While Measuring Gears: Gear Profile Inspection

Leads and involute profile curves from teeth gears are one of the most difficult surfaces to  measure, there are only a few measuring instruments in the market that are able to scan this particular surfaces such as blades, parallel axis gears, bevel gears, worms, worm wheels, shafts and gear production tools such as hobs.

Those mechanisms that are in charge of movement transmision and power between different shafts and are subjected to friction among them. Gear inspection is a commitment to be assumed by a different laboratory in order to control all the different defined parameters such tooth chordal width, backslash or clearance play.

There are two main fields of different gears, parallel cilindrical gears and cone shaped gears. Among the ones in the first family we can find straight, internal, helical, double helical, helical for crossed shafts and zipper ones. Between conical gears we also find straight, spiral, hipocycloid and worms.

1.- Parallel Gears

1.1.- Pitch diameter (Pd) is the diameter of circunference around teeth make contact between the mating gears, basis of all tooth dimensions. In cylindrical parallel shaft gears, the pitch diameter can be determined directly from the center to center distance and the number of teeth



1.2.- Pitch (p) is the length in between two consecutive teeth
1.3.- Outside Circle (Oc): The circle formed by the tops of the gear teeth.
1.4.- Outside Diameter (Od): The diameter the gear blank is machined to; the mean diameter of the gear.


1.4.- Gear modulus (m) is the ratio between the pitch diameter an the total teeth number (z).

1.5.- Addendum or Head height (ha) Addendum is defined as ha=pd/z
1.6.- Dedendum or Root height (hf)
1.7.- Tooth height (h) is then the sum of Addendum and Dedendum h=ha+hf

1.8- Gear pressure angle is defined by (αo) the angle in between the two profiles tangent line and the two gears center to center line.

1.9.- Root circle (rc) formed by the bottoms of the gear teeth
1.10.- Base Circle is the one that describes the involute line.
1.11.- Base Circle diameter db= d• cos αo
1.12.- Base Pitch is then pb= π•db/z=π•m•cos αo


1.13.- Circular Pitch (CP): Is the distance from a point on one tooth to a corresponding point on the next tooth is measured on the pitch circle.
1.12.- Circular Thickness (CT): One¬ half of the circular pitch.
1.13.- Chordal Thickness (tc): The thickness of the tooth measured at the pitch circle.
Chordal Thickness is tc= PD sin(90°/z)

Involute profile

In order to perform reliable gear and gear teeth measurements with the gear tooth Vernier, machinist should know gear tooth terminology and trigonometric formulation
Image Credits Source: www.waybuilder.net for more definition terms as clearance and backslash

2.- Parallel Straight Cilindrical Gear Inspection

2.1.- Chordal width teeth inspection
2.1.1.- Gear tooth Vernier Calliper: equipped with two graduated scales, horizontal for the tooth thickness and vertical for the tooth height modulator, both with a nonius in where you can adjust and read your lecture. The other sliding scale inserted in between the two jaws is used to read the chordal thickness of your gear tooth on the pitch circle.

How does it work?
By setting the addendum height in the modulator slider, search for the chordal addendum height on it and close the vertical screws to fix the vertical slider
Chordal addendum: h= m [ 1 + z/2 (1 – cos90°/z) ]
in the vertical graduated scale, once you’ve settled the h (chordal addendum) then search to make contact with external tooth diameter with the opened horizontal slider jaw, then slide the horizontal slider jaw till reaching contact with the tooth pitch diameter circle. Read in the horizontal nonius to get the tooth chordal measurement, CD.

2.1.2.- Vernier micrometer with plates to read CD measurement
2.1.2.- Vernier micrometer with plates to read CD measurement
How it works? First is to know (z, αo); that is the number of teeth to embrace to find out the flank contact within the plates to be just in the pitch diameter so that we can get a reliable measurement, by using the tabela below.
2.1.3.- mill comparator
To perform a trustly measurement by comparison gauge-blocks set points needed to be settled before any gear inspection operation.

2.2.- Tooth thickness (t) inspection: ‘Sykes’ or  ‘David Brown’ comparator
It consists of a comparator fixed in a support on which two sliders displace symmetrically to the probe along the two tracks.
The measuring tips are faced so that they form the interval of a zipper of one pressure angle α.

This interval is regulated by a special gauge.
The measurement of the teeth is carried out fitting them successively into the calibrated device.

If the comparator probe descends the fact is that the verified tooth thickness is major than the wished one and on the other hand if the comparator indicates less than the wished value then the tooth is thinner.

2.3.- Tooth to tooth interval inspection:
It is necessary to verify that the step is divided correctly in thickness of the tooth and hollow.
For it the interval is calculated by trigonometry from “A” distance between the rods placed in two diametrically opposite hollows; for an even teeth number gear is easier.

Measuring instrument comparator with interchangeable spherical contacts. Valid to measure the teeth interval inspection of internal or external gears:



2.4.- Involute profile inspection: sketch of a measuring instrument to measure the Involute profile inspection

2.5.- Spur Gear Inspection Inisde the profile projector: Inside the profile projector over the hi-mag image all the spur characteristics can be also measured.

2.6.- Radial runout inspection: Gear runout is the radial eccentricity of the pitch diameter and the reference workpiece axis, that is the radial distance in between the geometrical teeth axis and the workpiece center axis

2.6.1.- Radial runout inspection by means of a comparator and a calibrated wire:
2.6.2.- Radial runout inspection against a calibrated master gear gauge: Two mating gears, the calibrated gear gauge and the measured gear, running together against an applied center to center direction force.

The gauge turns around its fixed axis and a comparator indicates the sliding radial runout of the measured gear
During this principle measurement gears at matted within master gears clasified with differents quality classes according to DIN 3790 & DIN 58420. Their teeth after being tempered and grinded or hobbed are later on superfinished.

This measuring instrument configuration is modular. The basic unit is able to measure several different modulus fits by interchanging fits and fixations in the foundation.

CNC Instruments are nowadays used to inspect all freedom degrees from a Personal Computer under a customer friendly environment software package. Statistical packs are also available to deal with the big ammount of measurement data.


3.- Gear Inspection with Coodinate Measuring Machines:

5-axis CMM from M&M precision for CNC process control


Multiprobe CMM systems facilitate the gear inspection either by scanning or optical non-contact scanning systems and the postprocessing of measurement data.

3.- CMM Gear Measurement: Aplication


Sources: MITUTOYO, STARRET, BROWN & SHARPE, TESA, EMUGE and M & M Precision flyers and posters

Title: Curso de Metrología Dimensional.
By: Carro de Vicente Portela (Author).
Ed: E.T.S.I.I. de Madrid 1978. page 169 and next.

Title: Consejos de metrología de la A.E.C.C. (varios)
By: Comité de Metrología de la A.E.C.C. Madrid. (Authors).
Ed: Asociación Española de Control de Calidad.

Title: Clasificación de instrumentos de metrología dimensional.
By: Ministerio de Industria, Comercio y Turismo. Dirección General de Política Tecnológica.
Ed: Sección Publicaciones Ingenieros Industriales. Madrid, 1992.

Title: Metrologia básica
By: Manrique, E. (Author), Casanova, A. (Author).
Ed: Edebé

Title: Engranajes, Author: José Campabadal Martí, Ed: Ariel

EGA is registered as 14.302 Engineer at COITIM

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