Pitch Error Research Articles

РАЗРАБОТКА МЕТОДА ПРОГНОЗИРОВАНИЯ ТОЧНОСТИ СПИРОИДНЫХ КОЛЕС

The article considers the possible errors of the spiroid transmission based on mathematical modeling of the process of shaping the teeth of the spiroid wheel. Typical errors such as tooth profile error, tooth pitch error, tooth thickness error, tooth longitudinal line error are applicable to spiroid wheel tooth errors. Currently, the accuracy standards for spiroid transmissions are not standardized. It is shown that the mandrel of a cylindrical spiroid cutter for processing spiroid wheels has an increased length, which contributes to its greater squeezing from the spiroid wheel during the shaping process. Based on the components of the cutting forces, a graph of the vibrations of the milling cutter mandrel is presented. In the study of precision spiroid wheels on the basis of a comprehensive analysis of the formation of the tooth profile of spiroid wheel revealed that the geometric deviations of the lateral surfaces of the teeth of wheels due to the errors of gear cutting tools and technological factors.

Gear tolerancing for simultaneous optimization of transmission error and contact pressure

With electrification of vehicles comes an increasing demand on low noise, which for gears translates to transmission error. In this paper, static transmission error, STE, is found for a large number of manufacturing error combinations belonging to different tolerance classes, with focus on those typically used in the automotive industry. There is a lack of studies found in the scientific literature which investigate the link between STE, contact pressure, and manufacturing error tolerances. Therefore, the aim of the present study is to investigate this link. This is done by utilizing a novel simulation tool, developed by the authors, to compute STE for gear sets with pitch and profile slope errors combinations. The model uses a parametric description of the reference profile, includes tooth modifications, uses a hybrid method for compliance, and finds contact from equilibrium. The model handles contact outside the nominal line of action, including tip contact.A simplified method, with predictions based on simulated values, is shown to be accurate and suitable for estimations. Finally, STE is linked to contact pressure for better understanding of how STE and contact pressure interact as a consequence of manufacturing errors. It is shown how this can be used to optimize the gear set with respect to both STE and contact pressure simultaneously.

Influence of manufacturing error tolerances on contact pressure in gears

Gear manufacturing always results in some degree of manufacturing errors, i.e. deviations from the desired gear geometry. These errors alter how the gears mesh, typically causing increased contact pressure which in turn shortens service life. It is therefore crucial to choose tolerances such that excessive contact pressure, and especially tip contact, is avoided. With increasing demands due to electrification, this becomes even more important. The aim of this paper is to study how pitch error and profile slope error affect the contact pressure in spur gears sets. The meshing is simulated using a novel simulation approach that uses a parametric description of the reference profile and gear geometry, and a hybrid model for the compliance. The method includes tooth modifications such as tip relief, and uses the true geometry to find contacts. Thus, it also handles contact outside the nominal line of action, including tip contact. The study includes cases where a gear is subjected to both pitch error and profile slope error simultaneously. Numerical examples, relevant to the automotive industry, show the outcome of the simulations. It is shown how simulation-based tolerances for relevant industrial applications can be used to improve manufacturing outcome.

Extraction of melody from polyphonic music using modified morlet wavelet

In this paper, the extraction of melody for polyphonic music is discussed. The method proposes a simple but effective modification in the Morlet wavelet as a modified Morlet wavelet (MMW). The pitch detection concept is applied to the transformed wavelet music signal for primary melody estimation and extraction. The proposed method is then compared with three other methods reported in the literature (the method focused on Short Time Fourier Transform, multi-resolution Fast Fourier Transform, and Morlet Wavelet). The percentage gross pitch error (GPE) parameter is considered for purposes of comparison. In comparison, it is observed that the proposed approach has the lowest GPE. The simulation results also present a lower percentage error in the predominant pitch frequency estimation for the proposed method.

Effect of positional errors on the accuracy of cervical vertebrae maturation assessment using CBCT and lateral cephalograms

BackgroundThe objective of this study was to evaluate the effects of single plane and multiplane rotational errors in yaw, pitch, and roll of the head while recording the lateral cephalogram on CVM (cervical vertebrae maturity) assessment. MethodsA total of 40 cone-beam computed tomography (CBCT) scans and 360 lateral cephalograms were analyzed for patients with different rotations: Controls (no rotation), Y5 (yaw 5° rotation), Y10 (yaw 10° rotation), R5 (roll 5° rotation), R10 (Roll 10° rotation), P5 (pitch 5° rotation), P10 (pitch 10° rotation), YRP5 (yaw, roll, and pitch 5° rotation), and YRP10 (yaw, roll, and pitch 10° rotation). The C2, C3, and C4 concavity and their base-anterior ratio and posterior-anterior ratio were measured. In addition, maxillomandibular linear parameters, such as effective mandibular length and height, mandibular body length, effective midface length, and maxillomandibular differential, were also evaluated. ResultsY5, Y10, R5, and R10 led to overestimation of CVM in comparison with controls. Multiplane rotations (YRP5 and YRP10) led to more inaccuracies in CVM measurements than single plane rotations; 10° of rotation led to more inaccuracies than 5° of rotation while recording the lateral cephalogram, irrespective of the plane. Yaw rotational errors led to an underestimation of maxillomandibular linear measurements, whereas roll rotational errors led to an overestimation of the measurements; however, there were wide individual variations in the measurements between the different rotations and controls. ConclusionsRotational errors lead to overestimation of CVM assessment. Multiplane rotations cause higher inaccuracies than single plane rotations. Increased degree of rotations while capturing the lateral cephalograms lead to more inaccuracies in CVM assessment.

Polarization characteristic analysis of orthogonal reflectors with a side-scanning galvanometer in a laser communication terminal system.

An alignment tolerance allocation and alignment method of orthogonal reflectors with high polarization-maintaining characteristics is presented. A geometric optics vector model of orthogonal reflectors is established to derive the propagation vector of the output beam, including pitch angle error of the first mirror, the side-scanning angle of the galvanometer, and rotation angle error of the secondary mirror. The polarization transmission matrix of the orthogonal reflectors is derived based on the 3D polarization ray-tracing algorithm to present the relationship between assembly errors and diattenuation or retardance of the orthogonal reflectors. A calculation example of certain polarization ellipticity error is given to quantitatively distribute the orthogonal mirror assembly error. The optimal side-sway angle selection method of the galvanometer side-sway angle in a laser communication system is presented; further, effective measures to minimize the polarization ellipticity error is put forward.

A Novel Alignment Method for SINS with Large Misalignment Angles Based on EKF2 and AFIS.

In order to achieve the fine alignment of strapdown inertial navigation (SINS) under large misalignment angles, a novel filtering alignment method is proposed based on the second-order extended Kalman filter (EKF2) and adaptive fuzzy inference system (AFIS). Firstly, the quaternion is employed to represent the attitude errors of SINS. A second-order nonlinear state equation is made based on the nonlinear velocity error model and attitude error model, and the linear measurement equation is based on the velocity outputs from SINS. Then, the filtering scheme is designed based on EKF2 and AFIS. The error estimation and fine alignment can be achieved by using the proposed filtering scheme. The results of Monte Carlo Simulation show that the errors of pitch, roll and yaw misalignment angles quickly decrease to about 14″, 15″ and 7.62′ respectively in 350 s under the condition of any misalignment angles with pitch error from −40° to 40°, roll error from −40° to 40°, and yaw error from −50° to 50°. Even when the initial misalignment angles are all very large such as (80°, 120°, 170°), the proposed nonlinear alignment method still can converge normally by utilizing the adaptive fuzzy inference system (AFIS) to adjust the covariance matrix Pk/k−1. Finally, the turntable experiment was performed, and the effectiveness and superiority of the proposed method were further verified by compared with other nonlinear methods.

Robust Development of Electric Powertrain NVH for Compact Electric SUV

<div class="section abstract"><div class="htmlview paragraph">Electric vehicles (EV’s) present new challenges to achieving the required noise, vibration & harshness performance (NVH) compared with conventional vehicles. Specifically, high-frequency noise and unexpected noise phenomenon, previously masked by the internal combustion engine can cause annoyance in an EV. Electric motor (E-motor) whine noise caused by electromagnetic excitation during E-motor operation is caused by torque ripple and radial excitation. Under high speed and high load operating conditions, the overall sound level may be low, however high frequency whine noise can impair the vehicle level NVH performance. An example of a previously masked unexpected noise phenomenon is a droning noise that can be caused by manufacturing quality variation of the spline coupling between the rotor shaft of the E-motor and the input shaft of the reducer. It is dominated by multiple higher orders of the E-motor rotation frequency.</div><div class="htmlview paragraph">In this study, the high speed and high load condition whine noise problem was reproduced through electromagnetic and structural analysis. The countermeasures (E-motor geometry refinements to reduce the excitations and mechanical system transfer path modifications to reduce the vibration response) were defined and the effects investigated. Mechanical system modification to improve NVH performance without increasing the mass is challenging. However, E-motor air-gap geometry optimization, such as slot opening modulation and rotor notch modifications achieved significant noise reduction without critical trade-off of other performance.</div><div class="htmlview paragraph">This paper also describes the basic improvement plan proposed through the simulation of the droning noise behavior. The main two manufacturing errors (pitch error in the spline coupling and the alignment error between the rotor and the gearbox shafts) that are responsible for the unexpected droning noise were identified. Using simulation it was shown that the droning noise can be reduced through improved quality control and tolerance design optimization of factors such as axis self-alignment and spline gear tooth quality.</div></div>

Analysis and improvement of the positioning accuracy of rotary axes of compound machine tools based on pitch error compensation

A method for pitch error compensation analysis and parameter identification for a rotary axis with special structures is proposed to improve the positioning accuracy of the rotary axes of compound machine tools. The characteristics of the planar linkage mechanism of a rotary axis are analyzed. Then, the error compensation trend is obtained according to the corresponding relationship between the angle and the displacement. An angular positioning error piecewise function is used to represent the ideal effect and actual performance of the pitch error compensation of the rotary axis. The rotation positioning accuracy test of the rotary axis is completed with a laser interferometer and rotary calibration device. By the measured angular positioning error of the non-compensated points, the Levenberg–Marquardt algorithm is used to identify the parameter of the piecewise function, and the optimized linkage parameters of the rotary axis are obtained. By the measured angular positioning error of the integer points of the rotary axis, the pitch error compensation value is modified. The distribution of the calculated and measured angular positioning error of the rotary axis under the pitch error compensation is consistent. The compensation results show that the positioning accuracy of the rotary axis can be greatly improved and that it meets the work requirement of the compound machine. The piecewise function of pitch error compensation, linkage parameter identification and improved method of pitch error compensation proposed in this article offer certain reference and application value. The results can improve the rotation positioning accuracy of the rotary axes of machine tools with planar linkages.

A Multifrequency Heterodyne Phase Error Compensation Method for 3D Reconstruction

In view of the problem of “jumping points” in the phase unwrapping of the multifrequency heterodyne principle, this paper proposes a novel method to improve the multifrequency heterodyne. By solving the root-mean-square error of the original frequency function, it includes the relationship between the error and the adjacent phase in the condition of constrained phase unwrapping, and it compensates phase ±2π of the skip point. To ensure the accuracy of phase unwrapping, the function with a “jump point” after each phase unwrapping and the absolute phase curve of the principal value function are used to establish the threshold judgment model of the least square method, and the initial phase unwrapping of the principal value function with different frequencies is carried out continuously. The simulation analysis of phase compensation with the four-step phase-shifting method shows that the error is reduced to 36% under the set environment. The experimental result of 3D reconstruction by measuring the flatness of the plate shows that the error decreases by 41% after phase compensation compared with before phase compensation. The three-dimensional reconstruction experiment of pitch measurement with a nut shows that the nut after phase compensation is smooth without noise, and the pitch error is 0.033 mm, which verified the method is workable and effective.

Effect of detector installation error on the measurement accuracy of multi-degree-of-freedom geometric errors of a linear axis

A linear axis is the key component of several mechanical machines, especially of computer numerical control machine tools. The simultaneous measurement of the geometric motion errors of a linear axis is indispensable to compensate the machine errors, which improves the accuracy of machine tools. The principle of laser collimation is widely used for measuring the multi-degree-of-freedom (MDOF) geometric motion errors of a linear axis. However, installation errors of the detectors affect the measurement accuracy. In this study, we have proposed, for the first time, a measurement model for investigating the influence of all detector installation errors on the accuracy of the simultaneous measurement of MDOF geometric motion errors in a linear axis. The effect of detector installation errors on the horizontal straightness, vertical straightness, pitch, and yaw are analyzed using the homogeneous transformation method, which indicates that angular installation errors of detectors along the X0-axis direction can cause a crosstalk between the two straightness errors and between pitch and yaw errors. In addition, translational installation errors of position-sensitive detectors in the X0-axis direction, which is often called the defocusing amount, has a significant effect on the pitch and yaw measurements. To elucidiate the effect of defocusing, a measurement model was verified by both Zemax simulation and experiments. The experimental results indicate that the maximum deviation of the measured results obtained using the proposed model from that obtained using a Renishaw XL-80 interferometer can be greatly reduced by compensating the measurement errors induced by defocusing.

Study on the quality and tooth root load carrying capacity of the high contact ratio asymmetrical gear tooth machined using WCEDM process

ABSTRACT This work aims to report the quality of the high contact ratio asymmetrical gear tooth manufactured through wire cut electrical discharge machining(WCEDM) process and static load capacity of the gear tooth. The effect of various process parameters such as peak current (IP), pulse on time (Ton), pulse off time (Toff) and servo voltage (SV) on the performance parameters such as Surface roughness (Ra) and Kerf width (Kf) has been examined on the regular shaped specimen. Taguchi method was used with process parameters at three levels and the significance of WCEDM process parameters was studied through analysis of variance (ANOVA). Based on the significant process parameter values, the gears were manufactured and gear tooth errors such as profile, lead and pitch errors were estimated based on DIN3962 Standard using the Gleason inspection system and found that the range of quality of the gear obtained through this process was from Q8-Q11. The experimental test results conducted to explore the tooth root load carrying capacity of the gear tooth revealed that the gear with lower pressure angle at the non-drive side (17º-20º) has a maximum load carrying capacity and maximum yielding when compared to symmetric (20º-20º) and asymmetric gears with higher pressure angle at the non-drive side (22º-20º).

Sensitivity analysis of input errors to motion deviations of underwater glider based on optimized response surface methodology

This paper attempts to study the effects of control parameters errors and launching attitude errors on the motion of an underwater glider, and these errors are collectively called as input errors. The dynamics model of the underwater glider is established. To simplify the quantitative characterization of motion deviation, an evaluation parameter which can simultaneously characterize the path deviation and velocity deviation is proposed. On these bases, the motion deviations of the glider are quantitatively analyzed under two kinds of input errors. The control parameters errors include the net buoyancy adjustment amount error, the movable internal mass block translation amount error and the movable internal mass block rotation amount error. The launching attitude errors include the roll angle error, the yaw angle error and the pitch angle error. Then, an optimized response surface methodology (ORSM) is proposed to obtain the approximate function expressions between the input errors and the evaluation parameter of motion deviation. In the ORSM, the multi-island genetic algorithm (MIGA) is used to identify the key terms of polynomial. And the approximate function expressions are fitted by the polynomials including only the key terms, which can effectively weaken the polynomial wiggle. After that, the sensitivity analysis of input errors to motion deviations is achieved based on the above approximate function expressions. The results indicate that all control parameters errors and the yaw angle error should be small enough to avoid unacceptable motion deviations. In addition, the coexistence of particular input errors can offset motion deviations partially. The research results provide significant guidance for the accuracy design of underwater glider.

A Study of Pronunciation Errors in the Reading of Kanji Words in Cases with Pure Apraxia of Speech

In this study we investigated the pronunciation error patterns in Kanji words of two patients with pure apraxia of speech. We asked the patients to read aloud 80 visually presented Kanji words, half of which were homonymous and the rest non-homonymous. The words were presented at three different intervals (2, 1.5 and 1 sec.). Case A, a 68-year-old right-handed woman, produced a variety of sound errors - substitution, distortion and omission - and some errors of pitch position. Case B, a 73-year-old right-handed woman, omitted the prolonged vowels of each word, and produced many pitch errors, including pitch position errors and flattening of pitch. Each patient had different lesions in the left precentral gyrus - Case A from the posterior bank to the middle part of the left precentral gyrus, and Case B in the anterior bank and deep white matter of the left precentral gyrus. We speculated that Case A has difficulty mainly in the articulation process and vocalization, whereas Case B's deficit lies mainly in the phonation process, which relates to control of pitch and expiration.

High-resolution nonfluorescent imaging with structured illumination for patterned surface measurement

Surface patterning is widely performed in various applications, and hence high-resolution, high-throughput, and nondestructive measurement of patterned surfaces is required. The current optical methods used for such measurements are constrained, in terms of spatial resolution, by the diffraction limit. In this study, structured illumination was employed for high-resolution wide-field imaging measurements. Structured illumination microscopy is well known as a fluorescent bio-imaging technique. For nonfluorescent imaging and industrial measurement applications, however, speckle noise, generated by the structured illumination pattern, environmental vibrations, and thermal drift, causes problems for the high-precision positioning and control of the illumination pattern. To solve these problems, we developed a structured illumination microscope that detects the phase of the structured illumination as a fringe signal by using an additional interferometric measurement system. In this system, a low-coherence light source is employed for illumination pattern generation and high-resolution imaging with low speckle noise. The constructed optical system consists of multiple Michelson interferometers that allow the manipulation of low-coherence interference fringes at the sample position and the detection of the phase via another sensor. Robust imaging can be implemented by feeding back the structured illumination phase through super-resolution image processing. We experimentally achieved high-resolution nonfluorescent imaging with low speckle noise and resolved patterned surfaces beyond the diffraction limit without high-precision positioning stages. Furthermore, the image reconstruction algorithm typically used in structured illumination microscopy was improved by adopting a Fourier ptychography approach. Thus, artifact reduction, as well as decreases in luminance and pitch errors, was achieved, and this result represents a step forward in the development of practical measurement methods for patterned surfaces.

Simultaneous Constant Velocity Measurement of the Motion Errors of Linear Axes

The current standard for machine tool calibration supports the use of quasi-static measurement techniques. When measuring the six degrees of freedom motion errors, the measurements are typically taken consecutively. This introduces uncertainty when comparing the results due to machine deformation during individual measurements. Furthermore, quasi-static measurement techniques are known to be time consuming, a problem that is exacerbated as each degree of freedom must be measured separately. Additionally, the spatial resolution between the selected target positions can have an impact on calibration quality. In the following paper, the benefits of measuring the six motion errors simultaneously while the axis under test is traversing at a nominally constant velocity are presented. Firstly, the motivation for simultaneous continuous capture is presented. Secondly, continuous motion measurements are compared with quasi-static measurements for the six degrees of freedom motion errors showing sub-micrometer and sub-arcsecond correlation. The full effect of a ball screw pitch error is shown which can be missed using traditional quasi-static measurement techniques. Finally, wavelet analysis is performed for further spatial diagnostics along with correlation coefficients calculated to quantify the linear dependency between the six error motions.

Investigation on Sensorless Estimating Method and Characteristics of Friction for Ball Screw System

In this study, a novel sensorless method is developed to estimate the friction in a ball screw system using asynchronous experimental data for a worktable position (WP) and the servo motor torque current (SMTC), which is collected by the FOCAS library functions from a FANUC digital control system. The corresponding time stamps are retrieved by a high-resolution performance counter in Windows. The fluctuations in friction over the whole travel distance of the worktable (WTDOW) are analyzed using a piecewise polynomial fitting algorithm to extract the instantaneous average friction value (IAFV) and the friction fluctuating signal (FFS). The IAFVs can describe the effect of the WP and the pitch errors of the shaft on the friction. The FFT results of the FFS show that the friction depends on the rolling tool, the pitch of the shaft and the refeeding of the balls in the ball screw and linear ball rail guides. The experimental results show that the estimated friction can capture the characteristic spectra of the FFS. The effects of the feed velocity and direction, the effects of the WP on the IAFV, and the frequencies and amplitudes of the significant FFT components are discussed. The nonuniform pitch errors of the shaft impact the repeatability of the IAFVs at a given WP. The variations in the mean value of the IAFVs with the feed velocity for tests at a fixed WP show nonconventional Stribeck behavior. These results also demonstrate that the friction force varies with the WP, which is not captured by Stribeck characteristics. This study provides an effective method to evaluate the performance of a ball screw system and to predict the friction in that system without the use of sensors.

Influence of long-wave deviations on the quasi-static and dynamic excitation behavior at higher speeds

The scarcity of fossil fuels and increasing oil prices are among the factors that have led to a rising ownership of electric cars [1]. Noise reduction also plays a major role primarily in the drive train of motor vehicles. Noise and vibration excitation differ between a combustion engine and an electric motor. While the disturbing noises of auxiliaries, e.g. gear noise, have been largely masked by combustion engines, theses noises are no longer masked due to the use of electric motors [2]. Therefore, gear noise is perceived more pronounced. Considering the subjective perception and the excitation by rotational frequencies, that fall into the sensitive hearing range of high-speed gearboxes, the focus must be increasingly placed on manufacturing and assembly related long-wave deviations, such as wobble, pitch errors and eccentricities.This report investigates the effects of long-wave deviations of gears in gearboxes on the excitation and noise behavior. Quasi-static investigations were carried out to verify the influences of long-wave deviations on the long-wave excitation behavior. Therefore, the transmission error was measured, which describes the rotational fluctuation between input and output and represents the excitation.This investigation verifies according to the simulativ investigation by Brecher et al. that there is no transmission error dependency on the load [3]. In addition, this investigation proves the macro geometry-independent long-wave excitation in case of eccentricity. The reason for the invariant excitation behavior lies in the effective deviation in the gear mesh which in this case is independent of the mentioned parameters.In addition to the quasi-static tests, investigations of the structure-borne noise were carried out at higher speeds (input rotational speed up to nIn = 11,500 rpm). For these investigations, a two-stage gearbox with a test gear set was used and two different eccentricities and wobbles were manufactured. The analysis of these investigations confirm an increased excitation as a result of the deviations. Especially in natural frequency ranges, the excitation in the first rotational order is amplified by the considered long-wave deviations.The experimental results prove the importance of a function-oriented tolerance system for long-wave deviations, which lead to corresponding long-wave excitations. Furthermore, the findings constitute the first basis for the derivation of these tolerance limits.

Full-scale measurement of CNC machine tools

Geometric error measurement is crucial for error compensation and machining accuracy of CNC machine tools. However, traditional double-ball bar (DBB) method cannot be used for full-scale measurement of geometric errors due to the constant length of bars. In this paper, a full-scale measurement of geometric errors for CNC machine tools with high efficiency is carried out based on the double ball bar with a ball joint (J-DBB) method. Firstly, the principle of J-DBB is introduced. The J-DBB can be used for a full-scale measurement thanks to its freely measuring radius. Then, the equations of geometric errors which include squareness error, straightness error, roll error, pitch error, and yaw error of the axes are theoretically analyzed. In the end, we compared the theoretical trajectories of circular interpolation with the actual ones. The geometric errors between theoretical trajectories and actual ones can be measured and shown by J-DBB method. The results revealed that the J-DBB can be applied to conduct the full-scale measurement of geometric errors in CNC machine tools. Besides, the measurement range of geometric errors is extended from a two-dimensional circle to a three-dimensional sphere with a radius of 0.259L to 2L.

Error modeling and analysis of optomechanical platform based on multi-system theory

The quality of camera imaging is of great significance in aerial photography and space target detection, especially in the fields of military reconnaissance and geographic resource telemetry. There are many factors that affect the imaging quality of a camera mounted on the ground. One such factor is the optomechanical platform, as well as other related factors such as system control accuracy and optomechanical platform processing accuracy, where the optical axis pointing error is especially important for measuring the accuracy of a camera’s optomechanical platform. In this paper, to study the influence of the optical axis pointing error on the accuracy of the optomechanical platform, error traceability of a self-developed complex optomechanical platform is established, and based on the multi-body system theory, the spatial geometric error model of the platform and the mapping relationship between the optical axis pointing error and the geometric errors of the optomechanical platform are established. By analyzing the optical axis pointing error model, the influence of vertical axis errors of the pitch axis, azimuth axis, and rotation axis of the optomechanical platform on its optical axis is found. The results show that with the influence of the azimuth axis perpendicularity error, the pointing error decreases as the pitch angle increases, with the influence of the pitch axis perpendicularity error, the pointing error increases as the pitch angle increases, and with the influence of the rotation axis perpendicularity error, in the case of a smaller rotation angle, the pointing error increases as the pitch angle increases.