THE DESIGN AND MESHING EFFICIENCY ANALYSIS OF HELICAL SPUR GEAR REDUCER WITH SINGLE GEAR PAIR FOR ELECTRIC SCOOTERS

2015 ◽  
Vol 39 (3) ◽  
pp. 455-465 ◽  
Author(s):  
Long-Chang Hsieh ◽  
Tzu-Hsia Chen ◽  
Hsiu-Chen Tang
Keyword(s):  
Energy Conservation ◽  
Rotation Speed ◽  
Spur Gear ◽  
Efficiency Analysis ◽  
Gear Pair ◽  
Electric Scooter ◽  
Speed Range ◽  
Root Strength ◽  
Reduced Costs ◽  
Better Than

To achieve reduced costs and energy conservation, this paper proposes non-standard helical spur gear reducer with one gear pair (having reduction ratio 19.25) to be the gear reducer for electric scooter. This paper also focuses on the meshing efficiency analysis of non-standard helical spur gear pair. According to Buckingham’s research, the theoretical meshing efficiency formula of non-standard helical spur gear pair is derived. Three design cases of non-standard helical spur gear pair (4, 77) are proposed as examples for analyzing their meshing efficiencies at widely rotation speed range. The theoretical meshing efficiencies for the helical spur gear pair (4, 77) are between 96.47–99.26%. Its best meshing efficiency occurs at 800–1000 rpm of pinion. The meshing efficiencies of these three design cases are almost same, and their differences are less than 0.5%. Considering the root strength of pinion, Cases II and III are better than Case I.

Meshing Efficiency Analysis of Straight Spur Gear Pair

2015 ◽  
Vol 764-765 ◽  
pp. 314-318 ◽  
Author(s):  
Tzu Hsia Chen ◽  
Hsiu Chen Tang
Keyword(s):  
Power System ◽  
Rotation Speed ◽  
Spur Gear ◽  
Efficiency Analysis ◽  
Gear Train ◽  
Gear Pair ◽  
Friction And Lubrication

Due to shortage of energy, the meshing efficiency of gear train becomes an important factor of power system. This paper focuses on the meshing efficiency of straight spur gear pair. The analysis of gear meshing efficiency involves the involute theorem of gears, friction and lubrication, and other related issues. According to Buckingham’s research, the theoretical meshing efficiency equation of straight spur gear pair is proposed. One straight spur gear pair (15, 79) is proposed to be the example for analyzing meshing efficiencies at each rotation speed. The theoretical meshing efficiencies for the straight spur gear pair (15, 79) are between 98.36% ~ 99.79 %. Its best meshing efficiency occurs at pinion speed 600 rpm.

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

2015 ◽  
Vol 764-765 ◽  
pp. 374-378 ◽  
Author(s):  
Long Chang Hsieh ◽  
Tzu Hsia Chen ◽  
Hsiu Chen Tang
Keyword(s):  
Engineering Design ◽  
Spur Gear ◽  
Gear Transmission ◽  
Reduction Ratio ◽  
Gear Pair ◽  
Engineering Drawing ◽  
Electric Scooter ◽  
High Reduction ◽  
Cost Of Production ◽  
The Cost

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).

Analysis of parametric stability for a spur gear pair system considering the effect of extended tooth contact

2009 ◽  
Vol 223 (8) ◽  
pp. 1787-1797 ◽  
Author(s):  
Q Han ◽  
J Wang ◽  
Q Li
Keyword(s):  
High Speed ◽  
Floquet Theory ◽  
Gear Tooth ◽  
Spur Gear ◽  
Parametric Vibration ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Parametric Stability ◽  
Tooth Contact ◽  
Speed Range

In spur gear dynamic analysis, rectangular waves are often used to approximate the mesh stiffness alternating between one and two pairs of teeth in contact. But in actual practice, extended tooth contact (ETC) occurs due to gear tooth deflection under load. Considering the effect of ETC, the mesh stiffness in the pre-mature and post-mature contact regions is gradually rather than abruptly varying with time, which would influence the parametric stability of the geared system significantly. Therefore, research on parametric stability for a spur gear pair system considering the effect of ETC is carried out in this article. First, a torsional parametric vibration model for a spur gear pair system is established and the periodically time-varying mesh stiffness is approximated linearly by trapezoidal waveforms (with the effect of ETC) and rectangular waves (without the effect of ETC). Then, the Floquet theory for stability analysis (including two key elements: one is the derivation of state transition matrix (STM); the other is the stability criterion for parametric vibration system) is presented briefly. Based on these, the stabilities (stable and unstable regions) of a practically used high-speed and heavy-load spur gear pair with and without taking into account ETC are determined utilizing Floquet theory, respectively, and the differences between the two cases in three ranges of operating speeds for the system (low speed range, middle speed range, and high speed range) are contrasted in detail. In addition, various values of operating torques and mesh damping of the gear pair are also simulated and discussed for their influences upon unstable regions.

Effect of Contact Ratio on Spur Gear Dynamic Load With No Tooth Profile Modifications

1996 ◽  
Vol 118 (3) ◽  
pp. 439-443 ◽  
Author(s):  
Chuen-Huei Liou ◽  
Hsiang Hsi Lin ◽  
F. B. Oswald ◽  
D. P. Townsend
Keyword(s):  
Dynamic Load ◽  
Spur Gear ◽  
Tooth Size ◽  
Contact Ratio ◽  
Gear Dynamics ◽  
Wide Range ◽  
Gear Contact ◽  
Center Distance ◽  
Selection Of ◽  
Better Than

This paper presents a computer simulation showing how the gear contact ratio affects the dynamic load on a spur gear transmission. The contact ratio can be affected by the tooth addendum, the pressure angle, the tooth size (diametral pitch), and the center distance. The analysis presented in this paper was performed by using the NASA gear dynamics code DANST. In the analysis, the contact ratio was varied over the range 1.20 to 2.40 by changing the length of the tooth addendum. In order to simplify the analysis, other parameters related to contact ratio were held constant. The contact ratio was found to have a significant influence on gear dynamics. Over a wide range of operating speeds, a contact ratio close to 2.0 minimized dynamic load. For low-contact-ratio gears (contact ratio less than two), increasing the contact ratio reduced gear dynamic load. For high-contact-ratio gears (contact ratio equal to or greater than 2.0), the selection of contact ratio should take into consideration the intended operating speeds. In general, high-contact-ratio gears minimized dynamic load better than low-contact-ratio gears.

Influence of simultaneous time-varying bearing and tooth mesh stiffness fluctuations on spur gear pair vibration

2019 ◽  
Vol 97 (2) ◽  
pp. 1403-1424 ◽  
Author(s):  
Guanghui Liu ◽  
Jun Hong ◽  
Robert G. Parker
Keyword(s):  
Spur Gear ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness

Nonlinear dynamics of a spur gear pair with tooth root crack based on an amplitude modulation function

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nan Gao ◽  
Shiyu Wang ◽  
Muhammad Asad Ur Rehman Bajwa
Keyword(s):  
Nonlinear Dynamics ◽  
Amplitude Modulation ◽  
Spur Gear ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Chaotic Motions ◽  
Content Type ◽  
Modulation Function ◽  
Nonlinear Behaviors

PurposeGear transmissions are widely utilized in practice. This paper aims to uncouple the crack feature from the cracked time-varying mesh stiffness (TVMS) and investigate the effects of the crack on the nonlinear dynamics of a spur gear pair.Design/methodology/approachAn approximate method to simulate the cracked TVMS is proposed by using an amplitude modulation function. The ratio of mesh stiffness loss is introduced to estimate the TVMS with different crack depths and angles. The dynamic responses are obtained by solving a torsional model which takes the non-loaded static transmission error, the backlash and the cracked TVMS into account. By using the bifurcation diagram, the largest Lyapunov exponent (LLE) and dynamic mesh force, the influences of crack on nonlinear behaviors are examined. The dynamic characteristics are identified from the phase diagram, Poincaré map, dynamic mesh force, time series and FFT spectra.FindingsThe comparison between the healthy and cracked gear pairs indicates that the crack affects the system motions, such as the obvious changes of impact force and unpredictable instability. Besides, the additive and difference combination frequencies can be found in periodic-1 and -2 motions, but they are covered in periodic-3 and chaotic motions. Deeper crack is an important determinant of the nonlinear behaviors at a higher speed.Originality/valueThe research provides an interesting perspective on cracked TVMS and reveals the connection between crack and nonlinear behaviors of the gear pairs.

Neighboring periodic motion in spur gear pair and its identification methods

2021 ◽  
Author(s):  
Pengfei Liu ◽  
Lingyun Zhu ◽  
Xiangfeng Gou ◽  
Jianfei Shi ◽  
Guoguang Jin
Keyword(s):  
Periodic Motion ◽  
Spur Gear ◽  
Gear Pair ◽  
Identification Methods

A Theoretical Tribological Comparison Between Soft and Hard Coatings of Spur Gear Pairs

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Huaiju Liu ◽  
Caichao Zhu ◽  
Zhanjiang Wang ◽  
Ye Zhou ◽  
Yuanyuan Zhang
Keyword(s):  
Surface Deformation ◽  
Tribological Behavior ◽  
Elastohydrodynamic Lubrication ◽  
Spur Gear ◽  
Hard Coatings ◽  
Radius Of Curvature ◽  
Maximum Pressure ◽  
Gear Pair ◽  
The Coefficient Of Friction ◽  
Squeeze Effect

A thermal elastohydrodynamic lubrication (TEHL) model is developed for a coated spur gear pair to investigate the effect of soft coatings and hard coatings on the tribological behavior of such a gear pair during meshing. The coating properties, i.e., the ratio of the Young's modulus between the coating and the substrate, and the coating thickness, are represented in the calculation of the elastic deformation. Discrete convolution, fast Fourier transform (DC-FFT) is utilized for the fast calculation of the surface deformation. The variation of the radius of curvature, the rolling speed, the slide-to-roll ratio, and the tooth load along the line of action (LOA) during meshing is taken into account and the transient squeeze effect is considered in the Reynolds equation. Energy equations of the solids and the oil film are derived. The temperature field and the pressure field are solved iteratively. The tribological behavior is evaluated in terms of the minimum film thickness, the maximum pressure, the temperature rise, the coefficient of friction, and the frictional power loss of the tooth contact during meshing. The results show discrepancies between the soft coating results and hard coating results.

scholarly journals Nonlinear Dynamics of a Spur Gear Pair with Time-Varying Stiffness and Backlash

2004 ◽  
Vol 23 (3) ◽  
pp. 179-187 ◽  
Author(s):  
Shen Yongjun ◽  
Yang Shaopu ◽  
Pan Cunzhi ◽  
Liu Xiandong
Keyword(s):  
Nonlinear Dynamics ◽  
Spur Gear ◽  
Time Varying ◽  
Gear Pair
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