Mathematical Model of Helical Gear Topography Measurements and Tooth Flank Errors Separation

During large-size gear topological modification by form grinding, the helical gear tooth surface geometrical shape will be complex and it is difficult for the traditional scanning measurement to characterize the whole tooth surface. Therefore, in order to characterize the actual tooth surfaces, an on-machine topography measurement approach is proposed for topological modification helical gears on the five-axis CNC gear form grinding machine that can measure the modified gear tooth deviations on the machine immediately after grinding. Combined with gear form grinding kinematics principles, the mathematical model of topography measurements is established based on the polar coordinate method. The mathematical models include calculating trajectory of the centre of measuring probe, defining gear flanks by grid of points, and solving coordinate values of topology measurement. Finally, a numerical example of on-machine topography measurement is presented. By establishing the topography diagram and the contour map of tooth error, the tooth surface modification amount and the tooth flank errors are separated, respectively. Research results can serve as foundation for topological modification and tooth surface errors closed-loop feedback correction

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

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

Inertia matching of CNC cycloidal gear form grinding machine servo system

Reasonable ratio between the load inertia and servo motor inertia plays a decisive role for the dynamic performance and stability of the servo system, as well as the machining accuracy of the whole CNC machine. In order to improve the control performance and contour machining accuracy of the servo system of the CNC cycloidal gear form grinding machine, an optimization design method of the inertia matching for the CNC cycloidal gear form grinding machine servo system is proposed. The two-mass servo driving closed-loop PID control system is constructed, the influence of the different inertia ratios on the dynamic performance and contour errors of the servo system are deeply analyzed, and the inertia ratio is optimized to satisfied with the servo system performance requirements. Finally, the feasibility and practicability of the optimization design method of inertia matching are verified through the inertia ratio optimization grinding experiments of the cycloid gear in the CNC gear form grinding machine. This inertia matching optimization design method provides a valuable reference for the further design of CNC machine servo system

Digitized Modeling and Machining Simulation of Equal Base Bevel Gear

In order to achieve the NC machining to the equal base circle bevel gear with a standard cutter, to plan the machining path efficiently and to predict machining interference, based on the equal base circle bevel gear theory, the machining coordinate system for the bevel gear was established, according to gear tooth surface equations of the bevel gears, the tooth surface discretization function was derived, and through the calculation and get the discrete points, the gear surface was modeled in the software UG, and then the planning of the machining path, automatic programming and simulation processing were done. At last, simulation processing, analysis and comparison to the gear surface were carried on with the software VERICUT, improved that the gear surface modeling and NC machining methods were correct and feasible

Emergently Alteration of Procedural Strategy During Transcatheter Aortic Valve Replacement to Prevent Coronary Occlusion: A Case Report

BackgroundCoronary occlusion is an uncommon but fatal complication of transcatheter aortic valve replacement (TAVR) with a poor prognosis.Case PresentationA patient with symptomatic severe bicuspid aortic valve stenosis was admitted to a high-volume center specializing in transfemoral TAVR with self-expanding valves. No anatomical risk factors of coronary occlusion were identified on pre-procedural computed tomography analysis. The patient was scheduled for a transfemoral TAVR with a self-expanding valve. Balloon pre-dilatation prior to prosthesis implantation was routinely used for assessing the supra-annular structure and assessing the risk of coronary occlusion. Immediately after the tubular balloon inflation, fluoroscopy revealed that the right coronary artery was not visible, and the flow in the left coronary artery was reduced. The patient would be at high-risk of coronary occlusion if a long stent self-expanding valve was implanted. Therefore, our heart team decided to suspend the ongoing procedure. A transapical TAVR with a 23 mm J-valve was performed 3 days later. The prosthesis was deployed at a proper position without blocking the coronary ostia and the final fluoroscopy showed normal flow in bilateral coronary arteries with the same filling as preoperatively.DiscussionOur successful case highlights the importance of a comprehensive assessment of coronary risk and a thorough understanding of the TAVR procedure for the heart team. A short-stent prosthesis is feasible for patients at high risk of coronary occlusion. Most importantly TAVR should be called off even if the catheter has been introduced when an extremely high risk of coronary obstruction is identified during the procedure and no solution can be found

Three-Dimensional Imaging of Terahertz Circular SAR with Sparse Linear Array

Due to the non-contact detection ability of radar and the harmlessness of terahertz waves to the human body, three-dimensional (3D) imaging using terahertz synthetic aperture radar (SAR) is an efficient method of security detection in public areas. To achieve high-resolution and all aspect imaging, circular trajectory movement of radar and linear sensor array along the height direction were used in this study. However, the short wavelength of terahertz waves makes it practically impossible for the hardware to satisfy the half-wavelength spacing condition to avoid grating lobes. To solve this problem, a sparse linear array model based on the equivalent phase center principle was established. With the designed imaging geometry and corresponding echo signal model, a 3D imaging algorithm was derived. Firstly, the phase-preserving algorithm was adopted to obtain the 2D image of the ground plane for each sensor. Secondly, the sparse recovery method was applied to accomplish the scattering coefficient reconstruction along the height direction. After reconstruction of all the range-azimuth cells was accomplished, the final 3D image was obtained. Numerical simulations and experiments using terahertz radar were performed. The imaging results verify the effectiveness of the 3D imaging algorithm for the proposed model and validate the feasibility of terahertz radar applied in security detection

Perceived economic prospects during the early stage of COVID-19 breakout

How does a new epidemic affect individuals' expectations on economic prospects in the early stage of the breakout? We implemented an incentivized longitudinal online survey soon after the outbreak of the coronavirus disease 2019 (COVID-19) epidemic in China to answer this question. Results show that fewer new confirmed COVID-19 cases significantly increase individuals' expectations on gross domestic product and consumer price index growth rates. Our finding provides evidence that at the early stage of an unfamiliar epidemic, containing the spread of the disease may help to maintain positive economic expectations among individuals.Ministry of Education (MOE)Nanyang Technological UniversityWu thanks National Natural Science Foundation of China (No. 71373006 and 91546113) for financial support. Yan thanks Nanyang Technological University (NTU), Start Up Grant for financial support. Yan also thanks the Ministry of Education of Singapore (MOE) Tier 1 Grant (RG84/47) and CoHASS Research Support Grant for financial support