This paper presents a study regarding the gear hob’s rake face grinding possibilities and its consequences. A simple theoretical lined surface is considered. The mathematical model of the reciprocate ...meshing of surfaces was applied. It was proven that the proposed form of the rake face cannot be obtained because an undercut of inacceptable extent occurs. It is also proven and sustained by CAD modeling that using a simplified, flat grinding disk, the undercut is avoided, but the phenomenon of transection appears.
The present work aims to provide the readers with a bird’s-eye view of the general domain of cylindrical gear manufacturing technologies, including the cutting tools used, and related topics. The ...main scientific sources are explored to collect data about the subject. A systematization of the scientific works is completed, to emphasize the main issues the researchers have focused on in the past years in the domain. Several specific aspects are investigated: chip-forming process, cutting tool lifetime, the materials used to produce gear hobs, temperature and lubrication, the cutting tool geometry, cutting parameters, design methods, and optimization. Some gaps in the research have been identified, which are mainly related to the gear hob’s design. These gaps, the organization of knowledge, the current requirements of the industry, and the actual socio-economic priorities form the basis for identifying new scientific research directions for the future in the area of spur gears manufacturing technologies and cutting tools. The main output of this work is a frame to guide the development of scientific research in the domain of spur gear production.
Hobbing is one of the crucial gear manufacturing processes with high precision and high efficiency. In order to improve the accuracy of hobbing and hob relief grinding, more precise grinding wheels ...are demanded for relief grinding in the production of gear hobs. In this paper, a new and accurate mathematical method for calculating the axial profile of grinding wheel based on the corresponding gear hob to be ground is proposed. Considering that most researches have been conducted to focus on the optimization of hob geometric feature and only can be applied to a specific type of hand of helix and rake angle of gear hobs. The method in this paper can be served as a general algorithm for generating axial profile of grinding wheels on the basis of the spatial envelope theory, the principle of coordinate system transformation, and studies on normal profile of single-tooth. The accuracy of grinding hobs is based on applying the approach in practical manufacturing. Taking two typical different kinds of pre-grinding gear hobs as examples for calculation and experiment, the results of tooth profile errors strengthen the position that the validity and feasibility of this method, it can be employed for gear hob design and grinding processing.
In order to improve the cutting performance of toroidal worm gear hob and the tooth surface accuracy of hobbing worm gear, to control the absolute value of the side rake angle of each cutter tooth to ...be smaller and more balanced on the left and right sides, a method of developing the rake face of toroidal worm gear hob with spiral groove by using conical production surface is proposed. According to the theory of gear meshing rationality, the mathematical model of the rake face is established. The analysis and calculation example results show that the absolute value of the rake angle on both sides changes with the transmission ratio coefficient. By studying this change law, the optimal milling transmission ratio coefficient k = 0.886 is obtained. Meanwhile, the corresponding absolute value of the rake angle is between ±4.5°, which reduce the absolute value of the rake angles on both sides of the cutter teeth effectively and make the rake angles on the left and right sides be more balanced. The spiral groove was simulated, and the rake angle was measured in the simulation software. The measured results are consistent with the calculated results, which prove the correctness of this method.
Compared with single-enveloping worm gearing, double-enveloping worm gearing can provide the same load capacity with a more compact volume and a higher efficiency. However, that the relief grinding ...of its hob can not be finished automatically till now limits its applications because all of the cutting edges on the hob have different shapes and spiral angles. In this paper, a pioneering method is proposed to relief grind the planar double-enveloping worm gear hob by adding two additional translational motions of the generating plane in addition to the rotation motions of the hob and the generating plane. A mathematic model is built for the relief grinding of the hob. A series of related data of the four motion parameters when grinding different points of the land edges of the different hob teeth are solved out, and the relief surfaces of different hob teeth can be ground continuously by using the data. The method is verified by using software VERICUT. Furthermore, a worm gear hob is relief ground on a four-axis CNC enveloping worm grinding machine by using this method.
The performance of hourglass worm gear hob is influenced by two features of the rake angle: smaller absolute value and more balanced distribution on the left and right sides of each teeth. To meet ...the requirements of the rake angle, a method of machining the segmental spiral flute rake faces with a cylindrical milling cutter in different drive ratios is proposed. Firstly, a mathematical model of different drive ratios machining the rake face is established based on the principle of gear meshing. The initial point is determined using the point on the spiral face at the indexing ring position of the cutter tooth machined with a fixed drive ratio. The expression for the drive ratio is then calculated based on the machine movement relationship. Next, the optimum drive ratios were determined by studying the effect of drive ratio on the value of the rake angle and the machining position of the rake face. The design results show a significant improvement compared to the values of the rake angle for the fixed drive ratio. The maximum absolute value drops from 5.3° to 0.57°, and the difference between the rake angles of the two sides on cutter tooth is reduced from 7.47° to 0.15°. This implies that the cutting conditions have been substantially improved. Finally, the machining experiment is conducted. Measurement result shows the minimum difference between the experimental and theoretical values is 0.0167° and the maximum difference is 0.5451°. Verifying the correctness of the theoretical calculation and the feasibility of practical machining.
In order to improve the cutting performance of the hourglass worm gear hob and improve the cutting conditions of the teeth on both sides, it is necessary to constrain the absolute value of the rake ...angle of each tooth to be small and control the balance of the rake angles on the left and right sides. Based on the principle of enveloping tooth surface formation (Dong, 1989; Wu, 2009), this paper proposes a method of forming a spiral groove rake face with a variable transmission ratio, so that the rake face of each tooth is formed in segments to achieve the design requirements of small absolute value and balance on both sides. Taking the basic worm speed ω of the hob, the moving speed v of the machine tool cutter, and the installation offset Δx of the cutter as experimental factors, taking the rake angle on both sides of five teeth of the hob as response values, a three-factor three-level response surface analysis method is used to establish mathematical models between each experimental factor and the rake angle on both sides, and analyze the interaction between each factor. The results show that: The order of influence of the three selected factors on the rake angle on both sides is: basic worm speed, machine tool cutter moving speed, cutter installation offset; optimize and obtain the optimal parameter combination for each of five teeth in a spiral groove, perform simulation processing and measure rake angle. The results show that the rake angles on both sides of five teeth are controlled within ±0.3°, which is 94% lower than that when five teeth are processed simultaneously with a fixed transmission ratio. This indicates that rake faces of small rake angle can be designed by optimizing processing parameters, which is conducive to improving and balancing the cutting performance of hobs.
With the knowledge of the advantageous characteristics of the cylindrical worm gear drives having arched profile in axial section and the conical worm gear drives having linear profile in axial ...section, a new geometric type spiroid worm gear drive has been designed and then manufactured, and that is the spiroid worm gear drive having arched profile in axial section
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. We have developed the production technology of this new gear drive using classical machine. During the classical manufacturing process of conical thread surfaces with lathe center displacement, the worm shaft is driven with the help of the driving pin through the lathe fork. As a result of the shifting of the worm shaft by half cone angle, the path curve of the driving pin will be an ellipse path instead of a circle on the perpendicular plane to axis. The peripheral speed of the spindle is constant, but due to the ellipse path, the radius is constantly changing as a function of time. That is why the angular velocity and the rotation angle are also changing, and these cause pitch fluctuation during the manufacturing process of spiroid worms. During the manufacturing process, we have examined pitch errors which are caused by angular velocity fluctuation. In favour of angular velocity fluctuation, we have to ensure equal thread pitch during the manufacturing process of spiroid worms. That is why we have to design the geometrical shaping of the driving pin to solve the thread pitch fluctuation problem.
With the development of gear application technology,the higher requirements on gear precision are put forward,in order to achieve goals of high speed,high power,low noise and high transmission ...accuracy in gear transmission. In the gear hobbing process,if the tool geometry errors is ignored,the hob installation errors have become a major factor affecting the gear smooth precision. It starts from hob installation errors,the influence of hob installation errors on gear precision is analyzed. According to the principle of gear generating machining,the gear coordinate system and tool coordinate system are established,then by using the method of coordinate transformation,the gear tooth profile equation is deduced,which provides the design basis for 3D parametric gear precise modeling.
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