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.

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.

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.

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.

Considering Thermal Deformation in Gear Transmission Error Calculation

2013 ◽  
Vol 281 ◽  
pp. 211-215
Author(s):  
Yu Ning Wang ◽  
Zhi Li Sun ◽  
Ming Ang Yin
Keyword(s):  
Temperature Field ◽  
Body Temperature ◽  
Elastic Deformation ◽  
Vibration Amplitude ◽  
Thermal Deformation ◽  
Transmission Error ◽  
The Body ◽  
Gear Transmission ◽  
Contact Method ◽  
Error Calculation

This research analyze the gear for body temperature field, according to the body temperature field, it calculates comprehensive deformation of the loaded gear by using the contact method. It extracts the deformation of gear surface along the gear thickness and gear tall direction, calculating the gear non-involute error. It calculates the gear transmission error considering the thermal deformation. The results show that: Considering thermal deformation non-involute error of addendum is maximum, and there are no mutations in gear non-involute error the transmission error caused by mutation of elastic deformation mutate at single and double tooth alternating position. The bigger mutation becomes, the bigger vibration amplitude will be. The results of the study provide a solid basis to improve the motion transmission accuracy of gear.

Design Method of Vibrationally Optimum Tooth Flank Form for Involute Helical Gears With Scattering in Pressure Angle and Helix Angle Deviation

2000 ◽  
Author(s):  
Masaharu Komori ◽  
Aizoh Kubo ◽  
Yoshiki Kawasaki
Keyword(s):  
Vibrational Excitation ◽  
Helix Angle ◽  
Design Stage ◽  
Geometrical Shape ◽  
Contact Ratio ◽  
Design Algorithm ◽  
Actual Contact ◽  
Pressure Angle ◽  
Angle Deviation ◽  
Tooth Flank

Abstract The detail in geometrical shape of each tooth flank of a mass-production gear is usually not the same. Even a slight deviation of tooth flank form of several micrometers has a big influence on the running vibration/noise of transmission gear box. The influence of scattering in tooth flank form on the vibrational characteristics of gears must therefore be taken into consideration at the design stage to achieve low vibration gears. In this report, the influence of typical types of scattering, i.e. in pressure angle deviation and helix angle deviation, on the vibrational excitation is clarified in terms of the relationship between vibrational excitation and actual contact ratio. Those types of scattering decrease the actual contact ratio of a gear pair from that value of the tooth flank form designed on a draft. Gears with scattering in tooth flank form can run silenter, when some less amount of tooth flank form modification than the optimum one for gears without scattering is given. The design algorithm for optimum modification of tooth flank form with scattering is proposed.

Effects of Gear Dimensions and Tooth Surface Modifications on the Loaded Transmission Error of a Helical Gear Pair

1998 ◽  
Vol 120 (1) ◽  
pp. 119-125 ◽  
Author(s):  
M. Umeyama ◽  
M. Kato ◽  
K. Inoue
Keyword(s):  
Transmission Error ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Rotational Angle ◽  
Actual Contact ◽  
Transmission Errors ◽  
Effective Contact ◽  
Tooth Surfaces ◽  
Helical Gear Pair ◽  
Tooth Pair

Analysis of the loaded transmission error proved that the actual contact ratio and the effective contact ratios are the valid indices. In order to calculate the loaded transmission error, deformations of a pair of teeth are estimated using Hertzian formulas for the approach deformation and approximate formulas based on the FEM for the bending deflection. The actual contact ratio εr is defined using the rotational angle during which a tooth pair is actually in contact with each other. εr increases with the increase of applied loads. The effective contact ratio, εn, is determined geometrically by gear dimensions and modified tooth surfaces based on the path of contact. Adopting these ratios, the following characteristics are derived. 1) The loaded transmission error correlates to εr when it is smaller than εn and correlates to εn when εr exceeds εn. 2) Loaded transmission errors have their minimums and maximums at the same values of εr. 3) No load transmission error is the largest among the maximums. 4) Gear pairs with higher values of εn show lower loaded transmission error.

Gear transmission error outside the normal path of contact due to corner and top contact

1999 ◽  
Vol 213 (4) ◽  
pp. 389-400 ◽  
Author(s):  
R. G. Munro ◽  
L Morrish ◽  
D Palmer
Keyword(s):  
Dynamic Test ◽  
Theoretical Models ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission ◽  
The Novel ◽  
Transmission Systems ◽  
Helical Gears ◽  
Tooth Stiffness ◽  
Top Contact

This paper is devoted to a phenomenon known as corner contact, or contact outside the normal path of contact, which can occur in spur and helical gear transmission systems under certain conditions. In this case, a change in position of the driven gear with respect to its theoretical position takes place, thus inducing a transmission error referred to here as the transmission error outside the normal path of contact (TEo.p.c). The paper deals with spur gears only, but the results are directly applicable to helical gears. It systematizes previous knowledge on this subject, suggests some further developments of the theory and introduces the novel phenomenon of top contact. The theoretical results are compared with experimental measurements using a single flank tester and a back-to-back dynamic test rig for spur and helical gears, and they are in good agreement. Convenient approximate equations for calculation of TEo.p.c suggested here are important for analysis of experimental data collected in the form of Harris maps. This will make possible the calculation of tooth stiffness values needed for use in theoretical models for spur and helical gear transmission systems.

Experimental Study on a 3-Dimensional Hydro-Elastic Deformation of “Underwater Platform” With Multi-Towers in Waves

2016 ◽  
Author(s):  
Ken Haneda ◽  
Motohiko Murai ◽  
Jun Yamanoi
Keyword(s):  
Elastic Deformation ◽  
Body Motion ◽  
Offshore Wind ◽  
Elastic Response ◽  
Experimental Result ◽  
Elastic Model ◽  
Mooring Lines ◽  
3 Dimensional ◽  
Floating Offshore Wind Turbines ◽  
Head Waves

Underwater platform was proposed in OMAE 2015 for the purpose of enhancing productivity of various types of renewable energy converter on the sea and its feasibility study was carried out through 2 types of tank experiment [1]. The underwater platform which is a very large frame shape structure connects several floaters under the sea to share power cables and mooring lines and to keep relative distances between the floaters. In the experiment, 1/200 scale elastic model with three spar buoys was used. The buoys imitated spar type floating offshore wind turbines (FOWTs). From the experiment, it was shown that the platform with large draft can reduce its response in waves. In this paper, we report new result and knowledge obtained by additional model experiments use the 1/200 model. In the experiment, we changed the arrangement and draft of the model and measured hydro-elastic deformation of the underwater platform in waves. From the last experiment, relationship between draft settings and response was shown. In the experiment, relationship between wave angles and response was surveyed. From the experiment, we have confirmed followings: 1. Rigid-body motion is remarkable in beam waves, 2. Elastic response is remarkable in head waves, and 3. Remarkable torsional motion is occurred in 45 degrees’ waves. The more important thing, however, is that the experimental result indicated that the platform of large draft decreases its motion in the all the wave angles.

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