Linear Measurements

References :

1. handbok of dimensional measurement

2. http://fetweb.ju.edu.jo/staff/me/jyamin/3. http://www.phy.uct.ac.za/courses/c1lab/vernier1.html

• The measuring instrument / methods can be classified in various manner.

Direct / indirect measuring

1. Direct measuring : in which the measured value is determined directly.Example: micrometer, vernier caliper.

2. Indirect measuring: in which the dimension is determined by measuring other values functionally related to the required value.example: divider, caliper.

Absolute / comparative measuring

1. Absolute : here, the zero division of the instrument corresponds with the zero value of the measured dimension.

2. Comparative : Here, only the deviations of the measured dimensions from a master gauge are determined.

Contact / Contactless measuring

1. Contact: Here, the measuring tip of the instrument actually touches the surface to be measured.

2. Contactless: Here, no contact is required for measurement.

Linear / Angular measuring instrument

• Linear or (length) measuring instrument:

• Angular or (angle) measuring instrument:

Depending on the accuracy

1. Most accurate group includes light interference instruments.

2. Second group includes: optimeters, dial comparators.

3. Third group includes: dial indicator, vernier calipers.

• Measuring instrument can be divided based on their metrological properties, such as range of measurement scale, graduation value, scale spacing, sensitivity, and reading accuracy.

Range of measurement

• It indicated the size values between which measurements can be made on the given instrument.

• Example: micrometers are available for the following ranges. (0 to 25, 25 to 50, 50 to 75, 75 to 100, 100 to 125, 125 to 150)mm .

Scale division value

• It is the measured value corresponding to one division of the instrument scale.

Example: the scale division value of a micrometer is 0.01mm.

Sensitivity

• It is also called “ amplification factor” or “gearing ratio”

• It is the ratio of scale spacing to the scale division value.

• Example: on a dial indicator the scale spacing is 1.5 mm and the scale division value is 0.01 mm then the sensitivity is 150mm.

Types of length standards

• The distance may be expressed as the distance between two lines or the distance between two faces.

• The instruments used for the direct measurement if the linear dimensions fall into two categories:

1. Line standards.

2. End Standards.

Line Standards / End standards

• In the Line Standards. The measurement is made between two parallel lines engraved across the standard.

• In the End Standard. The measurement is made between two flat parallel faces.

Steel Rule

• Type: This is a low-resolution line-measuring instrument

• Operating principle: comparing an unknown length to a previously calibrated one.

• Construction: It consists of a strip of hardened steel having line graduations etched or engraved at intervals of fraction of standard unit of length. These graduations may not be uniform all throughout its length. This allows for multiple use for particular range as per accuracy required.

• Basic desirable qualities:

• (1) Clearly engraved lines.

• (2) Minimum thickness.

• (3) Good quality spring steel.

• (4)Graduations on both sides.

• (5) Low coefficient of thermal expansion.

• Degree of accuracy affected by:

• (1) Quality of rule.

• (2) Skill of user in estimation the parts of mm.

• Reliability of measurement when using scale for direct measurement depends on the proper positioning of the scale in relation to workplace.

Some accessories of Rules

Clamping shaft

Removable hooks

Some accessories of Rules

Center finder Right angle aligner

Errors1- Instrument limitations.

2-Geometric errors (flatness and parallelism).

3-Thickness of the grade line.

4-Least increment limitation.

5-Observation error.

6- Alignment error.

7- Parallax error (object not well aligned with scale).

Calipers

• Calipers are used to pick off diameters or distance from a workpiece.

• This setting is then measured with a scale, vernier caliper, or micrometer.

• They are known as “ transfer measuring instruments”.

Construction & Use:

• They consist of two legs hinged at the top with the ends of the legs span the parts to be inspected.

Types of calipers.

• Calipers can be classified as : Outside, Inside.

• Calipers can be classified as : Spring, Firm joint, Lock joint , Transfer.

firm joint calipers

Inside firm joint caliper Outside firm joint caliper

Spring caliper

Inside spring caliper outside spring caliper

• Operating principle: They are devices for comparing measurements against known dimensions.

• Construction: The legs are made from carbon & alloy steel containing not more than 0.05% Sulphur, and 0.05% Phosphorous with working ends suitably hardened and tempered to hardness of 400-500 HV and faces up to 650 + 50 HV. They are joined together by a rivet. They have rectangular cross section.

• Qualities: They should be free from cracks, seams, dirt, flaws and must have smooth bright finish.

• Nominal Size is the distance between the center of the rolling end and the extreme working end of a leg.

• Caliper’s Capacity is the maximum dimension that can be measured by the caliper. It should not be lesser than the nominal size.

• The accuracy depends on the sense and feel of the operator. Therefore, caliper should be held gently and square to the work with slight gauging pressure applied.

• Precision (medium resolution) linear measurement.

Characteristics of precise measuring instruments

(1) High degree of sensitivity.

(2) High degree of accuracy.

(3) Minimum inertia in moving part.

(4) Freedom from variance.

Vernier caliper

The basic components 1- Beam (line graduated)2- Fixed jaw3-Sliding jaw

Vernier Height scale

Vernier depth scale

• In metric systems, there are two variations of the Vernier Scale:

1. Where the main scale is graduated into mm and 0.5 mm.

2. Where the main scale is graduated in whole mm only.

• The relation between the size of the division on main scale and the size of a division on a vernier scale is :

nCCC

Cn

nC

CnCn

v

v

v

1)1(

• C = size of a division on main scale.

• Cv= size of a division on a vernier scale.

• n= number of total divisions on the vernier scale.

The small divisions on the rule span 1 mm.10 divisions on the vernier gauge span 9 divisions on the rule.Hence, the small divisions on the vernier span9/10 mm = 0.9 mm = 0.09 cm,and the difference between a small division on the vernier and a small division on the rule is1/10 mm = 0.1 mm = 0.01 cm.

Ref. http://www.wooster.edu/physics/lindner/Ph203_2000Labs/VernierCaliper.pdf

How to read a vernier caliper.

• The reading on the main scale just before the zero of the vernier is noted.This is called Main scale reading (M.S.R).The number of division on the vernier which coincides perfectly with any one of the main scale divisions is noted.This is called vernier coincidence (V.C).The verniercoincidence (V.C) is multiplied by least count to get the fraction of a main scale division.This is added to the main scale reading (M.S.R) to total reading.

Reference:http://www.phy.uct.ac.za/courses/c1lab/vernier1.html

Reference:http://www.phy.uct.ac.za/courses/c1lab/vernier1.html

• Graduation characteristics: they should be clearly engraved so that they are clearly visible.

• Sources of Errors with Vernier Caliper : Caliper not properly set to zero, Manipulation of the vernier scale reading, Wear in measuring tips, non-perpendicular plane between bar and jaws, or between jaws and workpiece.

Care to be taken in using the Vernier Scale :

• (1) Not to be treated as a wrench or hammer since they are not rugged.

• (2) Should not be dropped or tossed aside rather, handled with care.

• (3) Should be cleaned from dirt.

• Precautions :

• (1) Use the fixed jaw as the reference jaw,

• (2) Do not play with the sliding jaw on the scale in order not to lose accuracy,

• (3) Regularly check the tips of the jaws for possible wear.

Advances in Vernier calipers

Digital Caliper Dial Caliper

The Micrometer

The basic principle of the micrometerIs an extremely accurate screw thread with pitch (advancement with one rotation) equal to 0.5 mm. The measured part is placed between the anvil and the spindle. The Ratchet is used to reduce the fixing force on the part.

The measurement is read on the line graduation on the sleeve and the graduation on the thimble.

The accuracy of the micrometer is governed by the Lead error.

The calibration chart for the micrometer. X-axis is the value of the referenceY-axis is the error in measurement (reference – reading of the micrometer)

Question????

If the value of the measurand 0.45 in what is the expectedUncertainty or error inMeasurement?

Accuracy of the micrometer depends on

1- The parallelism and the flatness of theMeasuring surfaces2- The deflection of the frame (because of theHolding strength)3- The accuracy of the screw thread4- Heat transfer5- Lack of alignment with the object6- The reading error

The use of an optical flat to check The accuracy of the micrometer

Micrometer typesMicrometeraccessories

Micrometer types

Reading the micrometer

Fixed gauges

Fixed gauges are the pillers of interchangeability with efficient testing of the Manufactured part and adding the feel factor to the inspection process

Master gauges: Used forCalibration of measuring instrumentsIt takes the shape of full cylinder

Limit gauges: These usually establish the ends of the measurement And be adjustable

External (snap)

Internal (plug gauges)

Gauge blocksDisvered by johansson, a sweedish deligate to Mauser factory in Germany in 1985

He devised a techniques to produce any length from a build up of individual Fixed Master guages. The stacking is possible by a mechanised lapping process to the surface of the masters.

Block gauge set

The basic uses of the 0.5 and I block gauges are: a primary standard, as a reference standardFor calibrating other blocks and a working standard for calibrating sensitive measuringtools

The basic applications for II block gauges is in the setting of adjustable limit gaugesAnd for comparative length measurement

The basic use of the III block gauges is in the actual measurement and For calibrating measuring instruments

Usually the surfaces of the gauge blocks are subject to damages the following figureShows how to remove such minute damges

Other non-graduated instruments