Design of Formed Milling Cutter for Double-Helix Screw Based on Noninstantaneous Envelope Method
First Published January 1, 2013 research-article
Abstract:
The design theory and method of formed milling cutter for double-helix screw of progressing cavity pump are presented. Through analyzing the shape and characteristic parameters of double-helix screw, the helicoids equation and axial curve equation of double-helix screw were established. According to the relative position relations between formed milling cutter and double-helix screw in the machining process, the geometric mapping relationship of screw coordinate system and formed milling cutter coordinate system was established by using the coordinate transformation theory. Based on noninstantaneous envelope method and the meshing conditions between formed milling cutter and double-helix screw, the contact line equations were established by minimum value method. By analyzing the machining errors caused by resharpening the formed milling cutter, the tooth back curve equation was established based on spiral of Archimedes, and the profile equation of formed milling cutter with constant back angle was got. On this basis, the formed milling cutter of processing double-helix screw was designed, and the cutter head and tool post were manufactured, respectively. The measuring results have shown that this method can satisfy the requirements of machining accuracy for double-helix screw. So this is an effective method to get formed milling cutter profile for double-helix screw.
1. Introduction
With the difficulties increasing in oil exploitation, the traditional oil extraction equipment cannot satisfy the requirements of oil production. As one of the rising oil extraction equipment, the progressing cavity pump has been gradually applied in the oilfield exploitation with its superior performance. At present, the single-head progressing cavity pump is used in most oil field. However, theoretical calculation and experimental study show that the double-helix progressing cavity pump has more superior performance than the single-head progressing cavity pump. The output capacity of double-helix progressing cavity pump is greatly increased under the same structural parameters. Under the condition of same output capacity, its structure parameters correspondingly decreased. It is advantageous for improving the stress of rubber stator and prolonging the service life of progressing cavity pump. Therefore, the double-helix progressing cavity pump is the main development trend and research direction of progressing cavity pump [1,2].
Double-helix screw is a key part of the double-helix progressing cavity pump. Its curved shape and machining quality decide the technical performance indicators of progressing cavity pump, such as the meshing condition of the screw and spiral cavity, working pressure, rated flow, volumetric efficiency, and vibration noise. Therefore, the performance of progressing cavity pump depends on the design and manufacture of double-helix screw. There are many kinds of processing methods of screw, and they mainly include milling, hobbing, and grinding. The milling machining is most widely used, because of its high efficiency and good stability [3–7]. In screw milling processing, the precise calculation of cutter profile for formed milling cutter is the key to realize high precision machining, and it is also the foundation of manufacturing formed milling cutter [8–11]. According to the characteristic parameters of progressing cavity pump, Mimmi and Pennacchi had established the screw model and determined the contact line between cutter and screw to get the cutter profile [12]. And they analyzed the screw processing error which was caused by cutter wear [13]. Using the analytic method of coordinate transformation to design the cutter profile of rotary milling, Mohan and Shunmugam solved the over cutting problem of the screw [14]. Using multiple inserted cutter blades in roughing screw, Chiang and Fong established multiple insertion models to process screw, so that each blade of milling cutter has the same wear rate [15]. According to the envelop principle of milling cutter rolling surface and the spiral surface, Wu et al. had achieved the design on the contour of milling cutter in machining complex spiral surface [16]. According to the discrete point data on spiral surface work piece, Zhang had calculated mathematical model of formed milling cutter profile and analyzed the calculation error of formed milling cutter [17]. With the characteristics that the space position of contact line is unchanged, Peng et al. had deduced the geometry condition of helicoids space contact, and it had been applied to the design of screw hob blade [18].
Based on the above issues, a design method of formed milling cutter for double-helix screw of progressing cavity pump is proposed. Firstly, the helicoids equation and the axial curve equation of double-helix screw were established. Secondly, based on the noninstantaneous envelope method and minimum value method, the basic profile equation of formed milling cutter was established. By analyzing of machining error caused by resharpening formed milling cutter, the tooth back curve equation of formed milling cutter was established, and formed milling cutter profile equation with constant back angle was got. Finally, the design and manufacture of formed milling cutter are done to verify the design correctness.
2. Parametric Modeling of Double-Helix Screw
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