Free-Form Flank Correction in Helical Gear Grinding Using a Five-Axis Computer Numerical Control Gear Profile Grinding Machine

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Yi-Pei Shih ◽  
Shi-Duang Chen
Keyword(s):  
Correction Method ◽  
Computer Numerical Control ◽  
Numerical Control ◽  
Free Form ◽  
Profile Grinding ◽  
Wheel Profile ◽  
Grinding Machine ◽  
Tooth Flank ◽  
Five Axis ◽  
Gear Profile

To reduce form grinding errors, this paper proposes a free-form flank topographic correction method based on a five-axis computer numerical control (CNC) gear profile grinding machine. This correction method is applied not only to the five-axis machine settings (during grinding) but also to the wheel profile (during wheel truing). To achieve free-form modification of the wheel profile, the wheel is formulated as B-spline curves using a curve fitting technique and then normal correction functions made up of four-degree polynomials are added into its working curves. Additionally, each axis of the grinding machine is formulated as a six-degree polynomial. Based on a sensitivity analysis of the polynomial coefficients (normal correction functions and CNC machine settings) on the ground tooth flank and the topographic flank errors, the corrections are solved using the least squares method. The ground tooth flank errors can then be efficiently reduced by slightly adjusting the wheel profile and five-axis movement according to the solved corrections. The validity of this flank correction method for helical gears is numerically demonstrated using the five-axis CNC gear profile grinding machine.

Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator

2007 ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong
Keyword(s):  
Correction Method ◽  
Numerical Control ◽  
Cnc Machine ◽  
Hypoid Gears ◽  
Nc Code ◽  
Machine Errors ◽  
Highly Sensitive ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head

Because the contact bearings of spiral bevel and hypoid gears are highly sensitive to tooth flank geometry, it is desirable to reduce the flank deviations caused by machine errors and heat treatment deformation. Several methods already proposed for flank correction are based on the cutter parameters, machine settings, and kinematical flank motion parameters of a cradle-type universal generator, which are modulated according to the measured flank topographic deviations. However, because of the recently developed six-axis Cartesian-type computer numerical control (CNC) hypoid generator, both face-milling and face-hobbing cutting methods can be implemented on the same machine using a corresponding cutter head and NC code. Nevertheless, the machine settings and flank corrections of most commercial Cartesian-type machines are still translated from the virtual cradle-type universal hypoid generator. In contrast, this paper proposes a flank-correction methodology derived directly from the six-axis Cartesian-type CNC hypoid generator in which high-order correction is easily achieved through direct control of the CNC axis motion. The validity of this flank correction method is demonstrated using a numerical example of Oerlikon Spirac face-hobbing hypoid gears made by the proposed Cartesian-type CNC machine.

Probe Position Planning for Measuring Cylindrical Gears on a Four-Axis CNC Machine

2012 ◽  
Vol 579 ◽  
pp. 297-311
Author(s):  
Yi Hui Lee ◽  
Shih Syun Lin ◽  
Yi Pei Shih
Keyword(s):  
Mathematical Models ◽  
Gear Tooth ◽  
Experimental Result ◽  
Tooth Surface ◽  
Measuring Process ◽  
Profile Grinding ◽  
Cylindrical Gears ◽  
Large Size ◽  
Grinding Machine ◽  
Gear Profile

During large-size gear manufacturing by form grinding, the actual tooth surfaces will differ from the theoretical tooth surface because of errors in the clamping fixture and machine axes and machining deflection. Therefore, to improve gear precision, the gear tooth deviations should be measured first and the flank correction implemented based on these deviations. To address the difficulty in large-size gear transit, we develop an on-machine scanning measurement for cylindrical gears on the five-axis CNC gear profile grinding machine that can measure the gear tooth deviations on the machine immediately after grinding, but only four axes are needed for the measurement. Our results can serve as a foundation for follow-up research on closed-loop flank correction technology. This measuring process, which is based on the AGMA standards, includes the (1) profile deviation, (2) helix deviation, (3) pitch deviation, and (4) flank topographic deviation. The mathematical models for measuring probe positioning are derived using the base circle method. We also calculate measuring positions that can serve as a basis for programming the NC codes of the measuring process. Finally, instead of the gear profile grinding machine, we used the six-axis CNC hypoid gear cutting machine for measuring experiments to verify the proposed mathematical models, and the experimental result was compared with Klingelnberg P40 gear measuring center.

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.

scholarly journals Closed-Loop Feedback Flank Errors Correction of Topographic Modification of Helical Gears Based on Form Grinding

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Huiliang Wang ◽  
Jubo Li ◽  
Yang Gao ◽  
Jianjun Yang
Keyword(s):  
Closed Loop ◽  
Correction Method ◽  
Numerical Control ◽  
Grinding Wheel ◽  
Helical Gears ◽  
Form Grinding ◽  
Loop Feedback ◽  
Feedback Correction ◽  
Closed Loop Feedback ◽  
Tooth Flank

To increase quality, reduce heavy-duty gear noise, and avoid edge contact in manufacturing helical gears, a closed-loop feedback correction method in topographic modification tooth flank is proposed based on the gear form grinding. Equations of grinding wheel profile and grinding wheel additional radial motion are derived according to tooth segmented profile modification and longitudinal modification. Combined with gear form grinding kinematics principles, the equations of motion for each axis of five-axis computer numerical control forming grinding machine are established. Such topographical modification is achieved in gear form grinding with on-machine measurement. Based on a sensitivity analysis of polynomial coefficients of axis motion and the topographic flank errors by on-machine measuring, the corrections are determined through an optimization process that targets minimization of the tooth flank errors. A numerical example of gear grinding, including on-machine measurement and closed-loop feedback correction completing process, is presented. The validity of this flank correction method is demonstrated for tooth flank errors that are reduced. The approach is useful to precision manufacturing of spiral bevel and hypoid gears, too.

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