ComputerAided_Design_Engineering_amp_Manufactur.pdf
ComputerAided_Design_Engineering_amp_Manufactur.pdf
ComputerAided_Design_Engineering_amp_Manufactur.pdf
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
will introduce a way to propagate product specification into dimensional constraints of the part model.<br />
These dimensions are shown on the final drawings, and they are also the constraints used by 3-D<br />
variational geometry.<br />
Tolerance Propagation and Control<br />
In this section, we will briefly outline Bjorke’s (1989) theories on tolerance analysis. This will lead to the<br />
basis of tolerance propagation and control that help a designer attach dimensions to components.<br />
Tolerance control is the process of fitting a sum dimension tolerance to that specified by the designer;<br />
tolerance propagation allocates the specified tolerance to individual dimension tolerances. Tolerance<br />
propagation and control both require the identification of one or more sum dimensions. A sum dimension,<br />
or functional dimension, is any dimension that affects the functionality of the assembly more than<br />
the other dimension (Bjorke, 1989).<br />
The sum dimension tolerance (T_s) will be influenced by the tolerances on any individual dimension<br />
in the assembly, which affect the sum dimension. The relationship between these individual tolerances<br />
and the sum dimension tolerance is known as the fundamental equation. For a particular assembly, there<br />
may be several sum dimensions, each of which will have a fundamental equation of the form:<br />
where<br />
T_i is the ith sum dimension tolerance,<br />
T_j is the tolerance of the jth dimension influencing the sum dimension.<br />
The fundamental equations can be used to generate tolerance chains that can be shown visually using<br />
graphs in which arcs represent chain links and vertices represent the connections between the chain links.<br />
There are two types of tolerance chains of interest, namely the simple chain, in which no element is<br />
encountered twice, and the interrelated chain, which covers all other cases in which at least one endpoint<br />
is encountered twice.<br />
An ex<strong>amp</strong>le of an assembly generating an interrelated tolerance chain is shown in Figure 9.10. The<br />
dimensions S1 and S2 in the diagram denote sum dimensions, while the dimensions D1 to D3 show<br />
part dimensions. The data A and B, the tolerance on the sum dimensions, and the geometric tolerance<br />
of parallelism between faces A-F_1 and B-F_2 are originally specified by the designer when the assembly<br />
model is generated. Note that, due to the against- and clearance-fit spatial relationships and the riveting<br />
of parts B and C into position, any eccentricity between the holes in part A and the shafts of parts B and<br />
C will not affect the sum dimensions. This tolerance chain is interrelated. We see that the tolerances T_S1<br />
and T_S2 are propagated into T_D1, T_D2 and T_D3, while the tolerance TP_S1 is propagated into<br />
TP_D1 and TP_D2 such that TP_S1 � f(TP_D1, TP_D2). Proper datum selection by the designer is<br />
important since this is the basis of the determination of the individual dimensions affecting the sum<br />
dimension and hence the fundamental equations.<br />
The steps required in order to carry out tolerance propagation are as follows:<br />
1. Break down sum dimension to component dimension by analyzing dimension data and spatial<br />
relationships within the assembly that affect sum dimension.<br />
2. Establish a cost function by identifying the contribution of each individual tolerance to the manufacturing<br />
cost of the assembly.<br />
3. Prepare fundamental equations of sum tolerances.<br />
4. Solve fundamental equations that minimize cost function.<br />
It is envisaged that the ability to represent traditional and geometric tolerances will enable the analysis<br />
of the effect of a given geometric tolerance on a particular sum dimension, thus providing this tolerance<br />
analysis module.<br />
© 2001 by CRC Press LLC<br />
T_i �<br />
f_i(T_1,T_2,…T_j,…T_n)