Base curves of involute cylindrical gears via Aronhold’s first theorem

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1233-1242 ◽  
Author(s):  
Giorgio Figliolini ◽  
Hellmuth Stachel ◽  
Jorge Angeles
Keyword(s):  
Tooth Profile ◽  
Transmission Ratio ◽  
Cylindrical Gears ◽  
Pressure Angle ◽  
The Subject ◽  
Meshing Gears

The subject of this paper is the synthesis of the base curves of involute cylindrical gears, for uniform and non-uniform transmission ratio, by means of Aronhold’s first theorem and the return circle. The base curves can be generated in several ways, as reported in the literature, but this approach comes from the kinematics fundamentals; it is, thus, more straightforward than the alternatives for the case of non-uniform transmission ratio, which leads to non-circular gears. The base curves of circular and non-circular gears are obtained by intersecting, at each pitch point, the corresponding return circle with the line of action for a given pressure angle. This is possible for involute cylindrical gears since the tooth profile of the rack is represented by a line, and the conjugate profiles of the two meshing gears can be generated by its envelope.

Synthesis of the Pitch Surfaces of Non-Circular Skew-Gears

2010 ◽  
Author(s):  
Giorgio Figliolini ◽  
Pierluigi Rea ◽  
Jorge Angeles
Keyword(s):  
Transmission Ratio ◽  
Dual Algebra ◽  
Cylindrical Gears ◽  
Geometrical Characteristics ◽  
Variable Transmission ◽  
The Subject ◽  
Gear Engagement

The subject of this paper is the synthesis of the pitch surfaces of non-circular skew gears, intended to generate any motion program with a periodically varying transmission ratio. This is done by extending an existing algorithm, which was formulated through the application of dual algebra and the Principle of Transference. In particular, the variable transmission ratio of N-lobed elliptical and logarithmical cylindrical gears is expressed and analyzed along with their main characteristics to test the proposed algorithm, which is implemented in Matlab. The code generates the pitch surfaces of N-lobed elliptical and logarithmical skew gears, along with those of indexing skew gears. Finally, significant numerical and graphical results are shown to analyze the geometrical characteristics of the gear engagement. Not unexpectedly, cylindrical and bevel non-circular gears become particular cases thereof.

The Impact of Meshing Transmission of Arc Gear by Hobbing Method and Central Distance Error

2011 ◽  
Vol 295-297 ◽  
pp. 2534-2539
Author(s):  
Zhong Yi Ren
Keyword(s):  
Current Literature ◽  
Tooth Profile ◽  
Mesh Point ◽  
Transmission Ratio ◽  
Tooth Surface ◽  
Literature Report ◽  
Surface Equation ◽  
Distance Error ◽  
Pressure Angle ◽  
The Impact

The tooth profile of arc gear is no longer arc after hob process, it’s a section of curve which is similar to the arc. Although there have been confirmed that this curve which is similar to the arc can make sure that the transmission ratio and meshing point of two gears will not change ,pressure angle at the meshing point will certainly change, and there is also no literature report how much this curve has impact on pressure angle. The impact of meshing transmission of arc gear by central distance error researched by current literature is based on arc tooth profile, this study is not suitable for the tooth profile processed by hob, and there is no literature report how much central distance error has impact on transmission ratio, pressure angle and mesh point of arc gear which processed by hob. In this article, the author has work out this problem by use tooth surface equation.

Tooth Profile Design for Translational Meshing Motor

2013 ◽  
Vol 365-366 ◽  
pp. 14-18
Author(s):  
Rui Hua Li
Keyword(s):  
Design Method ◽  
Coincidence Degree ◽  
Tooth Profile ◽  
Transmission Ratio ◽  
The Novel ◽  
Pressure Angle ◽  
Involute Gears ◽  
Profile Design ◽  
Center Distance ◽  
Internal Meshing

As the reason for large transmission ratio, small center distance and interference on translational motor body, the design method of involute gear for translational meshing motor was proposed. In order to get appropriate tooth profile parameters, the trail calculation considering the conditions of interference and coincidence degree were applied using the tooth profile parameters calculated from given module, number of teeth, pressure angle and modification coefficient. The internal meshing gears was designed and processed based on proposed method. The novel translational meshing motor using designed involute gears operates successfully and efficiently which testify the validity and feasibility of proposed method.

The Research on Tooth Profile Total Deviation Measuring Method Based on Coordination Measuring Machine

2012 ◽  
Vol 184-185 ◽  
pp. 789-792
Author(s):  
Bing Li ◽  
Yu Lan Wei ◽  
Meng Dan Jin ◽  
Ying Ying Fan
Keyword(s):  
Mathematical Model ◽  
Data Processing ◽  
High Precision ◽  
Gear Tooth ◽  
Measuring Method ◽  
Tooth Profile ◽  
Cylindrical Gears ◽  
Total Deviation ◽  
Measuring Machine

Put forward a method that use scatter points which got in different places to measure the involution cylindrical gears, give a mathematical model that use the discrete points to sure the total deviation of gear tooth profile. The experience results show that this way is of high precision in measurement points, measurement an error data processing less intervention, etc.

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

Effects of Drive Side Pressure Angle on Gear Fatigue Crack Propagation Life for Spur Gears With Symmetric and Asymmetric Teeth

2019 ◽  
Author(s):  
Fatih Karpat ◽  
Oguz Dogan ◽  
Tufan Yilmaz ◽  
Celalettin Yuce ◽  
Onur Can Kalay ◽  
...  
Keyword(s):  
Fatigue Crack ◽  
Crack Propagation ◽  
Fatigue Crack Propagation ◽  
Tooth Profile ◽  
Spur Gears ◽  
Pressure Angle ◽  
Side Pressure ◽  
Machine Elements ◽  
Fatigue Crack Propagation Life ◽  
Initial Starting

Abstract Today gears are one of the most crucial machine elements in the industry. They are used in every area of the industry. Due to the high performances of the gears, they are also used in aerospace and wind applications. In these areas due to the high torques, unstable conditions, high impact forces, etc. cracks can be seen on the gear surface. During the service life, these cracks can be propagated and gear damages can be seen due to the initial cracks. The aim of this study is to increase the fatigue crack propagation life of the spur gears by using asymmetric tooth profile. Nowadays asymmetric gears have a very important and huge usage area in the industry. In this study, the effects of drive side pressure angle on the fatigue crack propagation life are studied by using the finite element method. The initial starting points of the cracks are defined by static stress analysis. The starting angles of the cracks are defined constant at 45°. The crack propagation analyses are performed in ANSYS SMART Crack-Growth module by using Paris Law. Four different drive side pressure angles (20°-20°, 20°-25°, 20°-30° and 20°-35°) are investigated in this study. As a result of the study the fatigue crack propagation life of the gears is increased dramatically when the drive side pressure angle increase. This results show that the asymmetric tooth profile not only decrease the bending stress but also increase the fatigue crack propagation life strongly.

Research for Tooth Profile Modification Technology and Slotting Process

2011 ◽  
Vol 328-330 ◽  
pp. 583-586
Author(s):  
Cong Gui Chen ◽  
Liang Bin Hu ◽  
Yao Bin Hu ◽  
Sheng Li
Keyword(s):  
Tooth Profile ◽  
Profile Modification ◽  
Development Status ◽  
Pressure Angle ◽  
Modification Process ◽  
Tooth Profile Modification ◽  
Grinding Machine

The development status of profile modification technology and slotting process are described, the paper proposed slotting profile modification process, in view of the advantages of slotting processing. The modification curve of modification gear is fitted in the form of multi-segment involutes by resembling the principle of tooth profile modification on the grinding machine by using generating principles and changing the pressure angle, the formula of modification pressure angles of slotting cutter corresponding sections of involutes deduced,the modification profile of slotting cutter is designed.

Synthesis of the Base Curves For N-Lobed Elliptical Gears

2004 ◽  
Vol 127 (5) ◽  
pp. 997-1005 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Differential Geometry ◽  
Tooth Profile ◽  
Spur Gears ◽  
Profile Angle ◽  
Pressure Angle ◽  
Base Circle ◽  
Noncircular Gears ◽  
The Right ◽  
First Time ◽  
Envelope Theory

Motivated by the need to synthesize the tooth profiles of noncircular gears, we approach the synthesis of the tooth profile of circular spur gears using their pitch circle, rather than their base circle. We do this by means of envelope theory. The proposed formulation gives the involute tooth profile and its well-known base circle for any pitch radius and profile angle of the rack cutter, which coincides with the pressure angle for circular gears. Then, the foregoing approach applies to the synthesis of the base curves of noncircular gears with involute tooth profiles and of their rack. We do this by resorting to basic differential geometry using the Euler–Savary Theorem, rather than to envelope theory. In particular, the formulation of both base curves for the right and left involute tooth profiles is obtained, for the first time, for N-lobed elliptical gears and their rack through the formulation of the pitch curves and their evolutes. The proposed formulation is illustrated with numerical results.

Modeling Research of Hypoid Gear Based on Real Machining Process

2010 ◽  
Vol 20-23 ◽  
pp. 1429-1433
Author(s):  
Xiu Ting Wei ◽  
Jing Cheng Liu ◽  
Qiang Du
Keyword(s):  
Tooth Profile ◽  
Modeling Method ◽  
Machining Process ◽  
Transmission Ratio ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Modeling Methods ◽  
Modeling Process ◽  
Generating Method

In this paper, two modeling methods, the forming method and the generating method, for hypoid gears with two kinds of transmission ratio are discussed by simulating the actual machining process. In the generating modeling method, the tooth profile of the gear is generated by boolean algorithm step by step after creating the models of the gear blank and the cutter and then rotating around their own axis by certain degrees until the cutter is outside the gear blank completely. In contrast with the generating modeling method, the tooth profile is formed by carrying out the boolean algorithm for one time after creating the models of the gear blank and cutter seperately in the forming modeling method. Then using feature instance, all the teeth are created both in the generating modeling method and in the forming modeling method. Using the two modeling methods given in this paper, the modeling process can be shortened and the modeling precision can be improved.

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