REPORT

Experiment 4: Dimensional Measurement

Student: Đỗ Tất Thành

Dimensional Measurement

1. Executive summaryThe aim of this experiment is to help the students have opportunity to use two

mechanical measuring instruments: Vernier caliper and Micrometer. Both of them are

used to take measure internal as well as external dimensions. However, they have

different characteristics and the users must be reasonble with specific objects.

At first, introduction will give basic idea about those two devices and the reason

why the students need to study with theories as well as train with experiment.

Secondly, it states more clearly about Vernier Caliper and Micrometer as well as

how to use or read them. Furthermore, after knowing the characteristics of both two

measurement devices, the students may have decisions when to use Vernier and when to

use the latter. The next part is for the sample object’s figure as well as table of data.

The third part is the analysis and dicussion. It is where the students interpret the

data with calculations. Also, applying 95% or 99% confidence, the sudents can know the

interval of the object’s dimension even the times of measuring the object is not enough to

ensure the mean is distributed in bell-shape.

2. IntroductionIn general, there will be errors of size in any machined work piece. This means

that the actual dimension will be different from nominal dimension. Many authors

mentioned about this problem and it is essential to solve or reduce the error in any

measure to get the more precise result. Guolo (2008) stated that ‘Measurement error

affecting the independent variables in regression models is a common problem in

many scientific areas’. In addition, according to Schennach (2000), ‘In a linear

econometric specification, a measurement error on the regressors can be viewed as a

particular type of endogeneity problem causing the disturbance to be correlated with

the regressors’. These errors should be within certain given limits by tolerances and

determined by the dimensional measurement to guarantee the product quality. So it is

important for Mechanical students to understand the constructions, operating

principle of measurement devices, and how to use them efficiently. In addition, it is

necessary to take the measurement several times to collect the data then calculate to

estimate the true value of dimension.

Vernier caliper

Vernier caliper is a precision instrument that can be used to measure internal and

external dimensions accurately.

Micrometer

A micrometer is commonly used for measuring the thickness and inside or outside

diameters of parts. Micrometers are also available for measuring depths. Micrometers

can be equipped with digital readout to reduce errors in reading.

3. Vernier caliper3.1 Introduction

Vernier calipers can measure internal dimensions (using the internal jaws),

external dimensions (using the external jaws), and depending on the manufacturer,

depth measurements by the use of a probe that is attached to the movable head and

slides along the centre of the body. This probe is slender and can get into deep

grooves that may prove difficult for other measuring tools. They include both metric

and inch measurements on the upper and lower part of the scale. Vernier calipers

commonly used in industry provide a precision to a hundredth of a milimetre or one

thousand of an inch.

The vernier caliper consists of a main scale engraved on a fixed ruler and an

auxiliary vernier scale engraved on a movable jaw. The movable auxiliary scale is

free to slide along the length of the fixed ruler. This vernier's main scale is calibrated

in centimeters with the smallest division in millimeters. The auxiliary scale has 10

divisions that cover the same distance as 9 divisions on the main scale. Therefore, the

length of the auxiliary scale is 9.0 mm.

1-Outside jaws: used to measure external diameter of width of an object

2-Inside jaws: used to measure internal diameter of an object

3-Depth bar blade: used to measure depths of an object or a hole

4-Main scale: gives measurements in quotient (in cm)

5-Main scale: gives measurements in quotient (in inch)

6-Vernier scale: gives measurements in fraction (in cm)

7-Vernier scale: gives measurements in fraction (in inch)

8-Retainer: used to block movable part to allow the easy transferring a

measurement

3.2 How to use Vernier caliper

- Step 1: Preparation to take the measurement, loosen the locking screw and move

the slider to check if the vernier scale works properly. Before measuring, do make

sure the caliper reads 0 when fully closed. If the reading is not 0, adjust the

caliper’s jaws until you get a 0 reading. If you can’t adjust the caliper, you will

have to remember to add to subtract the correct offset from your final reading.

Clean the measuring surfaces of Vernier caliper and the object, then you can take

the measurement.

- Step 2: Close the jaws lightly on the item which you want to measure. If you are

measuring something round, be sure the axis of the part is perpendicular to the

caliper. Namely, make sure you are measuring the full diameter. An ordinary

caliper has jaws you can place around an object, and on the other side jaws made

to fit inside an object. These secondary jaws are for measuring the inside diameter

of an object. Also, a stiff bar extends from the caliper as you open it that can be

used to measure depth.

3.3 How to read a measurement from the scales

1) The main metric scale is read first, this shows there are 13 whole divisions

before the 0 on the vernier scale.Therefore, the first number is 13.

2) Next read the fraction, only one division on the main scale lines up (aligns)

with a division on the vernier scale below it, whilst others do not. In this

figure, the 41st division on the vernier scale lines up exactly with a division on

the main scale.

3) The 41 is multiplied by 0.02 (the resolution of caliper) giving 0.82.

4) The 13 and the 0.82 are added together to give the final measurement of

13.82mm.

4. Micrometer4.1 Introduction

Micrometer is an instrument for making precise linear measurement of

dimensions such as diameters, thicknesses, and lengths of solid bodies. It is used

widely in mechanical engineering and machining as well as most mechanical trades

for precision measurement, along with other metrological instrument such as dial

calipers and vernier calipers.

Micrometer can measure more precisely than Vernier caliper can.

Micrometer construction

(0-25mm is the range of measurement

0.01mm is the resolution of this micrometer)

Thimble and Spindle face

Frame, Anvil face and Sleeve

Rachet stop

Ratchet stop is a device to help engineer to apply just enough torque to rotate the

thimble in a gentle manner. In principle, it allows continuous linear or rotary motion

in only one direction while preventing motion in the oppostite direction.

A ratchet consists of a round gear or linear rack with teeth, and a pivoting,

springloaded finger called a pawl that engages the teeth. The teeth are uniform but

asymmetrical, with each tooth having a moderate slope on one edge and a much

steeper slope on the other edge.

When the teeth are moving in the unrestricted direction, the pawl easily slides up

and over the gently sloped edges of the teeth, with a spring forcing it (often with an

audible ‘click click’) into the depression between the teeth as it passes the tip of each

tooth. When the teeth move in the opposite (backward) direction, however, the pawl

will catch against the steeply sloped edge of the first tooth it encounters, thereby

locking it against the tooth and preventing any futher motion in that direction.

4.2 How to use Micrometer

- Step 1: Carefully open the jaws by revolving the ratchet.

- Step2: Slightly place the item to be measured against the anvil of the micrometer.

Make sure the micrometer is perpendicular to the surfaces being measured.

- Step 3: Rotate the ratchet stop until the spindle contacts the item. Do not clamp

the micrometer tightly on to the workpiece. Use only enough pressure on the

ratchet stop to allow the item to just fit between the anvil and spindle. When you

hear “click click”, you can stop rotating the hatchet.

- Step4: Lock the lock nut on the micrometer to make sure that the figures can not

change any more.

4.3 How to read the measurement from the scales

Read the markings on the sleeve and the thimble, firstly, read the point which the

thimble stops at it on the right of the sleeve (It is 5.5mm here, because each line

above the centre long line represents 1mm while each line below the centre long line

represents 0.5mm). Secondly, read the markings on the thimble, it is 28. At last, add

all the reading up: 5.50mm + 28x0.01mm=5.78mm. So the total reading is 5.78mm.

5. Experimental Procedure5.1 Approach

5.2 Equipment list

5.2.1 Micrometer (Mitutoyo manufacturer)

- Range: 25-50mm.

- Resolution: 0.01mm.

5.2.2 Vernier caliper (Mitutoyo manufacturer)

- Range: 0-200mm.

- Resolution: 0.02mm.

5.2.3 Cylinder

2040

35 120

-0,2

-0,2

5-0

,2

-0,5

Ø30k7+ 0,023+0,002 ( )

Ø48

Ø28

0,1

AB

= O0,

030,

010,

05A

B

Rz1

2,5

Rz2

5

Rz3

,2R

z3,2

Rz2

0-0,25

-0,06

-0,2

III

IIV

VII

CD

E

Hìn

h 1

ABØ30k7( ) +0,002

+ 0,023

0,02

0,01

=OO =0,

010,

02

170

Ø42

5.3 Uncertainty: Room temperature, individual’s skill,

5.4 Experimental procedures

5.4.1 Use the Micrometer to measure 42 and 28.

- Before measuring, dry and clean sample and device. Wash and dry hand.

- Step 1: Keep the sample vertically.

- Step 2: Use the Micrometer as the instructions.

- Step 3: Collect data and analyze.

5.4.2 Use the Vernier caliper to measure L20 and L40 (By using Depth bar blade).

- Before measuring, dry and clean sample and device. Wash and dry hand.

- Step 1: Keep the sample vertically.

- Step 2: Keep the Vernier parallel to sample, slide slowly the Vernier scale

until the blade reaches surface C (when you measure L20), surface D

(when you measure L40). Note: the blade must be parallel to the sample.

- Step 3: Collect data and analyze.

6. Results and Discussion6.1 Data (in mm)

Parameters

TimesL20-0,2 L40-0,25 42-0,25 28-0,2

1 20.22 40.14 42.14 27.96

2 20.16 40.16 42.23 28.03

3 20.10 40.26 42.24 27.99

4 20.26 40.30 42.10 27.92

5 20.10 40.30 42.12 28.02

Mean x 20.17 40.23 42.17 27.98

6.2 Discussion and Analysis

With obtained results, the cylinder reaches the standard quality and can be used

for working.

Error: it is assumed that the sample mean is normal distribution because sample

size is 5<30

Sample standard deviation:

+L20: Sx = 0.072.

+L40: Sx = 0.077.

+42: Sx = 0.063.

+28: Sx = 0.045.

We have the equation:

When it is estimated that with 95% confidence, t4,0.025 is 2.776. Then the

population mean should be within:

+L20: x = 20.17 ± 0.089.

+L40: x = 40.23 ± 0.096.

+42: x = 42.17 ± 0.078.

+28: x = 27.98 ± 0.056.

With 99% confidence t4,0.005 is 4.604, then the population mean should be within:

+L20: x = 19.66 ± 0.148.

+L40: x = 39.84 ± 0.159.

+42: x = 47.86 ± 0.130.

+28: x = 27.81 ± 0.093.

7. Conclusion

By doing this experiment, students can know how use and read measurement

when using Vernier caliper and Micrometer.

x−tα /2 ,n−1s√n

≤μ≤x+t α /2, n−1s

√n

In order to get more precise result, it is needed to take more volume of measuring.

In addition, if there is not enough time to do that task, we can use longer range of

confidence interval to reduce the error.