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(9) where Fmaxpp is the maximum calculated cutting force on a tooth and Ftotalmax is the maximum possible cutting force, i.e. force available on the ram for a particular cutting speed. Step 6: (Selection of the number of simultaneously cutting teeth) mpm found in step 5 is chosen as the number of teeth in cut if it is greater than or equal to mmin or smaller than or equal to mmax. determined in step 2. If the force constraint allows cutting with more than mmax,, then mpm is taken as mmax, and we proceed to step 8. But if the force constraint requires mpm to be smaller than mmin then mmin is chosen as mpm, and we proceed to step 7 for a modification. Step 7: (Modification of the rise) In step 6, it was found that the force constraint required the cutting teeth number to be less than mmin. But, because of the pitch length constraint the minimum number of cutting teeth is mmin. Thus, mmin is to be selected as mpm. However, when this modification is done, the force per tooth must be decreased in order to remain within force constraint limits. That can be done by decreasing the chip area per teeth. Hence, the tooth rise is decreased. We may proceed to step 8 with the new values. However, we may also try width pision for this section which is another way of decreasing the chip area per tooth Step 8: (Pitch limits) Minimum and maximum possible pitch values are determined based on the simultaneously cutting teeth determined in Step 6. Step 9: (Graphs) The graphs that show stress, gullet-chip volume ratio and force variations are drawn. These variations are also expressed in terms of best-fit equations. Step10: (Gullet-chip volume ratio control) Chip-to-gullet volume indicates the space availability for the chips in the gullet. Monday [9] recommends this ratio to be less that 0.35 for good chip control. The volume ratio for the first tooth is checked. If there is no problem with the ratio, we directly proceed to step 11. But if the ratio is bigger than 0.35 then modifications must be done. First, the pitch is increased step by step until it reaches the value of maximum pitch corresponding to mpm and each time graphs in step 9 are updated. If the pitch modification is not enough to reduce the volume ratio to the acceptable levels, then the height modification starts each time turning back to step 9. Step 11: (Stress control) Tooth stress is checked. If it is higher than the acceptable stress level, then the rise is decreased. Step 12: (Number of teeth) From the force and stress variation graphs in step 9, maximum force level for each section is identified. Of course, it would be very much desirable to maintain uniform stress and force within a section, and also throughout the whole cycle. However, this is usually not possible due to the constraints. The number of the total teeth for a section is selected according to the force, stress and volume ratio predictions, and the geometry to be cut. The objective is to reach the maximum allowable force level, but if that is not possible a new reachable maximum force level is selected/ Based on this analysis, a section may be pided into several subsections. Then, each subsection is analyzed and designed separately. After a section is designed completely, the machined part geometry is checked to see if it has reached to its final form. If there is more material to be removed, we go back to step 4 to design the next broach section. If all cutting is over, the final design is used for simulations.
There are some special cases which may need additional steps or rules as they may yield better results. For example, if we need to use a small rise within a section because of the constraints, a width pision option in that section may produce better results. The tooth rise option 1 is used for that new section, and the same steps are followed step by step starting from step 4.
3 COMPUTER IMPLEMENTATION The models and algorithms developed are being implemented in computer program for practical use. The program will have two main functions when completed: Simulation of an existing broaching tool and optimal tool design for a specified work geometry, material, machine etc. The first, i.e. the simulation, part of the program has been completed and will be briefly described here. The program can be used to simulate the process with up to 20 tool sections. First of all, the geometry of the each section is entered. The window which is used to enter the general properties for each section can be seen in figure 5. In order to make this simple and fast, some common geometry templates are used in the input section of the program. Using there templates even very complex profiles such as fir-tree can be entered easily. Some profile examples can be seen in figure 6. Figure 5: General section properties window. Figure 6: A group of help window examples. Cutting force and tooth stress are simulated and displayed in the program.