A Novel Lengthwise Crowning Method for Face-Hobbed Straight Bevel Gears

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Yi-Pei Shih
Keyword(s):  
Mathematical Model ◽  
Numerical Control ◽  
High Productivity ◽  
Bevel Gears ◽  
Cutting Machine ◽  
Performance Indexes ◽  
Tooth Surfaces ◽  
Recent Addition ◽  
Machine Setting ◽  
The Many

A recent addition to the many milling processes used in manufacturing to cut straight bevel gears (SBGs) is a new face-hobbing (FH) method that uses a virtual hypocycloid straight-lined mechanism to produce straight-lined teeth. Despite earning much attention because of its high productivity, however, this method is unable to handle lengthwise crowning on tooth surfaces, which results in poor contact performance. This paper therefore proposes a novel lengthwise crowning method, applicable on a modern six-axis computer numerical control (CNC) bevel gear cutting machine, in which the gear blank performs a swinging motion during machining. This swinging motion is enabled by machine setting modifications, which here are derived from a mathematical model of a double (profile and lengthwise) crowned gear. After the model's correctness is confirmed using ease-off and tooth contact analyses, a final investigation examines the effect of two key parameters related to contact performance indexes whose interrelations are graphed to provide a designer reference.

Advanced Design and Manufacture of Face-Hobbed Spiral Bevel Gears

2009 ◽  
Author(s):  
V. Simon
Keyword(s):  
Gear Tooth ◽  
Numerical Control ◽  
Mutual Position ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Pinion Gear ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Crown Gear

The design and advanced manufacture of face-hobbed spiral bevel gears on computer numerical control (CNC) hypoid generating machines is presented. The concept of face-hobbed bevel gear generation by an imaginary generating crown gear is established. In order to reduce the sensitivity of the gear pair to errors in tooth-surfaces and to the mutual position of the mating members, modifications are introduced into the teeth of both members. The lengthwise crowning of teeth is achieved by applying a slightly bigger lengthwise tooth flank curvature of the crown gear generating the concave side of pinion/gear tooth-surfaces, and/or by using tilt angle of the head-cutter in the manufacture of pinion/gear teeth. The tooth profile modification is introduced by the circular profile of the cutting edge of head-cutter blades. An algorithm is developed for the execution of motions on the CNC hypoid generating machine using the relations on the cradle-type machine. The algorithm is based on the condition that since the tool is a rotary surface and the pinion/gear blank is also related to a rotary surface, it is necessary to ensure the same relative position of the head cutter and the pinion on both machines.

Tangential Follow System of High-Speed Leather Cutting Machine Modeling and Control Optimization

2011 ◽  
Vol 317-319 ◽  
pp. 649-654
Author(s):  
Yan Wei Zhao ◽  
Meng Sheng ◽  
Ting Li ◽  
Xin Min Wu ◽  
Shuo Jiang
Keyword(s):  
High Speed ◽  
Fitness Function ◽  
Numerical Control ◽  
Mechanical Transmission ◽  
Combined System ◽  
Evaluation Standard ◽  
Modeling And Control ◽  
Cutting Machine ◽  
Machine Modeling ◽  
Performance Indexes

As to the low dynamic response of tangential follow system, especially the poor dynamic follow ability when executing small arc rapid interpolation. Based on the principle of mechanical dynamics, the mathematical model of leather cutting machine tangential follow mechanical transmission system is built, considering a type of high-speed numerical control leather cutting machine as the research object. Joined mechanical model and servo motor model together, its electromechanical combined system diagram is created by Simulink. On the basis of this diagram, the dynamic characteristic is analyzed. The composite evaluation standard including multiple performance indexes is used for the fitness function, the three-ring PID control parameters of tangential follow system is optimized with genetic algorithm (GA). The results show that GA optimization is more superior and efficient, comparing with traditional PID setting method.

Mathematical Model for Face-Hobbed Straight Bevel Gears

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Yi-Pei Shih
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Tooth Contact Analysis ◽  
Rolling Circle ◽  
High Productivity ◽  
Bevel Gears ◽  
Straight Line ◽  
Base Circle ◽  
Straight Line Mechanism ◽  
Straight Lines

Face hobbing, a continuous indexing and double-flank cutting process, has become the leading method for manufacturing spiral bevel gears and hypoid gears because of its ability to support high productivity and precision. The method is unsuitable for cutting straight bevel gears, however, because it generates extended epicycloidal flanks. Instead, this paper proposes a method for fabricating straight bevel gears using a virtual hypocycloidal straight-line mechanism in which setting the radius of the rolling circle to equal half the radius of the base circle yields straight lines. This property can then be exploited to cut straight flanks on bevel gears. The mathematical model of a straight bevel gear is developed based on a universal face-hobbing bevel gear generator comprising three parts: a cutter head, an imaginary generating gear, and the motion of the imaginary generating gear relative to the work gear. The proposed model is validated numerically using the generation of face-hobbed straight bevel gears without cutter tilt. The contact conditions of the designed gear pairs are confirmed using the ease-off topographic method and tooth contact analysis (TCA), whose results can then be used as a foundation for further flank modification.

Mathematical Model of a Vertical Six-Axis Cartesian Computer Numerical Control Machine for Producing Face-Milled and Face-Hobbed Bevel Gears

2019 ◽  
Vol 142 (4) ◽  
Author(s):  
Ruei-Hung Hsu ◽  
Yi-Pei Shih ◽  
Zhang-Hua Fong ◽  
Chin-Lung Huang ◽  
Szu-Hung Chen ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Correction Method ◽  
Computer Numerical Control ◽  
Bevel Gear ◽  
Numerical Control ◽  
Numerical Illustration ◽  
Bevel Gears ◽  
Machine Stiffness ◽  
The Individual ◽  
Compact Design

Abstract Prior to the development of sophisticated computer numerical control (CNC), both face milling (FM) and face hobbing (FH), the two most popular technologies for bevel gear production, required cradle-type machines with diverse and complicated mechanisms. In the last two decades, however, the gear industry has replaced these traditional machines with six-axis CNC bevel gear cutting machines that have superior efficiency and accuracy. One such machine is a vertical six-axis machine with a vertical spindle arrangement, which offers two industrially proven advantages: compact design and maximum machine stiffness. The technical details of this machine, however, remain undisclosed; so, this paper proposes a mathematical model that uses inverse kinematics to derive the vertical machine's nonlinear six-axis coordinates from those of a traditional machine. The model also reduces manufacturing errors by applying an effective flank correction method based on a sensitivity analysis of how slight variations in the individual machine setting coefficients affect tooth geometry. We prove the model's efficacy by first using the proposed equations to derive the nonlinear coordinates for pinion and gear production and then conducting several cutting experiments on the gear and its correction. Although the numerical illustration used for this verification is based only on FM bevel gears produced by an SGDH cutting system, the model is, in fact, applicable in the production of both FM and FH bevel gears.

Fourth-Order Kinematic Synthesis for Face-Milling Spiral Bevel Gears With Modified Radial Motion (MRM) Correction

2005 ◽  
Vol 128 (2) ◽  
pp. 457-467 ◽  
Author(s):  
Pei-Yu Wang ◽  
Zhang-Hua Fong
Keyword(s):  
Fourth Order ◽  
Face Milling ◽  
Bevel Gear ◽  
Radial Motion ◽  
Numerical Control ◽  
Tooth Surface ◽  
Kinematic Synthesis ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel

The use of a fourth-order motion curve is proposed by Stadtfeld and Gaiser to reduce the running noise of a bevel gear set recently. However, the methodology of synthesizing the tooth surfaces was not clearly shown in the literature. In this work, we proposed a methodology to synthesize the mating tooth surfaces of a face-milling spiral bevel gear set transmitting rotations with a predetermined fourth-order motion curve and contact path. A modified radial motion (MRM) correction in the machine plane of a computer numerical control (CNC) hypoid generator is introduced to modify the pinion tooth surface. With MRM correction, an arbitrary predetermined contact path on the pinion tooth surface with predetermined fourth-order motion curve can be achieved. Parameters of MRM correction are calculated according to the predetermined contact path and motion curve. As shown by the numerical examples, the contact path and the motion curve were obtained as expected by applying the MRM correction. The results of this work can be applied to the pinion, which is generated side-by-side (for example, fixed setting method, formate method, and Helixform method) and can be used as a basis for further study on the motion curve optimizations.

A Study on the Tooth Geometry and Cutting Machine Mechanisms of Spiral Bevel Gears

1991 ◽  
Vol 113 (3) ◽  
pp. 346-351 ◽  
Author(s):  
Z. H. Fong ◽  
Bill Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Helical Motion ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Gear Cutting ◽  
Cutting Machine ◽  
The Matrix ◽  
Spiral Bevel

The tooth geometry and cutting machine mechanisms of spiral bevel gears are investigated. Based on the kinematics of titled head cutter, machine cradle, sliding base and work head, the matrix presentation of spiral bevel gear’s tooth geometry are developed. The relations between the parameters of the proposed mathematical model and the machine settings of existing spiral bevel gear cutting machines are also investigated. The tilt of head cutter axis, motion of generation, helical motion of sliding base, and nongenerating cutting of spiral bevel gears are taken into consideration. An example is given to illustrate the application of the proposed mathematical model.

Polishing of Large-Sized Spiral Bevel Gears Using Radial Bristle Brush

2017 ◽  
Vol 873 ◽  
pp. 48-53
Author(s):  
Kazumasa Kawasaki ◽  
Isamu Tsuji
Keyword(s):  
Surface Roughness ◽  
Cnc Machining ◽  
Numerical Control ◽  
Tooth Surface ◽  
Poly Vinyl Alcohol ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tool Mark ◽  
Tooth Surfaces ◽  
Spiral Bevel

A machining method of large-sized spiral bevel gears in cyclo-palloid system has been developed using a computer numerical control (CNC) machining center. As a result of trial machining, the tooth surfaces were rough and leprous tool mark occurred. Therefore, the tooth surfaces were polished using a poly-vinyl alcohol (PVA) elastic grindstone after machining in order to improve the surface roughness and the occurrence of leprous tool mark. However, the wear and clogging of the elastic grindstone occurred after polishing. In this paper, the tooth surfaces of the large-sized spiral bevel gears are polished using a radial bristle brush instead of a PVA elastic grindstone. The swarf cutting that was machined by the side of a tool was carried out in polishing in order to make the life of the radial bristle brush. After polishing, the tooth surface was observed and the surface roughness was measured. Afterwards, the surface roughness and the occurrence of leprous tool mark before and after polishing were compared. As a result, the surface roughness and the occurrence of leprous tool mark were improved.

A Lengthwise Modification for Face-Hobbed Straight Bevel Gears

2013 ◽  
Author(s):  
Yi-Pei Shih
Keyword(s):  
Tool Path ◽  
Point Contact ◽  
Contact Condition ◽  
Tooth Contact Analysis ◽  
High Productivity ◽  
Accuracy Requirement ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Gear Contact ◽  
Straight Line Mechanism

Face hobbing has been successfully applying in manufacturing straight bevel gears using a virtual hypocycloidal straight-line mechanism. This method is a continuous indexing and double-flank cutting process, and is recognized its high productivity and precision. In order to improve gear contact condition, three types of flank modifications are frequently used in gear industry: profile crowning, lengthwise crowning, and longitudinal twist. In the design of the spiral bevel and hypoid gear, under satisfying a specified accuracy requirement, three types of modifications are blended properly during gear design to absorb assembly and manufacture errors. Circular cutter blades are normally adopted to accomplish the first type modification. The second can be achieved by a cutter radius change or a cutter tilt with adjusted pressure angles. The last can be achieved by a cutter tilt or modified tool path (for example, helical motion and modified roll). This paper proposes a lengthwise crowning method for face-hobbed straight bevel gear (SBG) using a hypocycloidal mechanism. This modification is applied to the pinion only. A numerical example drive with point-contact tooth surfaces is adopted to validate the proposed mathematical model. Finally, two evaluations, ease-off topography and tooth contact analysis (TCA), are made to investigate the contact condition of this numerical case.

The Development of a Physico-Mathematical Model for the Functioning of an Underwater Waterjet Cutting Machine

2020 ◽  
Vol 75 (2) ◽  
pp. 167-174
Author(s):  
A. A. Ilukhina ◽  
V. I. Kolpakov ◽  
V. V. Veltishchev ◽  
A. L. Galinovsky ◽  
A. V. Khakhalin
Keyword(s):  
Mathematical Model ◽  
Waterjet Cutting ◽  
Cutting Machine
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