“…As the worm rotates about its axis k ! 1 , its tooth surfaces can form a family fΣ ðSÞ 1 g of the one-parameter surfaces in σ o1 , whose equations can be obtained from equation (11) employing the vector rotation technique as…”
Section: Is Placed On the Face Worm Gear To Indicate Its Current Posi...mentioning
confidence: 99%
“…The enveloping theory has been studied in depth in differential geometry 4 and the meshing theory. 5,6 Zhou et al 7–11 studied the manufacturing process and methods of the face gear, proposed a new geometric error compensation method, and completed the tooth contact analysis of the face gear drive by building an accurate measurement model. Figure 1. Schematic of face worm gear drive with hardened cylindrical worm.…”
This paper systematically establishes the computation method of the meshing limit line for the face worm gear drive with a hardened cylindrical worm. The meshing theory based on the reference point in the tooth surfaces is developed for the face worm gear drive. The reference point is reasonably determined based on the study of the meshing limit line characteristics. The calculation method of the coordinates of the reference point is proposed. The formula for the limit pressure angle at the reference point is obtained. Numerical results show that two meshing limit lines can be obtained on each flank of the worm tooth surface by iteratively solving the system of non-linear equations with four unknowns. These two meshing lines are near the inner end of the worm addendum. When the meshing limit lines are outside the worm tooth surface, the conjugacy of the worm tooth surface is good. Besides, studies of numerical examples find that poorly matched parameters of the face worm gear drive can result in the meshing limit line entering the worm tooth surface first from the inner end of the addendum, which reduces the conjugacy of the worm tooth surface. To avoid this, the conjugacy of the worm tooth surface can be checked by examining the limit pressure angle of the reference point when designing the face worm gear drive.
“…As the worm rotates about its axis k ! 1 , its tooth surfaces can form a family fΣ ðSÞ 1 g of the one-parameter surfaces in σ o1 , whose equations can be obtained from equation (11) employing the vector rotation technique as…”
Section: Is Placed On the Face Worm Gear To Indicate Its Current Posi...mentioning
confidence: 99%
“…The enveloping theory has been studied in depth in differential geometry 4 and the meshing theory. 5,6 Zhou et al 7–11 studied the manufacturing process and methods of the face gear, proposed a new geometric error compensation method, and completed the tooth contact analysis of the face gear drive by building an accurate measurement model. Figure 1. Schematic of face worm gear drive with hardened cylindrical worm.…”
This paper systematically establishes the computation method of the meshing limit line for the face worm gear drive with a hardened cylindrical worm. The meshing theory based on the reference point in the tooth surfaces is developed for the face worm gear drive. The reference point is reasonably determined based on the study of the meshing limit line characteristics. The calculation method of the coordinates of the reference point is proposed. The formula for the limit pressure angle at the reference point is obtained. Numerical results show that two meshing limit lines can be obtained on each flank of the worm tooth surface by iteratively solving the system of non-linear equations with four unknowns. These two meshing lines are near the inner end of the worm addendum. When the meshing limit lines are outside the worm tooth surface, the conjugacy of the worm tooth surface is good. Besides, studies of numerical examples find that poorly matched parameters of the face worm gear drive can result in the meshing limit line entering the worm tooth surface first from the inner end of the addendum, which reduces the conjugacy of the worm tooth surface. To avoid this, the conjugacy of the worm tooth surface can be checked by examining the limit pressure angle of the reference point when designing the face worm gear drive.
“…In terms of processing, face gears can be machined by grinding, CNC plunge milling, hobbing, and other processing methods [ 7 , 8 , 9 ]. The spur face gears, a simple type of face gears, can reach the desired accuracy level in the aerospace industry by grinding with “grinding-measurement-correction” [ 10 , 11 ]. The precision grade is evaluated by the measurement, so the reliable measurement of face gears is the basis of the correction of the machine tool settings in the processing.…”
Gears are usually measured by the contact metrology method in gear measuring centers or coordinate measuring machines. Recently, three-dimensional (3D) optical scanning, a non-contact metrology method, has been applied in the industry as an advanced measurement technology mainly due to its high efficiency. However, its applications to gears with complicated geometry, such as face gears, are still limited due to its relatively low accuracy and the void of related measurement solutions. In this work, an accurate measurement solution with 3D optical scanning is proposed for the tooth surface deviations of orthogonal face gears. First, point cloud collection is carried out by the 3D scanner. Furthermore, the measurement solution is implemented with a three-stage algorithm by aligning point clouds with the design model. Subsequently, 3D modeling is studied by numbering the points and reconstructing the real tooth surfaces. An example with a measurement experiment and loaded tooth contact analysis is given to show the validity of the proposed method.
“…How to generate the NC machining programme quickly and accurately is a key link to realise the gear cutting. With the rapid development of computer technology, great progress has been made in the fields of tooth surface precision modeling, simulation processing, error compensation, [16][17][18][19][20] etc. The development of five-axis NC machining technology [21][22][23] and its application in gear surface machining make it possible to NC machining this kind of split gear.…”
The purpose of this study is to realise numerical control (NC) gear cutting on the split wheel blank of equal-base bevel gears, based on the instantaneous cutter position information in tooth surface forming and NC machining theory, the coordinate system of split equal-base bevel gears is established. According to the movement of tool centre coordinate and its transformation, the linear motion of machine tool is solved. By the rotation and translation of the tool axis vector, the solution of the rotary motion of the machine tool is obtained. According to the different rotation direction and concave-convex property of tooth surface, the calculating model of the starting point of processing of each tooth surface is deduced. The complete machining trajectory is formed by analysis and extension of the tool starting point and terminal point of machining, and the automatic generation of the NC machining program is realised. Finally, the simulation of gear cutting on the split wheel blank is carried out using VERICUT software. The experimental and tooth surface measurement results show that the mathematical model of motion trajectory is correct and the machining method is feasible.
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