The development of gears technology used in rotary tables

Abstract

Abstract. The paper presents technology of forming of a face gear cooperating with cylindrical worm in spiroid gear drive application for rotation table. The method is based on application of a disc tool instead application of a hob. The solution is possible after application the CNC milling machine with five axis numeric system control. The method of forming face gear proposed in this article is based on application of the disc tool with a single blade edge and CNC milling machine. The method of forming the face gear cooperation with cylindrical worm on CNC milling machine with continuous divide and the scheme of the process kinematics have been presented in the paper. IntroductionInvention of face worm gear drives with conical worm by Saari [1] was a substantial contribution. Face gear cooperating with cylindrical worm in spiroid gear drive can be cut with conical or cylindrical hob cutter [1,2,3,4]. Litvin and coworkers [5] had proposed a tilted head-cuter for forming of face gear with cylindrical worm. Grajdek [6] developed a new technique of cutting a face gear on a CNC machine. He used the 4-axis vertical CNC milling machining incorporate a rotary table and a NC spindle. The generations are performed by a tilted tool edge with straight line profiles of blades.The authors of the paper [5] point out to big problems with sharpening hobbing cutters with small radius blades used for forming face gear and hob scale error that are transferred onto the gear. There is also a possibility of cutting the face gear with the use of a disc tool with a single blade tool [7,8,9]. For generation face gear used the 5-axis vertical CNC milling machine incorporate a rotary table and a NC spindle. The generations are performed by a tilted tool edge with straight line profiles of blades. Due to addition two rotational axes in 5-axis machining enables forming face gear and taken high surface quality. For numerically controlled milling machine a face gear can be shaped with different front lines of teeth [7]. While notching the teeth, workgroups of machine performs movements at a constant speed, the tracks are rectilinear or rotary (NC rotary table, spindle tool).Face gear cooperating with cylindrical worm in spiroid gear drive may have different type of involute teeth line used (elongated, shortened) with a modification of the teeth line and profile, in order to avoid edge contacts. All those involute teeth lines in face gear variations can be cut with the use of a disc tool on CNC machine tools.The Company Tool Works in Illinois -USA manufacture different types of spiroid gears. Figure 1 illustrates the idea of construction of a spiroid gear drive type duplex with two face gears cooperation with cylindrical worm application for rotation table.

Brief note on match and miss-match uncertainties

“…In case 𝓌 is unobservable, one might use disturbance estimator provided that the bounded of 𝓌is known (perhaps within a closed unit ball 𝓌 ≡ ℬ). Figure 3 shows affine function (2) where 𝓌 enters through the same input channel as 𝑢.…”

“…Uncertainties may introduce nonlinarity and need linearization to facilitate stabilization process [1]. Considering a mechanical rotational system in practice, the uncertainties in the modeling may be contributed by the backlash in the gearing teeth [2]. Many stabilization approaches available in the literature can be opted to perform tracking tasks as well as regulation tasks for such systems.…”