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.

Optimizing circumferential assembly angle of rotor parts connected by curvic couplings based on acquired tooth surface error data

Due to the excellent self-centering and load-carrying capability,curvic couplings have been widely used in advanced aero-engine rotors.However,curvic tooth surface errors lead to poor assembly precision.Traditional physical-master-gauge-based indirect tooth surface error measurement and circumferential assembly angle optimization methods have the disadvantages of high cost and weak generality.The unknown tooth surface fitting mechanism is a big barrier to assembly precision prediction and improvement.Therefore,this work puts forward a data-driven assembly simulation and optimization approach for aero-engine rotors connected by curvic couplings.The origin of curvic tooth surface error is deeply investigated.Using 5-axis sweep scan method,a large amount of high-precision curvic tooth surface data are acquired efficiently.Based on geometric models of parts,the fitting mechanism of curvic couplings is uncovered for assembly precision simulation and prediction.A circumferential assembly angle optimization model is developed to decrease axial and radial assembly runouts.Experimental results show that the assembly precision can be predicted accurately and improved dramatically.By uncovering the essential principle of the assembly precision formation and proposing circumferential assembly angle optimization model,this work is meaningful for assembly quality,efficiency and economy improvement of multistage aero-engine rotors connected by curvic couplings.

Effect of random surface errors on radiation characteristics of the side-fed offset Cassegrain antenna

In this paper the average power pattern of the side-fed offset Cassegrain(SFOC)dual reflector antenna is analyzed,and the effect of the random surface error on ra-diation characteristics of the antenna is introduced.Here,the random surface error is defined as the error of the stan-dard reflector in its normal direction and the errors in a small zone of the reflector are considered as equal.We also assume that the phase error on the aperture led by the ran-dom surface error obeys a Gaussian distribution with zero mean,under which the expression of the average power pattern is deduced.Finally,the data related to the radiation characteristics of the antenna are calculated and the corre-sponding curves are presented.The obtained results can be used for the user to determine the manufacturing accuracy of the reflector of the SFOC antennas.

ANALYSIS OF UN-COINCIDE COORDINATE ERROR IN SINGLE-AXIS ROTATING FIBER OPTIC STRAP-DOWN INERTIAL NAVIGATION SYSTEM

The un-coincide coordinate error in the single-axis rotating fiber optic strap-down inertial navigation system（SINS） is analyzed. Firstly, a rotating modulation technology is presented for SINS. The method provides the enhanced property of SINS when using the same-leveled inertial measurement units. Then, the rotating struc- ture modification is derived and augmented to resolve the un-modulated error-accumulated problem. As the insuf- ficient machine processing, the horizontal and the vertical errors on the machine surface are inevitable, and the in- volved coordinates are difficult to get the exact coincident. So, two major kinds of coordinate situation are stud- ied. The equivalent error models on gyro and acceleration outputs are built for each situation, and the impact is analyzed for compensation. The part of attitude and position error models caused by the built angle-rate error is established to calculate the un-eoincident impact. Considering these conditions of different gyro accuracy and mo- tion states simultaneously, numerical simulations are implemented. Results indicate that the SINS modulation ac- curacy is seriously affected by the combined factors on gyro accuracy and motion conditions.

ANALYSIS OF TOOTH FORM ERROR OF EQUAL BASE CIRCLE BEVEL GEAR

The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute

Facets of Uncertainty in Digital Elevation and Slope Modeling

This paper investigates the differences that result from applying different approaches to uncertainty modeling and reports an experimental examining error estimation and propagation in elevation and slope, with the latter derived from the former. It is confirmed that significant differences exist between uncertainty descriptors, and propagation of uncertainty to end products is immensely affected by the specification of source uncertainty.

Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

To deal with the staircase approximation problem in the standard finite-difference time-domain（FDTD） simulation,the two-dimensional boundary condition equations（BCE） method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.