Tooth Modification Research Articles

Determination of static transmission error of helical gears using finite element analysis

At present, increasing emphasis is being placed on low noise levels, especially in the automotive industry. One of the dominant sources of noise (and vibration) in vehicles (with an electric motor as well as an internal combustion engine) is the transmission system. In order to effectively reduce vibration and noise of gears and transmission systems, some important gear parameters should be determined / measured. One of these parameters is the static transmission error, which is addressed in this article. The evaluated parameter is the peak-to-peak value of the transmission error, which appears to be closely related to NVH (Noise Vibration and Harshness). The transmission error depends, inter alia, on the tooth macrogeometry (expressed by the contact ratio) and the tooth microgeometry (intentional tooth modifications), the influence of both has been analyzed and is presented in this article. The transmission error can be determined by virtual measurement (computationally) in software enabling finite element analysis or by technical experiments on a test rig. The results in this paper are based on the outputs of numerical simulations using the finite element method. This approach can be used at developing phase to find the optimal solution and to save a lot of time. In addition, no physical components are required and a wide range of arbitrary gear configurations can be analyzed. Nevertheless, the technical experiment is still necessary, thus the test rig will be designed/constructed in the near future, including the possibility of lubrication. The results will then be compared with numerical simulations.

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.

Multi-objective optimization of the manufacture of face-milled hypoid gears on numerical controlled machine tool

A new method is presented for advanced manufacture of hypoid gears on numerical controlled machine tool. The tool geometry and machine tool settings are determined to introduce the optimal tooth modifications into the teeth of hypoid gears. The goal is to reduce the maximum tooth contact stresses, angular displacement error of the driven gear, and energy losses in the oil film existing between tooth surfaces. The calculation is based on the optimal variation of machine tool settings on the classical machine tool for hypoid gear manufacture. The novelty of the method is that during the machining process of teeth surfaces, the variation of machine tool settings on the cradle-type hypoid generator is conducted by polynomial functions of fifth-order. By an algorithm, this variation of machine tool settings is transferred to the numerical controlled machine tool for hypoid gear manufacture (hypoid generator). The obtained results have shown that by applying the optimal manufacture process, considerable reductions in tooth contact stresses and angular displacement errors of the driven gear, and a moderate reduction in energy losses were obtained. Therefore, by applying this new method in practice, advanced manufacture of hypoid gears on CNC hypoid generator is made possible, resulting improved operating characteristics of the hypoid gear pair.

Modification of denture teeth for improved occlusal stability of a maxillary removable complete denture opposed by a mandibular implant-supported fixed complete denture: A clinical report

Wear of artificial teeth is the most common complication associated with an implant-supported fixed complete denture (ISFCD). This wear alters the occlusal scheme, with loss of eccentric occlusal balance and vertical dimension of occlusion (VDO). This clinical report describes the fabrication of a new maxillary removable complete denture opposing an existing ISFCD with occlusal modifications. Both prostheses received splinted zirconia crowns cemented with composite resin cement.

Geometrical design of variable ratio tooth profile based on Boolean subtraction operation and a novel modification method

Variable transmission ratio racks show great potential in rice transplanters as a key component of variable transmission ratio steering to balance steering portability and sensitivity. The objective of this study was to develop a novel geometrical design method to achieve quick, high-quality modeling of the free curvilinear tooth profile of a variable transmission ratio rack. First, a discrete envelope motion 3D model was established between the pinion-sector and the variable transmission ratio rack blank based on the mapping relationship between the rotation angle of the pinion-sector and the displacement of the rack, according to the variable transmission ratio function. Based on the loop Boolean subtraction operation, which removed the pinion-sector from the rack blank during all moments of the discrete motion process, the final complex changing tooth shape of the variable transmission ratio rack was enveloped. Then, since Boolean cutting residues made the variable ratio tooth surface fluctuant and eventually affected the precision of the model, this study proposed a modification method for establishing a smooth and continuous tooth profile. First, a novel fitting algorithm used approximate variable ratio tooth profile points extracted from the Boolean cutting marks and generated a series of variable ratio tooth profiles by utilizing B-spline with different orders. Next, based on a transmission stability simulation, the variable ratio tooth profile with optimal dynamic performance was selected as the final design. Finally, tests contrasting the transmission stability of the machining samples of the initial variable ratio tooth profile and the final variable ratio tooth profile were conducted. The results indicated that the final variable ratio tooth profile is more effective than the initial variable ratio tooth profile. Therefore, the proposed variable ratio tooth profile modeling and modification method for eliminating Boolean cutting residues and improving surface accuracy is proved to be feasible. Keywords: rice transplanter, steering, variable ratio tooth profile, variable ratio curve, Boolean subtraction operation, transmission stability DOI: 10.25165/j.ijabe.20201305.4884 Citation: Niu Z R, Li J L, Xin S, Zou L L, Li Y H, Hou J L, et al. Geometrical design of variable ratio tooth profile based on Boolean subtraction operation and a novel modification method. Int J Agric & Biol Eng, 2020; 13(5): 125–133.

Analysis on Dynamic Contact Performance and Microscopic Trimming Optimization of Pure Electric Bus Transmission Gears

Given the differing structure of transmissions for pure electric vehicles from the conventional ones, how to enhance the transmission performance is the key to improving their dynamic property and economical efficiency. In this work, a two-speed planetary transmission for a self-designed 10–12 m bus is studied. A simulation model of the transmission is created according to the gear meshing principle, and the load spectra are established by simulating the probable loads on the transmission in actual operation. The gear drive process of the transmission is analyzed, as along with the gear safety factors, damage rates and meshing dislocation. Trimming curves are derived based on the principles of axial and tooth profile modification, the trimming amounts are set, and the contact spots and transmission errors of gear meshing obtained before and after trimming are analyzed comparatively using the MASTA’s gear microscopic trimming module, thereby determining the reasonable method and quantity of trimming for the studied transmission gear. Comparison of the contact spots and transmission errors before versus after trimming finds greatly improved contact condition of gear and more stable gear transmission. With the methodology described in this paper, the shortcomings of traditional gear trimming, such as cumbersome process, long duration and nonlinear gear drive system, can be overcome, which improves the operational reliability.

Tool path active design for tooth modification of face-hobbed spiral bevel gears

An advanced design and manufacturing method called tool path active design for face-hobbed spiral bevel gears is mainly discussed in this paper. The method bases on the forming mechanism of extended epicycloids and utilizes an integrated cutter head without tilting, meanwhile, all its controlled parameters can be directly calculated according to the given meshing performances and modified conditions. Starting with the cutting principle of face-hobbing method, a tooth flank mending plan of altering tool path is developed, which detailed expressions are also given in functions. Then, the meshing performances which are used to determine the modification parameters are introduced and their formulas are also derived. Finally, the proposed method is validated by a numerical example of tooth contact analysis for a face-bobbed hypoid gear pair. As a further explanation, a numerical example of tooth contact analysis is done to validate the feasibility of the proposed method.

A general mathematical model for screw-rotor honing using an internal-meshing honing machine

This study proposes a general method to finish screw rotors using internal-meshing honing. During the honing process, the meshing between the screw rotor and the honing wheel is similar to that for a pair of crossed-axis internal-meshing helical gears with few teeth so the machining time can be reduced significantly. A normal rack that conjugates a pair of screw rotors is used to generate the honing wheel. The proposed mathematical model can also be used for screw rotor honing with a variable lead. The topography of the tooth surfaces of a screw rotor with a constant lead and a variable lead are used to show the accuracy and practicability of the proposed mathematical model. A honing wheel with a clearance that is generated using a modified normal rack is used to design the clearance for the male rotor. In addition, influence of additional movements for each machining axis on the tooth modification of screw rotor is investigated and discussed.

Geometric characteristics and tooth modification for variable speed pinion–rack drive

Variable speed steering system has been used by cars of various brands, including BMW and Toyota, with the purpose of improving the stationarity and controllability of the vehicle. Until now, relevant investigations are focused on the theory and traditional application, while the geometric characteristics and tooth modification for the rack are left untouched upon, hindering the prospect of a wider application. Focusing on this, the paper synthesizes the mathematical model, geometry characteristics, and tooth modification method for the variable pinion–rack drive. The major contributions lie in the contact analysis and the modification methodology for the pinion–rack drive, which combined forms a solid foundation for the application that has never been discussed.

Aerodynamic design optimization of an aircraft wing for drag reduction using computational fluid dynamics approach

The aircraft industry supports aviation by building aircraft and manufacturing aircraft parts for their maintenance. Fuel economization is one of the biggest concerns in the aircraft industry. The reduction in specific fuel consumption of aircraft can be achieved by a variety of means, simplest and more effective is the one to impose minor modifications in the aircraft main wing or the parts which are exposed to the air flow. This method can lead to a reduction in aerodynamic resistance offered by the air and have a smoother flight. The main objective of this study is to propose geometric design modifications on an existing aircraft wing which acts as a vortex generator and it can reduce the drag and increase lift to drag ratio, leading to lower fuel consumption. The NACA 2412 aircraft wing is modified and designed. Rigorous flow analysis is carried out using computational fluid dynamics based software Ansys Fluent. Results show that saw tooth modification to the main wing shows the best aerodynamic efficiency as compared to other modifications.

Aerodynamic design optimization of an aircraft wing for drag reduction using computational fluid dynamics approach

The aircraft industry supports aviation by building aircraft and manufacturing aircraft parts for their maintenance. Fuel economization is one of the biggest concerns in the aircraft industry. The reduction in specific fuel consumption of aircraft can be achieved by a variety of means, simplest and more effective is the one to impose minor modifications in the aircraft main wing or the parts which are exposed to the air flow. This method can lead to a reduction in aerodynamic resistance offered by the air and have a smoother flight. The main objective of this study is to propose geometric design modifications on an existing aircraft wing which acts as a vortex generator and it can reduce the drag and increase lift to drag ratio, leading to lower fuel consumption. The NACA 2412 aircraft wing is modified and designed. Rigorous flow analysis is carried out using computational fluid dynamics based software Ansys Fluent. Results show that saw tooth modification to the main wing shows the best aerodynamic efficiency as compared to other modifications.

A thermomechanical model for mesh deflection calculation of crown spur gear pair

An analytical model of evaluating tooth pair deflection along the line of contact is proposed in this paper to preliminarily determine the load distribution between tooth pairs contacting instantaneously for crown spur gears. Further, a three-dimensional thermomechanical point contact method is introduced for modeling the normal approach of two contacting teeth. Combined with tooth and fillet-foundation deflections, a coupled thermoelastic mesh deformation model for crown gears is developed. The influence of load, angular velocity and friction coefficient on the normal approach of the contact, load sharing ratio and transmission error during meshing are respectively investigated. It is suggested that without considering thermal influence, the vibration excitation of gears can be underestimated. Considering the coupled thermoelastic deformation of meshing gears may result in a better evaluation of transmission error and facilitate the subsequent tooth modification design and dynamic study.

Reliability sensitivity analysis of tooth modification on dynamic transmission error of helical planetary gears

As one of the most influential factors leading to gear vibrations, transmission errors of the engaging gears must be controlled to achieve a desirable dynamic performance for a power transmission system. It is well known that tooth modification is an effective way to reduce the fluctuations of the transmission error of a gear pair. The challenge is determining how to establish a quantitative relationship between the tooth modification parameters and the transmission error fluctuations of a gear pair. The present study aims to reveal the sensitivity of the tooth modification parameters on the transmission error fluctuations of a helical planetary gear train in a wind turbine gearbox. For this purpose, a sophisticated parametric three-dimensional contact model that included the micro-geometries of the tooth modification is developed in the ROMAX® environment. Based on this model, a loaded tooth contact analysis is carried out to compute the meshing characteristics, such as the contact pressure and transmission error of each gear pair in the planetary gear train. With the obtained meshing characteristics, the tooth modification amounts of the engaging gears were determined using empirical formulas. These modification amounts are designated as the mean values of the samples generated by the central composite method. After repeating the loaded tooth contact analysis process for each generated sample, a quadratic polynomial function is derived using the response surface method to describe the quantitative relationship between the tooth modification parameters and the dynamic transmission error fluctuations. A large number of random samples are generated using a Monte Carlo method, and the corresponding dynamic transmission error fluctuations are determined with the aforementioned quadratic polynomial function. Based on these samples, a reliability sensitivity analysis is carried out to demonstrate the effects of the tooth modification parameters on the dynamic transmission error fluctuations of the helical planetary gear train.

Simulation analysis of the tooth modification about wind power gearbox based on Romax software

At present, the gearboxes are faced with the problems of high failure rate, large vibration and noise, short service life etc. Gear modification is an effective means to reduce vibration and noise, extend life, which has been proved by practical experience at home and abroad for many years. With the introduction of some professional gear software or wind turbine analysis software from abroad, the work efficiency has been improved greatly and the extra cost due to experimental verification has also been reduced. With the use of Romax WIND excellent load distribution analysis function on the basis of the theory of gear modification, the static simulation analysis of the gearbox through the Romax WIND software was carried out under the equivalent loads. According to the load distribution on the tooth surface of gear, transmission errors and other parameters, the length, amount and curve of axial modification and the tooth profile of the high-speed pinion gear were analyzed and determined in the end. Conclusions can provide reference for gear modification.

Effects of tooth modifications on the dynamic characteristics of thin-rimmed gears under surface wear

Considering the thin rim structure and gear tooth modifications, a three-dimensional wear prediction model is proposed. Unitizing the proposed model, the contact pattern and the wear distribution are analyzed. For gear pairs with asymmetric rim structure, obvious stress concentration will lead to the severe wear on one edge of the gear tooth. Aiming at balancing the wear distribution and reducing vibration, an optimization scheme of the tooth modification (including the tip relief and the helix angle modification) is proposed. After adopting tooth modifications, the severe wear at one edge is almost eliminated. The fluctuation of the transmission error decreases significantly. The dynamic characteristics of thin-rimmed gears over the whole wear process are analyzed. It is found that the tooth modification is beneficial to shorten the running-in period and decelerate the failure process in the period of performance degradation.

Оценка долговечности подшипников опор сателлитов планетарных редукторов авиационных двигателей с учетом их динамической нагруженности

This paper presents a calculation method for assessing dynamic loading of bearings in satellites of planetary gearboxes of turbofan engines. The method is based on the analysis of a dynamic model of a planetary gearbox with lumped parameters for a planetary gear set with a fixed carrier. Simulation of the variable stiffness function of gear tooth meshing using the finite element method in a quasistatic formulation is employed for a more accurate assessment of the main source of excitation in the tooth meshing, that is the kinematic error, which includes both tooth deformations under load and technological deviations. Based on the comparison of the frequency response of the dynamic coefficient with and without tooth modification, it is established that the introduction of a modification reduces the dynamic coefficient in some modes by 2 times. The calculation results demonstrate that without taking into account the dynamic loading of the bearings, the bearing life is overestimated by about 11%. The design of a gearbox with satellite bearings on rolling bearings is considered.

Microscopic Trimming and Dynamic Contact Performance of Transmission Gears in Electric Bus

Different type of transmission structure is used for pure electric vehicles. Enhancing the transmission performance is the key to improve their dynamic property and economic efficiency. In this paper, a two-speed planetary transmission for a self-designed 10-12m bus is studied. A simulation model of the transmission is created according to the gear meshing principle and the load spectra are established by simulating the probable loads on the transmission during actual operation. The gear drive process of the transmission, as well as the gear safety factors, damage rates and meshing dislocation are analysed. Trimming curves are derived based on the principles of axial and tooth profile modification. The contact spots and transmission errors of gear meshing obtained before and after trimming are analysed comparatively using MASTA gear microscopic trimming module, thereby determining the reasonable method and quantity of trimming for the studied transmission gear.

Features of the glucose influence on the heart activity and the changes in the potentials of the stomach and the intestines at the heart insufficiency conditions

In acute rat experiments (thiopental sodium narcosis), it is established that introducing a 5 % glucose solution into the stomach lowers a frequency of heart rates (HR) and an amplitude of potentials of smooth muscles of the stomach and simultaneously raises doubtfully and shortly the potentials of sooth muscles (PSM) of the colon. Food additives used in the glutamate sodium, benzoate, tartrazine complex do not influence HR, but as before, reduces PSM of the stomach, and in the thick gut precise exciting or brake responses are marked. In the preliminarily developed heart insufficiency conditions, the glucose infusion into the stomach does not change HR. At the same time, the action of glucose, as well as of food additives, still results in reliable reactions of the stomach and the thick gut. Important is the present work information on the ability of glucose and food additives to modulate the heart activity estimated through the indicators of modification of electrocardiogram teeth. As appeared, the infusion of the specified irritants in the stomach of rats in control and heart insufficiency is accompanied by precise enough changes in such indicators as the RST duration, the amplitude and duration of the Т-wave, i. e. the prognostic attributes of the opportunity of occurrence of heart аrrhythmia, fibrillations.

Lower Back Pain and Forearm Tendinitis Linked to Irritation of Oral Mucosa by Teeth

We present a case of a woman with refractory lower back pain and forearm tendinitis, which improved dramatically after morphological modification of natural teeth. The subject was a 35-year-old Japanese woman, who was suffering from lower back pain when bending forward and she had severe pain from her right thumb to her wrist. These symptoms were not improved by massage and orthopedic treatment. On the other hand, once modifying the morphology of natural teeth, those symptoms improved dramatically. No side effects were observed, and the prognosis was good. Our observation suggested a close relationship between the oral situation and remote musculoskeletal conditions, and further multidisciplinary studies are needed to clarify the mechanisms.

Dynamic modelling and parametric optimisation of vibro-acoustic responses for power-split hybrid transmission

In this paper, vibro-impact induced gear whine radiated by full hybrid transmission equipped with a multi-mesh gear train is investigated. For accurate simulations of the reducer gear vibrations, an integrated dynamic model of the transmission is established using professional software MASTA, on which compliance effects of gear pairs, bearings, transmission shafts and gearbox housing are counted for. Numerical analyses are carried out for dynamic responses of the hybrid transmission. Bench tests are also conducted for the present model validation. Computational effort is made to recognise parametrically resonant patterns that cause gear whine in experiment. An optimal tooth modification design is presented for the real multi-mesh gear train. It is shown by test results using the optimised reducer that gear whine responses of the gearboxes are considerably improved.