Simplified permeable surface correction for frequency-domain Ffowcs Williams and Hawkings integrals

A simplified surface correction formulation is proposed to diminish the far-field spurious sound generated by the quadrupole source term in Ffowcs Williams and Hawkings(FW-H)integrals.The proposed formulation utilizes the far-field asymptotics of the Green’s function to simplify the computation of its high-order derivatives,which circumvents the difficulties reported in the original frequency-domain surface correction formulation.The proposed formulation has been validated by investigating the benchmark case of sound generated by a convecting vortex.The results show that the proposed formulation successfully eliminates the spurious sound.The applications of the proposed formulation to flows with some special parameters are also discussed.

Tooth surface error correction of hypoid gears machined by duplex helical method

In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.

Assessment of hybrid geoids in Chile and Spain,combining GGM and GNSS/Leveling observations

This research presents the results for analyses done to five geopotential global models(GGM),comparing them with ground data from GNSS and leveling in heterogenic zones from the geodetic perspective,in Chile and Spain.While the official and complete implementation of the International Height Reference Frame(IHRF)has not yet been established,the vertical geodetic system of many countries is not calculated on a global scale;instead,it is calculated by the variation of relative heights between one or more local tide gauges,such as in the case of Spain and Chile.This aspect creates regional and specific altimetry data,which disables the use of GGM to directly obtain the orthometric height of the vertical reference system(VRS)from the GNSS heights.Global models currently reach centimetric precision due to their high resolution but are directly incompatible for a local level.To solve this,we expose in this article the contrast between geometric geoidal undulation(ellipsoidal heights and orthometric data from the leveling networks in Spain and Chile)with the geoidal undulation in more recent models and higher resolution:Earth Gravitational Model 2008(EGM08),European Improved Gravity model of the Earth by New techniques(EIGEN6 C4),Gravity Observation Combination(GOCO05 C),Experimental Gravity Field Model(XGM2016),and Ultra-High Resolution Global Geopotential Model(SGG-UGM),adjusting the residual between both referential heights by different parametric models and polynomials of determined order.Once evaluated,their geoidal undulations are combined with GNSS/leveling data from the corresponding VRS to generate a correcting surface,which is also known as a hybrid geoid,resulting in a model of optimal adjustment for the combination of five parameters of the EIGEN-6 C4 with orthometric heights and ellipsoids of both Chile and Spain.The results show 2-3 cm precisions,which were statistically analyzed to determine the suitability for use.The final products are three grids of independent hybrid geoids,one for northern Spain and two for Chile(central and north),which allow continuous access to the VRS of each country using the GNSS’s full potential until the IHRF is available and ready for use.