Gear Manufacturing Errors Research Articles

Research of the deformability of the cantilever axis of the satellite of a multi-satellite planetary gear and its influence on the load distribution over power flows

A mathematical model of the axis of the satellite, cantilevered in the cheek of the carrier of the planetary gear, is presented. The axis of the satellite is presented in the form of a beam on an elastic base. The influence of the flexibility of the axle and the drive elements mated with it on the distribution of the load over power flows is considered. The Leibniz formulas and the Euler method were used to obtain the model. The coefficient of uneven load distribution over power flows is obtained by solving a system of displacement compatibility equations, including deformations of the wheel teeth, rolling bearing, satellite axle and mating parts, taking into account the initial non-adherence of the teeth due to gear manufacturing errors. The load capacity of a planetary gear with cantilever axes of satellites is analyzed depending on the number of power flows. Keywords: planetary gear, deformation, cantilever axle, load distribution. fplehanov@list.ru, alexandrsun4009@gmail.com

Influence Analysis of the Gear Manufacturing Error on Transmission Vibration Response

Influence Analysis of the Gear Manufacturing Error on Transmission Vibration Response

INVESTIGATION OF THE INFLUENCE OF GEAR ERRORS ON THE PERFORMANCE OF THE ROCKING MACHINE GEARBOX

This article presents the results of a study of the influence of gear manufacturing errors on the smooth operation of the reducer of the mechanical drive of the oil pumping unit based on a specially developed 3D modeling technique for the formation of kinematic error. This technique consists in constructing a three-dimensional solid-state model of a gear transmission with specified primary errors of the wheels and subsequent modeling of the gear engagement operation. Models of gears are obtained as a result of modeling the tooth-cutting process. This makes it possible to include manufacturing errors in the gear models caused by various technological reasons, such as, for example, fluctuations in the chain links of the machine, the beating of the cutting tool and the workpiece, errors in the cutting edges of the tool, errors in the installation of cutting tools, etc. The simulated graphs of the kinematic error of gears consisting of wheels are given, which contain the main manufacturing errors affecting the smooth operation of the reducer of pumping unit (errors in the lateral profile of the teeth, the error of the gearing step). Keywords: pumping unit, reducer, errors, working capacity.

Prognostics of Gear Manufacturing Errors for Planetary Gear Systems Based on Power Flow Theory

Abstract Gear manufacturing errors are key parameters in planetary gear trains and have effects on load sharing, tooth stress, and so on. Accurate estimation of manufacturing errors can help monitor the conditions of planetary gear systems. This study investigates the dynamic response sensitivity to model parameters for a nonlinear single-stage planetary gear set with coupled lateral and torsional motions. Power flow theory is introduced to assess the gear vibration and the parameter sensitivity. The response sensitivity equations are deduced with the direct method (DM). The influence of the rotating speed is considered in the sensitivity analysis. Then, the identifiability of the parameter estimation is investigated based on the sensitivity results. The Gauss-Newton method is applied to estimate the manufacturing errors. Gear meshing is a primary factor in gear vibration, so the sensitivities of its vibration power to the parameters are analyzed in this paper. The estimated results are accurate when the collected data contain a lower noise signal. The sensitivity and parameter estimation make it possible to provide support for the design and diagnosis of a planetary gear set.

Modulation sideband analysis of a two-stage planetary gear system with an elastic continuum ring gear

For a planetary gear system, the flexibility of its components can significantly affect mesh excitation, modal property, and dynamic behavior. However, current research has not revealed the influence of flexibility on the sidebands of vibration spectrum. For this purpose, in our earlier work, we addressed a new elastic-discrete planetary transmission model with an elastic continuum ring gear (originally presented in Wei Liu, Zhijun Shuai, Yibin Guo, Donghua Wang, Modal properties of a two-stage planetary gear system with sliding friction and elastic continuum ring gear. Mechanism and Machine Theory, 135 (2019) 251–270). The previous model study is solely based on free vibration without including sideband analysis. The present work aims to investigate modulation behavior of an elastic two-stage planetary gear (TSPG) system, thus expanding the previous work not only for modal property comparison but also for sideband analysis of the elastic planetary gear. First, gear mesh interface excitations with amplitude modulation (AM) and frequency modulation (FM) due to manufacturing errors are developed to analyze the sideband activity. Then, through loading gear mesh excitations with gear manufacturing errors on the previous model, acceleration spectra with and without sidebands are compared by an analysis with an example. To clearly show the modulation behavior, the effect of ring's elasticity and fluctuating torque on the sidebands is investigated. Finally, a TSPG test bench is proposed to measure the acceleration spectra. The measured spectra are compared to demonstrate the capability of the proposed model in predicting the sidebands of a planetary gear with manufacturing errors.

Vibration signal analysis of planetary gear with amplitude, frequency and phase modulation

In this paper, the vibration signal of planetary gear with amplitude, frequency and phase modulation is studied. The proposed mathematical model is employed to in- vestigate the modulation behavior of planetary gear. Based on this model, the ampli- tude modulation (AM) sidebands are analyzed to verify the correctness of theoretical calculation by Inalpolat and Kahraman. Then, the frequency modulation (FM) side- bands and phase modulation (PM) sidebands are also illustrated through an exam- ple analysis. The effects of parameters of planetary gear such as number of planets, teeth of sun and planet phasing relationships on the AM, FM and PM sidebands are analyzed. Finally, the specific expression of transmission error, time-varying mesh stiffness and dynamic mesh force including gear manufacturing error is developed. Time history signal and acceleration spectra of gear mesh interface excitations including AM, FM and PM are investigated for the meshes of sun-planet and ring- planet. The results show that gear parameters have important influence on the mod- ulation behavior. Additionally, manufacturing errors can be introduced to predict the sidebands of planetary gear. The amplitude, frequency and phase modulation study are extremely significant for the noise and vibration reduction, especially the fault diagnosis of planetary gear

Исследование напряженно-деформированного состояния щеки водила планетарной передачи

Planetary gears are commonly used in drive technology due to their high load capacity and good weight and size parameters. Among planetary gears, multi-satellite structures with a minimum number of excessive links are most widely used. They have a close to uniform distribution of the load in the engaged gears, which has a positive effect on the strength and bearing capacity of the drive. Such designs include planetary gears, the satellites of which are mounted on spherical bearings, and one of the main links (most often the sun gear) is self-aligning. This provides a theoretically uniform distribution of the load in the engaged gears when the mechanism has three satellites. However, high-loaded drives often use designs with a large number of satellites where the load is distributed unevenly due to gear manufacturing errors. The deformability of individual transmission elements has a significant positive effect on the distribution of the load in the gears, thus compensating for the manufacturing errors. In view of this, the authors propose a multi-satellite planetary gear with a carrier made with grooves in the cheeks, which reduces their rigidity and provides, with a rational choice of the parameters of the mechanism, an increase in the mechanism’s bearing capacity. When determining the carrier cheek’s compliance, two schemes of loading in the coupling zone with the axis of the satellite (uniform and nonuniform) are considered. The solution is obtained using Mohr’s integrals. A numerical analysis of the stressed-strain state of the carrier cheek performed using the finite element method in the SolidWorks environment showed that the results of the analysis were close to the theoretical ones. They corresponded to a uniform load distribution in the coupling zone of the satellite axis and the carrier cheek. The obtained dependences can be used in the design of a mechanical drive to determine the coefficients of the uneven load distribution over the planetary gear satellites and over the individual crowns of the satellite.

Modeling of manufacturing errors in external gear machines and experimental validation

Manufacturing errors are always unavoidable in actual machines. In external gear machines (EGMs), some of the manufacturing errors are typically on the same scale as the nominal clearances between the internal parts. These clearances are responsible for leakage flows that reduce the volumetric efficiency of EGMs and impact their overall performance. Current approaches of modeling the operation of EGMs neglect the manufacturing errors which limits their accuracy.This paper proposes a technique to study the operation of EGMs accounting for two common gear manufacturing errors: conicity and concentricity. Furthermore, an alternate technique to model these errors is proposed by defining an “effective gap height”. This latter technique can be used in any existing lumped parameter model as well as for quick estimations. To validate the approach, experiments are performed with gearsets exhibiting varying amounts of conicity and concentricity errors.The results from both the simulations and the experiments show that the volumetric efficiency decreases with an increase of the conicity error. Instead, by increasing the concentricity error, an increase in the volumetric efficiency is found, at least until the conditions of contact between the gears and the casing's internal surface are avoided.

Load-sharing analysis of two-stage three-branch star gearing based on deformation compatibility

A load-sharing analysis methodology was proposed for the multiple-branch star gear transmission which is composed of a number of closed-loop power flows. The moment equilibrium and deformation compatibility equations for the two-stage star gearing were derived, which are clearly different from that used in planetary gear transmission. Then the load-sharing analysis model was established and employed to systematically study the load-sharing behavior of the two-stage three-branch star gearing, some untouched aspects were investigated. Results show that the most sensitive directions of the central and star gear assembly errors on load-sharing are along the meshing line. The effects of the size and direction of the central gear–manufacturing errors on load sharing are the same for each branch, the initial directions of the central or a certain star gear–manufacturing errors will have no effect on the load-sharing coefficient of the system, but the initial directions of the assembly errors will. The conditions in which the load distribution curves repeat the first track were also obtained. Finally, a numerical example of a three-branch star gear aviation reducer was adopted to verify the feasibility of this proposed method, and the calculation results show good agreement with a previously published and validated model.

A manufacturing error measurement methodology for a rotary vector reducer cycloidal gear based on a gear measuring center

A manufacturing error of a cycloidal gear is the key factor affecting the transmission accuracy of a robot rotary vector (RV) reducer. A methodology is proposed to realize the digitized measurement and data processing of the cycloidal gear manufacturing error based on the gear measuring center, which can quickly and accurately measure and evaluate the manufacturing error of the cycloidal gear by using both the whole tooth profile measurement and a single tooth profile measurement. By analyzing the particularity of the cycloidal profile and its effect on the actual meshing characteristics of the RV transmission, the cycloid profile measurement strategy is planned, and the theoretical profile model and error measurement model of cycloid-pin gear transmission are established. Through the digital processing technology, the theoretical trajectory of the probe and the normal vector of the measured point are calculated. By means of precision measurement principle and error compensation theory, a mathematical model for the accurate calculation and data processing of manufacturing error is constructed, and the actual manufacturing error of the cycloidal gear is obtained by the optimization iterative solution. Finally, the measurement experiment of the cycloidal gear tooth profile is carried out on the gear measuring center and the HEXAGON coordinate measuring machine, respectively. The measurement results verify the correctness and validity of the measurement theory and method. This methodology will provide the basis for the accurate evaluation and the effective control of manufacturing precision of the cycloidal gear in a robot RV reducer.

Geometric Product Specification of Gears: The GeoSpelling Perspective

Gears as the key transmission parts of machineries are widely used in mechanical and aeronautical fields. GeoSpelling, a framework standardized as ISO 17450-2005 supported tolerancing process by a set of concepts and mathematical algorithms, is a coherent and complete model to manage the shape variations of geometrical parts. Considering current gear specification standards incline to inspection convenient ignoring tolerance quality control, so it is a realistic necessary to develop a coherent gear specification model based on GeoSpelling language. This model should not only consider integrating functional requirements involved in design stage but also be able to correspond to manufacturing and inspection procedures.In this paper a new approach based on discrete geometry is introduced to design gear specification model. It is also focus on a perspective discussion on how SSA (Statistical Shape Analysis) method could be a solution to analyze the gear integrated errors into different individual errors, such as tangential composite error, tooth-to-tooth tangential composite error, pitch accumulated deviation, tooth-to-tooth pitch accumulated deviation and geometric eccentricity.The fundamentals mentioned above provide a reliable methodology for analyzing gear manufacturing errors. As a result it is able to enhance the computational processing capability and metrological traceability for gear quality control.

Detection and Localization of Tooth Breakage Fault on Wind Turbine Planetary Gear System considering Gear Manufacturing Errors

Sidebands of vibration spectrum are sensitive to the fault degree and have been proved to be useful for tooth fault detection and localization. However, the amplitude and frequency modulation due to manufacturing errors (which are inevitable in actual planetary gear system) lead to much more complex sidebands. Thus, in the paper, a lumped parameter model for a typical planetary gear system with various types of errors is established. In the model, the influences of tooth faults on time-varying mesh stiffness and tooth impact force are derived analytically. Numerical methods are then utilized to obtain the response spectra of the system with tooth faults with and without errors. Three system components (including sun, planet, and ring gears) with tooth faults are considered in the discussion, respectively. Through detailed comparisons of spectral sidebands, fault characteristic frequencies of the system are acquired. Dynamic experiments on a planetary gear-box test rig are carried out to verify the simulation results and these results are of great significances for the detection and localization of tooth faults in wind turbines.

Effects of Gear Manufacturing Error on the Dynamic Characteristics of Planetary Gear Transmission System of Wind Turbine

The effects of gear manufacturing error on the dynamic characteristics of planetary gear transmission system of wind turbine are studied in this paper. Firstly, the static transmission error combined with manufacturing error of the gear is deduced. Then, the nonlinear dynamic model of planetary gear transmission system of wind turbine is set up with the consideration of time-varying mesh stiffness, backlash and manufacturing error. Finally, the statistical characteristics of Vibration displacement response process of each component of planetary gear transmission system are obtained by simulation analysis of the planetary gear system of 1.5MW Semi-direct drive wind turbine with the consideration of the torque fluctuation caused by wind speed. The research results lay a foundation for reliability design and optimizing of gear transmission system of wind turbine.

A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors

In this study, a nonlinear time-varying dynamic model is proposed to predict modulation sidebands of planetary gear sets. This discrete dynamic model includes periodically time-varying gear mesh stiffnesses and the nonlinearities associated with tooth separations. The model uses forms of gear mesh interface excitations that are amplitude and frequency modulated due to a class of gear manufacturing errors to predict dynamic forces at all sun-planet and ring-planet gear meshes. The predicted gear mesh force spectra are shown to exhibit well-defined modulation sidebands at frequencies associated with the rotational speeds of gears relative to the planet carrier. This model is further combined with a previously developed model that accounts for amplitude modulations due to rotation of the carrier to predict acceleration spectra at a fixed position in the planetary transmission housing. Individual contributions of each gear error in the form of amplitude and frequency modulations are illustrated through an example analysis. Comparisons are made to measured spectra to demonstrate the capability of the model in predicting the sidebands of a planetary gear set with gear manufacturing errors and a rotating carrier.

Influence of Carrier and Gear Manufacturing Errors on the Static Load Sharing Behavior of Planetary Gear Sets

In this paper, a state-of-the-art contact mechanics model of a planetary gear set is employed to study the effect of a number of manufacturing and assembly related carrier and gear errors on the load sharing amongst the planets. Three different groups of errors are considered: (i) time-invariant, assembly-independent errors such as carrier planet pinhole position errors, (ii) time-invariant, assembly-dependent errors such as planet tooth thickness errors, and (iii) time-varying, assembly-dependent errors such as gear run-out errors. With such errors present, planet load sharing characteristics of an n-planet system (n=3 to 6) is investigated for different piloting configurations under quasi-static conditions. Load sharing behavior as a function of key manufacturing errors is quantified and design guidelines are proposed for better planet load sharing behavior.

Analysis of tooth contact and load distribution of helical gears with crossed axes

This paper presents an approach for the analysis of tooth contact and load distribution of helical gears with crossed axis. The approach is based on a tooth contact model that accommodates the influence of tooth profile modifications, gear manufacturing errors and tooth surface deformation on gear mesh quality. In the approach the tooth contact load is assumed to be distributed along the tooth surface line that coincides with the relative principal direction of the contacting tooth surfaces. As compared with existing tooth contact (TCA) analysis model that assumes rigidity for the contacting surfaces, the model in this paper provides a more realistic analysis on gear transmission errors, contact patterns and the distribution of contact load. As a numerical example, the contact of a pair of helical gears with a small crossing angle is analyzed by the computer program that implements the approach. It is found from the analysis that helical gears with small crossing angles have meshing characteristics and load distribution similar to those of parallel-axis gears. The approach may be extended to other types of gearing.