scholarly journals Numerical Calculation Method of Meshing Stiffness for the Beveloid Gear considering the Effect of Surface Topography

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Hancheng Mao ◽  
Yongguo Sun ◽  
Tiantian Xu ◽  
Guangbin Yu
Keyword(s):  
Fractal Dimension ◽  
Surface Topography ◽  
Pitch Angle ◽  
Helix Angle ◽  
Mesh Stiffness ◽  
Meshing Stiffness ◽  
Pressure Angle ◽  
Beveloid Gears ◽  
Tooth Width ◽  
Fractal Roughness

The tooth surfaces of beveloid gears have different topography features due to machining methods, manufacturing accuracies, and surface wear, which will affect the contact state of the tooth surface, thereby affecting time-varying mesh stiffness between mating gear pairs. Therefore, a slice grouping method was proposed in this paper on the basis of potential energy to calculate the total meshing stiffness of beveloid gears with the surface topography. The method in this paper was verified by finite element method (FEM). Compared with the calculation results of this paper, the relative error is 5.9%, which demonstrated the feasibility and accuracy of the method in this paper. Then, the influence of parameters such as pressure angle, helix angle, pitch angle, tooth width, fractal dimension, and fractal roughness on meshing stiffness was investigated, of which results show that pressure angle, pitch angle, tooth width, and fractal dimension have an incremental impact on the mean value of mesh stiffness. However, the fluctuating value of mesh stiffness has also increased as the pressure angle, tooth width, and pitch cone angle increase. Both the helix angle and the fractal roughness have a depressive impact on the total stiffness. But the difference is that, with the increase of the helix angle, the fluctuation of meshing stiffness has been decreased. Conversely, with the increase of the fractal roughness, the fluctuation of meshing stiffness has been increased.

Improving the Characteristics of Gear Pumps: Part A — Discharge

2003 ◽  
Author(s):  
Ahmed M. M. El-Bahloul ◽  
Yasser Z. R. Ali
Keyword(s):  
Correction Factor ◽  
Helix Angle ◽  
Tooth Profile ◽  
Radius Of Curvature ◽  
Circular Arc ◽  
Pressure Angle ◽  
Face Width ◽  
Angle Change ◽  
Number Of Teeth ◽  
Gear Pumps

The main objective of this paper is to study the effect of gear geometry on the discharge of gear pumps. We have used gears of circular-arc tooth profile as gear pumps and have compared between these types of gearing and spur, helical gear pumps according to discharge. The chosen module change from 2 to 16 mm, number of teeth change from 8 to 20 teeth, pressure angle change from 10 to 30 deg, face width change from 20 to 120 mm, correction factor change from −1 to 1, helix angle change from 5 to 30 deg, and radii of curvature equal 1.4, 1.5, 2, 2.5, 2.75, and 3m are considered. The authors deduced that the tooth rack profile with radius of curvature equal 2.5, 2.75, 3m for all addendum circular arc tooth and convex-concave tooth profile, and derived equations representing the tooth profile, and calculated the points of intersections between curves of tooth profile. We drive the formulas for the volume of oil between adjacent teeth. Computer program has been prepared to calculate the discharge from the derived formulae with all variables for different types of gear pumps. Curves showing the change of discharge with module, number of teeth, pressure angle, face width, correction factor, helix angle, and radius of curvature are presented. The results show that: 1) The discharge increases with increasing module, number of teeth, positive correction factor, face width and radius of curvature of the tooth. 2) The discharge increases with increasing pressure angle to a certain value and then decreases with increasing pressure angle. 3) The discharge decreases with increasing helix angle. 4) The convex-concave circular-arc gears gives discharge higher than that of alla ddendum circular arc, spur, and helical gear pumps respectively. 5) A curve fitting of the results are done and the following formulae derived for the discharge of involute and circular arc gear pumps respectively: Q=A1bm2z0.895e0.065xe0.0033αe−0.0079βQ=A2bm2z0.91ρ10.669e−0.0047β

Low excitation spur gears with variable tip diameter

2021 ◽  
Vol 263 (5) ◽  
pp. 1275-1285
Author(s):  
Joshua Götz ◽  
Sebastian Sepp ◽  
Michael Otto ◽  
Karsten Stahl
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Axial Forces ◽  
Tooth Width ◽  
Drive Trains ◽  
Static Transmission Error

One important source of noise in drive trains are transmissions. In numerous applications, it is necessary to use helical instead of spur gear stages due to increased noise requirements. Besides a superior excitation behaviour, helical gears also show additional disadvantageous effects (e.g. axial forces and tilting moments), which have to be taken into account in the design process. Thus, a low noise spur gear stage could simplify design and meet the requirements of modern mechanical drive trains. The authors explore the possibility of combining the low noise properties of helical gears with the advantageous mechanical properties of spur gears by using spur gears with variable tip diameter along the tooth width. This allows the adjustment of the total length of active lines of action at the beginning and end of contact and acts as a mesh stiffness modification. For this reason, several spur gear designs are experimentally investigated and compared with regard to their excitation behaviour. The experiments are performed on a back-to-back test rig and include quasi-static transmission error measurements under load as well as dynamic torsional vibration measurements. The results show a significant improvement of the excitation behaviour for spur gears with variable tip diameter.

Coupled Bending-Torsion Vibration of Geared Rotors

1995 ◽  
Author(s):  
J. S. Rao ◽  
J. R. Chang ◽  
T. N. Shiau
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Mesh Stiffness ◽  
Present Program ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Torsion Vibration ◽  
Gear Mesh Stiffness

Abstract A general finite element model is presented for determining the coupled bending-torsion natural frequencies and mode shapes of geared rotors. Uncoupled bending and torsion frequencies are obtained for examples available in literature and the present program is verified against these. The effect of the gear box is considered to determine the coupled frequencies. Parameters studied include the pressure angle, gear mesh stiffness, and bearing properties. The gear pressure angle is shown to have no effect on the natural frequencies of rotors supported on isotropic bearing supports. Several case studies with bending-torsion coupling are considered and the results obtained are compared with those available in literature. The results of a general rotor system with 8lodes are also presented.

Research on dynamic modeling and simulation verification of a new type of FT pin-cycloid transmission

2019 ◽  
Vol 233 (17) ◽  
pp. 6276-6288
Author(s):  
Liang Xuan ◽  
Chao Xie ◽  
Tianmin Guan ◽  
Lei Lei ◽  
Heng Jiang
Keyword(s):  
Dynamic Model ◽  
Industrial Robot ◽  
Torsional Stiffness ◽  
Mesh Stiffness ◽  
Lagrange Method ◽  
Input Shaft ◽  
Meshing Stiffness ◽  
Theoretical Support ◽  
Bearing Stiffness ◽  
New Type

A new type of FT pin-cycloid transmission reducer is widely used in the industrial robot field due to the high transmission accuracy. In addition, the complex working conditions bring about vibration, which affects the transmission accuracy of the robot. Therefore, it is necessary to study the dynamic characteristics of FT reducer at the transmission joint. In this paper, based on the analysis of its transmission principle and structure, the dynamic model of FT transmission is established by necessary assumptions. The stiffness mathematical models of different meshing positions are obtained from the dynamic model, and the differential equations of the system are established by Lagrange method. In order to solve the natural frequency of the system, the stiffness of meshing positions of the system is solved, including input shaft torsional stiffness, involute gear meshing stiffness, bearing stiffness, cycloid gear and pin torsional stiffness. Considering the output of FT transmission, a “3+ i” model is proposed to obtain the mesh stiffness between the cycloid gear and output pins. Finally, the correctness of the model is proved by choosing parameters such as transmission ratio and force on parts and components by simulation. The research results will provide theoretical support for the optimal design of FT transmission.

scholarly journals Improvement on Meshing Stiffness Algorithms of Gear with Peeling

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 609
Author(s):  
Lingli Cui ◽  
Tongtong Liu ◽  
Jinfeng Huang ◽  
Huaqing Wang
Keyword(s):  
Simulation Analysis ◽  
Gear Tooth ◽  
Gear Wheel ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Involute Gears ◽  
Gear Mesh Stiffness ◽  
Meshing Process

This paper investigates the effect of a gear tooth peeling on meshing stiffness of involute gears. The tooth of the gear wheel is symmetric about the axis, and its symmetry will change after the gear spalling, and its meshing stiffness will also change during the meshing process. On this basis, an analytical model was developed, and based on the energy method a meshing stiffness algorithm for the complete meshing process of single gear teeth with peeling gears was proposed. According to the influence of the change of meshing point relative to the peeling position on the meshing stiffness, this algorithm calculates its stiffness separately. The influence of the peeling sizes on mesh stiffness is studied by simulation analysis. As a very important parameter, the study of gear mesh stiffness is of great significance to the monitoring of working conditions and the prevention of sudden failure of the gear box system.

Coupled Dynamic and Vibration Analysis of Beveloid Geared System

2012 ◽  
Vol 215-216 ◽  
pp. 917-920
Author(s):  
Rong Fan ◽  
Chao Sheng Song ◽  
Zhen Liu ◽  
Wen Ji Liu
Keyword(s):  
Transmission Error ◽  
Time Varying ◽  
Spur Gears ◽  
Dynamic Coupling ◽  
Nonlinear Dynamic Model ◽  
Mesh Stiffness ◽  
Hypoid Gears ◽  
Helical Gears ◽  
Beveloid Gears ◽  
Vibration Model

Dynamic modeling of beveloid gears is less developed than that of spur gears, helical gears and hypoid gears because of their complicated meshing mechanism and 3-dimsional dynamic coupling. In this study, a nonlinear systematic coupled vibration model is created considering the time-varying mesh stiffness, time-varying transmission error, time-varying rotational radius and time-varying friction coefficient. Numerical integration applying the explicite Runge-Kutta formula and the implicit direct integration is used to solve the nonlinear dynamic model. Also, the dynamic characteristics of the marine gear system are investigated.

Investigation of Tool Errors and Their Influences on Tooth Surface Topography for Face-Hobbed Hypoid Gears

2019 ◽  
Vol 142 (4) ◽  
Author(s):  
Chengcheng Liang ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Yawen Wang ◽  
Siyuan Liu ◽  
...  
Keyword(s):  
Surface Topography ◽  
Rake Angle ◽  
Tooth Surface ◽  
Maximum Deviation ◽  
Angle Error ◽  
Hypoid Gears ◽  
Pressure Angle ◽  
Deviation Analysis ◽  
Surface Deviation ◽  
The Impact

Abstract Tool errors are inevitable in an actual gear-manufacturing environment and may directly affect the accuracy of machined tooth surfaces. In this paper, tool errors including spheric radius, pressure angle, rake angle, regrind angle, and cutting side relief angle errors for three-face blade are defined and considered to establish the accurate tooth surface mathematical model for face-hobbed hypoid gears based on the manufacturing process and the meshing theory. The simulation flowchart for tooth surface modeling and tooth surface topography deviation analysis are proposed and performed. Results show that the tooth surface deviation is positive with positive spheric radius and rake angle errors and contrary results can be found for other three tool errors. In addition, the impact of the pressure angle error is the strongest. In addition, the rake angle error has the weakest effect and the influence of spheric radius error on the tooth surface deviation is unsubstantial. For location of tooth surface deviation, the maximum deviation is at the top on the heel and the minimum deviation is at the middle on the toe for spheric radius error. The maximum and minimum deviations are at the top and the middle tooth on the heel for other factors, respectively.

CONSISTENCY ANALYSIS OF WORN SURFACE TOPOGRAPHY AND FRICTION FORCE BASED ON PHASE TRAJECTORY AND RECURRENCE ANALYSIS

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950130
Author(s):  
XUE ZUO ◽  
MINGLONG PENG ◽  
YUANKAI ZHOU
Keyword(s):  
Fractal Dimension ◽  
Surface Topography ◽  
Friction Force ◽  
Phase Trajectory ◽  
Small Volume ◽  
Surface Profile ◽  
Recurrence Plots ◽  
Recurrence Analysis ◽  
Wear Process ◽  
Worn Surface

The dynamic evolutions of friction force and worn surface profile were qualitatively analyzed by phase trajectory and recurrence plots and quantitatively characterized by fractal dimension and percent determinism. The results show that phase trajectories first shrink to a small volume, then stabilize at a minimum volume, finally expand to a large volume in the wear process. The white areas on the recurrence plots increase with the wear time. The fractal dimension first increases, then stabilizes at a high value, and finally decreases rapidly. The percent determinism first decreases, then fluctuates in a certain range, and finally increases. It demonstrates that friction force and worn surface topography derived from one tribology system evolve in a similar but not exactly the same way. They have the consistent evolution law in the wear process. Specially, friction force is much more sensitive to the variation of wear states than the worn surface.

Investigating the effect of helix angle and pressure angle on bending stress in helical gear under dynamic state

2018 ◽  
Vol 15 (4) ◽  
pp. 478-488
Author(s):  
Prashant Jaysing Patil ◽  
Maharudra Patil ◽  
Krishnakumar Joshi
Keyword(s):  
Gear Tooth ◽  
Helix Angle ◽  
Helical Gear ◽  
Dynamic State ◽  
Load Carrying Capacity ◽  
Bending Stress ◽  
Content Type ◽  
Gear Design ◽  
Pressure Angle ◽  
Load Carrying

Purpose The aim of this paper is to study the effect of pressure angle and helix angle on bending stress at the root of helical gear tooth under dynamic state. Gear design is a highly complex process. The consistent demand to build low-cost, quieter and efficient machinery has resulted in a gradual change in gear design. Gear parameters such as pressure angle, helix angle, etc. affect the load-carrying capacity of gear teeth. Adequate load-carrying capacity of a gear is a prime requirement. The failure at the critical section because of bending stress is an unavoidable phenomenon. Besides this fact, the extent of these failures can be reduced by a proper gear design. The stresses produced under dynamic loading conditions in machine member differ considerably from those produced under static loading. Design/methodology/approach The present work is intended to study the effect of pressure angle and helix angle on the bending stress at the root of helical gear tooth under dynamic state. The photostress method has been used as experimental methods. Theoretical analysis was carried out by velocity factor method and Spott’s equation. LS DYNA has been used for finite element (FE) analysis. Findings The results show that experimental method gives a bending stress value that is closer to the true value, and bending stress varies with pressure angle and helix angle. The photostress technique gives clear knowledge of stress pattern at root of tooth. Originality/value The outcomes of this work help the designer use optimum weight-to-torque ratio of gear; this is ultimately going to reduce the total bulk of the gear box.

Sign in / Sign up

Export Citation Format

Share Document