Spur Gear Transmission Research Articles

Theoretical analysis and experimental measurement of spur gear transmission error

Theoretical analysis and experimental measurement of spur gear transmission error

Nonlinear dynamic analysis of a coupled lateral-torsional spur gear with eccentricity

In this study, the dynamic behaviors of gear system are systematically analyzed with coupled lateral-torsional vibration caused by the gear meshing. A 4-degree-of-freedom (DOF) lumped parameter dynamic model for a spur gear, considering gravity, backlash, eccentricity, transmission errors, external excitation, is proposed. Parametric studies are performed to understand the influence of key parameters such as rotational speed ω, backlash b and error fluctuation er on the nonlinear dynamic behavior. The frequency response characteristics of spur gear system show that lateral resonance frequency and torsional resonance frequency simultaneously exhibit in lateral direction. In addition, other nonlinear phenomena including various forms of periodic, quasi-periodic and chaotic vibrations are analyzed. The results show that the nonlinear dynamical behaviors such jump discontinuous phenomena, single-sided impact and double-sided impact are strongly attributed to interaction between backlash, eccentricity and error fluctuant amplitude. Significantly, the appropriate rotational speed and decrease error fluctuant amplitude could effectively control the nonlinear vibration. Whereas the backlash has a complicated effect on the nonlinear dynamical characteristics. The results presented in this paper show that an analysis of the coupled lateral-torsional vibration (CLTV) of the spur transmission gear system. Some research results presented in this paper are useful to dynamic design and vibration control of spur gear transmission system.

Nonlinear dynamics analysis of the spur gear system for railway locomotive

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

Investigation on coupling effects between surface wear and dynamics in a spur gear system

A dynamic wear prediction methodology is proposed to investigate the coupling effects between surface wear and dynamics of spur gear systems. The overall computational scheme combines a quasi-static wear model and a translational-rotational-coupled nonlinear dynamic model. The worn surfaces are represented by modulated mesh excitations and introduced into the dynamic model to investigate the effects of surface wear on system׳s dynamic characteristics. The dynamic gear mesh forces are converted into an equivalent load by using the Miner rule to reveal the effects of dynamics on wear behaviors. A spur gear transmission is taken as an example system to demonstrate the interactions between surface wear and dynamic behaviors. The simulations indicate that surface wear and gear dynamics are highly interacted.

Frictional effects on the dynamic responses of gear systems and the diagnostics of tooth breakages

ABSTRACTTo develop accurate diagnostic techniques, this study examines the dynamic responses of spur gear transmission system with including frictional effects on a tooth mesh process. An 8-degree-of-freedom model is developed to include the effects of supporting bearings, a driving motor and a loading system. Moreover, it takes into account not only the time-varying stiffness, but also the time-varying forces and moments due to the frictional effect. The latter causes additional vibration responses in the direction of the off-line-of-action (OLOA). To show the quantitative effect of the friction, vibration responses are simulated under different friction coefficients. It shows that an increase in friction coefficient value causes a nearly linear increase in the vibration features of diagnostics. However, features from torsional responses and the principal responses in the line-of-action show less changes in the vibration level, whereas the most significant increasing is in the OLOA direction. Furthermore, the spectral peaks at the rotational and sideband frequencies are influenced significantly by small breakage defects, especially when the friction effect is taken into account. In addition, the second and third harmonics of the mesh frequency are more influenced than the first harmonic component for all motions, which can be effective features for both indicating lubrication deterioration and improving conventional diagnostic features.

On-line detection of incipient trend changes in lubricant parameters

Purpose– The purpose of this paper is to present a data fusion methodology for online oil condition and wear particles monitoring for assessment of a mechanical spur gear transmission system.Design/methodology/approach– In this work, a background understanding of the tribological phenomena behind oil degradation and wear on the contact surface of mechanical elements is presented. Experimental results were obtained from oil continuously sampled from an operating a single-stage gearbox. Sampling was done by a multi-sensor automated prototype and online analysis performed by algorithms implemented in a C-code programmed graphical user interface.Findings– Two sets of experiments were performed to observe different fault events frequently occurred in an industrial environment. Fault detection was achieved in appropriate time under constant operating conditions. Under variable operating conditions, same results were obtained by adjusting analysis parameters to critical operation conditions.Originality/value– The value of this research work is the integration of the hardware and software necessary for online monitoring of oil condition and mechanical wear. The setup integrates online sampling with data acquisition, wireless communication, change detection and fault recognition computation. The approach has application in non-destructive online condition-based maintenance.

Coupled multi-DOF dynamic contact analysis model for the simulation of intermittent gear tooth contacts, impacts and rattling considering backlash and variable torque

Variable torque conditions in geared powertrain applications are known to lead to tooth contact loss, contact reversal, tooth impacts, rattling vibration and noise. Displacements/ deflections dominate the low-torque high-vibration responses and, besides backlash, the real-time dynamic lateral deflections of the gear bodies and the occurrence of simultaneous double-sided tooth contact influence the instantaneous mesh excitation strongly. The faster deterministic and stochastic analytical models do not consider this coupling, whereas the numerical models that do so implicitly by simulating the contact of discretised tooth surfaces/ volumes are significantly limited by the accuracy and computational overhead of their discrete meshes. To provide a both fast and accurate solution of the contact problem, especially in displacement-dominated operating conditions, this work analyses the dynamic contact of gears starting from basic principles and derives an accurate analytical model for the coupling between the compliance, contact geometry, the backlash, and the torsional and lateral displacements and deflections in the general three-dimensional multi-DOF system. This serves as a foundation for a series of dynamical simulations of a single-stage spur gear transmission under different variable-torque excitations to predict tooth contact loss and contact reversal and the basic interactions that lead to impacts and rattling vibration. This approach can be used to predict critical torque fluctuation levels, beyond which these phenomena emerge.

Advanced model for the calculation of meshing forces in spur gear planetary transmissions

This paper presents a planar spur gear planetary transmission model, describing in great detail aspects such as the geometric definition of geometric overlaps and the contact forces calculation, thus facilitating the reproducibility of results by fellow researchers. The planetary model is based on a mesh model already used by the authors in the study of external gear ordinary transmissions. The model has been improved and extended to allow for the internal meshing simulation, taking into consideration three possible contact scenarios: involute–involute contact, and two types of involute-tip rounding arc contact. The 6 degrees of freedom system solved for a single couple of gears has been expanded to 6 + 3n degrees of freedom for a planetary transmission with n planets. Furthermore, the coupling of deformations through the gear bodies’ flexibility has been also implemented and assessed. A step-by-step integration of the planetary is presented, using two typical configurations, demonstrating the model capability for transmission simulation of a planetary with distinct pressure angles on each mesh. The model is also put to the test with the simulation of the transmission error of a real transmission system, including the effect of different levels of external torque. The model is assessed by means of quasi-static analyses, and the meshing stiffness values are compared with those provided by the literature.

The Engineering Design of Helical Spur Gear Transmission with Single Gear Pair for Electric Scooter

Traditionally, the reduction ratio of a spur gear pair is limited to 4 ~ 7. For a spur gear transmission with reduction ratio more than 7, it is necessary to have more than two gear pairs. Consider the cost of production, this paper proposes a helical spur gear reducer with one gear pair having reduction ratio 19.25 to substitute the gear reducer with two gear pairs. Based on the involute theorem, the gear data of helical spur gear pair is obtained. According to the gear data, its corresponding engineering drawing is accomplished. This manuscript verify that one spur gear pair also can have high reduction ratio (20 ~ 30).

On the theoretical foundation of flanking and profile modification of spur gear transmissions

In a theoretical justification, it is shown that a flanking and profile modification of spur gear transmissions is needed. It is proposed to make a profile modification of gear teeth based on mathematical modeling.

Analysis of Stochastic Nonlinear Dynamics in the Gear Transmission System with Backlash

Abstract In order to study the different backlash, gear damping ratio and random disturbance on dynamic behavior of gear transmission system, stochastic dynamic equations of the three-degree-of-freedom spur gear transmission system are established considering random disturbances of a low-frequency external excitation induced by torque fluctuation, gear damping ratio, gear backlash, excitation frequency and meshing stiffness. Using bifurcation diagram, phase diagram, time course diagram, Poincaré map and power spectrum of the system, the dynamic characteristics of the gear transmission system with different backlash under gear damping ratio changing, and the influence of the random disturbance of gear damping ratio on the bifurcation characteristic of system are analyzed. Numerical simulation shows that the gear transmission system will be from periodic motion with a noisy disturbance to chaotic-like motion by period-doubling bifurcation with decreasing gear damping ratio. In the small damping ratio range, the backlash has great effect on the motion characteristics. Random disturbance has an important effect on the bifurcation characteristics.

Contact between Logarithmic Crowned Teeth of Spur Gear Transmission

Gear tooth modification such as lead crowning can reduce stress concentration at the edges of the gear teeth; therefore prolong the fatigue life of gears. A logarithmical lead profile was applied on spur gears and the surface coordinate equation of logarithmic crowned tooth for manufacturing was established. On the basis of the contact mechanics model, the deformation equation of compatibility and load equilibrium equation were solved with an iterative numerical algorithm, and the corresponding programs were developed in Matlab to calculate the distributions of contact stress and von Mises stress field inside the subsurface layer at any meshing position. The numerical results of some typical examples show that the level of stress concentration before modification changes with the engaging locations of the gear teeth, and so does the amount of logarithmic modification along the line of contact, which can completely eliminate the edge effects of tooth surface at every meshing position during the spur gear transmission process, and thus improves the fatigue resistance of gear teeth surfaces.

Gear Diagnostics – Fault Type Characteristics


 
 
 To date, the majority of existing Condition Indicators for gears are based on various statistical moments of a recorded time history. A supplementary analysis proposed in this study, shall suggest an approach that may, in the future, enable the identification of faulty gearwheel and possibly fault type in the system. In this work, a combined analytical and empiric approach is applied. This approach is based on the assumption that reliable dynamic models can be utilized to predict the effects of faults on vibrational patterns. Dynamic model generated signatures are used to verify experimental findings. Moreover, discrepancies between simulated and actual results, combined with understanding of the assumptions and omissions of the model, are helpful in understanding and explaining the experimental results.A spur gear transmission setup was used for experiments, along with an electric AC motor and a friction belt loading device. The experimental runs were conducted at varying speed settings. Two types of faults, a tooth face fault and a tooth root fault, were seeded in the experimental transmission and into the model. The effect on extracted signal features is examined.
 The purpose of this study is to evaluate fault detection capabilities of proposed diagnostic tools at the presence of two seeded faults of varying severity, verified by a dynamic model. Observed differences between examined fault types and their manifestation will be discussed. A basis for future work on prognostics capabilities is laid by a varying degree of tooth root fault.
 
 

Modeling and Solution of a Nonlinear Vibration Model of the Bending-Torsion Coupled Spur Gear Transmission System Based on Lumped Mass Method

After comprehensive considerations of the influences of stiffness excitations, deviation excitations, meshing impact excitations, friction of tooth surfaces, gap changes and other kinds of nonlinear factors, it established a nonlinear vibration model of the bending-torsion coupled spur gear driven system based on Lumped Mass Method (LMM). By transforming the model to dimensionless form and using fifth order adaptive variable step (Runge-Kutta) method to solve the nonlinear vibration model of the system, it can get the time domain charts, spectrum charts, phase charts, Poincare charts, FFT charts and the system bifurcation figures. And then it discussed the influence of system parameter vibrations on its dynamic characteristics, and this could provide a foundation for system dynamic optimization design

Near-Field Beamforming Source Localization for Gear Transmission in a Semi-Anechoic Room

In this study, we discussed the sound sources localization and characterization for a spur gear transmission, which deals with a vibro-acoustic surveillance for predictive maintenance. The technique uses is based on the near-field Beam forming using Bartlett and Capon estimators. The measurements done on the gear transmission with a rectangular phased array of microphones were performed in acoustics and vibration laboratory (LVA) of the INSA of Lyon, in a semi-anechoic room. The gear transmission was considered sometimes open and sometimes closed. The results are presented as an image showing the acoustic field distribution radiated by the gear transmission at the most energetic frequencies. Both estimators have satisfactory results, but even better for the method with high resolution capon.

Analysis of effect of random perturbation on dynamic response of gear transmission system

In order to investigate the effects of random perturbation of a low-frequency excitation caused by torque fluctuations, gear damping ratio, gear backlash, meshing frequency and meshing stiffness, the random dynamic model of a single pair of three-degree-of-freedom spur gear transmission system is established. With gear meshing frequency changing, the dynamic characteristics of the gear transmission system were analyzed by bifurcation diagram, phase diagram, time course diagram and Poincaré map of the system. The effects of random perturbation caused by a low-frequency excitation caused by torque fluctuations, gear damping ratio, gear backlash, meshing frequency and meshing stiffness were comparative analyzed. Numerical simulation shows that the gear transmission system with nonlinear clearance exists rich period-doubling bifurcation phenomenon. With the increasing of the gear meshing frequency, gear transmission system will be from the chaotic motion to periodic motion by inverse period-doubling bifurcation. The effect of the meshing frequency random perturbation on the gear transmission system movement is largest. On the contrary, the effect of the meshing stiffness random perturbation on the system is minimum.

Influence of disk brake friction on the dynamic behaviour of a directly coupled spur gear transmission

Purpose– The purpose of this paper is to study the influence of friction phenomenon generated by a disc brake on the dynamic behaviour of a one-stage spur gear.Design/methodology/approach– A theoretical model is proposed and is based on both theories of Coulomb and Dahl in order to analyse the influence of disc brake friction phenomenon on the dynamic behaviour of one-stage spur gear transmission.Findings– The influence of brake friction on the dynamic behaviour of the transmission is investigated using the proposed model and leads to observe higher vibration levels when the braking is occurring as well as the emergence of significant efforts at the gear teeth.Originality/value– A new numerical model based on the implicit numerical integration technique of Newmark coupled with Newton-Raphson method is proposed to study the influence of friction phenomenon of a disc brake on the dynamic behaviour of one-stage spur gear.

Topological modeling of a one stage spur gear transmission

Finding a basis of unification for the modeling of mechatronic systems is the search subject of several works. This paper is a part of a general research designed to the application of topology as a new approach for the modeling of mechatronic systems. Particularly, the modeling of a one stage spur gear transmission using a topological approach is tackled. This approach is based on the concepts of topological collections and transformations and implemented using the MGS(modeling of general systems) language. The topological collections are used to specify the interconnection laws of the one stage spur gear transmission and the transformations are used to specify the local behavior laws of its different components. In order to validate this approach, simulation results are presented and compared with those obtained with MODELICA language using Dymola solver. Since good results are achieved, this approach might be used as a basis of unification for the modeling of mechatronic systems.

Gear transmission dynamic: Effects of tooth profile deviations and support flexibility

In this work a non-linear dynamic model of spur gear transmissions previously developed by the authors is extended to include both desired (relief) and undesired (manufacture errors) deviations in the tooth profile. The model uses a hybrid method for the calculation of meshing forces, which combines FE analysis and analytical formulation, so that it enables a very straightforward implementation of the tooth profile deviations. The model approach handles well non-linearity due to the variable meshing stiffness and the clearances involved in gear dynamics, also including the same phenomena linked to bearings. In order to assess the ability of the model to simulate the impact of the deviations on the transmission dynamics, an example is presented including profile deviations under different values of transmitted torque. Several results of this example implementation are presented, showing the model’s effectiveness.

Planet position errors in planetary transmission: Effect on load sharing and transmission error

In this paper an advanced model of spur gear transmissions developed by the authors is used to study the influence of carrier planet pin hole position errors on the behaviour of the transmission. The model, initially conceived for external gear modeling, has been extended with internal meshing features, and thus increasing its capabilities to include planetary transmission modeling. The new features are presented, along with the summary of the model general approach. The parameters and characteristics of the planetary transmission used in the paper are introduced. The influence of carrier planet pin hole position errors on the planet load sharing is studied, and several static cases are given as examples in order to show the ability of the model. Tangential and radial planet pin hole position errors are considered independently, and the effect of the load level is also taken into account. It is also given attention to the effect on the transmission error of the transmission. Two different configurations for the planetary transmission are used, attending to the fixed or floating condition of the sun, and the differences in terms of load sharing ratio are shown.