Analysis of General Characteristics of Transmission Error of Gears With Convex Modification of Tooth Flank Form Considering Elastic Deformation Under Load

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Edzrol Niza Mohamad ◽  
Masaharu Komori ◽  
Hiroaki Murakami ◽  
Aizoh Kubo ◽  
Suping Fang
Keyword(s):  
Power Transmission ◽  
Transmission Error ◽  
Elastic Model ◽  
Qualitative Characteristic ◽  
Contact Ratio ◽  
Factors Affecting ◽  
Specific Loading ◽  
Tooth Flank ◽  
Form Deviation ◽  
Peak Value

The vibration/noise of power transmission gears is a serious problem for vehicles including automobiles, and therefore many studies on gear vibration have been reported. These studies, however, were carried out by investigation using numerical simulations in which gears with specific dimensions and tooth flank modifications under specific loading were considered. Therefore, the general characteristics of the transmission error of gears have not been clarified theoretically. In this report, a general model for the tooth meshing of gears is proposed; in which a quasi-infinite elastic model composed of springs with stiffness peculiar to the gear is incorporated. The transmission error of gears is formulated by theoretical equations. An investigation on the factors affecting the general characteristics of transmission error is accomplished using the formulated equations. The qualitative characteristic of the transmission error of gears with convex tooth flank form deviation is determined by the actual contact ratio and qualitative elements of gears, i.e., tooth flank form deviation and the distribution of stiffness. Even if the amplitude of torque, the amount of tooth flank form deviation, and other quantitative elements are not determined, the qualitative characteristic of transmission error can be derived. The peak-to-peak value of transmission error increases proportionately to the amount of tooth flank form deviation.

Effect of Convex Tooth Flank Form Deviation on the Characteristics of Transmission Error of Gears Considering Elastic Deformation

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Edzrol Niza Mohamad ◽  
Masaharu Komori ◽  
Hiroaki Murakami ◽  
Aizoh Kubo ◽  
Suping Fang
Keyword(s):  
Elastic Deformation ◽  
General Model ◽  
Transmission Error ◽  
Gear Transmission ◽  
Elastic Model ◽  
Contact Ratio ◽  
Actual Contact ◽  
Tooth Flank ◽  
Form Deviation ◽  
Peak Value

The transmission error of gears is an important factor for power transmissions, particularly automotive. Consequently, a lot of research has been conducted on the gear transmission. However, in contrast, there remains relatively little research clarifying the characteristics of gear transmission error and its relationship to the tooth flank form. The authors have proposed a general model for tooth meshing between gears. This expresses the transmission error theoretically from a quasi-infinite elastic model, which is composed of springs with stiffness specific to the gears. In this report, the influence of tooth flank form deviation on transmission error is further investigated by using this model. It is shown that the form of the ridge curve of the tooth flank form deviation greatly influences the actual contact ratio at the minimum point of peak-to-peak value of transmission error. The peak-to-peak value of transmission error is affected by the amplitude and the form of the ridge curve.

Tooth flank modification to reduce transmission error and mesh-in impact force in consideration of contact ratio for helical gears

2020 ◽  
pp. 095440622097506
Author(s):  
Chao Jia ◽  
Zongde Fang ◽  
Ligang Yao ◽  
Jun Zhang
Keyword(s):  
Impact Force ◽  
Transmission Error ◽  
Contact Analysis ◽  
New Method ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Modification Method ◽  
Tooth Modification ◽  
Tooth Flank

In this paper, a new tooth modification method considering the contact ratio of gears and a new method for calculating the mesh-in impact force of modified helical gears are proposed. The new method for calculating the mesh-in impact force is based on tooth contact analysis and loaded tooth contact analysis. The mesh-in impact position can be calculated accurately via the new method. First, the procedures for creating the new tooth modification and the details of calculation method of the mesh-in impact force are exhibited. Second, the optimal modification of the tooth flank is achieved by solving the optimization problem. Third, a dynamic model of the gear system considering the loaded transmission error and the mesh-in impact force is used to study the dynamic characteristics. Ultimately, numerical examples are presented and the simulation results suggest that the amplitude of the loaded transmission error and the mesh-in impact force can be reduced more effectively based on the introduced new tooth modification method. And the mesh-in impact effects should not be neglected in gear dynamic analysis, regardless of whether the tooth modified or not, especially for high-speed gears.

Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

2016 ◽  
Vol 231 (11) ◽  
pp. 2025-2041 ◽  
Author(s):  
Shijing Wu ◽  
Haibo Zhang ◽  
Xiaosun Wang ◽  
Zeming Peng ◽  
Kangkang Yang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Transmission Error ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Contact Ratio ◽  
The Impact

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

scholarly journals Quasi-Static Characteristics and Vibration Responses Analysis of Helical Geared Rotor System with Random Cumulative Pitch Deviations

2020 ◽  
Vol 10 (12) ◽  
pp. 4403
Author(s):  
Bing Yuan ◽  
Geng Liu ◽  
Lan Liu
Keyword(s):  
Degrees Of Freedom ◽  
Transmission Error ◽  
Rotor System ◽  
Dynamic Responses ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Long Period ◽  
Light Load ◽  
Vibration Responses ◽  
Loaded Tooth Contact Analysis

As one of the long period gear errors, the effects of random cumulative pitch deviations on mesh excitations and vibration responses of a helical geared rotor system (HGRS) are investigated. The long-period mesh stiffness (LPMS), static transmission error (STE), as well as composite mesh error (CMS), and load distributions of helical gears are calculated using an enhanced loaded tooth contact analysis (LTCA) model. A dynamic model with multi degrees of freedom (DOF) is employed to predict the vibration responses of HGRS. Mesh excitations and vibration responses analysis of unmodified HGRS are conducted in consideration of random cumulative pitch deviations. The results indicate that random cumulative pitch deviations have significant effects on mesh excitations and vibration responses of HGRS. The curve shapes of STE and CMS become irregular when the random characteristic of cumulative pitch deviations is considered, and the appearance of partial contact loss in some mesh cycles leads to decreased LPMS when load torque is relatively low. Vibration modulation phenomenon can be observed in dynamic responses of HGRS. In relatively light load conditions, the amplitudes of sideband frequencies become larger than that of mesh frequency and its harmonics (MFIHs) because of relatively high contact ratio. The influences of random cumulative pitch deviations on the vibration responses of modified HGRS are also discussed.

scholarly journals Analysis on Meshing Characteristics and Transmission Error of Elliptic Gears

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Changbin Dong ◽  
Yongping Liu ◽  
Yongqiao Wei ◽  
Beibei Yun ◽  
Dawei Li ◽  
...  
Keyword(s):  
Great Influence ◽  
Transmission Error ◽  
Spur Gear ◽  
Analysis Model ◽  
Contact Ratio ◽  
Cylindrical Gear ◽  
Pressure Angle ◽  
Object Based ◽  
Meshing Characteristics ◽  
Eccentricity Error

As an important parameter to distinguish noncircular gear from cylindrical gear, eccentricity is very important for the meshing characteristics and transmission error of noncircular gear. In order to study the transmission characteristics of the elliptic gear, a pair of elliptic gear in the reversing device of a new type of drum pumping was taken as the research object. Based on the analysis of the transmission pressure angle and instantaneous contact ratio of the elliptic gear, the eccentricity error was introduced into the analysis model of transmission error. The influences of the eccentricity on the transmission pressure angle, instantaneous contact ratio, and transmission error were analyzed, and the analysis accuracy is verified by the finite element method. The results show that the eccentricity has a great influence on the transmission pressure angle, instantaneous contact ratio, and transmission error of the elliptic gear, and the eccentricity error has a significant influence on the transmission error. In order to ensure the normal meshing condition of the elliptic gear, the eccentricity should be less than 0.7071, and the maximum instantaneous contact ratio is 1.809. The research results can provide some guidance for the following noncircular spur gear transmission test and transmission error research.

Design and analysis of high contact ratio spiral bevel gears by modified curvature motion method

2017 ◽  
Vol 232 (19) ◽  
pp. 3396-3409 ◽  
Author(s):  
Yanming Mu ◽  
Zongde Fang
Keyword(s):  
Transmission Error ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Contact Ratio ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Curvature Motion ◽  
Seventh Order ◽  
Spiral Bevel ◽  
Motion Method

This paper presents a new method to design a seventh-order transmission error for high contact ratio spiral bevel gears by the modified curvature motion method to reach the purpose of reducing or eliminating gear vibration and noise. In this paper, firstly, based on the predesigned seventh-order transmission error, the polynomial coefficients of transmission error curve can be obtained. Secondly, a method named modified curvature motion method is used to generate the spiral bevel gear with the predesigned transmission error. Lastly, based on TCA and LTCA, we verify the feasibility of the modified curvature motion method to generate spiral bevel gear with seventh-order transmission error, and the meshing impact of gear set with the seventh-order and second-order function of transmission error is analyzed and compared. The results of a numerical example show that the seventh-order transmission error acquired by the modified curvature motion method can effectively reduce the meshing impact of spiral bevel gears. The tooth modification method and meshing impact analysis method can serve as a basis for developing a general technique of flank modification for spiral bevel gears.

scholarly journals An experimental method to measure gear tooth stiffness throughout and beyond the path of contact

2001 ◽  
Vol 215 (7) ◽  
pp. 793-803 ◽  
Author(s):  
R. G. Munro1 ◽  
D Palmer ◽  
L Morrish
Keyword(s):  
Gear Tooth ◽  
Contact Region ◽  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Extended Contact ◽  
Tooth Stiffness ◽  
Simplifying Assumptions ◽  
Tooth Pair ◽  
Usual Problem

A method is presented that allows the accurate measurement of the tooth pair stiffness of a pair of spur gears. The method reveals the stiffness behaviour throughout the full length of the normal path of contact and also into the extended contact region when tooth corner contact occurs. The method makes use of the properties of transmission error plots for mean and alternating components over a range of tooth loads (Harris maps). It avoids the usual problem when measuring tooth deflections that deflections of other test rig components are difficult to eliminate. Also included are predicted Harris maps for a pair of high contact ratio spur gears, showing the effects of various simplifying assumptions, together with a measured map.

Transmission Error Analysis of External Gear Drive Based on Form and Position Errors

2014 ◽  
Vol 614 ◽  
pp. 36-39
Author(s):  
Ke Ke Li ◽  
Yu Shu Bian ◽  
Bing Dong Liu
Keyword(s):  
Error Analysis ◽  
Statistical Method ◽  
Probability Distributions ◽  
Transmission Error ◽  
Calculation Formula ◽  
Key Factors ◽  
Factors Affecting ◽  
Gear Drive ◽  
Position Errors ◽  
Gear Mechanism

The key factors affecting the transmission error of gear mechanism are analyzed and the calculation formula of transmission error based on parts’ form and position errors is derived in this paper. Since the errors have different kinds of probability distributions, this paper calculate the expectation and variance of transmission error by statistical method, gives final transmission error value, and verify it by an example.

Optimizing involute gear design for maximum bending strength and equivalent pitting resistance

2007 ◽  
Vol 221 (4) ◽  
pp. 479-488 ◽  
Author(s):  
V Spitas ◽  
C Spitas
Keyword(s):  
Bending Strength ◽  
Power Transmission ◽  
Optimization Procedure ◽  
Contact Ratio ◽  
Element Analysis ◽  
Gear Design ◽  
Involute Gear ◽  
Involute Gears ◽  
High Power Transmission ◽  
Complex Algorithm

Standard involute gear designs dominate high-power transmission applications because they combine sufficient bending strength with high pitting resistance, while retaining an adequate contact ratio. In this paper, a non-standard, optimal alternative involute gear design has been presented, which has the same pitting resistance as the standard involute gears but exhibits maximum resistance to bending. The optimization procedure is based on the complex algorithm, where the root stress, as calculated through tabulated boundary element analysis values, is the objective function and the active constraints include all of the kinematical, manufacturing and geometrical conditions, which must be satisfied by the optimal design, including the pitting resistance. The results indicate that optimal designs can achieve up to 8.5 per cent reduction of the fillet stress. Two-dimensional photoelasticity was used to verify the optimization results.

Sign in / Sign up

Export Citation Format

Share Document