Gears and Gearing Part 1 Types of Gears Types of Gears

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Gears and Gearing

Part 1

Types of Gears
Types of Gears

Spur
Helical

Bevel
Worm

Nomenclature of Spur-Gear Teeth

Fig. 13–5

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Rack

 A rack is a spur gear with an pitch diameter of infinity.  The sides of the teeth are straight lines making an angle to the line

of centers equal to the pressure angle.

Fig. 13–13

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Tooth Size, Diameter, Number of Teeth

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Tooth Sizes in General Industrial Use

Table 13–2

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How an Involute Gear Profile is constructed

A₁B₁=A₁A₀, A₂B₂=2 A₁A₀, etc Pressure Angle Φ has the values of 20° or 25 ° 14.5 ° has also been used.

Gear profile is constructed from the base circle. Then additional clearance are given.

Relation of Base Circle to Pressure Angle

Fig. 13–10

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Standardized Tooth Systems: AGMA Standard

 Common pressure angles f : 20º and 25º  Older pressure angle: 14 ½º

 Common face width:

3p  F  5p



P p 

3

5

P
 F 

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Gear Sources

• Boston Gear

• Martin Sprocket

• W. M. Berg • Stock Drive Products

….

Numerous others

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Conjugate Action

 When surfaces roll/slide against each other and

produce constant angular velocity ratio, they are said

to have conjugate action.

 Can be accomplished if

instant center of velocity

between the two bodies remains stationary between the grounded instant centers.

Fig. 13–6

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Fundamental Law of Gearing:

The common normal of the tooth

profiles at all points within the mesh

must always pass through a fixed point on the line of the centers called pitch point. Then the gearset’s velocity ratio will be constant through the mesh and

be equal to the ratio of the gear radii.

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Conjugate Action: Fundamental Law of Gearing

 Forces are transmitted on line of action which is normal to the contacting surfaces.

 Velocity. V_Pof both gears is the

V_P

same at point P , the pitch point

 Angular velocity ratio is inversely proportional to the

radii to point P , the pitch point.

 Circles drawn through P from each fixed pivot are pitch

circles, each with a pitch radius.

Fig. 13–6

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Gear Ratio

V_Pof both gears is the same at point P , the pitch (circle contact) point

푉_푃= 휔₁푟₁=휔₂푟₂

Gear Ratio >1

ꢀꢀ

= =

ꢁ

푁

ω₂

ω₂rotates opposite of ω₁

r₁

r₂

ω₁

Pitch Circle of Gears

N₂
N₁

Nomenclature

Smaller Gear is Pinion and Larger one is the gear

In most application the pinion is the driver, This reduces speed but it increases torque.

Simple Gear Trains

 For a pinion 2 driving a gear 3, the speed of the driven gear is

V_P

n₃=ω₃

r₂

r₃

n₂=ω₂

N₃
N₂

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Simple Gear Trains (Gear 2 to Gear 4)

Fig. 13–27

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Compound Gear Train

 A practical limit on train value for one pair of gears is 10 to 1  To obtain more, compound two gears onto the same shaft

Fig. 13–28

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Compound Gear Trains

n₅
N₃

 ( )( )( )

n₁N₂N₄N₅

N₁
N₄

Example 13–3

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Example 13–4

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Example 13–4

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Example 13–5

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Example 13–5

Shigley’s Mechanical Engineering Design

Example 13–5

Shigley’s Mechanical Engineering Design

Example 13–5

Shigley’s Mechanical Engineering Design

Example 13–5

Shigley’s Mechanical Engineering Design

Recommended publications

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Design of Involute Spur Gears with Asymmetric Teeth & Direct Gear

International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 1 Issue 6, August - 2012 Design of Involute Spur Gears with Asymmetric teeth & Direct gear Design G. Gowtham krishna 1, K. Srinvas2,M.Suresh3 1.P.G.student,Dept. of Mechanical Engineering, DVR AND DHM college of Engineering and technology, Kanchikacherla, 521180,Krishna dt, A.P. 2.Associat.professor, Dept of Mechanical Engineering,DVR AND DHM college of Engineering and technology, Kanchikacherla, 521180,Krishna dt, A.P. 3.P.G.student,Dept. of Mechanical Engineering,BEC,Bapatla,Guntur,A.P. Abstract-- Design of gears with asymmetric teeth that production. • Gear grinding is adaptable to custom tooth shapes. enables to increase load capacity, reduce weight, size and • Metal and plastic gear molding cost largely does not depend vibration level. standard tool parameters and uses nonstandard on tooth shape. This article presents the direct gear design tooth shapes to provide required performance for a particular method, which separates gear geometry definition from tool custom application. This makes finite element analysis (FEA) selection, to achieve the best possible performance for a more preferable than the Lewis equation for bending stress particular product and application. definition. This paper does not describe the FEA application for comprehensive stress analysis of the gear teeth. It sents the engineering method for bending stress balance and minimization. Involute gear Introduction Conventional involute spur gears are designed with symmetric tooth side surfaces . It is well known that the conditions of load and meshing are different for drive and coast tooth's side. Application of asymmetric tooth side surfaces enables to increase the load capacity and durability for the drive tooth side.
Interactive Involute Gear Analysis and Tooth Profile Generation Using Working Model 2D

AC 2008-1325: INTERACTIVE INVOLUTE GEAR ANALYSIS AND TOOTH PROFILE GENERATION USING WORKING MODEL 2D Petru-Aurelian Simionescu, University of Alabama at Birmingham Petru-Aurelian Simionescu is currently an Assistant Professor of Mechanical Engineering at The University of Alabama at Birmingham. His teaching and research interests are in the areas of Dynamics, Vibrations, Optimal design of mechanical systems, Mechanisms and Robotics, CAD and Computer Graphics. Page 13.781.1 Page © American Society for Engineering Education, 2008 Interactive Involute Gear Analysis and Tooth Profile Generation using Working Model 2D Abstract Working Model 2D (WM 2D) is a powerful, easy to use planar multibody software that has been adopted by many instructors teaching Statics, Dynamics, Mechanisms, Machine Design, as well as by practicing engineers. Its programming and import-export capabilities facilitate simulating the motion of complex shape bodies subject to constraints. In this paper a number of WM 2D applications will be described that allow students to understand the basics properties of involute- gears and how they are manufactured. Other applications allow students to study the kinematics of planetary gears trains, which is known to be less intuitive than that of fix-axle transmissions. Introduction There are numerous reports on the use of Working Model 2D in teaching Mechanical Engineering disciplines, including Statics, Dynamics, Mechanisms, Vibrations, Controls and Machine Design1-9. Working Model 2D (WM 2D), currently available form Design Simulation Technologies10, is a planar multibody software, capable of performing kinematic and dynamic simulation of interconnected bodies subject to a variety of constraints. The versatility of the software is given by its geometry and data import/export capabilities, and scripting through formula and WM Basic language system.
VIRTUAL HOBBING E. BERGSETH Department of Machine Design, KTH, Stockholm, Sweden SUMMARY Hobbing Is a Widely Used Machining Proc

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The Kinematics of Conical Involute Gear Hobbing

The Kinematics of Conical Involute Gear Hobbing Carlo Innocenti (This article fi rst appeared in the proceedings of IMECE2007, The technical literature contains plenty of information the 2007 ASME International Mechanical Engineering regarding the tooth fl ank geometry (Refs. 8–9) and the setting Congress and Exposition, November 11–15, 2007, Seattle, of a hobbing machine in order to generate a beveloid gear Washington, USA. It is reprinted here with permission.) (Refs. 10–15). Unfortunately, the formalism usually adopted makes determination of the hobbing parameters a rather involved process, mainly because the geometry of a beveloid Management Summary gear is customarily—though ineffi ciently—specifi ed by It is the intent of this presentation to determine all rigid-body positions of two conical involutes that resorting to the relative placement of the gear with respect mesh together, with no backlash. That information to the standard rack cutter that would generate the gear, even then serves to provide a simple, general approach in if the gear is to be generated by a different cutting tool. To arriving at two key setting parameters for a hobbing make things worse, some of the cited papers on beveloid gear machine when cutting a conical (beveloid) gear. hobbing are hard reading due to printing errors in formulae A numerical example will show application of the and fi gures. presented results in a case study scenario. Conical This paper presents an original method to compute the involute gears are commonly seen in gearboxes parameters that defi ne the relative movement of a hob with for medium-size marine applications—onboard respect to the beveloid gear being generated.
Dynamic Behavior of Planetary Gears Dr.-Ing

TECHNICAL Dynamic Behavior of Planetary Gears Dr.-Ing. Burkhard Pinnekamp, Dr.-Ing. Michael Heider, and M.Sc. Andreas Beinstingel Introduction Besides power density, reliability and efficiency, noise is always an important criterion for a successful gear design. In many theoretical and experimental in- vestigations and papers, the influences and potential remedies were discussed. For example, in (Ref. 6) the importance of a large overlap ratio, achieved by a large helix angle is described as the most important factor for reducing gear noise. In planetary gear systems of high power density and high gear ratio, heli- cal gears create undesirable tilting mo- ments on the planet gears; therefore, Figure 1 Noise: generation, transmission and radiation. spur gears are still preferred for plan- etary gears — a special challenge with respect to noise. Specifically, the dif- ferent behavior of planetary gears with sequential and symmetric gear mesh is explained in this paper. As described (Ref. 10), the variable mesh stiffness along the path of con- tact in the tooth contact leads to oscil- lating forces on the shafts and bearings, which are transmitted to the casing. The casing vibrations radiate airborne noise (Fig. 1). The influence of tooth geometry on the excitation behavior is determined by the geometry parameters, such as Figure 2 Contributions to single tooth contact deflection along path of contact (Source: FZG TU Munich). profile and overlap ratios, flank modifi- cations and manufacturing deviations. For design to low noise emission, the knowledge of the elastic and dynamic behavior of the transmission system and the excitation mechanisms of the gear mesh is required.
Engineering Information Spur Gears Gear Nomenclature

Engineering Information Spur Gears Gear Nomenclature ADDENDUM (a) is the height by which a tooth projects GEAR is a machine part with gear teeth. When two gears beyond the pitch circle or pitch line. run together, the one with the larger number of teeth is called the gear. BASE DIAMETER (Db) is the diameter of the base cylinder from which the involute portion of a tooth profile is generated. HUB DIAMETER is outside diameter of a gear, sprocket or coupling hub. BACKLASH (B) is the amount by which the width of a tooth space exceeds the thickness of the engaging tooth on the HUB PROJECTION is the distance the hub extends beyond pitch circles. As actually indicated by measuring devices, the gear face. backlash may be determined variously in the transverse, normal, or axial-planes, and either in the direction of the pitch INVOLUTE TEETH of spur gears, helical gears and worms circles or on the line of action. Such measurements should be are those in which the active portion of the profile in the corrected to corresponding values on transverse pitch circles transverse plane is the involute of a circle. for general comparisons. LONG- AND SHORT-ADDENDUM TEETH are those of BORE LENGTH is the total length through a gear, sprocket, engaging gears (on a standard designed center distance) or coupling bore. one of which has a long addendum and the other has a short addendum. CIRCULAR PITCH (p) is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth. KEYWAY is the machined groove running the length of the bore.
Basic Fundamentals of Gear Drives

Basic Fundamentals of Gear Drives Course No: M06-031 Credit: 6 PDH A. Bhatia Continuing Education and Development, Inc. 22 Stonewall Court Woodcliff Lake, NJ 07677 P: (877) 322-5800 [email protected] BASIC FUNDAMENTALS OF GEAR DRIVES A gear is a toothed wheel that engages another toothed mechanism to change speed or the direction of transmitted motion. Gears are generally used for one of four different reasons: 1. To increase or decrease the speed of rotation; 2. To change the amount of force or torque; 3. To move rotational motion to a different axis (i.e. parallel, right angles, rotating, linear etc.); and 4. To reverse the direction of rotation. Gears are compact, positive-engagement, power transmission elements capable of changing the amount of force or torque. Sports cars go fast (have speed) but cannot pull any weight. Big trucks can pull heavy loads (have power) but cannot go fast. Gears cause this. Gears are generally selected and manufactured using standards established by American Gear Manufacturers Association (AGMA) and American National Standards Institute (ANSI). This course provides an outline of gear fundamentals and is beneficial to readers who want to acquire knowledge about mechanics of gears. The course is divided into 6 sections: Section -1 Gear Types, Characteristics and Applications Section -2 Gears Fundamentals Section -3 Power Transmission Fundamentals Section -4 Gear Trains Section -5 Gear Failure and Reliability Analysis Section -6 How to Specify and Select Gear Drives SECTION -1 GEAR TYPES, CHARACTERISTICS & APPLICATIONS The gears can be classified according to: 1. the position of shaft axes 2.
Gears & Gear Drives

GEARS AND GEAR DRIVES GEAR TYPES .....................................................A145 GEAR TYPES 99%. Some sliding does oc- GEAR BASICS ...................................................A153 cur, however. And because ears are compact, SPEED REDUCERS ............................................A158 contact is simultaneous positive-engagement, across the entire width of G power transmission SELECTING GEAR DRIVES................................A162 the meshing teeth, a contin- elements that determine ANALYZING GEAR FAILURES...........................A168 uous series of shocks is pro- the speed, torque, and di- duced by the gear. These rection of rotation of driven rapid shocks result in some machine elements. Gear types may be objectionable operating noise and vi- grouped into five main categories: bration. Moreover, tooth wear results Spur, Helical, Bevel, Hypoid, and from shock loads at high speeds. Noise Worm. Typically, shaft orientation, ef- and wear can be minimized with ficiency, and speed determine which of proper lubrication, which reduces these types should be used for a partic- tooth surface contact and engagement ular application. Table 1 compares shock loads. these factors and relates them to the specific gear selections. This section on gearing and gear drives describes the major gear types; evaluates how the various gear types are combined into gear drives; and considers the principle factors that affect gear drive selection. Spur gears Spur gears have straight teeth cut Figure I — Involute generated by parallel to the rotational axis. The unwrapping a cord from a circle. tooth form is based on the involute curve, Figure 1. Practice has shown the tool traces a trochoidal path, Fig- Figure 2 — Root fillet trochoid generated that this design accommodates ure 2, providing a heavier, and by straight tooth cutting tool.
Optimal Choice of the Shaft Angle for Involute Gear Hobbing Carlo Innocenti

Optimal Choice of the Shaft Angle for Involute Gear Hobbing Carlo Innocenti Management Summary With reference to the machining of an involute spur or helical gear by the hobbing process, this paper suggests a new criterion for selecting the position of the hob axis relative to the gear axis. By adhering to the proposed criterion, the hob axis is set at the minimum distance from the gear axis, thus maximizing the depth of the tooth spaces of the gear. The new criterion is operatively implemented by solving a univariate equation, which stems from a new, synthetic analysis of the meshing of crossed -axis, involute gears. A numerical example shows application of the suggested procedure to a case study and compares the optimal hob setting to the customary one. Introduction 4 and 5—do not question the standard choice Hobbing of both spur and helical gears is of the hob setting angle as the sum of the gear generally done by setting the axes of the gear pitch helix angle and of an angle that charac- and the hob at an angle that is the algebraic terizes the hob. sum of the pitch helix angles of gear and hob This paper first revises the kinematics of (Refs.1–2). Such a standard way of determin- meshing two crossed- axis, involute helical gears ing the shaft angle—although conducive to sat- (Refs. 3 and 6), and presents an original, concise isfactory results—does not rely on a convinc- relationship for determining the meshing back- ing rationale. Suffice it to say that any referral lash in terms of the gear dimensions, shaft ax- to pitch helix angles is questionable because is distance and shaft axis angle.
Transmission Error in Spur Gears: Static and Dynamic

Transmission Error in Spur Gears: Static and Dynamic Finite-Element Modeling and Design Optimization By Raul Tharmakulasingam BEng. MSc. (Eng) Submitted in accordance with the requirements for the degree of Doctor of Philosophy School of Engineering and Design Brunel University United Kingdom October 2009 ACKNOWLEDGEMENTS “Success is sweet: the sweeter if long delayed and attained through manifold struggles and defeats.” I would like to take this opportunity to thank everyone who has helped me in my pursuit of success in my PhD. Firstly; I would like to thank my supervisor Dr. Giulio Alfano for helping me shape my research and motivating me at the right times with a timely reminder of how much we have achieved. I would also like to Dr Mark Atherton for bringing a fresh perspective to everything we did during the research, and always providing a kind ear and an objective view to all our problems. I am also very grateful to Prof. Luiz Wrobel for providing me with the opportunity to undertake my PhD research, and also helping me with my numerous problems while carrying out my research. To the colleagues who helped me with moments of respite during a hard day’s work, inspiration by example, and lasting friendships, I thank you from the bottom of my heart and look forward to keeping in touch. My family who have endured my worst and celebrated my best of times during my PhD also receive a heartfelt embrace and acknowledgement for everything they have done for me. My dear friends who constantly reminded me of my duty to hand in my Thesis by the incessant question “Have you submitted yet?”.
Gear Noise and Vibration – a Literature Survey

GEAR NOISE AND VIBRATION – A LITERATURE SURVEY Mats Åkerblom [email protected] Volvo Construction Equipment Components AB SE–631 85 Eskilstuna, Sweden Abstract This paper is a survey of the literature on gear noise and vibration. It is divided into three parts, “Transmission error”, “Dynamic models” and “Noise and vibration measurement”. Transmission error (TE) is considered to be an important excitation mechanism for gear noise and vibration. The definition of transmission error is “The difference between the actual position of the output gear and the position it would occupy if the gear drive were perfectly conjugate”. Dynamic models of the system consisting of gears, shafts, bearings and gearbox casing are useful in order to understand and predict the dynamical be- haviour of a gearbox. Noise and vibration measurement and signal analysis are important tools when experimentally investigating gear noise because gears create noise at specific frequencies, related to number of teeth and the rotational speed of the gear. Keywords: gear, noise, vibration, transmission error, dynamic models. CONTENTS 1 TRANSMISSION ERROR.................................................................................................2 1.1 Introduction to transmission error....................................................................................2 1.2 Transmission error theory................................................................................................2 1.3 Transmission error measurement.....................................................................................5