Laser Interferometric Measuring Method of Involute Artifact and Stabilization of Measurement

2011 ◽  
Vol 5 (2) ◽  
pp. 144-149
Author(s):  
Masaharu Komori ◽  
◽  
Fumi Takeoka ◽  
Aizoh Kubo ◽  
Hiroshige Fujio ◽  
...  
Keyword(s):  
Gear Tooth ◽  
Measuring Method ◽  
Tooth Profile ◽  
National Standard ◽  
Helical Gears ◽  
Involute Gears ◽  
Measuring Machine ◽  
Form Quality ◽  
Tooth Flank ◽  
Laser Interferometric

Vibration and noise are serious problems with involute spur and helical gears used, e.g., in drivetrains of vehicles such as automobiles. The gear tooth flank form of micrometer order markedly affects gear vibration and noise; therefore, the tooth flank form quality must be strictly controlled to maximize gear performance. Tooth profile measuring machines used in calibration for form error inspection of involute gears usually use an involute artifact, which itself must be calibrated highly accurately. However, it is typically difficult for current tooth profile measuring machine using contact stylus to calibrate the involute artifact with a high accuracy while satisfying traceability to a national standard. A highly precise and traceable measuring technology for the involute artifact is therefore required. The direct measurement of the involute artifact we propose uses a laser interferometer, whose measurement stability is confirmed in experiments measuring the detailed form of an involute tooth flank.

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.

Laser Holographic Measurement of Tooth Flank Form of Cylindrical Involute Gear: Part 2 — For Helical Gear Tooth

1992 ◽  
Author(s):  
H. Fujio ◽  
A. Kubo ◽  
S. Tochimoto ◽  
H. Hanaki ◽  
S. Saitoh ◽  
...  
Keyword(s):  
Gear Tooth ◽  
Measuring Method ◽  
Helix Angle ◽  
Helical Gear ◽  
Helical Gears ◽  
Error Surface ◽  
Tooth Flank ◽  
Form Deviation ◽  
Laser Holography ◽  
Holographic Measurement

Abstract The interferometry using laser holography is applied to measure the form deviation of tooth flank of involute helical gears. One problem of this method is that the increase of helix angle reduces the region of the flank to which the laser beam can irradiate at a same time. To solve this problem, following method is developed: The objective tooth flank is divided into some regions, and the interferometry measurement is worked out for each region. The measured values for the form deviation of each region of the tooth flank are transformed to the values on the plane of action of this gear. These values for each region of the tooth flank are then concatenated successively until they result the curved surface for the form deviation of the whole tooth flank of the helical gear. The error surface of the tooth flank of helical gear obtained by this procedure is compared with that of conventional measuring method using contacting stylus.

A parameterized numerical method for generating discrete helical gear tooth surface allowing non-standard geometry

2008 ◽  
Vol 222 (6) ◽  
pp. 1033-1038 ◽  
Author(s):  
J Hedlund ◽  
A Lehtovaara
Keyword(s):  
Gear Tooth ◽  
Numerical Approach ◽  
Helical Gear ◽  
Tooth Surface ◽  
Tool Profile ◽  
Standard Geometry ◽  
Gear Manufacturing ◽  
Involute Gears ◽  
Gear Geometry ◽  
Tooth Flank

Gear analysis is typically performed using calculation based on gear standards. Standards provide a good basis in gear geometry calculation for involute gears, but these are unsatisfactory for handling geometry deviations such as tooth flank modifications. The efficient utilization of finite-element calculation also requires the geometry generation to be parameterized. A parameterized numerical approach was developed to create discrete helical gear geometry and contact line by simulating the gear manufacturing, i.e. the hobbing process. This method is based on coordinate transformations and a wide set of numerical calculation points and their synchronization, which permits deviations from common involute geometry. As an example, the model is applied to protuberance tool profile and grinding with tip relief. A fairly low number of calculation points are needed to create tooth flank profiles where error is <1 μm.

A Method for Constructing Standard Involute Gear Tooth Profile

2018 ◽  
Author(s):  
Edward E. Osakue ◽  
Lucky Anetor
Keyword(s):  
Gear Tooth ◽  
Contact Point ◽  
Contact Angles ◽  
Tooth Profile ◽  
Computer Design ◽  
Solid Models ◽  
Module Size ◽  
Involute Gears ◽  
Base Circle ◽  
Involute Curve

A simple but accurate combined computationaland graphical method for creating drawings and solid models of standard involute gears is presented. The method is predicated on the fact that the gear tooth angle at the base circle is fixed for a gear of specified module or size. As the contact point moves along the involute curve from the base circle point through the pitch point to the addendum circle point; the involute and gear tooth contact angles change continuously but their sum is fixed at the value it was at the base circle. This allows the coordinates of points on the involute curve to be generated analytically without employing the roll angle as current available methods. The generated data can be implemented in any computer design drafting (CDD) package platform to create an accurate gear tooth profile. The computations are done with Microsoft Excel which generates the graphical data for the gear tooth profile that are used in the CDD package. The required inputs to the Excel spreadsheet are the gear module size, the pressure angle, the number of teeth and the radial number of steps. A gearset example is considered and created with this method. The solid model of the example gearset in mesh and 2D drawing of the pinion are presented.

Geometric Calculations of the Chamfered Tip and the Protuberance Undercut of a Tooth Profile

2011 ◽  
Author(s):  
Milos Nemcek ◽  
Zdenek Dejl
Keyword(s):  
Mass Production ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Measuring Device ◽  
Car Industry ◽  
Industry Standard ◽  
Tooth Flank ◽  
Computing Method ◽  
Circle Diameter

Nowadays special modified tools are mostly used for rough or semi-finishing milling in the mass production of ground or shaved gears today. These modifications ensure the desired chamfer at the head or the undercut at the bottom of the gear tooth. Diameters of the beginning and the end of the operational involute (exact knowledge of them is necessary for the calculation of important meshing parameters) are found by using several techniques. The first one is the simulation of the generating action of a hob tooth using suitable graphic software with the subsequent measuring of these diameters from the envelope of hob tooth positions which was created. The second one is measuring directly on the gear manufactured using a measuring device. These simulations or measuring are often not performed and the tool with recommended parameters of the protuberance or the ramp is simply chosen by an educated guess [1]. But it is not an acceptable technique in a mass production (car industry). Standard DIN 3960 [2] gives a certain manual for the determination of these diameters. It suggests the iterative method for the calculation of the chamfer beginning circle diameter but without a reliable guideline. And as regards the protuberance, it refers to the correct calculation only in theory. This paper deals with the computing method to determine diameters of the beginning and the end of the function part of a tooth flank involute. It is designed for a specified tool with modifications for creating the chamfer or the protuberance undercut. The paper also takes into account the necessary shaving (grinding) stock or the backlash. Furthermore it refers to possible problems when the basic profile of the generating tool with the protuberance is designed from the basic rack tooth profile.

Revisiting Plane-Generated Gear Tooth Surfaces: A Novel Design Perspective

2015 ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani
Keyword(s):  
Gear Tooth ◽  
Transmission Function ◽  
Tooth Surface ◽  
Generation Process ◽  
Noise Emission ◽  
Helical Gears ◽  
Beveloid Gears ◽  
Tooth Surfaces ◽  
Involute Gears ◽  
The One

The teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known: in particular, the motion transmission function is insensitive to center distance variations, and contact lines (or points, when a corrective surface mismatch is applied) evolve along a fixed plane of action, thereby reducing vibrations and noise emission. As a result, involute gears are easier to manufacture and assemble than non-involute gears, and silent to operate. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis): the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to investigate this type of generation-by-envelope process and to profitably use it to explore new potential design layouts. In particular, with some similarity to the basic principles underlying conical involute (or Beveloid) gears, but within a broader scope, we propose a generalization of these concepts to the case of involute surfaces for motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the theoretical possibility of involute profiles transmitting motion between skew axes through line contact and, perihaps more importantly, they lead to apparently novel geometric designs featuring insensitivity of transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples.

A Novel Design Procedure for Reducing Vibration and Noise in Gears

1993 ◽  
Author(s):  
K. Y. Yoon ◽  
S. S. Rao
Keyword(s):  
Gear Tooth ◽  
Design Procedure ◽  
Transmission Error ◽  
Tooth Profile ◽  
Profile Modification ◽  
Noise Characteristics ◽  
Spline Curves ◽  
Involute Gears ◽  
Static Transmission Error ◽  
Novel Design

Abstract A new method is proposed for reducing vibration and noise of involute gears. The method is based on the use of cubic spline curves for gear tooth profile modification. The tooth profile is constrained to assume an involute shape during the loaded operation. Thus the new gear profile assures conjugate motion at all points along the line of action. The new profile is found to result in a more uniform static transmission error compared to standard involute profile thereby contributing to the improvement of vibration and noise characteristics of the gear.

A Novel Finish Hobbing Methodology for Longitudinal Crowning of a Helical Gear With Twist-Free Tooth Flanks by Using Dual-Lead Hob Cutters

2014 ◽  
Author(s):  
Van-The Tran ◽  
Ruei-Hung Hsu ◽  
Chung-Biau Tsay
Keyword(s):  
Computer Simulation ◽  
Longitudinal Direction ◽  
Helical Gear ◽  
Tooth Profile ◽  
Second Order ◽  
Order Function ◽  
Helical Gears ◽  
Pressure Angle ◽  
Dual Lead ◽  
Tooth Flank

In the gear finish hobbing process, to obtain a twist-free tooth flank of helical gears, a novel hobbing method for longitudinal crowning is proposed by applying a new hob’s diagonal feed motion with a dual-lead hob cutter. Wherein the hob’s diagonal feed motion is set as a second order function of hob’s traverse movement and tooth profile of hob cutter is modified in a dual-lead form with pressure angle changed in it’s longitudinal direction. The proposed method is verified by using two computer simulation examples to compare topographies of the crowned work gear surfaces hobbed by the standard and dual-lead rack cutters. The results reveal the superiority of the proposed novel finish hobbing method.

Laser Holographic Measurement of Tooth Flank Form of Cylindrical Involute Gear

1994 ◽  
Vol 116 (3) ◽  
pp. 721-729 ◽  
Author(s):  
H. Fujio ◽  
A. Kubo ◽  
S. Saitoh ◽  
M. Suzuki ◽  
S. Tochimoto ◽  
...  
Keyword(s):  
Laser Beam ◽  
Incident Angle ◽  
Measuring Method ◽  
Helical Gears ◽  
Phase Stepping ◽  
Interference Fringes ◽  
Phase Stepping Method ◽  
Tooth Flank ◽  
Form Deviation ◽  
Holographic Measurement

The form deviations of tooth flanks of spur and helical gears obtained by using a laser holographic interferometer are compared with the results of the conventional measuring method using a contacting stylus. The objective tooth flank which has a rough finish compared with optical parts is irradiated with a laser beam in a large incident angle to obtain the reflected ray from it. Image patterns of the interference fringes for tooth flanks with various types of form deviation are obtained, and they are transformed to the form deviations from the target tooth flank form. The algorithm of this transformation is shown: the brightness information of the image of the interference fringe on the CRT is converted to the amplitude of form deviation defined on the plane of action of the gear according to the phase difference of light beam by using the phase stepping method. A partial measuring procedure for helical gears is proposed which achieves the same level of accuracy as the conventional method using a stylus.

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