scholarly journals Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

2021 ◽  
Vol 6 (7 (114)) ◽  
Author(s):  
Serhii Pylypaka ◽  
Tetiana Kresan ◽  
Tatiana Volina ◽  
Iryna Hryshchenko ◽  
Liubov Pshenychna ◽  
...  
Keyword(s):  
High Reliability ◽  
Gear Tooth ◽  
Logarithmic Spiral ◽  
Acute Angle ◽  
Machine Building ◽  
Radius Vector ◽  
Transfer Number ◽  
Friction Forces ◽  
Number Of Teeth ◽  
Coordinate Origin

Toothed gears are the most common mechanical gears in machine building, which are characterized by high reliability and durability, a constant transfer number, and which can transmit high torque. During toothed gear operation, the surfaces of the teeth slide, which gives rise to friction forces and wears their working surfaces. To prevent this, the surfaces of the teeth need constant lubrication. This paper considers the design of a gear tooth engagement, which does not have friction between the surfaces of the teeth since they roll over each other without slipping. The profile of the tooth of such a gear is outlined by congruent arcs, symmetrical relative to the line that connects the center of rotation of the toothed wheel with the top of the tooth. These symmetrical curves at the top of the tooth intersect at the predefined angle. In the depressions of the wheel, adjacent teeth also intersect at the same angle. Such a condition can be ensured by a curve that at all its points crosses the radius-vector emanating from the coordinate origin, also at a stable angle equal to half of the given one. This curve is a logarithmic spiral. If the number of teeth of the drive and driven wheels is the same, then their teeth are congruent. Otherwise, the profiles of the teeth would differ but they could be outlined by congruent arcs of the same logarithmic spiral of the same length taken from different areas of the curve. The minimum possible angle at the top of the teeth is straight. At acute angle, the toothed gear operation is impossible. To build gear wheels with a right angle at the top of the tooth, it would suffice to set the number of teeth of the drive and driven wheels. The center-to-center distance is calculated using the derived formula. The transfer number of such a gear is variable but, with an increase in the number of teeth, the range of its change decreases. The algorithm of wheel construction is given.

Design and Test of Differential Planetary Gear System for Open Rotor Power Gearbox

2013 ◽  
Author(s):  
Hideyuki Imai ◽  
Tatsuhiko Goi ◽  
Kenichi Kijima ◽  
Tooru Nishida ◽  
Hidenori Arisawa ◽  
...  
Keyword(s):  
Performance Test ◽  
High Efficiency ◽  
High Reliability ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Design Concept ◽  
Gear System ◽  
Open Rotor ◽  
Planetary Gear System ◽  
Validation Tests

The open rotor engine is a next generation aero-engine that satisfies the demand for high fuel efficiency and low CO2 emission. A differential planetary gear system is incorporated in the open rotor engine to connect the turbine output shaft and fan rotors in order to counter-rotate the fan rotors as well as allow the turbine and fan rotors to operate at more efficient speeds. The open rotor gear system is required to have not only 20,000 hp high power transmission, but also an increasingly high efficiency, high reliability and light weight. To achieve these requirements, the following design works were conducted; (1) a low misalignment and lightweight carrier, (2) a flexible structure to absorb the displacement caused by the flight load, (3) an optimum gear tooth modification and (4) reduction of oil churning and windage losses. Also, extensive analyses and simulations such as lube oil flow CFD, FEA and tooth contact analysis were conducted. A full scale prototype gear system was manufactured and validation tests were conducted using a newly constructed test rig to validate the design concept. A slow roll test, rated performance test and efficiency test were conducted. And the design concept was found to be valid. This paper describes details of the prototype design and the results of the validation tests.

Logarithmic Spiral Bevel Gear Tooth Contact Inspection

2010 ◽  
Vol 44-47 ◽  
pp. 1345-1349
Author(s):  
Qiang Li ◽  
Wen He ◽  
Hong Bo Yan ◽  
Hong Xiang Zhang
Keyword(s):  
Contact Area ◽  
Detection Method ◽  
Gear Tooth ◽  
Logarithmic Spiral ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Tooth Contact ◽  
Ideal Number ◽  
Spiral Bevel ◽  
Gear Contact

Introduction of spiral bevel gear tooth contact detection method, detection method based on the principle of EPG in the Y9550-type bevel gear roll tester on a pair of spiral bevel gear tooth contact area of sample detection experiment, obtained by experiment logarithmic spiral bevel gear contact area of the location, shape and size of the result. The experimental results with the Gleason spiral bevel gear contact area and the ideal number of spiral bevel gears on the contact area were compared, obtained on the number of spiral bevel gear tooth contact of the correlation.

A Novel Loaded Tooth Contact Analysis Procedure with Application to Internal-External Straight Bevel Gear Mesh in Pericyclic Drive

2020 ◽  
pp. 1-22
Author(s):  
Tanmay D. Mathur ◽  
Edward C. Smith ◽  
Robert C. Bill
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Bevel Gear ◽  
Gear Train ◽  
Initial Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Gear Mesh ◽  
Number Of Teeth ◽  
Loaded Tooth Contact Analysis

Abstract A comprehensive numerical loaded tooth contact analysis (LTCA) model is proposed for straight bevel gears that exhibit large number of teeth in contact, well beyond involute line of action limits. This kind of contact is observed when the meshing gears have conformal surfaces, as in a Pericyclic mechanical transmission, and is traditionally analysed using finite element simulations. The Pericyclic drive is kinematically similar to an epicyclic bevel gear train, and is characterized by load sharing over large number of teeth in an internal-external bevel gear mesh, large shaft angles (175° - 178°), nutational gear motion, and high reduction ratio. The contact region spreads over a large area on the gear tooth flank due to high contacting surface conformity. Thus, a thick plate Finite Strip method (FSM) was utilized to accurately calculate the gear tooth bending deflection. Based on tooth deformation calculation model, and accounting for initial surface separation, a variational framework is developed to simultaneously solve for load distribution and gear tooth deformation. This is followed by calculation of contact stress, bending stress, mesh stiffness, and transmission error. The results demonstrate the high power density capabilities of the Pericyclic drive and potential for gear noise reduction. The model developed herein is applied with real gear tooth surfaces, as well.

Research on Involute Gear Undercutting with Mechanical Mechanics Based on Neural Network

2014 ◽  
Vol 540 ◽  
pp. 92-95
Author(s):  
Xu Lei Deng ◽  
Jun Xiao ◽  
Jia Ning He ◽  
Wu Xing Ma ◽  
Yan Li ◽  
...  
Keyword(s):  
Neural Network ◽  
Gear Tooth ◽  
Nonlinear Mapping ◽  
Matlab Simulation ◽  
Amount Effect ◽  
Number Of Teeth ◽  
Involute Gear ◽  
The Neural Network ◽  
Relationship Model ◽  
Tooth Number

This paper is based on the neural network nonlinear mapping characteristics. The involute gear tooth number, modulus and their relationship model of cutting the amount effect are established respectively. Through MATLAB simulation gets the relation curve between the number of teeth and modulus. These curves can intuitive reflect the tooth number and modulus effects on cutting amount change, which provides valuable theoretical reference for the design of the involute gear.

scholarly journals INSTALLATION AND ME TION AND METHODOLOGY FOR DE OGY FOR DETERMINING OF TERMINING OF ANTIFRICTIONAL PROPER AL PROPERTIES OF AN TIES OF ANTISTATIC-HEA TIC-HEATCONDUCTING COMPOSI TING COMPOSITE POLYMERIC M YMERIC MATERIALS INTERACTING WI TING WITH FIBROUS M TH FIBROUS MASS (CO ASS (COTTON-RAW)

2018 ◽  
Vol 2 ◽  
pp. 20-23
Author(s):  
S Negmatov ◽  
◽  
N Abed ◽  
G Gulyamov ◽  
Q Eshkabilov
Keyword(s):  
Flat Surface ◽  
Rotating Disk ◽  
Machine Building ◽  
Polymer Materials ◽  
Heat Conducting ◽  
Friction Forces ◽  
Friction Zone ◽  
Electrostatic Charges ◽  
Antifriction Properties ◽  
Disk Sample

The paper Presents a disk tribometer installation and allows to determine the antifriction properties of machine-building composite antistatic-heat-conducting polymer materials working in interaction with the fibrous mass (raw cotton). A method for determining the friction force, temperature and electrostatic charge values arising in the friction zone is developed. The friction of the fibrous material is carried out on the flat surface of the rotating disk sample from the material under study at specified clamping pressures and sliding speeds. Values of friction forces, temperatures and values of electrostatic charges of the tested sample in a zone of friction with cotton-raw are measured by means of sensors.

scholarly journals Theoretical background for the bionic substantiation of parameters of the stubble cultivator working bodies

2019 ◽  
Vol 20 (2) ◽  
pp. 183-191
Author(s):  
L. F. Babitsky ◽  
I. V. Sobolevsky ◽  
V. A. Kuklin
Keyword(s):  
Soil Layer ◽  
Logarithmic Spiral ◽  
Theoretical Background ◽  
Radius Vector ◽  
Plant Residues ◽  
Industrial Complex ◽  
Resource Saving ◽  
Angle Of Internal Friction ◽  
Working Surface ◽  
Working Bodies

In the southern regions of Russia, the technology of cultivation of grain crops in the variant of partial sowing has been widely used. In this regard, it became necessary to create effective working bodies of a stubble cultivator that would have fundamentally new resource-saving ways of influencing the area under cultivating and meet the requirements of modern advanced technologies. The shapes of the working bodies surfaces of the cultivators were improved taking into account the mechanic-bionic approach. The main parameters of the toothed cutting surface were determined by the method of bionic comparisons, with a scarab beetle as a bionic prototype. Use of the serrated shape of the cutting edge is consistent with the bionic principle of multi-contact exposure and leads to the fact that the tops of the teeth become stress concentrators and, with a significantly smaller indentation force, cause soil destruction processes, which reduces the energy costs of cutting the soil layer. The optimal curvilinear shape of the working surface made in the form of a logarithmic spiral, is characterized by a constant value of the angle between the normal and the radius vector, and the value of this angle, equal to the angle of internal friction of the soil φ2, will ensure the sliding of the soil and plant residues with minimal energy consumption. The number (n = 4), height (h = 5...7 mm) and tooth placement step (S = 10...12 mm) of the bit tip of the stubble cultivator are analytically justified. The shape of the profile of the working surface of the stubble cultivator bit in the form of a logarithmic spiral with a variable angle of crumbling is proposed. The studies were conducted in the period from September to October 2018 in the soil channel of the research Laboratory of Bionic Agroengineering of the Department of Mechanization and Technical Service in Agro-Industrial Complex. They have shown the decrease in the traction resistance of the proposed working body of the stubble cultivator by 16.5% in comparison with the traction resistance of the serial sample.

Performance Rating and Optimization of Spur Gear Drives With Small Number of Teeth

2000 ◽  
Author(s):  
M. A. Sahir Arikan
Keyword(s):  
Gear Tooth ◽  
Spur Gear ◽  
Maximum Length ◽  
Performance Rating ◽  
Tooth Root ◽  
Contact Ratio ◽  
Geometry Factor ◽  
Factor I ◽  
Number Of Teeth ◽  
Gear Drives

Abstract Performance rating of spur gear drives with small number of teeth is made and variations of contact ratio, circular tooth thicknesses at pinion and gear tooth tips, lengths of the pinion addendum and dedendum portions of the line of action, AGMA geometry factor J for the pinion and the gear and their ratio, and AGMA geometry factor I with addendum modification coefficient are determined. Thus, it is made possible to design gear drives with properties such as, maximum possible contact ratio, maximum length of the pinion addendum portion of the line of action, maximum length of the pinion dedendum portion of the line of action, equal AGMA geometry factors J for the pinion and the gear (i.e. equal pinion and gear tooth root stresses), and maximum AGMA geometry factor I (i.e. minimum tooth contact stress). Rack cutter tip fillet radius and rack cutter geometry are considered in the analysis, which are the basic factors that determine the gear tooth fillet profile.

scholarly journals Influence of the movement of involute profile gears along the off-line of action on the gear tooth position along the line of action direction

2021 ◽  
Vol 23 (4) ◽  
pp. 736-744
Author(s):  
Łukasz Jedliński
Keyword(s):  
Analytical Model ◽  
Frictional Force ◽  
Gear Tooth ◽  
Gear Ratio ◽  
Spur Gears ◽  
Tooth Position ◽  
Pressure Angle ◽  
Number Of Teeth ◽  
The Impact

When gears change their distance along the off-line of action (OLOA) direction, this affects the distance between the working surfaces of the meshing teeth along the line of action (LOA). This effect is usually neglected in studies. To include this effect precise equations are derived for spur gears. The analysis is carried out for the general case of spur gears with shifted profiles frequently used in the industry. The influence of OLOA gear displacement on LOA direction is also a function of gears parameters. An analysis is conducted, and the impact of parameters such as module, pressure angle, gear ratio, and the number of teeth is determined. As an example, a simulation of a 12 DOF analytical model is presented. The movement of gears along OLOA is caused by a frictional force that can be high during tooth degradation e.g. scuffing. Results show that when the movement of gears along the OLOA direction is significant, its influence on the distance between the mating teeth should not be neglected.

Digital Conjugate of Tooth Surface of Logarithmic Spiral Bevel Gear

2014 ◽  
Vol 556-562 ◽  
pp. 1079-1082
Author(s):  
Qiang Li ◽  
Yun Long Diao
Keyword(s):  
Gear Tooth ◽  
Logarithmic Spiral ◽  
Bevel Gear ◽  
Conjugate Points ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Surface Meshing ◽  
Spline Fitting ◽  
Spiral Bevel ◽  
Surface Precision

Based on the surface of the envelope principle and the digital conjugate surface theory, The taper logarithm helical gear meshing theory further perfect. According to the mathematical model of logarithmic spiral bevel gear tooth surface meshing, using MATLAB powerful scientific analysis and calculation visual features and functions for the conjugate tooth surface equation to get the enveloping surface discrete conjugate points and draw out the conjugate tooth surface. Again through the optimization of surface get rid of the noise, end up with conjugate tooth surface precision, and can B spline fitting. Said for further analysis of spiral bevel gear drive are very valuable.

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