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He demonstrated that for most of the tools analyzed, the load distribution among the broaching sections were quite non uniform resulting in uneven wear, potential quality problems and overloaded sections. He also suggested that the process models can be used to improve the load distribution which may result in shorter tool length, and thus lower cycle time. Following with this idea, Budak and Ozturk [17] presented a model for simulation of the broaching process which can be used for improved tool design. They considered fir-tree broaching as it represents one of the most complex broaching processes due to the geometry and difficult-to-cut work material, waspaloy. In this paper, an optimization method is presented for broach tool design based on the previously developed process and structural models. The paper is organized as follows. The optimization procedure together with the constraints are explained in the second section. The computer implementation is presented in section 3. The procedure is demonstrated on a tool design application. The paper is concluded by the overview of the optimization procedure and the future work. 2 BROACHING PROCESS OPTIMIZATION 2.1 Broaching variables There are several important variables that must be considered in the optimization of broaching tools. They strongly affect the process mechanics and the machined part quality. These variables are interrelated, and the governing equations are implicit and nonlinear. Thus, they cannot be optimized in a straightforward manner. In this section, the important variables considered in broach tool design will be briefly reviewed. There are several limitations related to tool stress, force, power or part quality that will be considered in the optimization process. The difficulty of the optimization procedure for broaching is the number of feasible solutions for a given part geometry. Figure 1 shows general broaching tool geometry. In broaching, the material is removed by successive cutting teeth on a broach tool section. There may be more than one section in a tool set which is moved through the work in a linear motion. Increased size or rise of the tooth with respect to the previous one defines the chip thickness. Similar to other machining processes, chip thickness affects the cutting process strongly, and thus has to be selected properly. Pitch is the distance between two successive teeth, and it determines the number of teeth in the cut at a time. Smaller pitch would reduce the tool length at the cost of increased total broaching force. Another important variable is the gullet space between the teeth, which depends on the tooth height and land, root radius and gullet depth. Chip-to-gullet space ratio is important for chip storage during broaching, and thus it must be maintained at a certain acceptable level. Figure 1: General broach tool geometry. The optimization of the broaching process is complicated due to several reasons. First of all, all of these parameters are interrelated, thus modification of one would affect others strongly. For example, if the pitch is decreased, the number of simultaneously cutting teeth may increase resulting in higher cutting force and power. This in turn may require lower rise to be used. Combination of these may result in a shorter or longer broach section depending on other parameters and the constraints. This is only for a single section. Considering that for complex geometries like a fir-tree there are multiple broach sections with different profiles, the selection of number of sections and properties of each section make the optimization process further complicated. The volume to be broached must be distributed among broaching sections, and there is large number of feasible solutions. However, each section selection would affect the rest of the tools, both in profile and in cutting parameters. This is a unique optimization problem which cannot be addressed using the common methods. This partially explains why this problem has never been attacked in the literature before. The approach used for this purpose will be presented in the following sections of the paper. 2.2 Objective function The objective function is based on the maximum production rate, or the material removal rate (MRR). The MRR depends on the cycle time, and thus the stroke, or tool length, and the cutting speed. In broaching, an economical cutting speed is usually selected for an application based on machinability of the material, tool setup time and wear rate. Therefore, the cutting speed will be assumed as given and will be left out of the optimization process. Thus, the only way to minimize the production time is by using the shortest possible total tool length. Min L (1) or as Ozturk stated [17]: :1:1(1)ssNii iiNiiiwtbnMax MRR Vwnp =+−∑∑ (2) where MRR is the material production rate, V is the cutting speed, w is the cutting depth, ti is the chip thickness, bi is the chip width, pi is the pitch for the ith teeth, Ns is the number of sections and ni is the number of cutting teeth. The tool length can be expressed as follows: ():11s NiiiL np =− ∑