Effect of Meshing Parameters on the Dynamic Loads of a Mechanism With Spur Gears

1993 ◽  
Author(s):  
Boris G. Belnikolovsky ◽  
Bozhidar I. Cheshankov ◽  
Bader A. Abuid
Keyword(s):  
Equations Of Motion ◽  
Variable Stiffness ◽  
Gear Ratio ◽  
Dynamic Loads ◽  
Spur Gears ◽  
Contact Ratio ◽  
Pitch Error ◽  
Tooth Width ◽  
Tooth Modification ◽  
Gear Wheels

Abstract In the model used inertias of motor, machine and the gear wheels, stiffness of shafts and bearing and damping are considered. In the meshing zone, the variable stiffness of teeth, pitch error, tooth deflection, tooth modification and impact between teeth are included. Differential equations of motion are written and solved analytically and numerically. Based on the good agreement between the analytical and the numerical results, a dynamic analysis for the effect of many parameters of meshing, such as pitch error, tooth modification, module, contact ratio, tooth width and the gear ratio on the dynamic loads is made.

Analytical Model of the Efficiency of Spur Gears: Study of the Influence of the Design Parameters

2011 ◽  
Author(s):  
Miguel Pleguezuelos ◽  
Jose´ I. Pedrero ◽  
Miryam B. Sa´nchez
Keyword(s):  
Load Distribution ◽  
Gear Ratio ◽  
Design Parameters ◽  
Spur Gears ◽  
Transmitted Power ◽  
Power Losses ◽  
Contact Ratio ◽  
Complete Study ◽  
Uniform Model ◽  
Analytical Expressions

An analytic model to compute the efficiency of spur gears has been developed. It is based on the application of a non-uniform model of load distribution obtained from the minimum elastic potential criterion and a simplified non-uniform model of the friction coefficient along the path of contact. Both conventional and high transverse contact ratio spur gears have been considered. Analytical expressions for the power losses due to friction, for the transmitted power and for the efficiency are presented. From this model, a complete study of the influence of some design parameters (as the number of teeth, the gear ratio, the pressure angle, the addendum modification coefficient, etc.) on the efficiency is presented.

scholarly journals Analytical Expressions of the Efficiency of Standard and High Contact Ratio Involute Spur Gears

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Miguel Pleguezuelos ◽  
José I. Pedrero ◽  
Miryam B. Sánchez
Keyword(s):  
Friction Coefficient ◽  
Contact Point ◽  
Load Sharing ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Transmission Parameters ◽  
Constant Friction ◽  
Analytical Expressions ◽  
Approximate Expressions

Simple, traditional methods for computation of the efficiency of spur gears are based on the hypotheses of constant friction coefficient and uniform load sharing along the path of contact. However, none of them is accurate. The friction coefficient is variable along the path of contact, though average values can be often considered for preliminary calculations. Nevertheless, the nonuniform load sharing produced by the changing rigidity of the pair of teeth has significant influence on the friction losses, due to the different relative sliding at any contact point. In previous works, the authors obtained a nonuniform model of load distribution based on the minimum elastic potential criterion, which was applied to compute the efficiency of standard gears. In this work, this model of load sharing is applied to study the efficiency of both standard and high contact ratio involute spur gears (with contact ratio between 1 and 2 and greater than 2, resp.). Approximate expressions for the friction power losses and for the efficiency are presented assuming the friction coefficient to be constant along the path of contact. A study of the influence of some transmission parameters (as the gear ratio, pressure angle, etc.) on the efficiency is also presented.

Studies on the Dynamic Performance of a Spur Gear With Hollow Teeth

1992 ◽  
Author(s):  
A. Ramamohana Rao ◽  
B. Srinivasulu
Keyword(s):  
Damping Ratio ◽  
Dynamic Performance ◽  
Spur Gear ◽  
Dynamic Loads ◽  
Response Analysis ◽  
Spur Gears ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Direction Parallel ◽  
Gear Teeth

Abstract Performance of spur gears largely depends on the magnitude and nature of variation of dynamic loads occuring between mating teeth. Variable tooth mesh stiffness is one of the primary sources causing parametric excitations resulting in dynamic loads. The usual method of varying the mesh stiffness to reduce dynamic loads is to use high contact ratio and profile modified gears. In this paper, a new type of tooth design to improve the dynamic performance of spur gears is presented. In this, a through hole is drilled in each tooth in a direction parallel to the gear axis. The diameter of the hole and its position on the tooth centre line are variable. Such a gear is called a hollow gear. Dynamic analysis is carried out for the mesh of hollow pinions mating with solid gears. The results are compared with solid pinions (no holes in teeth) meshing with solid gears. Finite element method is used for the analysis. For estimation of the dynamic load variation in hollow-solid and solid-solid gear meshes, a model incorporating the varying mesh stiffness and damping of gear teeth is used. Governing differential equations are solved using unconditionally stable Newmark-beta algorithm. The dynamic loads obtained are used as an input time varying loads for the determination of dynamic fillet and hole stress response of solid and hollow gear teeth whichever is applicable. Modal superposition technique is used for transient response analysis. The study shows that for the same damping ratio, dynamic loads in hollow-solid meshes are nearly the same as in a solid-solid mesh. In reality, the dynamic loads in a hollow-solid mesh are less than a solid-solid mesh due to its inherent higher material damping.

Determination of Addendum Modification Coefficients for Spur Gears Operating at Non-Standard Center Distances

2003 ◽  
Author(s):  
M. A. Sahir Arikan
Keyword(s):  
Gear Tooth ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Performance Variables ◽  
Practical Design ◽  
Gear Drives ◽  
Maximum Contact ◽  
Center Distance

Although it is possible to find some recommended conventional values both for the sum of the addendum modification coefficients and for the allocation of the sum of the addendum modification coefficients (e.g. ISO/TR 4467), a detailed analysis is necessary to determine the addendum modification coefficient values for the desired optimization criteria and the performance since the main objective of the above mentioned sources is to facilitate practical design of non-standard gear drives which will not have problems while operating. They give practical average values within a safe range. In this study, by considering the required gear ratio, center distance and the desired backlash, alternative gear pairs are determined and corresponding gear performance variables are calculated in order to allocate the addendum modification coefficients for the pinion and the gear by using criteria such as: not having undercut or pointed (or excessively-thinned-tip) tooth, having desired proportions for the lengths of the dedendum and addendum portions of the line of action, having maximum contact ratio, having sufficient bottom clearance, having minimum contact stresses, having balanced pinion and gear tooth root stresses, having equal pinion and gear lives, etc.

A systematic approach to profile relief design of low and high contact ratio spur gears

1999 ◽  
Vol 213 (6) ◽  
pp. 551-562 ◽  
Author(s):  
N Yildirim ◽  
R G Munro
Keyword(s):  
Experimental Validation ◽  
Systematic Approach ◽  
Variable Stiffness ◽  
Transmission Error ◽  
Uniform Motion ◽  
Spur Gears ◽  
Contact Ratio ◽  
Simplifying Assumptions ◽  
Manufacturing Tolerances ◽  
Parameter Values

This is the first of a series of papers on the design of the tooth profile relief of both low and high contact ratio spur gears and its effects on transmission error (TE) and tooth loads. A systematic approach to profile relief design is introduced. The process of profile relief analysis is based on a number of simplifying assumptions to ease the understanding of the relief design. Useful relief cases determined during the simplified analysis are further investigated, with realistic parameter values such as variable stiffness, manufacturing tolerances and so on, in other papers of the series. Experimental validation of the cases proven to be good are also given in forthcoming papers. In the present paper, the systematic approach is applied to low contact ratio (LCR) spur gears first with some design regions and to high contact ratio (HCR) spur gears with some new and promising design regions and rules. Several smooth transmission error curves at different loads are shown to be possible for the relief designed, hence allowing a range of loads with uniform motion transfer. The advantages of HCRG over LCRG in terms of smooth TE curves and tooth load values are noted.

Simplified Calculation Method for the Efficiency of Involute Spur Gears

2009 ◽  
Author(s):  
Jose´ I. Pedrero ◽  
Miguel Pleguezuelos ◽  
Marta Mun˜oz
Keyword(s):  
Friction Coefficient ◽  
Load Distribution ◽  
Gear Ratio ◽  
Spur Gears ◽  
Uniform Load ◽  
Contact Ratio ◽  
Cylindrical Gear ◽  
Transmission Parameters ◽  
Uniform Model ◽  
Simplified Calculation

The traditional methods for computation of the efficiency of cylindrical gear transmissions are based on the hypotheses of constant friction coefficient and uniform load distribution along the line of contact. However, the changing rigidity of the pair of teeth along the path of contact produces a non–uniform load distribution, which has significant influence on the friction losses, due to the different relative sliding at any point of the line of contact. In previous works, the authors obtained a non-uniform model of load distribution based on the minimum elastic potential criterion. This load distribution was applied to compute the efficiency of spur and helical gears, resulting in slightly greater values of the efficiency than those obtained if the load distribution along the line of contact is assumed to be uniform. In this work, this non-uniform model of load distribution is applied to study the efficiency of involute spur gears with transverse contact ratio between 1 and 2 (i.e., the load is shared among one or two pairs of teeth), assuming the friction coefficient to be constant along the path of contact. Analytical expressions for the power losses due to friction, for the transmitted power and for the efficiency are presented. A study of the influence of some transmission parameters (as gear ratio, pressure angle, etc.) on the efficiency is also presented.

Optimization of fillet stress to enhance the bending strength through non-standard high contact ratio spur gears

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1139-1148 ◽  
Author(s):  
P Marimuthu ◽  
G Muthuveerappan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Parametric Study ◽  
Bending Strength ◽  
Spur Gear ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Element Analysis ◽  
Gear Drives

The present study aims to determine the improvement in the bending strength of the non-standard high contact ratio spur gears based on the balanced (optimum) fillet stress of the pinion and gear. The average number teeth in contact is more than two for high contact ratio gear drives. In the non-standard high contact ratio spur gears, the rack cutter tooth thickness factor is more than 0.5, whereas the standard rack cutter tooth thickness factor is 0.5. The maximum fillet stresses of the pinion and gear is not equal for non-standard high contact ratio spur gear drives when the gear ratio increases. In order to avoid the fatigue failure of the gear, the fillet stresses of the pinion and gear should be balanced. This balanced stress is predicted as the optimum fillet stress. Hence, the present study focuses to optimize the fillet stress with respect to the rack cutter tooth thickness factor of the pinion and gear through finite element analysis. Also, a parametric study is carried out to obtain the influence of some gear parameters, such as gear ratio, teeth number in the pinion, pressure angle, addendum height and corrected gear drives (S+, S− and So) on the optimum fillet stress with respect to the rack cutter tooth thickness factor of the pinion and gear.

A new type of profile relief for high contact ratio spur gears

1999 ◽  
Vol 213 (6) ◽  
pp. 563-568 ◽  
Author(s):  
N Yaldirim ◽  
R G Munro
Keyword(s):  
Systematic Approach ◽  
Transmission Error ◽  
Uniform Motion ◽  
Spur Gears ◽  
Contact Ratio ◽  
Advantages And Disadvantages ◽  
Design Load ◽  
Pitch Error ◽  
New Type ◽  
Overall Performance

The second of a series of papers on the systematic approach to the profile relief design of both low contact ratio (LCR) and high contact ratio (HCR) spur gears and its effects on transmission error (TE) and tooth loads. Basics of the approach are given in the previous paper of the series. Application of the approach to HCR spur gears has produced two promising design cases, namely the short and long reliefs, with advantages and disadvantages. In this paper a new relief type, double relief, is introduced by making use of the two promising cases. Advantages of the two are brought together, with some compromise. The overall performance of the new relief type, however, is superior to the others in terms of peak-to-peak TE value, maximum tooth load value, rate of tooth loading and number of smooth TE curves, and hence in terms of the range of transmitted load with nearly uniform motion transfer. A procedure for compensation for adjacent pitch error (PE) with smooth TE curve at off-design load is also included.

Dynamic Analysis of High-Contact-Ratio Spur Gears With Asymmetric Teeth

2008 ◽  
Author(s):  
F. Karpat ◽  
S. Ekwaro-Osire
Keyword(s):  
Numerical Technique ◽  
Spur Gear ◽  
Dynamic Loads ◽  
Spur Gears ◽  
Load Carrying Capacity ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Load Carrying ◽  
Gear Contact

In this research, a numerical technique is used to study the performance of high-contact-ratio (HCR) spur gears with asymmetric teeth. Asymmetric teeth have been shown to minimize dynamic loads and to increase the load carrying capacity. This is due to the fact that these teeth have a larger pressure angle on the drive side compared to the coast side. In literature, symmetric gear teeth with HCR have been shown to also yield low dynamic loads and high load capacities. HCR gears have these positive attributes because for gears in a mesh, the number of tooth pairs sharing the transmitted load alternates between two and three. In this study, the separate benefits of an HCR gear and asymmetric teeth are unified into a spur gear with asymmetric teeth. In this case, the effect of the gear contact ratio, addendum factor, mesh stiffness, pressure angles, and operation speeds on dynamic tooth loads are considered. The influences of these parameters on dynamic response are presented and discussed. A comparison between standard and non standard gear pairs in literature is also presented, with respect to dynamic tooth loads. Sample simulation results, which were obtained by using an in-house computer program, are discussed. The results obtained are shown to match well with some related analytical and experimental results in literature. It is further demonstrated that HCR spur gears with asymmetric teeth do provide a marked advantage compared to the conventional spur gears with symmetric teeth.

scholarly journals A Variable Parameter Ambient Vibration Control Method Based on Quasi-Zero Stiffness in Robotic Drilling Systems

Machines ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 67
Author(s):  
Laixi Zhang ◽  
Chenming Zhao ◽  
Feng Qian ◽  
Jaspreet Singh Dhupia ◽  
Mingliang Wu
Keyword(s):  
Vibration Control ◽  
Vibration Isolation ◽  
Control Method ◽  
Control Strategies ◽  
Equations Of Motion ◽  
Variable Parameter ◽  
Harmonic Balance Method ◽  
Variable Stiffness ◽  
Ambient Vibration ◽  
Robotic Drilling

Vibrations in the aircraft assembly building will affect the precision of the robotic drilling system. A variable stiffness and damping semiactive vibration control mechanism with quasi-zero stiffness characteristics is developed. The quasi-zero stiffness of the mechanism is realized by the parallel connection of four vertically arranged bearing springs and two symmetrical horizontally arranged negative stiffness elements. Firstly, the quasi-zero stiffness parameters of the mechanism at the static equilibrium position are obtained through analysis. Secondly, the harmonic balance method is used to deal with the differential equations of motion. The effects of every parameter on the displacement transmissibility are analyzed, and the variable parameter control strategies are proposed. Finally, the system responses of the passive and semiactive vibration isolation mechanisms to the segmental variable frequency excitations are compared through virtual prototype experiments. The results show that the frequency range of vibration isolation is widened, and the stability of the vibration control system is effectively improved without resonance through the semiactive vibration control method. It is of innovative significance for ambient vibration control in robotic drilling systems.

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