# Squareness (Metrology)

7.8.
First we shall be dealing with the squareness of straight lines and planes and then the
perpendicularity of motion.
Two planes, two straight lines or a straight line and a plane are said to be perpendicular
when the error of parallelism in relation to a standard square does not exceed a given value.
The reference square may be a metrological square or a right angle level or may consists of
kinematic planes or lines. The permissible errors are specified as ‘Errors relating to the right
angle: ± … ^ or mm on a given length’ and if the error is determined in relation to another part
of the machine then the permitted direction of error should also be specified, such as, ‘Free
end of spindle inclined only towards the support’.
We shall be considering the following cases for the measurement of squareness of lines
and planes.

### Squareness of an axis of rotation with a given plane

For this test the dial indicator is mounted on an
arm which is attached to the spindle representing the
axis of rotation. The plunger of the dial indicator is
touch the plane. As the spindle revolves, the dial gauge
(or the end of plunger if revolving freely into air)
describes a circumstances, the plane of which is per-
pendicular to the axis of rotation. When no testing
plane is specified the dial gauge is rotated by 360° and
the variation in the readings of instrument represents
the deviation of parallelism between the plane of the
circumstances and the plane to be tested. However, if
planes are specified (e.g. planes 1 and 2) then the
difference of the readings in the position of the dial
gauge, 180° apart is noted for each of these planes
(Fig. 7.20).
The deviation is expressed in relation to the
diameter of the circle of rotation of the instrument.
The effect of periodical axial slip of the spindle
can be eliminated by repeating the above test after
moving the dial gauge through 180° relative to the
spindle and average of two sets taken. The effect of
minimum axis play can be eliminated by means of a
suitable axial pressure.

Fig. 7.20. Testing squareness.
7.8.1.

### Checking of Perpendicularity of Motion.

The term ‘perpendicularity of
motion’ refers to the successive positions on the trajectory of a point on a moving part of the
machine in relation to a plane (support or slide way), or a straight line (axis of intersection of
two planes), or to the trajectory of a point on another moving point.
The checks for testing the perpendicularity of motion become the tests of parallelism by
the use of a square suitable for the given conditions. As the tests of parallelism, have already
been discussed in details, these are not being repeated. As in the tests for parallelism, here
also, the moving part should be driven in the usual way so as to allow for the effects of play
and errors in slideways.
7.8.2.

### Squareness Testing.

The angle of 90° is probably the most important angle in
engineering applications. It is assigned several names as square, normal, right angle and it is
represented for most practical purposes by squares, rectangular blocks etc. Probably the
achievement of modern sciences would have not reached the present state of advancement if
right angle was unattainable to within a close degree of accuracy. Its importance is realised
from the following applications. The cross slide of lathe must move exactly at 90° to the spindle
axis in order to produce a flat face during facing operation. The spindle of depth micrometer
must be square to the locating face in order to avoid any errors in measurement. The column
and table of milling machine must be at 90° to each other.
For most of the purposes where high degree of accuracy is not desired, the workpiece
can be tested against an engineer’s square or square block. It simply shows whether the two
surfaces of a workpiece are at right angle or not and judgement is purely based on eye. In order
to know the amount of error and for checking squares and square blocks, the following methods
can be used.
7.8.2.1.

### Indicator Method.

This method is particularly suitable for checking the
squareness of a block whose opposite faces are supposed to be parallel. It is assumed that the
squareness of the block has already been assured to a reasonable accuracy by the use of square
etc., as otherwise the full sensitivity of the method can’t be obtained. The instrument for this
purpose is designed by N.P.L. and is very suitable for checking squareness while manufactur-
ing a square block. The instrument consists of parallel strip (framework) and a flat base. A
knife edge and some form of indicator is mounted on the framework as shown in Fig. 7.21.
The other tests of squareness of lines and planes are given below in the tabular form.

 Condition Test set up Method in brief (i) Two planes (1 and 2) at 90° to each other Squareness of two planes 1 and 2 is checked by placing the square on one plane and then checking the parallelism of 2nd plane with the free arm of the square by sliding the dial indicator (mounted on a base) along 2nd plane and its feeler moving against free arm of the square. (ii) Two axes at 90° to each other (a) Both axes fixed
 (b) One axis being axis of rotation and other fixed. The dial gauge mounted on arm and fixed on the mandrel is brought into contact with the cylinder representing fixed axis at two points 1 and 2,180° apart and deviation expressed in relation to distance between 1 and 2. (c) Both the axes being axes of rotation. The test is conducted in the same way as (ii)-(b) but the cylinder representing 2nd axis of rotation is brought into the mean position of the run out in the plane of measurement. (iii) An axis at 90° to a plane. (a) axis is fixed. Test set up is self explanatory, but the test is carried out in two perpendicular directions. (h) Axis being the axis of rotation. This test has already been described. (iv) An axis at 90° to the intersection of two planes. (a) Axis is fixed. The test set up is self explanatory.
 (b) Axis being the axis of rotation. First reading is taken by making the feeler of the dial indicator to touch on a V-block resting on two intersecting plane surfaces. (The dial in- dicator is mounted on the spindle). The second reading is noted by rotating the spindle along with dial by 180° and moving the V-block so as to bring the feeler into contact with the same point on the block. (v) Intersection of two planes is at 90° to another plane. In this test, either the square or the dial indicator fitted with a suitable base is allowed to rest on the intersecting planes and the dial indicator is moved with its feeler resting against the arms of dial gauge. The test is made in two perpendicular planes. (vi) Two straight lines, each formed by the in- tersection of two planes, are at 90° to each other. Test is self explanatory.

In this method, means are also available to produce and measure parallel surfaces by
some form of grinder and a comparator respectively. The height of the indicator is adjusted
such that it makes contact near the top of the side of the square block. The block is then placed
against the knife edge as shown in Fig. 7.21 (a) and a reading is noted on the indicator. The
block is then turned so that now the opposite side is facing the knife edge [Fig. 7.21 (&)] and
again a reading is noted on the indicator. If two sides AD and BC are truly parallel then the
two readings will be same for true right angle. In case the faces are not exactly at right angles,

Fig. 7.21. Squareneindicator method.ss testing by
then the two readings will be equally above and below the reading for a true right angle. Thus
the differences of two readings is double the error in squareness of work over the length T
between the two contact marks.
7.8.2.2.

### Correction for squareness Error.

The purpose of determining the error in
squareness of a workpiece is that it may be corrected, otherwise knowing the error will not be
of much value. Let us assume that the two readings obtained as described previously are l±
and l2, and the distance between the contact points is I. Let the length of the square block AD

from D and nothing being removed from A. Similarly 23 must be brought down by same amount,
no metal being removed at C. For this, block is set up on a surface grinder, face AD being
uppermost and cut of the above said
amount is taken across this face as shown
in Fig. 7.22 (a). The block is then turned
over as shown in Fig. 7.22 (b) and a cut
taken to clean up face .BC which will then
be square with reference to AB and CD.
The face AD can then be ground parallel
to face BC and all the four faces will be
square to each other.

Fig. 7.22. Correction for squareness error.
The two readings taken by in-
dicator could also be taken by using auto-collimator in which case a slip gauge is held against
the surface to be tested and reading on auto-collimator taken. This thus becomes a still
sensitive method.
7.8.2.3.

### Engineer’s Square Tester

Its design is also devised by N.P.L. It consists of
a bar or a tilting frame having a pair of hardened and ground steel cylinders of precisely the
same size as shown in Fig. 7.23. A plane reflector is mounted upon the bar and the instrument
is set up on a flat reference plane of suitable degree of accuracy.
The square is then placed on the same flat reference plane and the two cylinders just
square as shown in Fig. 7.23 and
down. The square as then placed
on the other side as shown and
again the bar so tilted such that
the two cylinders just touch the
ing in auto-collimator is noted
down. Then half the difference in
the two readings gives the an-
gular error in the squareness of
the square.
In order to check whether
two machined surfaces are exact-
ly at right angles to each other or
not, the use of optical square and the auto-collimator can also be made.
7.8.2.4.

### Optical Tests for Squareness.

Squareness of any two machined surfaces can
be easily checked by using the auto-collimator. The axis of the incident beam from the auto-
collimator forms the measuring datum. An optical square is utilised for turning the incident
bean through exactly 90°. In this test, it is assumed that the two surface faces are perfectly
straight. A stainless steel mirror block with a flat base is used for the horizontal surface for
aligning the collimator with the surface. A reading is thus taken in collimator at position A

Fig. 7.23. Testing squareness with engineer’s square tester.
(Fig. 7.24). The mirror with
base is then transferred to the
vertical surface and the optical
square placed in the angle as
then taken in position B. The
of the two mirror positions will
indicate whether the
machined surfaces are ac-
curately at right angles, if not

Fig. 7.24. Optical test for squareness.
the reading will show the direction and amount of error.
7.8.3.

### Focusing telescope.

Focusing telescope, also known as micro-alignment tele-
scope, is an important and powerful optical instrument to check and ensure geometrical
integrity of components and their assembly. The optical methods have the advantage of
simplicity, non-contact measurements, versatility, cost effectiveness, and in some cases the
only feasible solutions. Focusing telescope is based on the concepts of geometric optics and is
simple and straight forward to use. It enables geometric problems to be solved from first
principles. It is a portable instrument and requires simply power supply and thus can be
conveniently used at site and in every area of the workshop/factory.
Micro-alignment telescope is used to measure deviation from straight line of sight to set
and check alignment, squareness, straightness, flatness, parallelism, vertically and level. The
focussing telescope is also used for achieving precise alignment settings on large engineering
components and structures. The ability to move the focussing lenses with freedom from
transverse movement or tilts is a critical element of
the telescope design, determining the accuracy of
the resultant line of sight. Horizontal and vertical
displacement from a true line of sight are measured
via a two-axis tilting plate micrometer coupled to
graduated drums. (Refer Fig. 7.25 for schematic
drawing of focusing telescope).
The Micro-Alignment Telescope is presently
available to read directly to um and is able to focus
down to zero distance from the front objective. The
primary optical axis is concentric with and parallel
to the outside of the tube to within 6.4 (ira and 3
seconds of arc respectively. The tube itself is
cylindrical to within 5 urn. In practice one can readily
achieve a setting accuracy of 50 fxm at a distance of
30 meters and proportionally for longer and shorter
distances down to 3 metres.
Alignment Telescope focuses from zero to in-
finity and incorporates an optical micrometer to
measure deviations from a line of sight in two direc-
tions at right angles to each other.
The Micro-Alignment Telescope generates a
straight line of sight which is the basic reference for
all measurements. A prism is used to deviate the
straight line to generate squareness, and a rotating
prism generates flatness. The telescope is specially
designed to facilitate autoreflection and autocol-

Fig. 7.25. Simplified general arrangement
of the Micro-Alignment Telescope.
limation providing for squareness and angular measurement using reflection targets or
polygons.
Focusing telescope becomes a powerful measurement tool to handle a vast range of
applications when used in conjunction with a wide variety of accessories like mechanical
mounting, targets and target holders, sweep optical square, optical squares, levels, beam
dividing prisms etc. These accessories enable the focusing telescope to define straight lines of
sight in related directions and to sweep out datum planes.
Mounting accessories are used for various requirements. Targets and target holders
include mirror targets for auto-reflection and autocollimation. Sweep optical square is used to
sweep out a reference plane at 90° to the telescope axis, from which errors of flatness can be
measured. Optical squares are used to deviate the line of sight through 90 degrees to within
1 second of arc and to check squareness of axes. Optical squares are also used for setting out
right angles lines of sight like checking that a machine column is square to the bed. Spherical
mounts in conical seatings are used extensively to define a fixed point (the centre of the sphere)
through which the telescope line of sight or target always passes irrespective of tilt. Telescope
lamp house accessory or separate collimator unit is used to achieve angular setting and
measurement from a datum. Well fixturing of the telescope is essential for most of the
applications.

### Applications of Focusing Telescope System

Typical applications include the measurement and setting of bearing alignment ;
alignment and squareness of axles, spindles and bores; straightness, flatness and squareness
of bedways and slides ; alignment of engines with shafting, gearboxes and compressors ;
parallelism and squareness of rollers and conveyors ; squareness and alignment of assembly
jigs and alignment to foundation blocks.

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