Comparison Of Screw Rotor Profiles From A Manufacturing Perspective

Two different rotor profiles are compared based on their manufacturing characteristics. The comparison is based on application of a profile manufacturing simulation which is used to analyze the effect of variability in the profile finishing. A Monte Carlo model is used to create sample outputs of the simulated manufacturing process with defined elemental process step capabilities. Rotors are compared on the basis of the difference in the number of useable profiles in a production run of 1,000 samples. INTRODUCTION A good rotor profile represents a balance between characteristics such as blowhole size and seal line length on the one hand and manufacturability on the other. We need the right design features for performance and noise considerations. At the same time, we must insure that the profile can be made economically and consistently to our target tolerances. In addition to a capable rotor finishing process, it is important to understand the interactions between the profile and the manufacturing process so that during the profile and tool design process, each can be rationalized to the other to provide the best rotor possible. Some of this understanding can come from use of a computer simulation of the rotor profile finishing process. Use of this process to study the effect of extremes in the variation of selected manufacturing process parameters on rotor profile form and rotor pair clearances has been reported in /1/ and /2/. For this study, a different approach is taken. Here, we will use the simulation to look directly at the effect of random manufacturing process variations on individual profiles produced over time – the time span being represented in the study by the simulation of the manufacture of 1,000 profiles. In this study, we will simulate the manufacture of male and female rotors of two different profile designs. The profiles are designated K and E. The E profile is an older design used in R22 compressors; the K is a third generation design for R134a compressors. The K is a derivative of the J profile which was compared to the E profile in /2/. Both profiles are defined by first specifying the shape of a generating rack, which is then used to generate the theoretical male and female rotor profiles. These profiles are then modified to produce a desired rotor pair clearance distribution. Simulation of 1,000 samples of male and female rotors of two different designs means we will have 4,000 separate profiles to look for this study. Thus, it becomes necessary to define rotor quality measures that are simple yet meaningful. A clearance limit quality chart and a drive band location parameter are introduced in this report to serve this purpose. The manufacturing process simulation is briefly reviewed in the next section. Profile quality assessment methods are then introduced followed by a discussion of the set-up of the Monte Carlo model of the process. Results of application of the simulation to the K and E rotors are then presented using the quality measurements proposed. The paper concludes with some closing comments about the rotors and the use of the simulation process. PROFILE FINISHING PROCESS SIMULATION The profile finishing process simulation has been described in /1/ and /2/ so only a brief review will be presented here. As reported in these references, the original modeling system was made up of four computer programs. These programs in the simulation system are: a) Rotor profile design Theoretical profiles and profiles modified to provide for the desired rotor pair clearance distribution are computed. Profile data is written to files for use by other programs. b) Cutting tool design The shape of the milling cutter or grinding wheel profile is computed from the profile data and specifications of nominal manufacturing process parameters. c) Profile finishing simulation The tool form and specified values of the manufacturing process parameters are used to compute a rotor profile form. If the nominal tool form and nominal values of the process parameters are used, the result is a computation of the nominal profile defined in program a). However, if variations from the nominal process are defined, a different profile will result. d) Profile comparison This is a “numerical CMM”. The profile as made in program c) is compared to the nominal defined in program a). Deviations are computed and the results stored in files for subsequent analysis. For the analyses in /1/ and /2/, a limited number of values for selected manufacturing process parameters were evaluated and the programs c) and d) were run manually to simulate the process. For this study, 4000 separate cases are to be run, so a new program was written. This program combines the functions of the profile finishing and profile comparison steps. The program reads the cutter profile and nominal rotor profile data, then reads from a file of manufacturing process parameter specifications. This new input file has one line for each profile to be made. The values of the process parameters are read from one line at a time; the profile is made, compared to the nominal and results are written to a data file for subsequent processing. This process will make as many profiles as there are input lines in the process parameter definition file. The methods for calculation of the rotor and tool profiles are those developed by Stošić, et al /3/. There are numerous manufacturing parameters and three have been selected for this study. The tool and rotor engaged for the profile finishing operations are illustrated in Figure 1. The cutting wheel setting angle, β, the location of the wheel on its spindle, Z, and the distance between the wheel and rotor axes, R, are the three manufacturing process parameters chosen for investigation. These are the same parameters used in the study reported at the 2000 International Compressor Engineering Conference at Purdue /2/. Figure 1: Rotor Profile Manufacturing Setup and Parameters The approach taken to selection of the process parameter variation is also the same as used in /2/. The K profile design is selected as the baseline. The manufacturing simulation is then used to determine the amount of variation in each of the parameters that will, alone, produce a maximum deviation of 10μm Z Z R Profile Finish Tool