19-01-2013, 11:53 AM
Geometric parameter optimization in multi-axis machining
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ABSTRACT
This paper presents a systematic method for the determination of optimal geometric machining
parameters in multi-axis machining. Machining accuracy is considered to be determined by a set of
geometric parameters: the design parameters of the cutter, the positioning of the cutter, the orientation of
the cutter etc. First, we formulate the general nonlinear constrained optimization model of the machining
process. The optimal machining result is expected to produce the least deviation between the designed
surface and the actual surface. This objective is accomplished by minimizing the deviation between the
designed surface and the actual surface during machining. The details of how to characterize and calculate
the deviation is then discussed for both ruled surface milling and general free-form surface milling. The
swept surface is developed based on robotic manipulation and is used to model the actual surface. A
signed distance function is constructed to perform the comparison which returns the signed distance
from each sampled point to the designed surface. The direct search algorithm (Nelder–Mead simplex
algorithm and pattern search algorithm in this paper) is used to solve our optimization problems due to
possible discontinuity of the objective function and large nonlinearity of the problem. Three numerical
examples and necessary comparisons are given to demonstrate the effectiveness of our method. The
first example shows the generation of the swept volume of a filled-end cutter.
Introduction
Multi-axis NC machines have vast applications in modern
industry especially in machining workpieces with sculptured
surfaces such as ship impellers, turbine blades and propellers
[1–3]. Engineers are now faced with more choices of machining
parameters such as the setup of the workpiece on the mounting
table, and positioning of the cutter. They can even choose some
specially designed cutters. Different combinations of machining
parameters might produce large variations in the final product
quality. However, most of current CAM software has not yet
proposed a systematic method of determining optimal machining
parameters. Experimental study before actual machining is timeconsuming
and not cost-effective. And machining planning based
on experience may not fully exploit the power of available
machines to achieve the highest machining accuracy.
Calculation of objective function for general free-form surface
machining
Free-form surface milling involves surfaces with relatively
complex shapes. As pointed in Section 2.1, deviation analysis
between the desired surface and the swept surface requires large a
number of distance calculations and analysis of geometric features.
Using the method in Section 2.2.1 is not flexible in dealing with
this situation. A robust method is expected for the evaluation of
deviation for optimization in this type of milling. A signed distance
function has been proposed in Section 2.1 to define the deviation.
The main job of formulating the objective function is to obtain this
signed distance function ary.
Cutter geometry
In order to compute the swept volume, the cutter shape definition
and corresponding properties should be known. Commonly
used cutters can be classified into four types: ball-end mill, flat-end
mill, tapered-end mill, and fillet-end mill. All four types of cutter
can be derived from the definition of a generalized cutter which is
often referred to as an APT-like cutter (see in Fig. 4
Conclusion and future work
Machining accuracy is related to a set of pre-determined parameters
such as the parameters of the cutter, positioning of the cutter,
and cutter orientation. This paper focuses on geometric machining
parameter optimization to improve machining accuracy. The problem
of geometric machining parameter optimization is formulated
as a constrained nonlinear programming problem. The goal is to
maximize the similarity between the desired surface and the actual
surface under constraints such as non-interference conditions,
geometrical design requirements of the cutter, and scallop height
requirement. Here, the signed distance function is constructed to
calculate the point-surface distance which is used to describe the
similarity. The pattern search with a Nelder–Mead simplex algorithm
can be applicable to solve the nonlinear programming problem
formulated in this paper. Comparing with traditional iterative
search algorithms, the proposed examples in this paper show that
the pattern search algorithm is robust, easily implemented and
more likely to give a global minimum in dealing with highly nonlinear
problems.