# A Novel Optimization Design Method of Form Ginding Wheel for Screw Rotor
## 5 Conclusions  
This paper proposed a novel optimization design method of form wheels that considers installation parameters. This method has been employed to select the correct range for the installation angle and center distance. According to coordinate transformation and engagement theory, a profile generation model was established, based on which numerical simulation was subsequently carried out. The numerical cases show that the slope and curvature of the grinding wheel shaft profile as well as the length of contact line will change with the installation parameters. Grinding experiments for a female rotor by introducing different installation parameters were performed in order to verify the results of the numerical cases. Several important conclusions are drawn from this work, as follows:  
1. The installation parameter optimization design model was established based on geometric transformation and engagement theory. The ranges of the installation angle and center distance satisfying meshing conditions were obtained.
2. The characteristics of the contact line and the profile features of the wheel grinding under different installation parameters were investigated. The numerical relationship between the slope and curvature of the shaft section profile of the grinding wheel, as well as the length of the contact line  
Figure 12: The effects of the installation angle on screw rotor profiles (mm). (**a**) Installation angle, \(44.09^{\circ}\). (**b**) Installation angle, \(45.09^{\circ}\). (**c**) Installation angle, \(46.09^{\circ}\). (**d**) Installation angle, \(47.09^{\circ}\).  
and the installation parameters have been clarified. Error-sensitive factors were also identified. The installation angle is a relatively sensitive factor that must be controlled in priority.
3. The evaluation criteria for the profile characteristics of the grinding wheel were established, and female rotor grinding experiments were conducted. The new installation angle was compared with the empirical approach (lead angle), and the profile precision was found to have increased from \(\pm 8\)\(\upmu\)m to \(\pm 6\)\(\upmu\)m.  
The above conclusions show that the proposed optimization design method is accurate and reliable for selecting the precision installation parameters for a certain twin screw compressor's profile. Previously, there was no applicable method and theory for selecting the installation parameters of the forming tool in the process of screw rotor manufacture, which leads to the difficulty in improving the machining accuracy. In this paper, the internal relationship between the grinding performance of a forming wheel and its installation parameters is studied for the first time, and an optimization design method of installation parameters is proposed. This paper also provides a new viewpoint for the selection of installation parameters for form tools used in form machining. In future work, the optimization design method could also be extended to other types of form machining. Practical optimization design software for this approach could also be developed to improve the efficiency of precision design of form grinding wheels.  
Conceptualization, Z.L.; Data curation, Z.L.; Funding acquisition, Q.T.; Investigation, N.L.; Project administration, Q.T.; Validation, P.H.L. and W.L.  
This work was financially supported by The National Key Research and Development Program of China (grant number 2018 YFB1701203), the National Natural Science Foundation of China (grant number 51575069), the Doctoral Funding of Chongqing University of Chongqing Technology and Business University (grant number 1956029), The opening project of the international joint research center for health care in service of china-canada equipment system (grant number KFJ)2019061).  
The authors declare no conflict of interest.