End mill design and machining via cutting simulation
Introduction
High-speed machining (HSM) technology using ball-ended milling tools has been widely adopted due to its various advantages, such as productivity, machining accuracy, surface quality, and production cost. The cutting tool used in a CNC (Computer Numerical Control) machine plays a vital role in accomplishing a successful HSM process; it directly affects the quality of a machined surface. In addition, it is practical to develop cutting tools with high performance and long product life at a low price [1].
The material, coating, and shape of an end mill are key factors in improving cutter performance, where the shape mainly affects the machining accuracy and dynamic stability. The shape elements of an end mill include relief angle, rake angle, and helix angle; these are the main determinants of machinability and they are interrelated [3].
It is difficult to model the exact three-dimensional shape of an end mill because a certain part of the shape (e.g., the helical groove) is not determined until the actual machining stage. If we have no three-dimensional solid model of the designed end mill, we need to make a physical prototype and carry out cutting tests in order to improve the cutter shape [2]. Therefore, it would reduce the cost and time for designing an end mill if we could use its three-dimensional solid model. In addition, it is also beneficial for the required grinding wheel geometry and CL data to be computed using the solid model. One of the methods to predict a proper three-dimensional shape is cutting simulation: a helical groove shape and sectional profiles can be obtained by grinding simulation for the given wheel geometry and CL data (i.e., wheel paths), where a series of Boolean operations between the wheel and the cylindrical blank (i.e., raw stock) is performed. Major design parameters–rake angle, inner radius and cutter width–can then be evaluated from the sectional profile curve, which facilitates digital interrogation of cutter geometry and prediction of the required wheel geometry and CL data computation for machining as well.
It is also required that the machining condition (i.e., wheel geometry and positioning data) to fabricate the end mill that satisfies given dimensional parameters (e.g., rake angle) be determined, which is called the ‘inverse problem’ [2]. It is necessary to predict the helical groove shape as accurately as possible because it determines the rake angle, etc. However, it is the combination of the grinding wheel geometry and its positioning data that generates the helical groove shape, which makes it difficult for a designer to predict the shape analytically. So it is usual for a designer to determine the required machining conditions using a trial and error method that requires many very tedious hours of manual work. More efficient way of predicting machining conditions should be presented.
There are a few previous studies on predicting the profile curve for the helical groove of an end mill, which can be categorized into two methodologies: direct method and analytical analysis. The ‘direct method’ approximates the grinding wheel as a set of a finite number of thin disks whereby the intersections of primitive wheels and the workpiece are calculated to obtain a profile curve [2], [3], [8], [9], [11], and leads to graphical visualization [4]. Alternatively, the latter method tries to find the profile curve based on mathematical constraints such that the common normal vector at the contact point of a wheel and the workpiece should meet the rotational axis of the wheel [5], [6], [10], [12].
Clearly, the cutting simulation approach in this paper is basically same as the direct method in a respect that it tries to obtain a machined result. However, the main difference is that our approach creates a complete three-dimensional solid model, and thereby facilitates accurate geometric analysis but also further engineering analysis such as with the finite element method (FEM).
Considering the inverse problem, we can find relevant works for finding wheel setting conditions and wheel geometry data [2], [3], [7] by use of a numerical search method. Some previous work successfully demonstrated the practical use of developed software by adopting the direct method [2], [3]. In our approach, the geometric interrelationship among the design parameters of an end mill, a grinding wheel and wheel positioning data was investigated; thereby a straightforward search becomes possible. In addition, the cutting simulation approach was adopted in calculating the geometric parameters of the end mill during the search flow. So it possibly performs a more efficient and accurate prediction of the required wheel geometry and positioning data. Section 2 describes the basic dimensional parameters and their relationships in a typical end mill and grinding wheel, followed by three-dimensional solid modeling of the cutter using the cutting simulation mentioned in Section 3. The prediction of wheel geometry, positioning data, and grinding tool-path generation are presented with some illustrative examples in the following sections.
Section snippets
Dimensional parameters
Fig. 1 and Table 1 show the geometric dimensions that define the shape of end mills. It should be noted that the helical groove and neck groove shape will not be determined by the design parameters but by other factors, such as grinding wheel shape and grinding positions. Therefore, it is not straightforward to analytically verify the dimension of the helical flute and neck groove shape (see Fig. 2).
Cutter shape modeling
The three-dimensional shape of an end mill is constructed by sweeping the sectional profile curve of the helical groove along the predefined helix (see Fig. 2). We adopted the cutting simulation approach where the end mill shape is divided into shank, neck, and flute. First, the shank model is based on the dimensional parameters of the wheel and the relative position of the grinding wheel and workpiece (see Fig. 3). The neck is then modeled by a cutting simulation of the blank and grinding
Prediction of wheel geometry and positioning data
It was shown in Section 3 that we can construct a solid model of end mills by simulating the machining operation where the machining conditions–the grinding wheel geometry and the CL or wheel positioning data (i.e., wheel setting angle, center point and offset value shown in Fig. 3(b))–are provided. Conversely, it is also a requirement that we should determine the machining conditions to fabricate an end mill that satisfies given dimensional parameters, such as rake angle, etc. It is well known
Grinding tool path generation
In general, NC (numerical control) machining of a target shape for the given cutter geometry requires a computation process of CL (cutter location) data that will be post-processed into NC codes for a specified NC machine. The CL data at a given CC (cutter contact) point are defined by the cutter position and orientation (i.e., cutter axis vector). Therefore, tool-paths for the variable-axis machining are obtained. Moreover, the machining of helical groove shapes in drilling or end mills
Illustrative example
We developed the described system on a basis of Unigraphics® Open API in an MS Windows® environment. The main functions applied in this system include end mill shape modeling, prediction of wheel geometry and positioning data, tool-path generation, and verification that can be summarized as follows:
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Shape modeling by cutting simulation
It constructs a solid model in end mills by simulating real machining operations where the geometry and positioning data of the grinding wheel (i.e., machining
Conclusions
We developed an end mill design methodology using cutting simulation, in which a solid model of the cutter was obtained. Also, the cutter geometry (e.g., rake angle) can be interrogated. The solid model facilitates graphical and numerical verification of the cutter shape without constructing a physical prototype. It can also be used as an input model for FEM analysis, etc.
Secondly, we investigated the relationship between the cutter geometry, wheel geometry, and positioning data. A simple
Acknowledgements
This research was supported by the Program for the Training of Graduate Students in Regional Innovation (No. AROOKB-2201-220107) conducted by the Ministry of Commerce, Industry and Energy of the Korean Government.
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