scholarly journals Optimal Tooth Numbers for Compact Standard Spur Gear Sets

1982 ◽  
Vol 104 (4) ◽  
pp. 749-757 ◽  
Author(s):  
M. Savage ◽  
J. J. Coy ◽  
D. P. Townsend
Keyword(s):  
Optimal Design ◽  
Objective Function ◽  
Design Space ◽  
Spur Gear ◽  
Gear Ratio ◽  
Contact Ratio ◽  
Bending Fatigue ◽  
Gear Mesh ◽  
Compact Design ◽  
Center Distance

The design of a standard gear mesh is treated with the objective of minimizing the gear size for a given ratio, pinion torque, and allowable tooth strength. Scoring, pitting fatigue, bending fatigue, and the kinematic limits of contact ratio and interference are considered. A design space is defined in terms of the number of teeth on the pinion and the diametral pitch. This space is then combined with the objective function of minimum center distance to obtain an optimal design region. This region defines the number of pinion teeth for the most compact design. The number is a function of the gear ratio only. A design example illustrating this procedure is also given.

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.

Optimal Design of 6-UPU Parallel Mechanism

2011 ◽  
Vol 480-481 ◽  
pp. 1055-1060
Author(s):  
Guang Hua Wu ◽  
Lie Hang Gong ◽  
Xin Wei Ji ◽  
Zhong Jun Wu ◽  
Yong Jun Gai
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimal Design ◽  
Objective Function ◽  
Parallel Mechanism ◽  
Design Space ◽  
Jacobian Matrix ◽  
Optimal Model ◽  
The Real ◽  
Universal Joints

The methodology of the optimal design for the 6-UPU parallel mechanism (PM) is presented based on genetic algorithms. The optimal index which expressed by Jacobian matrix of the PM is first deduced. An optimal model is established, in which the kinematic dexterity of a parallel mechanism is considered as the objective function. The design space, the limiting length of the electric actuators and the limit angles of universal joints are taken as constraints. The real-encoding genetic algorithm is applied to the optimal design of a parallel mechanism, which is proved the validity and advantage for the optimal design of a similar mechanism.

Formulation for an optimal design problem of spur gear drive and its global optimization

2012 ◽  
Vol 227 (8) ◽  
pp. 1804-1817 ◽  
Author(s):  
Zhong Wan ◽  
ShaoJun Zhang
Keyword(s):  
Global Optimization ◽  
Optimal Design ◽  
Design Problem ◽  
Optimization Method ◽  
Spur Gear ◽  
Global Optimization Method ◽  
Contact Ratio ◽  
Gear Drive ◽  
Variable Space ◽  
Global Optimal

In this article, an optimal design problem of spur gear drive with a fixed load factor is formulated as a nonlinear optimization model. Three methods are presented to find the globally optimal design scheme on the structure of the spur gear pair. By suitable variable transformation, the constructed model is first converted into a linear program with mixed variables. By developing an algorithm of global optimization for solving a binary linear programming with mixed variables, all global optimal solutions are found for the original design problem. Taking into account the modification of the contact ratio factors, a specific global optimization method is provided to optimize the design of spur gear drive with soft tooth flank in a continuous variable space. On the basis of enumeration of the discrete variables and utilization of the monotonicity in the optimal model, another global optimization method is designed to search for the global optimal solutions in the mixed variable space, which does not depend upon whether the modification of contact ratio factor exists or not. Case studies are employed to demonstrate the validity and practicability of the constructed model and the proposed methods.

Dimensionless Solution to the Optimal Design of Spur Gear Sets

1989 ◽  
Vol 111 (2) ◽  
pp. 290-296 ◽  
Author(s):  
R. K. Carroll ◽  
G. E. Johnson
Keyword(s):  
Optimal Design ◽  
Material Properties ◽  
Design Space ◽  
Problem Formulation ◽  
Stress Constraints ◽  
Spur Gear ◽  
Minimum Size ◽  
New Approach ◽  
Materials Used ◽  
Standard Sets

In some earlier papers (Savage, Coy, and Townsend, 1982; Carroll and Johnson, 1984), the design of spur gear sets based on minimum size has been addressed considering the interaction of bending and contact stress constraints. In this paper, we present a new approach to the spur gear problem. The new method makes use of some newly defined dimensionless parameters. In the resulting design space, the optimal dimensionless design (which defines the optimal tooth geometry) is independent of load and speed requirements of the gear set. However the optimum is dependent on the physical properties of the materials used. We introduce a new quantity called the Material Properties Relationship Factor, CMP. In the problem formulation presented here, we show that the optimum will always be constraint bound and it will occur at one of three possible constraint intersections. CMP is used to identify which of three possible constraint intersections is the correct one. After the dimensionless optimum is found, we present an example which shows how to transform the solution back into the real design space considering the load and speed requirements of the gear set along with discrete value constraints on the number of teeth and the diametral pitch. Tabulated optimal dimensionless designs are included for some standard sets of tooth proportions.

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.

Effect of Involute Contact Ratio on Spur Gear Dynamics

1999 ◽  
Vol 121 (1) ◽  
pp. 112-118 ◽  
Author(s):  
A. Kahraman ◽  
G. W. Blankenship
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Design Guidelines ◽  
Forced Response ◽  
Contact Ratio ◽  
Test Rig ◽  
Response Curves ◽  
Gear Mesh ◽  
Dynamic Transmission Error ◽  
Selection Of

The influence of involute contact ratio on the torsional vibration behavior of a spur gear pair is investigated experimentally by measuring the dynamic transmission error of several gear pairs using a specially designed gear test rig. Measured forced response curves are presented, and harmonic amplitudes of dynamic transmission error are compared above and below gear mesh resonances for both unmodified and modified gears having various involute contact ratio values. The influence of involute contact ratio on dynamic transmission error is quantified and a set of generalized, experimentally validated design guidelines for the proper selection of involute contact ratio to achieve quite gear systems is presented. A simplified analytical model is also proposed which accurately describes the effects of involute contact ratio on dynamic transmission error.

scholarly journals Effect of Contact Ratio on Spur Gear Dynamic Load

1992 ◽  
Author(s):  
Chuen-Huei Liou ◽  
Hsiang Hsi Lin ◽  
Fred B. Oswald ◽  
Dennis P. Townsend
Keyword(s):  
Dynamic Load ◽  
Spur Gear ◽  
Tooth Size ◽  
Contact Ratio ◽  
Gear Dynamics ◽  
Wide Range ◽  
Gear Contact ◽  
Center Distance ◽  
Selection Of ◽  
Better Than

Abstract 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 2.0), increasing the contact ratio reduced the 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.

scholarly journals Optimal Design of Compact Spur Gear Reductions

1992 ◽  
Author(s):  
M. Savage ◽  
S. B. Lattime ◽  
J. A. Kimmel ◽  
H. H. Coe
Keyword(s):  
Optimal Design ◽  
Search Algorithm ◽  
Spur Gear ◽  
Optimal Designs ◽  
Continuous Variables ◽  
Gear Mesh ◽  
System Life ◽  
Optimal Configurations ◽  
System Volume ◽  
Selection Of

Abstract The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to the gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.

Compact Design of High-Contact-Ratio Spur Gears

2020 ◽  
Author(s):  
Tuan H. Nguyen
Keyword(s):  
Spur Gear ◽  
Operating Parameters ◽  
Spur Gears ◽  
Bending Stress ◽  
Contact Ratio ◽  
Dynamic Design ◽  
Compact Design ◽  
Profile Errors ◽  
Tooth Profile Errors ◽  
Root Stress

Abstract This study presents a computer simulation for the dynamic design of compact high-contact-ratio spur gear transmissions. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented in this work was performed by using the NASA gear dynamics code DANST (Dynamic Analysis of Spur Gear Transmissions). In the analysis, the addendum ratio (addendum/diametral pitch) was varied over the range 1.30 to 1.40 to obtain a contact ratio of 2.00 or higher. The constraints of bending stress limit and involute interference provide the main criteria for this investigation. Compact design of high-contact-ratio gears with different gear ratios and pressure angles was investigated. Comparison of compact design between low-contact-ratio and high-contact-ratio gears was conducted. With the same operating parameters, high-contact-ratio gears appear to have much more compact design than low-contact-ratio gears. For compact design of high-contact-ratio gears, a diametral pitch of 6.00 appears to be the best choice for an optimal gear set.

Optimal Design of Bourdon Gage Mechanisms

1987 ◽  
Vol 109 (4) ◽  
pp. 524-527
Author(s):  
L. Beiner
Keyword(s):  
Optimal Design ◽  
Objective Function ◽  
Operating Conditions ◽  
Center Line ◽  
Number Of Teeth ◽  
Design Variables ◽  
Line Inclination ◽  
Center Distance

The paper deals with the optimization of lever-segment gear-pinion mechanisms used in the construction of Bourdon gage manometers. The number of teeth of the pinion (which is rigidly attached to the manometer hand) is used as an objective function in order to maximize accuracy. Design variables are the gear-pinion center distance and center line inclination and various constraints are imposed in order to satisfy operating conditions and constructive limits. An example is presented showing that the objective function is maximized by the highest feasible value of the center distance and is less sensitive to variations of the center line inclination.

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