Civil Engineering Reference
In-Depth Information
The use of the tolerance is inevitable due to the impossibility of producing two parts that have precisely
the same dimensions. This could be attributed to the fact that many uncontrollable or random factors
often exist during the production process. Tolerances specified on the blueprint by design engineers
are specifications targeted to ensure a product's functional performance, and are often designed in
such a way that the critical dimensions are specified with strict allowable tolerances, which then become
the quality criteria of the final product inspection. Assigning tolerance to the nominal dimension of
a component is one of the important factors to ensure that the product assembled will be within the
functional requirements, and assembly tolerance stackup can be either worst-case or statistical. The
worst-case tolerance stackup assumes that all components are produced within the tolerance limit; as
a result, 100% inspection is needed to eliminate the possibility of using any nonconforming component
in an assembly. Mathematically, the addition of the component tolerances shall be less than or equal
to the assembly tolerance specification. On the other hand, the statistical tolerance stackup accepts
slight defective assemblies; this matches the reality more closely. However, the assembly tolerance must
be normally distributed and the component dimensions must be independent. Mathematically, the
square root of the addition of the squared component tolerances shall be less than or equal to the
standard deviation of the assembly tolerance. When the finalized blueprints of components are dis-
tributed for production from the research division, the process engineer designs a sequence of oper-
ations in order to produce the component as required. This is called process planning, which includes
various tasks such as design of jig and fixture, tooling, NC program, standard operation sheet, etc.
One of the important tasks in planning a process is the assignment of the tolerance to the working
dimension of each operation. The process tolerance represents the control limits that should be strictly
complied to by each operation to ensure that the final accumulated dimension of the component is
within the blueprint specification. The amount of stock removal needed for each operation to reach
the required precision, the machining accuracy of the equipment, the identification of the tolerance
chain linking the consecutive reference and processed surfaces, and the tolerance stackup resulting
from a series of operations must be considered while assigning process tolerances to various operations.
The machining accuracy refers to the limitation or attainable tolerances of individual operation, and
is frequently expressed in terms of the upper lower tolerance bounds. Specifically, these tolerance
bounds represent the economical precision that can be held by a specific machine, and the engineers
should design products with these tolerances in mind. Process tolerances are usually designed based
on intuition and best guess of the engineers, thus being vulnerable to overestimation or underestima-
tion. Loosely estimated tolerances may cause problems in the succeeding operations, while unneces-
sarily tight tolerances, on the other hand, escalate the manufacturing cost. One of the techniques used
to widen the overestimated tolerances is called tolerance chart balancing, which can be performed
either manually [11, 12, 13] or mathematically [2, 4, 14, 15, 16, 17, 18, 19, 22]. Among several other
techniques, Nagarwala et al. [2] have proposed a slope-based method for solving the tolerance-process
selection problem, wherein the cost function is approximated by a sequence of linear functions. Ngoi
and Seng [4] designed tolerances by concurrently minimizing the nonlinear manufacturing cost and
maximizing the working dimensions. Wei and Lee [10] have included the process capability index of
the machinery in their tolerance design problem; therefore, the scrap rate of each operation and the
entire process can be predicted with respect to the tolerances assigned. Ngoi [14] has proposed a linear
programming model, coupled with identification schemes of tolerance chain, to determine the total
additional tolerances to be added to the existing process tolerances. A weighting system is involved to
evaluate the relative importance of operations. Unfortunately, this model does not consider the process
capability of the equipment, thereby rendering the allocated tolerance to be uneconomic. Lee et al.
[18] have used nonlinear design functions to determine the coefficients of the nonlinear cost equation.
Lin et al. [19] have proposed a tolerance-process selection formulation using nonlinear objective
function and constraints, wherein a genetic algorithm is applied to obtain the least-cost tolerances
allocation. This article limits the discussion to process tolerance; therefore, the tolerance, hereafter,
means process tolerance.
