as narrow field of vision lens assembly. In a particular version of the proposed design, the thickness of Lens 1 a is 0.3±0.001 inches, the radius of curvature of the surface of Lens 1, noted as b, is 10.72+0.022 inches. Lens 1 is held against an inclined surface c. The lens is in contact with the surface c at a particular point. The angle between the inclined surface c and the axis, also called as lip angle, is 84.8°. The retainer flange depth e is 0.5±0.001 inches, and the retainer radius fis 1.03±0.0005 inches. The housing length h is 7.07±0.002 inches, and the depth of Lens 2, noted as i, is 0.47±0.001 inches. The 2D tolerance analysis techniques [1,2] can be used to investigate the spatial variation of the distance g between the two lens surfaces (Fig. 1). It is noted that in order to restrict the analysis to 2D and to simplify the analysis, the following assumptions can be applied to the precision assembly (Fig. 1): i) the lenses have no tilting; and ii) the contact between the housing and the retainer is circular.
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(2025)
References
[1] Gao, Y., 2025, "Precision Manufacturing Technologies", Lecture Notes, HKUST, Hong Kong.
[2] Zhang, H.C., 1997, "Advanced Tolerancing Techniques", John Wiley and Sons, New York.
[3] Parker, M., 1991, "Manual of British Standards in Engineering Drawing and Design", Stanley Thornes, England.