Principle of auto collimator:

Auto collimator is an optical instrument of small angular differences. For small angular measurement, auto collimator provides a very sensitive and accurate approach. Auto collimator is actually a infinity telescope and a collimator combined into one instrument. The instrument is designed to measure small angular defection and may be used in conjuncture with a plane mirror or other reflecting device. If a scale is provided on the graticule the tilt of the reflecting

surface, so that a direct two to one reading is obtained. The light rays thus reflected are linearly displaced from the target by a amount of 20f.

Fig4.4

Figure shows the diagrammatic representative principle of a autocollimator. The gratitude GH is focused in the principal focal plane of the objective lens is illuminated from a suitable light rays parallel to the optic axis. If a reflecting mirror AA is situated at right angle to the optical axis, then the light rays will be reflected back on their original paths and the returned image of the object will coincide with the object at G.

If the mirror is deflected about ‘O’ through an angle θ to the position BB’ and therefore to be at right angles to the optical axis, the graticule, an image of the object, giving a displacement x from G. the distance x is a measure of angle 2θ and which is twice the angle deflection of the mirror.

If

X distance traveled by the image from the initial position of the object.

F focal length of the lens.

θ the angle of tilt of the reflecting mirror and considered to be small.

Then,

2θ = x/f where x = 2fθ . The points to be noted are:

1. The position of the final image does not depend upon the objective lens.

2.

If the reflector is completely moved back i.e. if θ become gauge, the reflected rays will completely miss the lens and no image will be formed.

3. For high sensitivities i.e. for large value of X for smaller angular deviation a long focal length is required.

Autocollimator Applications :

i. The measurement of straightness & flatness

ii. Precise angular indexing in conjunction with polygons iii. Comparative measurement using master angles

iv. Assessment of square ness & parallelism of components v. Measurement of small linear dimensions

Angle Dekkor:

This is also a type of an autocollimator. It contains a small illuminated scale in the focal plane of the objective lens. This scale in normal position is outside the view of the microscope eye piece as shown in the fig: The illuminated scale is projected as a parallel beam by the collimating lens which after a striking the reflector below the instrument is re-focused by the lens in the field of view of the eye piece. In the field of view of the microscope there is another datum scale fixed across the center of screen & the reflected image of the illuminated scale is received at right angle to this fixed scale & the two scales, in this position intersect each other. Thus the reading on the illuminated scale measures angular deviation from one axis at 90⁰ to the optical axis & the reading on the fixed datum scale measures the deviation about an axis mutually perpendicular to the other two. In other words, changes in angular position of the reflector in two planes are indicated by changes in the point of intersection of the two scales.

Readings from scale are read direct to 1’ without the use of a micrometer. The whole of the optical system is enclosed in a tube, which is mounted on an adjustable bracket. There is a lapped flat & reflective base on which all these things are placed. It is mostly used as a Comparator. The instrument measures by comparing the readings obtained from a standard, a sine bar or combination of angular gauges with that from the work under test. Though this is not a precise instrument in comparison to autocollimator, it has wide field of application for general angular measurement, as angular variations are read direct without the operation of a micrometer.

Fig 4.5

CHAPTER - 5

Screw Thread and Gear Measurement Terminology:

Fig 5. 1

Screw thread: a screw thread is the helical ridge produced by forming a continuous helical groove of uniform section on the external or internal surface of a cylinder or a cone. A screw thread formed on a cylinder is known as straight or parallel screw thread, while the one formed on a cone is known as tapered threads.

External thread: a thread formed on outside of a work piece is known as external thread. Example: on bolts or studs etc.

Internal thread: a thread formed on inside of a work piece is known as internal thread. Example: on a nut or female screw gauge.

Multiple-start screw thread: forming two produces this or more helical grooves equally spaced and similarly formed in an axial section on a cylinder. This gives

‘quick traverse’ without sacrificing core length.

Axis of a thread: this is imaginary line running longitudinally through the center of the screw.

Hand (right or left hand thread): Suppose a screw is held such that the observer is looking along the axis, if a point moves along the thread in clockwise direction and thus moves away from the observer, the thread is right hand: and if it moves towards the observer the thread is left hand.

Form of thread: this is the shape of the contour of one complete thread as seen in axial section.

Crest of thread: this is defined as the prominent part of thread, whether it is external or internal.

Root of thread: this is defined as bottom of the groove between the two flanks of the thread, whether it is external or internal.

Flanks of thread: these are straight edges, which connect the crest with the root.

Angle of thread (included angle): this is the angle between the flanks and slope

of the thread measured in an axial plane.

Flank angle: the flank angles are angles between individual flanks and the perpendicular to the axis of the thread which passes through the vertex of the fundamental angle. The flank angle of a symmetrical thread is commonly termed as the half angle of thread.

Pitch: the pitch of the thread is the distance, measured parallel to the axis of the thread, between corresponding points on the adjacent forms in the same axial plane and on the same side of the axis. The basic pitch is equal to the lead divided by the number of the thread starts. On drawings of thread sections, the pitch is shown as the distance from the center of one thread crest to the center of next, and this representation is correct for single start as well as multi-start threads.

Lead: lead is the axial distance moved by the threaded part when it is given one complete revolution about it’s axis with respect to fixed mating thread. the uniformity of pitch measurement does not necessarily assure uniformity of lead.

variations in either or pitch cause the functional or virtual diameter of thread to differ from the pitch diameter.

Thread per inch: this is the reciprocal of pitch in inches.

Lead angle: on straight threads, lead angle is the angle made by the helix of the thread at the pitch line with plane perpendicular to the axis. The angle is measured in actual plane.

Helix angle: on a straight thread, the helix angle is the angle made by the helix of the thread at the pitch line with the axis. the angle is measured in an axial plane.

Depth of thread: this is the distance from the crest or tip of the thread to the root of the thread-measured perpendicular to the longitudinal axis. This could also be defined as the distance measured radially between the major and minor cylinders.

Axially thickness: this is the distance between the opposite faces of the same thread measured on the pitch cylinder in the direction parallel to the axis of the thread.

Truncation: a thread is sometimes truncated at the crest or at the root or at both crest and root. Truncation at crest is the radial distance from the crest to nearest apex of the fundamental triangle. Similarly the truncation at the root is the radial distance from the root to the nearest apex.

Addendum: for an external thread, this is defined as the radial distance between the major and pitch cylinders. For an internal thread this is the radial distance between the minor and pitch cylinders.

Dedendum: this is radial distance between the pitch and minor cylinder for an external thread and for internal thread, this is radial distance between the major and pitch cylinders.

Major diameter: in case of a straight thread, this is the diameter of the major cylinder (imaginary cylinder, coaxial with the cylinder, which just touches the roots of an internal thread). It is often referred to as root diameter or cone diameter of external threads.

Effective diameter or pitch diameter: in case of straight thread, this is the diameter of the pitch cylinder (the imaginary cylinder which is coaxial with the axis of the screw and intersects the flank of the threads in such a way as to make the width of the threads and width of the spaces between the threads equal.). If the pitch cylinder were imagined as generated by the straight line parallel to the axis of the screw that straight line is referred to as pitch line. Along the pitch line the widths of the threads and the widths of the spaces are equal on a perfect thread. This is the most important dimension as it decides the quality of the fit between screw and nut.

Functional (virtual) diameter: for an external or internal thread, this is the pitch diameter of the enveloping thread of perfect pitch, lead and flank angles having full depth of engagement but clear at crest and root. This is defined over a specified length of thread. This may be greater than the effective diameter by an amount due to errors in pitch and angle of thread. The virtual diameter being the modified effective diameter by pitch and angle errors is the most important single dimension of a screw thread gauge. In case of a taper screw thread, the cone angle of taper, for measurement of effective diameter and whether the pitch is measured along the axis or along the pitch code generator also needs to be specified.

Errors in threads:

In case of plain shafts and holes, there is only one dimension, which has to be considered, and errors on this dimension if exceed the permissible tolerance, will justify the rejection of the part. While in case of screw threads there are at least five important elements, which require consideration, and error in any one of these can cause rejection of the thread. In routine production all of these elements (major dia, minor dia, effective dia, pitch and angle of thread form) must be checked and method of gauging must be able to cover all these elements.

Errors on the major and minor diameters will cause interference with the mating thread. Due to errors in these elements, the root section and wall thickness will be less, also the flank contact will be reduced and ultimately the component will be weak in strength. Errors on the effective diameter will also result in weakening of the assembly due to interference between the flanks.

Similarly pitch and angle errors are also not desirable as they cause progressive tightening and interference on assembly. These two errors have a special significance as they can be precisely related to effective diameter.

Pitch errors in screw threads:

A point cutting tool generates Generally screw threads. In this case, for pitch to be correct, the ratio of linear velocity of tool and angular velocity of work must be correct. This ratio must be maintained constant; otherwise pitch errors will occur.

If there is any error in the pitch the total length of thread engaged would be either too great or too small, the total pitch in overall length of the thread being called the cumulative pitch error. Various pitch errors are:

Progressive pitch error Periodic pitch error Drunken error Irregular errors

Drunken error: this is the one having erratic pitch, in which the advance of the helix is irregular in one complete revolution of the thread. Thread drunkenness is a particular case of a periodic pitch error recurring at intervals of one pitch. In such a thread, the pitch measured parallel to the pitch measured parallel to the thread axis will always be correct, the error being that the thread is not cut to the true helix. If the screw thread be regarded as an inclined plane wound around the cylinder and if the thread be unwound from the cylinder, (that is development of the thread be taken) then the drunkenness can be visualized. The helix will be a curve in the case of drunken thread and not a straight line as shown in the figure.

Fig 5.2.

It is very difficult to determine such errors and moreover they do not have any great effect on the working unless the thread is of very large size.

Progressive pitch error: this error occurs when the tool work velocity ratio is incorrect, though it may be constant. It can also be caused due to pitch errors in the lead screw of the lathe or other generating machine.

The other possibility is by using an incorrect gear or an approximate gear train between the work and lead screw. E.g. while metric threads are cut with an inch pitch lead screw and a translatory gear are not available. A graph between the cumulative pitch error and the length of thread is generally a straight line in case of progressive error.

Periodic pitch error: this repeats itself at regular intervals along the thread. In this case, successive portions of the thread are either shorter or longer than the mean. This type of error occurs when the tool work velocity ratio is not constant.

This type of error also results when the thread is cut from a leads crew, which lacks square ness in the abutment causing the leads crew to move back and forth in each revolution. Thus the errors due to these cases are cyclic in nature and so the pitch increases to a maximum value, decreases to the mean and then to the minimum value and so on. The graph between the cumulative pitch error and length of threads for this error will, therefore, be of sinusoidal form.

Irregular errors: these arise from the disturbances in the machining setup, variations in the cutting properties of material etc. thus they have no specific causes and correspondingly no specific characteristics also. These errors could be summarized as follows:

Erratic pitch: this is irregular error in pitch and varies irregularly in magnitude over different lengths of thread.

Progressive error: when the pitch of a screw is uniform, but is shorter or longer than its nominal value, it is said to have progressive error.

Periodic error: if the errors vary in magnitude and recur at regular intervals, when measured from thread to thread along the screw are referred to as periodic errors.

Screw threads measurements:

There are a large number of different standard forms of screw threads in common use. A few important measuring types of screw thread elements are discussed here. Here the nomenclature of the screw threads is not discussed here.

Full diameter: for measuring the full diameter of a screw, an ordinary micrometer with anvils of a diameter sufficient to span two threads may be used.

To eliminate the effect of errors in the micrometer screw and the measuring faces, it is advisable first to check the instrument on a cylindrical standard of about the same diameter as the screw. For such purposes a plug gauge is useful.

Core diameter: the diameter over the root of a thread may be checked by means of a special micrometer adapted with shaped anvils, or an ordinary micrometer may be used in conjunction with a pair of vee pieces. The second method is more universal in application, and a diagram showing the arrangement is given in the figure. It is important that while making the test the micrometer is positioned at right angles to the axis of the screw being measured.

The vee pieces used for this test are of hardened steel with an angle of about 45⁰ finished with a radius less than that of the root of the thread. The back faces should be finished flat, perpendicular with the axis of the vee and parallel with the edge of the radius.

Effective diameter: the only reliable means of inspecting the effective diameter of a screw is to use some method, which enables a reading to taken from the straight, sloping flanks of the threads.

This is accomplished in a simple manner by using small cylindrical test wires, which rest in the thread angle and make contact with the sloping sides. If means

are available (e.g. a floating micrometer) for maintaining the micrometer at the right angles to the screw axis, two opposite wires may be used; or else three wires are required to align the micrometer, and this method is the rule when using an ordinary micrometer. The wires should be hardened and polished and their surfaces should be round, straight, parallel, and uniform to a high degree of accuracy.

Three-wire method: checking the effective diameter when a screw is measured over wires is given below for general case. One side of the screw is shown in the figure, where w= distance over the wires and DE the effective diameter. The wire is designated with radius r and diameter d.From this general formula we may apply the special adaptation for common threads.

Fig 5.4

Pitch:

An error in the pitch requires a compensating reduction in effective diameter of approximately twice the amount; pitch errors are to be reduced to absolute minimum. A pitch-measuring device consists of a bed with centers at each end to support the screw, with alternative means for holding nuts and sleeves when internal threads are to be tested. Sliding along the bed and moved by an accurate micrometer is head which carries a feeler piece or stylus shaped to fit in the vee of the thread provided with an indicator which shows when it is bedded home centrally in the vee (i.e. in its lowest position). When making a test, the head is moved along causing the stylus to seat itself successively in each of the threads over the length being examined. Observation and analysis of the micrometer reading obtained then enables the pitch of the thread to be determined. A diagrammatic sketch of the stylus is shown in the figure.

An error in the pitch requires a compensating reduction in effective diameter of approximately twice the amount; pitch errors are to be reduced to absolute minimum. A pitch-measuring device consists of a bed with centers at each end to support the screw, with alternative means for holding nuts and sleeves when internal threads are to be tested. Sliding along the bed and moved by an accurate micrometer is head which carries a feeler piece or stylus shaped to fit in the vee of the thread provided with an indicator which shows when it is bedded home centrally in the vee (i.e. in its lowest position). When making a test, the head is moved along causing the stylus to seat itself successively in each of the threads over the length being examined. Observation and analysis of the micrometer reading obtained then enables the pitch of the thread to be determined. A diagrammatic sketch of the stylus is shown in the figure.

In document 18424933 Metrology and Measurements (Page 30-45)