Development Of A Design For A Tool Machine

Development of a Design Tool for Machine Tools Combining Conceptual Design Support and Detail Design Method
Nozomu Mishima, Advanced Manufacturing Research Institute, AIST, 1-2 Namiki, Tsukuba, Ibaraki,305-8564 JAPAN T: +81-29-861-7227 F: +81-29-861-7201 Email: n-mishima@aist.go.jp

1 Backgrounds
Machine tool design has been a rather experience-based procedure. However, the products machinedby those machine tools tend to have more varieties and quantity deviation. In response to the situation, not only the products design, but also the machine tools design should have efficiencies. For that purpose, a design tool which can review machine tools design in its early stage whether the design is appropriate or not, will be helpful. The design tool does not need to be too accurate inpredicting machine tool performance. But it should review machine tool design without prototyping or precise modeling. In order to support machine tool design, the author proposed a design tool [1][3] combines the form-shaping theory [4] of machine tools and the Taguchi method [5]. Originally, the form-shaping theory assumes that the structural components of the machine tool are rigid objects. However,deformation of the machine tool structures such as deformation caused by static force or heat affect the machine tool performance significantly. The proposed design tool offers a simplified method to consider those deformations of machine tool structure, combining with component errors which are also critical for machine tool performances. By this extension, the design tool can clarify whicherror factors of machine tools have considerable effect on the performance. By doing this, it can support systematic design of machine tools.

movement parallel to the x-axis being 1, and so on. When the homogeneous transformation matrices Ai are represented by the transformations ji, (= 1 to 6), and the amount of each motion is represented by li, we define A(i)(ji)(li) as the expression of thematrices. Vector r0 represents the relative displacement between the product and the tool, and the tool shape vector

rt

is also defined. The relation between r0 and

rt

is as given by equation (1), and r0 is the definition of the

form-shaping function that expresses the cutting motions of the machine tool. The theory that expresses cutting motions mathematically is called form-shapingtheory. Actual machine tools have imperfect alignment, and experience thermal deformation, wear, and many other sources of error. In order to describe actual cutting motions, one must take these errors into account. Such errors may for convenience's sake be treated as errors in transformations between elements. I defined another homogeneous transformation matrix A i (eq. (2))to generally representtransformation error between elements. By inserting the error component matrix A i between A(i)(ji)(li) and A(i+1)(ji+1)(li+1) into equation (1), the form-shaping function including errors, r 0 is written as equation (3). The form-shaping error function r0 , expressing the error as a quantitative deviation from the target value, is defined as the difference between the formshaping function with andwithout errors, as equation (4). The form-shaping error function r0 is a 4 dimensional vector which has error lengths in the x, y, z directions for the first three elements. The last element of r0 is 0, because
r0 is defined as the difference between r0 and r 0 .

2 Design evaluation method
A machine tool structure can be thought of as a chain of directly linked rigid components extendingfrom the product through the cutting tool. An orthogonal coordinate system Si corresponding to element i (i = 0 to k) is defined. The translation from Si to Si+1 is represented by a coordinate transformation. Form-shaping theory represents these respective coordinate transformations by homogeneous transformation matrices [7]; Ai. In an ordinary machine tool, Ai is represented by a parallel...