Eccentricity Error Research Articles

Analysis on Meshing Characteristics and Transmission Error of Elliptic Gears

As an important parameter to distinguish noncircular gear from cylindrical gear, eccentricity is very important for the meshing characteristics and transmission error of noncircular gear. In order to study the transmission characteristics of the elliptic gear, a pair of elliptic gear in the reversing device of a new type of drum pumping was taken as the research object. Based on the analysis of the transmission pressure angle and instantaneous contact ratio of the elliptic gear, the eccentricity error was introduced into the analysis model of transmission error. The influences of the eccentricity on the transmission pressure angle, instantaneous contact ratio, and transmission error were analyzed, and the analysis accuracy is verified by the finite element method. The results show that the eccentricity has a great influence on the transmission pressure angle, instantaneous contact ratio, and transmission error of the elliptic gear, and the eccentricity error has a significant influence on the transmission error. In order to ensure the normal meshing condition of the elliptic gear, the eccentricity should be less than 0.7071, and the maximum instantaneous contact ratio is 1.809. The research results can provide some guidance for the following noncircular spur gear transmission test and transmission error research.

A cylindrical profile measurement method for cylindricity and coaxiality of stepped shaft

The cylindricity and coaxiality of the stepped shaft are important parameters reflecting the vibration characteristics of the rotating machines system. In order to evaluate the cylindricity and coaxiality of the stepped shaft accurately, the paper proposes a cylindrical profile measurement model, which takes into account five kinds of systematic errors and analyzes the combined effects of five systematic errors on cylindrical profile measurement results. Based on the proposed measurement model, the distribution of sample angle deviation caused by five systematic errors is studied. A non-uniform spline filter is designed, and the effect of uniform and non-uniform spline filter methods on the cylindricity and coaxiality of stepped shaft are analyzed. In order to verify the effectiveness of the cylindrical profile measurement model with five systematic errors and the spline filter method proposed in the paper, a rotary measuring instrument with high precision is built. The experimental results show that compared with the traditional measurement method, the measurement accuracy of cylindricity and coaxiality can be improved by 11.43 μm and 8.99 μm for stepped shaft with large radius on the proposed method, respectively. The proposed method is suitable for small probe radius and large eccentricity error, probe offset error, workpiece tilt error, and guide rail tilt error, especially for stepped shaft with large radius, such as aerospace engine, gas turbine, and machine tools.

Vibration characteristic analysis of gearbox based on dynamic excitation with eccentricity error

In this study, the vibration characteristics of gearbox considering the eccentricity error and the friction excitation of helical gear pair were evaluated theoretically and experimentally. A geometric model of a single-stage helical gear pair with eccentricity error was established to obtain the calculation formula of the length of the dynamic contact line and the friction excitation. The multi-degree-of-freedom dynamic model of the transmission system was established considering the influences of tooth friction, support stiffness and damping, meshing stiffness and damping, static error, and dynamic tooth backlash. Then, the dynamic meshing forces of the system were obtained and applied to the gearbox for vibration response analysis using mode superposition method. A correlation test rig was developed to measure vibration under different operating conditions for verifying the correctness of the simulation models. Comparison between simulation and test was performed to demonstrate the accuracy of the proposed model in predicting vibrations. Results showed that eccentricity greatly influenced the overall vibration characteristics. The relative error between measurement and prediction can be significantly reduced by considering the eccentricity error in the dynamic model of transmission system.

High-efficiency full-surface defects detection for an ICF capsule based on a null interferometric microscope

Laser inertial confinement fusion (ICF) triggers a nuclear fusion reaction via the evenly compressed capsule containing deuterium tritium fuel with a high-power laser. However, isolated defects on the surface of the capsules reduce the probability of ignition. In this paper, we present a full-surface defects detection method based on a null interferometric microscope (NIM) to achieve high-precision, high-efficiency, and full-surface defects detection on ICF capsules. A dynamic phase-shifting module is applied to the NIM to achieve a single-shot measurement in a single subaperture. With the capsule controlling system, the capsule is rotated and scanned along a planned lattice to get all subapertures measured. The eccentricity error can be measured from wavefront aberrations and compensated online to guarantee the measurement accuracy during the scanning process. After the scanning process, all of the surface defects are identified on the full-surface map. Theories and experimental results indicate that for the capsule with 875-µm-diameter, the lateral resolution could reach 0.7 µm and the measurement time is less than 1 h. The number of sampling points can reach about 50 million. To the best of our knowledge, our proposed system is the first to achieve full-surface defects detection of ICF capsules with such high efficiency and high resolution at the same time.

The influence of the geometric eccentricity on the dynamic behaviors of helical gear systems

Geometric eccentricity error is unavoidable in gear systems, resulting that the center of mass and center of rotation do not coincide with each other. The gear center distance and condition of gear tooth engagement are time-varying during the process of gear meshing. The effect of the geometric eccentricity should be involved in both the quasi-static and dynamic analysis. An improved loaded tooth contact analysis method considering geometric eccentricities is proposed and the mesh stiffness is validated by the result in a published literature. The contact state changes significantly during the process of meshing because of the geometric eccentricity. Then the dynamic model of the gear system is established. It is found that there are sideband frequencies around the meshing frequency of the gear pair with geometric eccentricities. This feature is consistent with the experimental results. Finally, the dynamic response under different initial eccentric phase is discussed.

A Machine Vision Method for Correction of Eccentric Error Based on Adaptive Enhancement Algorithm

In the procedure of surface defects detection for large-aperture aspherical optical elements, it is of vital significance to adjust the optical axis of the element to be coaxial with the mechanical spin axis accurately. Therefore, a machine vision method for eccentric error correction is proposed in this article. Focusing on the severe defocus blur of reference crosshair image caused by the imaging characteristic of the aspherical optical element, which may lead to the failure of correction, an adaptive enhancement algorithm (AEA) is proposed to strengthen the crosshair image. AEA consists of the existed guided filter dark channel dehazing algorithm (GFA) and the proposed lightweight multiscale densely connected network (MDC-Net). The enhancement effect of GFA is excellent but time-consuming, and the enhancement effect of MDC-Net is slightly inferior but strongly real time. As AEA will be executed dozens of times during each correction procedure, its real-time performance is very important. Therefore, by setting the empirical threshold of definition evaluation function SMD2, GFA and MDC-Net are, respectively, applied to highly and slightly blurred crosshair images so as to ensure the enhancement effect while saving as much time as possible. AEA has certain robustness in time-consuming performance, which takes an average time of 0.2721 and 0.0963 s to execute GFA and MDC-Net separately on ten 200 pixels $\times200$ pixels region of interest (ROI) images with different degrees of blur, and also, the eccentricity error can be reduced to be within $10~\mu \text{m}$ by our method.

On-Line Measurement Method for Diameter and Roundness Error of Balls

This paper presents an on-line measurement method for the diameter and roundness error of balls. An easy-installation rotary scanning system, which integrates the principles of the diameter and the roundness measurements, is constructed. The rotary scanning system consists of a rotary stage, a linear stage, and two sensors with a flat probe. Two sensors are initially installed on the linear stage and contact each other. The outputs of two sensors are reset to zero at first. The ball is then mounted on the rotary stage and positioned between two flat probes. The variations of the diameter and the roundness error of the ball at each angular position can be directly recorded by two sensors when the ball is rotated by the rotary stage. Substituting the outputs of two sensors into the proposed mathematical models, the diameter and roundness error can be evaluated. The effects of the alignment error induced by the spindle error of the rotary stage and the titling error and the eccentric error of the ball on the measurement accuracy can be self-separated in the proposed on-line measurement method. A series of experiments are carried out to verify the effectiveness and the capability of the proposed on-line measurement method and the designed rotary scanning system. The designed system is easy to construct both in the laboratory environment and the factory field.

Experimental Study on Investigating the Influence of Combination Combining Eccentricity with Different Orientations for Process System of Milling Center

There are several critical factors which have adverse effects on the workpiece surface finish, dimensional accuracy, tool life, etc. Eccentricity is one of them which can be manipulated when the spindle, tool holder and milling cutter revolve around the line parallel to their cutting axes and crop up due to clamping deviation and geometric imperfections. This work was driven by the observation that there should an approach through which final eccentric error can be reduced as other researchers only displayed the effects of eccentricity on cutting forces, etc. This task was carried out through performing numerous experiments on the CNC milling center and measuring geometric imperfections from the whole body of machining elements at different orientations with dial gauge to find out whether different orientations of elements have effects on the eccentricity. If they have noticeable effects then such orientations of elements exhibiting the minimum eccentricity can be selected which in turn may improve the accuracy and precision of workpieces and reduce the final cutting edge error. Our observation showed that orientations have remarkable effects on the eccentricity pretending lowest final eccentric error which is unable to be ignored.

Optimisation of Compression Moulding Parameter for NR/EPDM Material

Natural Rubber/Ethylene Propylene Diene Monomer (NR/EPDM) elastomeric has gaining popularity in the automotive industry owing to the fact in term of sustainability. With extensive studies and an increasing number of applications for future advancement, the need for an accurate and reliable guide in processing this type of elastomer has increased enormously. The present work deals with the study of compression moulding parameters (i.e. temperature, pressure, heating time and pressure time) and its effects against NR/EPDM elastomeric mechanical properties (i.e. ultimate tensile strength (UTS), cross-link density and eccentricity error) aim on establishing optimized processing parameters setup. The optimizations are achieved through the Response Surface Methodology (RSM) and mathematical model for each response is developed to access the relationship between the parameters. Adequacy of models is analysed statistically using analysis of variance (ANOVA) in the determination of significant input variables and possible interactions. Lastly, multi objectives optimization is performed through numerical optimization and predicted results are validated. Strong agreement between experimental and the selected solution are found in between 93% and 96%, thus validating the solution as an optimal run condition. The findings suggest that temperature and heating time is the main factor affecting ultimate tensile strength, whereas for cross-link density there is only one significant parameter which is temperature. UTS and cross-link density decrease with the increases of the temperature and heating time due to the degradation (temperature too high for NR/EPDM working temperature). Therefore, it is recommended to start the process below the NR/EPDM degradation point to avoid the scissoring rubber take place and subsequently improving the mechanical properties

Calibration, Compensation and Accuracy Analysis of Circular Grating Used in Single Gimbal Control Moment Gyroscope.

The accuracy of the circular grating is the key point for control precision of the single gimbal control moment gyroscope servo system used in civilian micro-agile satellites. Instead of using the multi reading heads to eliminate eccentricity errors, an algorithm compensation method based on a calibration experiment using a single reading head was proposed to realize a low-cost and high accuracy angular position measurement. Moreover, the traditional hardware compensation method using double reading heads was also developed for comparison. Firstly, the single gimbal control moment gyroscope system of satellites was introduced. Then, the errors caused by the installation of the reading head were studied and the mathematic models of these errors were developed. In order to construct the compensation function, a calibration experiment using the autocollimator and 24-sided prism was performed. Comparison of angle error compensation using the algorithm and hardware method was presented, and results showed that the algorithm compensation method proposed by this paper achieved the same accuracy level as the hardware method. Finally, the proposed method was further verified through a control system simulation.

Two-Sided Contact Mesh Stiffness and Transmission Error for a Type of Backlash-Compensated Conical Involute Gear Pair

Both the drive- and back-side contact mesh stiffnesses (two-sided contact mesh stiffness) for a new type of conical involute gear (NTCIG) is developed analytically. Instead of the conventional spring preload anti-backlash method, an active control strategy to eliminate the time-varying backlash is presented by adjusting the axial displacement of the driven gear. The dynamic transmission error (DTE) of the gear pair is calculated under different load excitations to analyze the differences between the drive- and back-side meshes under a time-varying backlash with anti-backlash conditions based on the NTCIG model with an eccentricity error. Considering the additional rotational angle caused by the anti-backlash and the differences from the two-sided contact, the theory of no-load transmission error for the NTCIG is modified by agreeing considerably well with the low component of the DTE. Moreover, the DTE curve under varying load excitations showed that the dynamics of the NTCIG improved considerably after backlash compensation. The drive- and back-side tooth meshes were analyzed according to the DTE of NTCIG with backlash control under various external excitations at different speeds and variable initial phases, frequencies, and amplitudes of the sinusoidal load.

Test bed for rotation-based triboelectric nanogenerators.

The triboelectric nanogenerator (TENG) has been attracting attention for electronic devices and sensors consuming low power. Among the few operating modes of the TENG, the rotation-based TENG provides a more continuous and smoother output than the linear-motion-based TENG. To evaluate the output performance of the rotation-based TENG precisely and quantitatively, a test bed that adjusts the eccentricity error, tilt angle error, contact force, and rotational speed is proposed. The test bed includes a motor, torque sensor, 2-axis planar stage, 2-axis tilting stage, 1-axis vertical stage, 3-degree-of-freedom force/torque (3-DOF F/T) sensor, and voice coil actuator. With the proposed test bed, the effects of the eccentricity error, tilt angle error, contact force, and rotational speed on the electrical output performance of the rotation-based TENG are analyzed. The test bed is expected to be used for quantitative performance analysis and comparative study of various rotation-based TENGs, and it can help improve the performance and reliability of rotation-based TENGs.

Influence of tool eccentricity on surface roughness in gear skiving

Gear skiving is a state-of-the-art technique for machining internal gears with high efficiency. Numerical simulation method being able to analyze the eccentricity error e of cutter is critical to the understanding on the formation of surface roughness in skiving process. In this work, we proposed a novel Z-map-based numerical model to calculate the surface of gear flanks with eccentricity errors up to 9 μm. Correlation between eccentricity error and gear flank profile was clarified by numerical simulation and supported by experimental verification. The results show that the eccentricity error imposed a low-frequency motion during the generation of scallop height, leading to a surface roughness with a maximal error about four times that of the theoretical roughness. The e-induced scallop height became the majority factor account for variation of surface roughness when e exceeds 1.4 and 2.3 μm for feed rates of 0.4 and 0.8 mm/rev, respectively. The experimental result further supported the capability of proposed simulation model in providing detail surface features of gear flanks in skiving process.

The Effects of the Planet–Gear Manufacturing Eccentric Errors on the Dynamic Properties for Herringbone Planetary Gears

In the presence of manufacturing errors, the dynamic properties of herringbone planetary gear train (HPGT) can be altered from the originally designed properties to have undesired behavior. In this paper, by considering the herringbone gear actual structure characteristics, manufacturing eccentric errors of members (i.e., carrier and gears) and tooth profile errors of gears, time-varying meshing stiffness, bearing deformation, and gyroscopic effect, a novel lateral–torsional–axial coupling dynamic model for the herringbone planetary gear system is formulated by using the lumped-parameter method, which is able to be employed in the dynamic feature analysis of the HPGT with an arbitrary number of planets and different types of manufacturing errors. By applying the variable-step Runge–Kutta algorithm, the dynamic response of a HPGT system is studied for cases with and without planet–gear eccentric error excitations. The dynamic contact forces of gears and bearings are analyzed for the two cases in time and frequency domains, respectively. Moreover, the effect of the planet–gear eccentricity on the vibration accelerations of the HPGT system is also discussed. The obtained results indicate that manufacturing error excitations such as the planet–gear eccentricity have a pronounced influence on the dynamic behavior of the HPGT system.

Design of the portable fiber-optic current transformer for electrolytic aluminum industry

A portable fiber-optic current transformer (P-FOCT) based on the Faraday effect utilizing the fiber jumper and the flexible sensing coil is proposed to enhance the portability and improve the design for disassembly of FOCT in the electrolytic aluminum industry. To ensure the accuracy of P-FOCT, the polarization crosstalk of fiber jumper and the conductor eccentric error are studied. According to the theoretical analysis and experimental results, the relative error of P-FOCT would decrease as the distance between the current conductor and the non-closed node of the sensing coil increases. A new sensing head is designed and experiments show that the error is 0.31 % at variable temperature from 233K to 343K, which meets the requirement for accuracy in the electrolytic aluminum industry.

Research on the transmission error of swing-rod movable teeth transmission system

Using the two-tooth difference swing-rod movable teeth transmission system satisfying the drive function of large optical instruments as the study object, the influence of each component error on system transmission error is analysed. Each component error is presented by the vector method, and then it is transformed into equivalent error in the direction of the meshing action line based on the equivalent meshing error principle. The instantaneous transmission ratio of the system is obtained by the instantaneous velocity center method, and the system transmission error model is established. Using numerical analysis, the influence of each component error on the system transmission error is obtained. The transmission error test platform is used to test and analyze the transmission error of the two-tooth difference swing-rod movable teeth transmission system. The research results show that the swing-rod length error and the wave generator eccentric error have a great influence on the transmission error of the system among the six types of error factors, so they should be strictly controlled during design, processing and assembly. This study provides a theoretical basis for the rational allocation of machining errors and assembling errors of the two-tooth difference swing-rod movable teeth transmission system.

Influence of transmission errors to load sharing behaviour in Ravigneaux planetary gear sets

Ravigneaux planetary gear sets are widely applied in automotive, national defense, shipbuilding industry, etc.In this paper, orthogonal experiment method and variance analysis are utilized, to quantitatively analyze the influence of three typical transmission errors on the load sharing behaviour of Ravigneaux planetary gear sets. A 30 DOF translational-torsional coupling dynamic model of Ravigneaux planetary gear sets has been derived. Both qualitative and quantitative analysis indicate that load sharing coefficients of different meshing pairs are sensitive to different kinds of errors. As a result, key errors and key members which affect load sharing behaviour most are found out: the position error of short planetary gear, the installation error of small ring gear, and the eccentric error of sun gear. At the end, several fitting formulas are innovatively proposed in order to obtain load sharing coefficient, the results of proposed fitting formulas show great consistency with the calculation results of software Maple.

Load Sharing Behavior of Double-Pinion Planetary Gear Sets Considering Manufacturing Errors

The unequal load sharing of double-pinion planetary gear sets (PGSs) would take place because of manufacturing errors. A quasi-static model, suitable for any planet train number and support condition, was proposed considering manufacturing errors. The load sharing ratio of double-pinion PGSs with four planet trains was simulated for various planet position errors, whose results show that the radial planet position error has different effects on the load sharing behavior from simple PGSs. The mechanics for this phenomenon was revealed. The effect of the planet train number on the load sharing behavior in the presence of different planet position errors was then simulated by introducing the equivalent error variable. Finally, the effect of gear eccentricity errors on the load sharing behavior were simulated and some important characteristics were revealed such that the planet eccentricity error has worse impacts than position errors, and the effect of the eccentricity error of sun gear could be eliminated by floating the sun gear.

An On-Orbit Dynamic Calibration Method for an MHD Micro-Angular Vibration Sensor Using a Laser Interferometer.

The magnetohydrodynamic (MHD) micro-angular vibration sensor is a significant component of the MHD Inertial Reference Unit (MIRU) and measures micro-amplitude and wide frequency angular vibration. The MHD micro-angular vibration sensor must be calibrated in orbit since the ground calibration parameters may change after lift-off. An on-orbit dynamic calibration method for the MHD micro-angular vibration sensor is proposed to calibrate the complex sensitivity of the sensor in high frequency. An absolute calibration method that combines a homodyne laser interferometer and an angular retroreflector was developed. The sinusoidal approximation method was applied, and the calibration system was established and tested using a manufactured MHD sensor. Furthermore, the measurement principle and installation errors were analyzed, including the eccentric installation error of the retroreflector, the tilt installation error of the retroreflector, and the optical path tilt error. This method can be realized within a rotation range of and effectively avoid the installation error caused by mechanical errors. The results indicate that the calibratable angular vibration frequency range is 25–800 Hz, and the angular velocity range is –7590 mrad/s. The expanded uncertainties of the sensitivity amplitude and phase shift of the calibration system for the MHD micro-angular sensor are and .

Influence of installation error on roundness error measurement

The installation tilt causes the actual measured circular contour to be an elliptical contour [1], and the installation eccentricity causes the sampled points uneven [2], which can both affect the measurement accuracy of the roundness error [3, 4]. The tilt and eccentricity error must be separate from the measured data when measuring the cylindrical workpiece roundness error with a cylindricity measuring instrument to obtain the true contour information of the cylindrical workpiece itself. In this paper, the mathematical models of the workpiece installation tilt and eccentricity are established based on the least square roundness error evaluation algorithm. The influence of the workpiece installation tilt and eccentricity on the roundness error measurement are simulated by MATLAB, and an actual measurement is analysed. The results show that after leveling and centering the workpiece, the influence of the tilt and eccentricity error of the workpiece installation on roundness error measurement can be neglected when the Taylor565H type cylindricity measuring instrument is used for micron order roundness error measurement.