Gear Deformation Research Articles

Investigation of the Effects of Design Parameters on Tooth Profile Formation and Operating Performance in Cycloidal Reducers

Cycloidal reducers have a unique and complex tooth profile design compared to conventional gear systems. Unlike standardized gear profiles, cycloidal reducers provide significant flexibility in design parameters such as module, profile modification coefficient, and eccentricity. However, these parameters interact in a complex manner, affecting both tooth profile formation and the overall performance of the reducer. Inaccuracies in selecting parameters may lead to problems such as excessive contact stress, gear deformation or reduced load transfer efficiency. This study aims to investigate the effects of design parameters on the formation of cycloidal tooth profiles and the operating performance of reducers. By analyzing the relationships and interactions between these parameters, the research provides a deeper understanding that will improve design processes, enhance performance, and contribute to future standardization efforts. As a result, this study aims to contribute to the development of cycloidal reducers that are structurally robust, efficient and suitable for high-performance operation.

Extended influence coefficient method for meshing stiffness evaluation of spur gears considering rotor flexibility

Rotor-supported gears are applied in transmission systems, and the rotor flexiblility leads to the misalignment of the gear pair with multiple degrees of freedom, which ultimately leads to the decrease of meshing stiffness. To evaluate the meshing stiffness of rotor-supported gears, the extended influence coefficient method (EICM) is proposed in this paper. Firstly, the gear contact position adjustment under misalignment condition is carried out. Then, the extended influence coefficients of bending, shearing, axial compression, Hertzian contact and fillet foundation deformation of gears are derived to obtain the extended influence coefficient matrix. Afterward, the load-deformation equations under different contact states are obtained, and the meshing stiffness is calculated. Subsequently, a cantilever rotor-gear coupling dynamic model is established by the rigid body element-extended influence coefficient method (RBE-EICM), and the dynamic meshing stiffness considering rotor flexibility is obtained. The accuracy of EICM and RBE-EICM is verified by comparison with finite element method, literature methods and experimental data, respectively. Finally, the effects of supporting layout, input torque and rotor diameter on the dynamic characteristics of cantilever rotor-supported gears are discussed.

Loaded tooth contact analysis for helical gears with surface waviness error

Meshing characteristics are crucial for the transmission performance of vibration noise and strength of gear systems. Gear transmission error has been acknowledged as a prominent excitation in vibration systems, but the surface waviness deviations that directly affect it in contact analysis are generally ignored. This study proposes a comprehensive model for quasi-static analysis of tooth surfaces with waviness error. The model reconstructs the actual tooth surface in reverse based on the gear Fourier measurement principle. Instead of solving the meshing equations to pre-assume contact position, the problem of normal contact between surfaces with deviations is solved by an innovative multiscale grid and a local iterative numerical algorithm. Combining the finite element numerical method and surface integral of the Boussinesq solution determines gear deformation and develops a loaded contact model. The validity of the model is verified through numerical examples. Furthermore, the proposed model is applied to discuss the tooth surfaces with different waviness amplitudes, frequencies, and distribution angles for the first time. It explains the interaction between local microscale and global scale introduced by waviness error on tooth surfaces and reveals the mechanism of the waviness error on meshing performance.

THE INFLUENCE OF THE OPTIMIZATION OF THE SPUR GEAR BODY ON THE MESHING STIFFNESS

The design of the body shape of spur gears has an effect on the deformation and thus also the stiffness of the gearing. The stiffness of the gearing is a parameter that significantly affects the noise level of transmission mechanisms. Determining the gear stiffness is difficult due to the shape of the gear teeth. The paper examines the influence of the shape and size of individual gear body parameters on gear deformation. Deformation is solved by finite element method. On the basis of the deformation of the gearing, the stiffness of the gearing is determined.

Using high sensitivity DC accelerometers for torque estimation on a wind turbine gearbox

In this paper we propose a novel approach to estimate the torque on a wind turbine gearbox using single-axis high sensitivity DC accelerometers. The torque estimator uses an Augmented Extended Kalman Filter (AEKF), combining physics-based models with measurement data. The accelerometer sensor model is derived by analysing the measurements, leading to the identification of two torque-driven acceleration contributions: acceleration due to force excitation and acceleration due to a change in measurement direction. For the latter, two different sources, with distinct frequency content, are capable of changing the measurement direction. The first source corresponds to rigid body motion (f < 0.15Hz), the second one to ring gear deformation (0.15 < f < 4Hz). Using this information, the measured signal can be filtered to target specific acceleration contributions. The first torque estimation approach targets frequencies from 0.15 to 4Hz and produces a Normalised Mean Absolute Error (NMAE) of 2.12%. The second approach targets frequencies up to 0.15Hz, and will estimate the rigid body deflection angle. The torque is calculated through a linear identified relation between the rigid body angle and applied input torque. This approach yields an NMAE of 2.59%. This leads to the conclusion that high sensitivity DC accelerometers are a valid option for estimating torque on a wind turbine gearbox. These torque monitoring approaches will pave the way for advanced condition monitoring strategies and the calculation of remaining useful lifetime of the gearbox.

Research of the influence of element deformation and manufacturing errors of planetary gears on the load distribution among satellites

A technologically advanced multi-satellite design of a toothed planetary gear is studied, in which the carrier is made in the form of two cheeks, which are connected to each other by the axes of the satellites, which act as jumpers. The problem of the stress-strain state of mating elements is solved using differential equations of the curved axis of the satellite, represented by a beam on an elastic foundation. The distribution of the load across the satellites is determined taking into account the deformation of the gear segments and the non-adherence of the gear teeth caused by errors in its manufacture. Keywords:planetary gear, non-rigid carrier, compliance of segments, load distribution Alexandrsun4009@gmail.com

Gear error control and response of electric vehicle transmission gearing based on gear trimming

The lightweight development of electric vehicle motors is a prominent future trend, with the challenge of transmission vibration and noise acting as a key bottleneck that limits the enhancement of power and speed in electric vehicle drive systems. The noise generated by electric vehicle transmissions is primarily associated with the transmission system and gear structure. In line with this, the present study proposes an analysis of transmission error and response mechanisms through gear modifications. The research delves into the analysis of gear deformation and error generation characteristics. It further investigates methods for parametric equation modeling, tooth profile modification, deformation imprint analysis, and vibration response modeling to examine excitation response analysis and noise reduction techniques pertaining to transmission errors. The findings demonstrate that, under 40 % torque, the shaped gear exhibited a maximum reduction in transmission error of 34.2 %, resulting in an overall error improvement of over 5.7 %. Moreover, the maximum error difference after tooth profile and tooth direction shaping exceeded 2 %. The gear-shaping-based electric vehicle transmission showcased favorable economic and technical performance, while its excitation response mechanism provided valuable guidance for mass production. Overall, these results highlight the significance of analyzing transmission errors through gear modifications in achieving lightweight electric vehicle motors. By addressing transmission vibration and noise issues, this research contributes to overcoming limitations and promoting advancements in power and speed within electric vehicle drive systems.

Limitations of the Check Calculation for Tooth Deformation of Plastic Gears According to Gear Design Guideline VDI 2736.

An in situ gear test rig has been developed at the Institute of Polymer Technology (LKT) to characterize the deformation of plastic gears during operation. It analyses timing differences between following index pulses of rotary encoders on the input and output shaft. This measurement principle enables the continuous measurement of the elastic tooth deformation and permanent deformations and wear at operating speed by switching between a high and low torque. Gear tests using a steel-polybutylene terephthalate (PBT) gear set were performed at different rotational speeds and tooth temperatures to analyze the tooth deformation during operation. The results were compared to the calculated deformation according to gear design guideline VDI 2736. Moreover, the results of the gear tests were correlated with the results of a dynamomechanical analysis (DMA). Both, the DMA and the in situ gear tests show that the effect of temperature on deformation is much higher than the effect of frequency or rotational speed. However, the experimentally measured tooth deformation is significantly higher (up to 50%) than the calculated at lower speed. Thus, the check calculation according to VDI 2736 underestimates the actual tooth deformation at lower speeds. Therefore, the guideline should be adjusted in the future.

Influence of single phase NiS nanoparticles as lubricant additive in microscale deformation of copper gear

ABSTRACT Demand for miniature gears is increasing daily due to huge development in MEMS and microdevices. As a result of this drive towards miniaturisation, microsystem technologies are becoming increasingly important. In this concern, researchers are interested in developing a micro forming process to manufacture highly accurate micro gears, improved operational and functional characteristics, capacity to perform in hazardous environmental conditions, and longer service life. Single-phase NiS nanospheres were developed using a high-temperature wet chemical method and were dispersed in engine oil (SAE 20 W-40) for further forming process. During plastic deformation (micro-scale), the combined grain size effects and NiS nanoparticle added lubricant on formability and interfacial friction of the micro gear are investigated. The grain size effect significantly impacts the micro gear’s formability during micro forming. The grain size and orientation significantly influence the microscale deformation process. Due to the size effect, the microhardness value at the centre and the tooth varies considerably. Due to the existence of NiS nano additive lubricant, the surface quality of micro gear improved significantly. The findings of this work help to comprehend the properties of nano additive lubricant and how it behaves tribologically throughout the micro-forming process.

A New Fast Calculating Method for Meshing Stiffness of Faulty Gears Based on Loaded Tooth Contact Analysis

Gear transmission systems are widely used in various fields. The occurrence of gear cracks, tooth pitting, and other faults will lead to the dynamic characteristics deterioration of the transmission system. In order to calculate the meshing stiffness of faulty gear pairs more effectively and precisely, this article improves the loaded tooth contact analysis (LTCA) method by analyzing the influence of different fault types on gear deformation, including bending-shearing deformation and contact deformation, which combines the accuracy of the finite element method (FEM) and the rapidity of the analytical method (AM). The improved LTCA method can model the fault areas accurately and optimize the deformation coordination equation under the actual meshing situation of the faulty gear tooth, making it suitable for calculating the meshing stiffness of faulty gears. Based on the calculation results of the finite element method, the accuracy of the improved meshing stiffness calculation method has been verified, and the sensitivity of different fault type parameters on meshing stiffness has been studied.

DIC analysis of gears in bending condition

Thin rim gears present a complex strain and stress field due to its particular geometry, above all in bending problems. From this point of view, the position of the most stressed point and the corresponding equivalent stress value are useful for an accurate design of thin rim gears. More in detail, in case of bending failure, both crack initiation point and corresponding propagation path are strictly related to the gear’s geometry.In this work, an experimental analysis was performed to evaluate how light weight gears geometry may influence the strain field close to the tooth root.To this aim, an experimental activity was carried on by a dedicated equipment for bending tests and the gear deformation was monitored by using the 3D Digital Image Correlation (DIC) technique.The local strain field in both tooth and web portions was measured for two types of gears (standard gear and thin-rim gear) in order to identify the stress condition due to the bending loading. A particular attention was devoted to point out the most stressed point for both gears. Results were also compared with XFEM model available in literature.

A Study on the Influence of Plasma Nitriding Technology Parameters on the Working Surface Deformation of Hypoid Gears

This paper presents the results of the research on the influence of plasma nitriding technology parameters on the working surface deformation of hypoid gears. Blue light technology with non-contact measuring devices is used to determine the working surface deformation of hypoid gears after plasma nitriding. The study has determined a regression equation showing the influence of plasma nitriding technology parameters on the deformation of the working surface of the hypoid gear. The minimum deformation optimization value at the planning area is 0.0071746 at permeation temperature TL=4.89oC, permeation time h=510h, and gas flow 1 G1=6.02L/h.

In situ investigation of the influence of varying load conditions on tooth deformation and wear of polymer gears

A new method for in situ deformation and wear measurement of polymer gears has been developed at the LKT and validated for polyamide-66 (PA66) gears at constant loading torque and rotational speed. This contribution contains a more comprehensive validation of the newly developed test method by examining polybutylenterephtalate (PBT) gears under varying loading conditions. The deformation test method is based on measuring and analysing the timing differences between the index pulse signals of rotary encoders on the input and output shaft of the test rig. Since the total tooth deformation is a combination of different effects, such as elastic and plastic deformation, thermal expansion and wear, different testing modes with a low and a high torque level are implemented to separate the effects of elastic deformation on the one hand and plastic deformation and wear on the other hand. As a consequence, the new test rig design allows a deeper understanding of the wear and deformation behaviour of polymer steel gear sets over time. This potential is used to analyse the interactions of different loading conditions on the time-dependent deformation of plastic gears. The influence of both, different transmitting torques and rotational speeds is examined.The test method shows good correlation with well-established ex situ measurements for different combinations of rotational speeds and loading torques and thus could be validated. Long-term gear tests under varying rotational speeds and loading torques show increasing wear and deformation at higher speeds and torques confirming the state of the art described in the literature. In addition, the time dependent deformation behaviour at different load conditions due to superposition of wear and plastic deformation could be analysed in detail.

Deformation and Response Analysis of Spur Gear Pairs with Flexible Ring Gears and Localized Spalling Faults

For the analysis on the deformation of flexible ring gears in spur gear pairs, the complete flexible ring is discretized, and the boundary condition is added to the connecting points to develop a calculation method for the flexible deformation. The ovality index is used to describe the deformation degree of flexible ring gears, then the influences of ring-gear width and the spalling defects on the flexible deformation of ring gears are discussed. The result shows that the flexible deformation of ring gears is caused by the gear pair meshing force, and the deformed shape is close to an ellipse. In the single-tooth meshing interval of gear pairs, the main form of deformation is being stretched, and while in the double-tooth meshes, the main form is bending deformation. When the width of the ring gear rims is increased, the flexible deformation of the ring gears can be effectively suppressed, and the vibration amplitude of the gear pairs can be reduced. Additionally, when there is a localized spalling fault on gear pairs, the sudden changes in the deformation of flexible ring gears are generated by the shock of the meshing force. Finally, through the finite element analysis model and the experiment, the mathematical model of gear pairs with flexible rings is confirmed.

Study of the glass fibres and internal lubricants influence in a polyamide 66 matrix on the wear evolution of polyacetal and polyamide 66 based gears in a meshing process

When designing gear systems, it is crucial to select materials to meet functional requirements of the application. It is necessary to know characteristics of the materials that will be integrated into drive components of the entire system to ensure a precise calculation of the system. In gear applications, system performance does not depend on a single material, but on material pairs that form a gear system. Therefore, it is desirable to test gears of different polymer materials to obtain relevant information regarding material data which are integrated into advanced virtual models to optimize mechanical structure. Gears are usually exposed to cyclic fatigue spectrum load, which causes degradation of the tooth flanks shape, and consequently increased teeth flanks wear, which results in lower load-carrying capacity. In this paper, wear behavior of gear pairs POM-PA66 and POM-PA66 reinforced with 30% of glass fibres with internal lubricants (PTFE and silicone oil) are analyzed and discussed considering load conditions. The results showed higher wear rate on the POM gears in comparison to PA66 based gears. It has been deduced that wear progression is nearly connected to more elastic material properties related with higher elongation and coefficient of linear thermal expansion for POM material in comparison to to PA based materials. Wear coefficients for POM and PA based materials imply that wear and deformation of gears are inversely proportional with durability. When observing materials at higher loads, it can be noticed that POM/PA66 GF30 TF15 Si has longer lifetime compared to POM/PA66 and vice versa at lower load. The authors concluded that lower wear and deformation of gear teeth have a decisive influence on good durability performance of gears.

Analytical models for thermal deformation and mesh stiffness of spur gears under steady temperature field

Thermal effect is an important cause of engineering failure of gear system. However, the lack of accurate model limits the research on the thermal behavior of gear transmission system. Here, based on the linear thermal expansion theory, involute profile theory and energy method, the thermal expansion model, the mesh stiffness model, the load sharing ratio model and the loaded static transmission error model of spur gears are proposed which comprehensively consider the thermal changes of material properties, theoretical involute, thermal profile error and actual contact positions. The corresponding finite element models are established to verify the accuracy of the proposed model and published models. The results indicate that the proposed model is accurate enough. The increase of temperature leads to the decrease of mesh stiffness, the unevenness of load sharing ratio and the increase of loaded static transmission error, accompanied by the phenomenon of earlier meshing. The hub bore radius has obvious influences on the thermal profile error and mesh stiffness, and the load torque also has apparent influences on mesh stiffness. The research provides supports for gear thermal effect analysis and gear system design.

Study on the influencing factors of the deformation in the process of gear shaping

Ring gear is an important part of high power transmission system. Because of its thin wall and low stiffness, it is easy to cause deformation in the process of gear shaping, which affects its accuracy. Therefore, how to ensure the quality of gear ring gear insertion is an urgent research topic. In this paper, the influence of cutting parameters of gear shaper on the deformation of gear ring is studied by finite element simulation and practical test. The results show that the influence of main cutting parameters on the deformation of 42CrMo ring gear is radial feed, circumferential feed, stroke speed, and cutting depth. In the actual gear shaping process, the cutting parameters can be adjusted according to this deformation law, so as to control the deformation of the ring gear.

Parametric Design on Solving the Maximum Deformation of Traction Helical Gear on Locomotive

The helical gear for locomotive traction has a popular application in the locomotive transmission system due to its excellent transmission performance. The maximum amount of deformation needs to be taken into consideration when performing the tooth profile modification on helical gear. The tooth profile design and corresponding calculation process tend to be tedious since the variation of the contact ratio of gear might lead to the change of logarithm in meshing tooth. In this paper, starting from the effect of the contact ratio on the logarithm of meshing teeth, the mesh-stiffness of helical gear can be solved by cross-section deformation formula based on the similarity of helical gear and spur gear. And then the general calculation formula governing the variation on the length of contact line is derived regarding the moment when gear tooth just engages. On the basis of actual production requirements, the solution equation for inter-tooth load distribution coefficient is derived. As a result, the general mathematical model for maximum deformation of helical gear which can perform parameterized calculation is established. The theory provides a significant theoretical guide in the field of tooth profile modification on locomotive traction helical gear.

Development and verification of a computationally efficient stochastically linearized planetary gear train model with ring elasticity

This paper develops a hybrid dynamic model for the analysis of nonlinear stochastic vibration of a wind turbine’s planetary gear train (PGT) with an elastic ring gear. The elastic deformation of ring gear is considered and incorporated into the model through the finite element model. Moving loads are used to incorporate the meshing loads between the planet-ring gear pairs. In addition, the model includes both the stiffness variation and the backlash nonlinearity between meshing gears. The backlash is linearized using the statistical linearization technique, and a linear set of equations is obtained based on which simulation is carried out with PGT parameters in wind turbines. A parametric study is conducted, and the results demonstrate that the statistical linearization method is accurate enough to study the nonlinear stochastic PGT. The results reveal that the moving mesh has a strong effect on PGT when the ring gear elasticity is considered. The influence of rim thickness on PGT dynamics was analyzed, and the results show that the effect is significant. Monte Carlo simulations are used to verify the accuracy of the proposed method.

EHL Analysis of Spiral Bevel Gear Pairs considering the Contact Point Migration due to Deformation under Load

The actual contact point of a spiral bevel gear pair deviates from the theoretical contact point due to the gear deformation caused by the load. However, changes in meshing characteristics due to the migration of contact points are often ignored in previous studies on the elastohydrodynamic lubrication (EHL) analysis of spiral bevel gears. The purpose of this article is to analyze the impact of contact point migration on the results of EHL analysis. Loaded tooth contact analysis (LTCA) based on the finite element method is applied to determine the loaded contact point of the meshing tooth pair. Then, the osculating paraboloids at this point are extracted from the gear tooth surface geometry. The geometric and kinematic parameters for EHL simulation are determined according to the differential geometry theory. Numerical solutions to the Newtonian isothermal EHL of a spiral bevel gear pair at the migrated and theoretical contact points are compared to quantify the error involved in neglecting the contact point adjustment. The results show that under heavy-loaded conditions, the actual contact point of the deformed gear pair at a given pinion (gear) roll angle is different from the theoretical contact point considerably, and so do the meshing parameters. EHL analysis of spiral bevel gears under significant load using theoretical meshing parameters will result in obvious errors, especially in the prediction of film thickness.