# A Novel Optimization Design Method of Form Ginding Wheel for Screw Rotor  
[PERSON]  
1 Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing 400067, China; [EMAIL_ADDRESS]  
[PERSON]  
2 State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China; [EMAIL_ADDRESS] (Q.T. ); [EMAIL_ADDRESS] (P.L. ); [EMAIL_ADDRESS] (W.L.) [PERSON]  
3 Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore 31  
rotor with high profile precision, it is essential to optimally design the profile of the form grinding wheel through its installation parameter settings. Both the design principle of the screw rotor form tool and the theoretical mathematical modeling of the tool profile design have been extensively studied in the existing literature. [PERSON] and [PERSON] [PERSON] and [PERSON] (2005) extended an enveloping method to gear design and manufacture. Subsequently, [PERSON] (2005) advanced the design principle by figuring out the governing equation describing the contact status between the form tool and screw rotor. [PERSON] et al. (2007) proposed a method to determine the theoretical shape of the disk cutter for a screw pump rotor. [PERSON] and [PERSON] [PERSON] and [PERSON] (2008) demonstrated a new method of grinding process that could efficiently make the concave profile of the worm thread smooth. These studies reviewed the methods used in the design of screw rotor form tools in detail, but they did not discuss the selection methods for the installation parameters. In another sense, these works also provided some reference for follow-up studies of the design of the form tool for screw rotors. For example, [PERSON] et al. [PERSON] _et al._ (2008); [PERSON] _et al._ (2008) proposed a method to determine the grinding wheel profile and its setup for use in finishing cylindrical gears with an evolvent profile by using the meshing principle and enveloping theory. [PERSON] et al. [PERSON] _et al._ (2008), who proposed a radial-ray shooting (RRS) method to simulate the form grinding process for screw rotors, obtained an accurate simulation profile for screw rotors. Based on discrete point teeth and the gear meshing principle under stable-contact conditions, [PERSON] et al. [PERSON] _et al._ (2008) proposed a form-position geometric method. With the proposed method, the precise design of a cutter at the cusp of the screw profile could be solved. Further, a novel calculation method was proposed by [PERSON] _et al._ (2010), who calculated the wheel profile using a predetermined groove model and wheel axis setting parameters. While these studies have provided valuable information about the design principles used in form tools, they have not reported on the effect of installation parameters on the profile error in the process of form grinding. In contrast, extensive studies have reported on the profile accuracy (or error) of screw rotors. For example, [PERSON] (2008) calculated the tool wear amount of a milling cutter in screw rotor machinery and estimated errors using a tool-rotor transformation method. In this method, the relative movements of the tool and screw rotor were taken into consideration, since different movements would lead to different tool wear. To investigate the influence of grinding wheel installation on the rotor profile, a numerical method considering various installation errors (e.g., installation angle error, center distance error, and axial position error) was presented by [PERSON] et al. [PERSON] _et al._ (2010). Using the computer numerical control (CNC) method, [PERSON] et al. [PERSON] _et al._ (2010) investigated the precision grinding via an analysis of the major grinding parameters (e.g., center distance, swivel angle, and initial phase angle) and screw rotor profile. The authors managed to improve the screw rotor profile accuracy with a novel grinding wheel segmentation dressing method. Grinding experiments successfully verified the correctness of the results evaluated by this method.