VIET NAM NATIONAL UNIVERSITY, HO CHI MINH CITY
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY
Report of Tolerance and Measurement (LAB)
Instructor: PhD. Bành Quốc Nguyên
Group: CC01
No
Student Name
Student ID
1
Nguyễn Phúc Anh
2052029
2
Bùi Công Đức
2052958
3
Nguyễn Quý Hưng
2152101
4
Chung Minh Gia Hy
2152104
5
Lao Vĩnh Khang
2152107
6
Trần Ngọc Vĩnh Quyền
2153755
7
Nguyễn Quốc Thắng
2152984
Ho Chi Minh City, 2025
CONTENTS
LAB 1: VERIFY SHAPE DEVIATION OF A SMOOTH CYLINDRICAL PART IN
HORIZONTAL AND VERTICAL CROSS SECTIONS ...........................................1
I. OBJECTIVE ............................................................................................................1
II. APPARATUS ..........................................................................................................1
III. INTRODUCTION TO THE APPARATUS ..........................................................1
IV. PROCEDURE .......................................................................................................2
1. Measure the shape deviation in the vertical cross section (Fig. 1.2) ..................2
2. Measure the shape deviation in the horizontal cross section (Fig. 1.3) ..............3
V. EVALUATE AND COMMENTS ON THE RESULTS .........................................4
LAB 2: RADIAL AND FACE RUNOUT MEASUREMENT OF CYLINDRICAL
PART ...........................................................................................................................6
I. OBJECTIVES ..........................................................................................................6
II. OVERVIEW OF MEASURING INSTRUMENTS ...............................................6
III. PROCEDURE .......................................................................................................7
IV. EXPERIMENT DATA ..........................................................................................7
V. EVALUATION AND COMMENT ON MEASUREMENT RESULTS ................7
LAB 3: MEASUREMENT AND INSPECTION OFSTRAIGHTNESS, FLATNESS,
AND PERPENDICULARITY ....................................................................................9
I. OBJECTIVES ..........................................................................................................9
II. MEASURING INSTRUMENTS ...........................................................................9
III. INTRODUCTION OF THE MEASURING INSTRUMENTS ............................9
1. Dial indicator .......................................................................................................9
2. Dial indicator fixture ...........................................................................................9
IV. PROCEDURE .......................................................................................................9
1. Checking the flatness and straightness................................................................ 9
2. Checking the perpendicularity ..........................................................................10
V. EXPERIMENT DATA .......................................................................................... 11
VI. RESULT EVALUATION ....................................................................................12
LAB 4: DETERMINATION OF SAMPLE SIZE.....................................................13
I. OBJECTIVE ..........................................................................................................13
II. APPARATUS ........................................................................................................13
III. INTRODUCTION TO THE APPARATUS ........................................................13
1. Conception of measuring sample ......................................................................13
2. Samples combination principle .........................................................................14
3. Use and storage of measuring samples ............................................................. 15
IV. PROCEDURE .....................................................................................................16
V. EXPERIMENT RESULTS ...................................................................................17
VI. REVIEW AND COMMENT THE RESULT ......................................................17
LAB 5: MEASURING THE TAPER HOLE BY INDIRECT METHOD ................19
I. OBJECTIVES ........................................................................................................19
II. MEASURING INSTRUMENTS .........................................................................19
III. MEASURING TAPERED HOLE WITH SPHERICAL BALL .........................20
IV. PROCEDURE .....................................................................................................21
V. RESULT OF THE EXPERIMENT.......................................................................23
VI. COMMENT ........................................................................................................23
LAB 6: MEASURE THE GEAR RUNOUT ............................................................ 24
I. OBJECTIVE ..........................................................................................................24
II. APPARATUS ........................................................................................................24
III. PROCEDURE .....................................................................................................24
1. Diagram Measurement ......................................................................................24
2. Method ..............................................................................................................24
IV. EVALUATE .........................................................................................................25
V. COMMENT ..........................................................................................................25
LAB 7: MEASURE GENERAL NORMAL LENGTH ............................................26
I. OBJECTIVE ..........................................................................................................26
II. GENERAL INTRODUCTION OF PRINCIPLES ...............................................26
III. PROCEDURE .....................................................................................................26
IV. EVALUATE AND REVIEW THE RESULT ......................................................27
V. COMMENT ..........................................................................................................27
LAB 8: SURVEY THE CHARACTERISTICS OF DYNAMOMETER BASED ON
PRINCIPLE OF DEFORMATION ...........................................................................28
I. OBJECTIVE ..........................................................................................................28
II. APPARATUS ........................................................................................................28
III. PROCEDURE .....................................................................................................28
IV. REPORT ..............................................................................................................29
LAB 10: MEARSURE DEFORMATION USING STRAIN GAUGE ....................32
I. OBJECTIVE ..........................................................................................................32
II. INSTRUMENTS ..................................................................................................32
III. WHEATSTONE BRIDGE CIRCUIT .................................................................32
IV. BAR WITH ONE FIXED END ..........................................................................34
1. Relationship between force, stress, and deformation ........................................34
2. Experimental model ..........................................................................................34
3. Strain gauge (tension variable resistor) ............................................................. 35
V. HOLLOW TUBE WITH ONE FIXED END .......................................................35
VI. PROCEDURE .....................................................................................................38
VII. RESULT TABLE ............................................................................................... 39
VIII. REPORT ...........................................................................................................39
LAB 11: MAKING A DRAWING FROM A SAMPLE ...........................................42
I. OBJECTIVE ..........................................................................................................42
II. APPARATUS ........................................................................................................42
III. PROCEDURE .....................................................................................................42
IV. REPORT ..............................................................................................................43
LAB 13: SURVEY THE HEAT MEASUREMENT SYSTEM ................................ 45
I. OBJECTIVE ..........................................................................................................45
II. APPARATUS ........................................................................................................45
III. PROCEDURE .....................................................................................................45
IV. EXPERIMENT RESULTS ..................................................................................45
V. REVIEW AND COMMENT THE RESULTS .....................................................46
REFERENCES ..........................................................................................................48
LAB 1: VERIFY SHAPE DEVIATION OF A SMOOTH CYLINDRICAL PART
IN HORIZONTAL AND VERTICAL CROSS SECTIONS
I. OBJECTIVE
- Be able to use a micrometer and a dial indicator.
- Be able to check the shape deviation of a smooth cylindrical part.
II. APPARATUS
- Granite surface plate
- V- block
- Micrometer
- Dial indicator
III. INTRODUCTION TO THE APPARATUS
Micrometer
Micrometer is a widely used apparatus in mechanical manufacturing factories. The
apparatus operates by turning rotary motion to linear motion by using a pair of threaded
screws. The measurement apparatus is made up of two parts including the fixed part (1)
and the moveable part (2).
Figure 1.1 Structure of a micrometer
The fixed part (1) has a sleeve scale (Fig. 1.1). The sleeve scale has two row scale
divisions,the upper scale is marked in 1mm interval, the lower scale is also marked like
the upperscale, but the mark of the lower scale is between the two marks of the upper
scale, the two row make up the sleeve scale with the interval of 0.5 mm, equal to the
pitch of the pair of screws. The moveable part (2) has the barrel scale with 50 divisions.
When it completes a rotation, it also moves linearly an interval equal to the pitch of the
1
screw (0.5 mm). Therefore, after a complete rotation the scale moves a length of 0.5mm.
The division on the scale is:
i=
0.5
= 0.01 mm
50
IV. PROCEDURE
1. Measure the shape deviation in the vertical cross section (Fig. 1.2)
Check the conicity, cylindricity, and curvature.
Figure 1.2 Diagram of measuring the shape deviation in the vertical cross section
Mark the position of the cross section to check I-I, II-II, III-III, the two cross section
I-I, III-III is 10mm away from the edge.
Put the part on the granite surface plate so that the dial indicator touches the part,
zeroing the gauge or read the value at point A (of cross section I-I), then slide the dial
indicator to point A of the cross section II-II and read the value from there. Slide the
gauge to point A of cross section III-III and read the value. Write the values into the
table. Mind that point A of the three cross section I-I, II-II, III-III must be on the same
generator line that is parallel to the center of the part.
Repeat the experiment for the other lines by turning the part an angle of 90° and 45°.
Table 1.1 Part number 6
Detail number
Generator line
1
Generator line
2
Generator line
3
Cross section I-I
Cross section II-II
Cross section III-III
AA’
AA’
AA’
BB’
CC’
0
BB’
CC’
0.07
0
0.07
0.07
2
CC’
0.08
0.07
0
BB’
0.07
2. Measure the shape deviation in the horizontal cross section (Fig. 1.3)
Measure the ovality
- Check the “zero” of the micrometer.
- Use the micrometer to measure the diameter AA’, BB’, CC’, DD’. Mind that
AA’ ⊥ BB’, CC’ ⊥ DD’.
(In each horizontal cross section, measure the diameter pair perpendicular to each
other).
Figure 1.3 Diagram of measuring the shape deviation in the horizontal cross section
Table 1.2 Part number 6
Part number
AA’
BB’
CC’
DD’
Cross section
I-I
27.97
27.97
28.01
28
Cross section
II-II
28.04
28.03
28.04
28.05
Cross section
III-III
28.03
28.03
28.03
28.03
∆𝑜𝑣𝑎𝑙= 𝑑𝑚𝑎𝑥 − 𝑑𝑚𝑖𝑛 (𝑎𝑡 𝑒𝑎𝑐ℎ 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛)
Measure the polygon type deviation
- Put the part on the V block and then put them on the granite surface plate.
- Put the dial indicator to touch the part at point 𝐴1 , after that rotate the part180° to
point 𝐴2, at the same time observe the value of the dial indicator at point 𝐴1 and 𝐴2, the
difference between the two values is ∆ℎ. The value ∆ℎ is not only dependent on the
number of sides of the part, but also depends on the 2𝜑 angle of the V-block.
- If 2𝜑 = 60°, the polygon type deviation:
3
Δ𝑐 =
Δℎ
3
- If 2𝜑 = 90° & 120°, the polygon type deviation:
Δ𝑐 =
Δℎ
2
Figure 1.4 Diagram of measuring the polygon type deviation
Table 1.3 Part number 6
Δℎ at each cross section
Detail number
Cross sections
I-I
II-II
III-III
A-A’
0
0.01
0.02
B-B’
0
0
0.02
C-C’
0
0
0.01
V. EVALUATE AND COMMENTS ON THE RESULTS
Measure the ovality
Section I-I:
∆𝑜𝑣𝑎𝑙 = 28.01 − 27.97 = 0.04
Section II-II:
∆𝑜𝑣𝑎𝑙 = 28.05 − 28.03 = 0.02
Section III-III:
∆𝑜𝑣𝑎𝑙 = 28.03 − 28.03 = 0
So, the part has the ovality level, and each section has a different value of ovality.
Measure the polygon type deviation
Section I-I:
4
∆𝑑𝑐 =
∆h 0.01 + 0.02
=
= 0.015
2
2
Section II-II:
∆𝑑𝑐 =
∆h 0.02
=
= 0.01
2
2
∆𝑑𝑐 =
∆h 0.01
=
= 0.005
2
2
Section III-III:
Therefore, the speciment is the polygon type deviation.
5
LAB 2: RADIAL AND FACE RUNOUT MEASUREMENT OF CYLINDRICAL
PART
I. OBJECTIVES
- Have knowledge of using a dial indicator and measurement jig.
- Know how to check the positional error of a cylindrical part.
II. OVERVIEW OF MEASURING INSTRUMENTS
A dial indicator is a type of mechanical measuring instrument that is widely used in
manufacturing, despite having some disadvantages compared to optical, electrical, or
pneumatic measuring devices. These disadvantages include lower accuracy due to the
presence of many mechanical transmission elements, which introduce backlash and
friction; decreasing reliability over time due to wear; a limited range of comparison; and
a higher likelihood of reading errors.
Figure 2.1 The structural diagram of a commonly used dial indicator with
an accuracy of 0.01 mm and a measuring range of 10 mm
The structural principle of the 0.01 mm dial indicator is illustrated in Figure 2.1. Shaft
number 1 is pulled downward by spring 2. The shaft has a rack of teeth along its body.
Gear shaft 4 is mounted with a small needle 3 (indicating millimeter values) and gear 9,
which has 100 teeth and meshes with gear 8, which has 10 teeth. On the shaft of gear 8,
the measuring needle 5 (indicating 0.01 mm values) is mounted. Therefore, when the
small needle 3 rotates 1/10 of a full turn (36 degrees), the measuring needle 5 completes
one full revolution (360 degrees). Gear 8 also meshes with gear 7, whose shaft is
connected to an Acximet spring 6. This spring continuously applies torque to ensure that
needle 5 follows the movement of shaft number 1.
6
III. PROCEDURE
The part to be checked according to Figure 2.2:
- Mount the part between the two center points.
- Place the gauge fixture on the edge of the table.
- Put the indicator in contact with the shaft surface or the end face to be tested.
- Rotate the part 360 degrees.
- Record the maximum and minimum values indicated during the full 360-degree
rotation.
Figure 2.2 Diagram of radial runout and face runout of the cylindrical part
IV. EXPERIMENT DATA
(part no.2, unit: mm)
Table 2.1
Part
Face runout
No. 2
max
min
Radial runout
Section 1
Section 2
Section 3
max
min
max
min
max
min
Trial 1
0.51
0
0.11
-0.02
0.03
-0.02
0.08
-0.02
Trial 2
0.52
0
0.1
-0.02
0.03
-0.01
0.07
0
Trial 3
0.53
0
0.11
-0.02
0.02
-0.02
0.09
-0.01
V. EVALUATION AND COMMENT ON MEASUREMENT RESULTS
Face runout:
∆1 = 𝑚𝑎𝑥1 − 𝑚𝑖𝑛1 = 0.51 − 0 = 0.51 (𝑚𝑚)
∆2 = 𝑚𝑎𝑥2 − 𝑚𝑖𝑛2 = 0.52 − 0 = 0.52 (𝑚𝑚)
∆3 = 𝑚𝑎𝑥3 − 𝑚𝑖𝑛3 = 0.53 − 0 = 0.53 (𝑚𝑚)
7
∆𝑡𝑏 =
∆1 + ∆2 + ∆3 0.51 + 0.52 + 0.53
=
= 0.52 (𝑚𝑚)
3
3
The required face runout tolerance for the part is 0.01 mm, but the actual measured
value is 0.52 mm; therefore, the part does not meet the requirement.
Radial runout (calculated as the average value of 3 measurements for 3 cross-sections:
∆𝑠𝑒𝑐𝑡𝑖𝑜𝑛1 = 0.13 (𝑚𝑚)
∆𝑠𝑒𝑐𝑡𝑖𝑜𝑛2 = 0.04 (𝑚𝑚)
∆𝑠𝑒𝑐𝑡𝑖𝑜𝑛3 = 0.09 (𝑚𝑚)
The required radial runout for the part is 0.01 mm. The actual measured values for
the three cross-sections are 0.13 mm, 0.04 mm, and 0.09 mm, respectively; therefore,
the part does not meet the requirement.
8
LAB 3: MEASUREMENT AND INSPECTION OFSTRAIGHTNESS,
FLATNESS, AND PERPENDICULARITY
I. OBJECTIVES
- Know how to measure and test straightness and flatness.
- Be able to determine straightness and flatness.
- Know how to check perpendicularity.
- Know how to use a dial indicator.
II. MEASURING INSTRUMENTS
- Surface plate
- Feeler gauge (range 0.05 – 1 mm)
- Precision straightedge
- Dial indicator fixture
- Set-square
- Dial indicator
III. INTRODUCTION OF THE MEASURING INSTRUMENTS
1. Dial indicator
(Figure 2.1)
2. Dial indicator fixture
Mount the dial indicator onto the holder (Figure 3.1).
Figure 3.1 Dial indicator fixture
IV. PROCEDURE
1. Checking the flatness and straightness
Rectangular part with dimensions (150 × 100 × 40) mm.
Method 1: using a precision straightedge.
- Place the straightedge along the edges or along the intersection lines of the surfaces
of the block (Fig. 3.2) and use a feeler gauge to check for any clearance between the
straightedge and the surface of the block.
9
Figure 3.2 Diagram for checking straightness and flatness using a feeler gauge
Method 2: using surface plate and dial indicator.
- Slide the dial indicator along the edges of the part to check for flatness (Fig. 3.3).
- Each surface is measured in six directions, and each direction is measured twice.
- Determine the flatness of the surface: flatness is defined as the maximum deviation
from a perfectly flat plane.
Figure 3.3 Diagram for checking straightness and flatness using suface plate
and dial indicator
2. Checking the perpendicularity
- The part to be inspected requires perpendicularity between its surfaces (Fig. 3.4).
Figure 3.4 The test part
- Perpendicularity is measured using a set-square and a feeler gauge to determine the
minimum and maximum gap ∆min, ∆max (Fig. 3.5). The measurement is performed
three times along each specified straight line segment (L = 50 mm) at different positions.
10
Figure 3.5 Checking perpendicularity using a square and feeler gauge
V. EXPERIMENT DATA
Part no.
202 (face 4)
Surface no.
Line
Precision straightedge
Straightness
and feeler gauge
Dial indicator
1
2
3
4
5
6
0
0
0
0
0.03
0.03
0.07
0.07
0.02
0.03
0.04
0.06
Precision straightedge
Flatness
0.03
and feeler gauge
0.07
Dial indicator
Face 2 perpendicular to face 1
Perpendiculatity
Feeler gauge and setsquare
Trial 1
Trial 2
∆max
∆min
∆max
∆min
∆max
∆min
0.04
0.03
0.1
0.03
0.16
0.04
Part no.
202 (face 2)
Surface no.
Line
Precision straightedge
Straightness
and feeler gauge
Dial indicator
1
2
3
4
5
6
0.07
0.07
0
0
0.06
0.07
0.02
0.03
0.08
0.1
0.03
0.06
Precision straightedge
Flatness
Trial 3
0.07
and feeler gauge
0.08
Dial indicator
Perpendiculatity
Face 3 perpendicular to face 1
11
Feeler gauge and setsquare
Trial 1
Trial 2
Trial 3
∆max
∆min
∆max
∆min
∆max
∆min
0.05
0.03
0.05
0.03
0.05
0.03
VI. RESULT EVALUATION
The straightness of the part is different.
The flatness of the plane is the greatest non-linearity.
The perpendicular:
(0.04 − 0.03) + (0.1 − 0.03) + (0.16 − 0.04)
= 0.07
3
(0.05 − 0.03) + (0.05 − 0.03) + (0.05 − 0.03)
∆2 =
= 0.02
3
∆1 =
The required perpendicularity of surface 2 with respect to surface 1 is 0.02 mm, but
the actual measured result is 0.06 mm; therefore, it does not meet the requirement. The
required perpendicularity of surface 3 with respect to surface 1 is 0.01 mm, but the actual
measured result is 0.02 mm; thus, it also fails to meet the requirement.
12
LAB 4: DETERMINATION OF SAMPLE SIZE
I. OBJECTIVE
- Be able to use round type dial gauge.
- Be able to use types of gauges.
- Be able to select and preserve the sample.
II. APPARATUS
- Round type dial gauge.
- Round type dial gauge holder with reference plane.
III. INTRODUCTION TO THE APPARATUS
1. Conception of measuring sample
Measuring sample is a type of part manufactured with high precision according to
certain nominal dimensions. Depending on the manufacturing accuracy achieved,
people are divided into precision levels 0, 1, 2, 3, ... Accuracy level decreases from 0÷3.
Common measurement patterns such as length samples, angle samples. Length gauges
are usually made in the form of triangular plates, quadrilaterals or polygons. These
samples are generally in the form of plates, so they are collectively referred to as plate
samples. Usually in production or called the plate sample as the template because
sometimes people use it to measure the gaps, the height dimensions are not convenient
because when it is necessary to measure the crankshaft, for example.
Measuring samples with two working faces, also called measuring faces, are
machined with high precision and low surface roughness: for samples with size ≤ 0.4
mm, the working surface needs to achieve 𝑅𝑧 = 0.063 𝜇𝑚 size samples >0.4 mm need
to reach 𝑅𝑧 = 0.032 𝜇𝑚.
The nominal size of the specimen measures the length of the perpendicular distance
between the two working faces of the specimen, measured at the center of the specimen.
The nominal size of the specimen is indicated on the non-working side of the specimen
for specimens larger than 5.5 mm. Samples less than 5.5 mm are marked on the work
surface.
The measuring sample is made of the high-quality alloy steel with the requirements
of thermal stability, anti-fouling, anti-rust. Allows fabrication of models ≤ 10mm in
length with hardened alloy steel.
13
Samples are made in sets. The long models come in sets of 122, 87, 42, 12 and 10
patterns, the angle models come in sets of 93, 33, and 24.
Uses of the gauges:
- Securing and transmitting dimensions from the unit of measure to the quantities to
be measured, For example, for testing and calibration of gauges and measuring
instruments, graduations for new machines.
- Used as the ‘0’ calibration for the gauge in the comparison measurement.
- Use direct measurement of dimensions requiring high accuracy.
- Use for precise marking or for cutter adjustment.
- Samples used for checking and grading instruments and meters are called reference
samples.
- Gauges used in routine measurement are called working samples.
2. Samples combination principle
Each gauge has only a certain size, usually only these dimensions do not satisfy the
required dimensions while measuring. In order to get the desired size, it is necessary to
proceed to stitch the existing samples together.
When grafting, it is necessary to wipe the sample clean, rub the two working sides
gently on each other. Due to the very high surface smoothness of the sample, the two
sides of the sample breathe into each other. To facilitate checking when matching
samples, large sizes need to be put down, first, numbers to turn to the left, small models
to be connected later, so that the dial is facing up. The more certain the composite sample
set, the more accurate the size of the gauge set.
The measuring sample also has an error called the test error, so the sample itself has
a systematic error, the more multiple samples in the sample set, the higher the
cumulative error. Therefore, the calculation of sample matching needs to be done to
minimize the number of samples.
In general, the number of composite samples should be less than 4 when using a set
of 87 samples and less than 5 when using a set of 42 samples.
How to calculate sample size:
Select in the sample box, the largest sample size that can satisfy the smallest odd digit
of the required size.
14
Take the difference between the required size and the selected sample size, we will
get the second required size. Continue selecting as stated in the two steps until the
required size is exhausted.
Example: Combination of sample size 28,786 in box of 87 samples:
Select:
I: 28.785-1.005=27.780
II:27.78-1.28=26.5
III:26.5-6.5=20
IV:20-20=0
3. Use and storage of measuring samples
- The measured sample after use should be washed with gasoline, alcohol, ether,
dried, then coated with a thin layer of neutral grease to prevent rust, then stored in a
sealed container, in a dry place. Samples that are not used frequently should be cleaned
once a month. When using samples to avoid collisions, a lot of friction for sample
matching reduces the accuracy and rust resistance of the samples. Absolutely avoid
touching the work surface of the specimen with your hand. Meanwhile, unused or
washed samples should be left on a soft cloth, or cotton or smooth paper to avoid
scratching the sample. Small samples need to be washed first, kept separate, do not put
large and small samples together to wash together will damage the small sample.
- When grafting samples, it is necessary to pay attention to dust, gently crush two
sample plates together, the sample will be attracted to each other, not strong, difficult to
match, may damage the surface of the sample.
- When the measurement is complete to separate all samples, gently push each plate
out. Avoid breaking the specimen apart by hand or forcefully peeling off individual
plates as this will result in a mutual force between the very smooth surface which will
cause blistering of the work surfaces.
- After removing the samples to be used from the box, the sample box should be
closed to avoid dust. Do not leave the sample in a place with high temperature such as
in the sun, under a lamp, next to an oven.
- A sample that meets the accuracy requirements should be used. No need to use highprecision sample boxes in common measurement, only used when there is a requirement
for high-accuracy measurement and verification.
15
IV. PROCEDURE
Details need to check the size according to Fig. 4.1.
Choose one of the 8 available specimens with the dimensions to be tested given in
the Table 4.1
1. Based on the size to be checked, combine the dimensions of the measured sample
so that it is the correct size to be checked. (level of accuracy of size 𝐴±0.04 ,
𝐵±0.05 , 𝐶±0.06).
Figure 4.1
2. Place the sample base on the counter clock (Figure 4.2)
Figure 4.2
3. Let the counter in contact with the size sample base. Read the odometer (or set ‘0’
for the meter)
4. Keep the dial in position, remove the sizing pad and place the part to be tested in
(Fig. 4.3). Read the indicator on the meter.
Figure 4.3
16
5. The only difference between two measurements is the error of the sample size
compared to the size to be checked.
Table 4.1
Size needs to verify
No.
A
B
C
1
69.847
60.158
50.129
2
69.678
59.947
49.926
3
69.872
60.277
50.141
4
69.864
59.980
50.065
5
69.963
59.679
49.738
6
69.860
60.022
50.060
7
69.781
59.758
49.999
8
70.001
59.876
50.008
V. EXPERIMENT RESULTS
Specimen 8
Table 4.2
No. 8
Errror
A
B
C
1
-0.12
- 0.05
- 0.26
2
- 0.11
- 0.06
- 0.25
3
- 0.10
- 0.04
- 0.24
4
- 0.12
- 0.05
- 0.25
5
- 0.11
- 0.05
- 0.26
Calculate sample size
A = 50 + 19 + 1.001
B = 50 + 6 + 1.8 + 1.07 + 1.006
C = 25 + 24 + 1.008
− 0.12 − 0.11 − 0.10 − 0.12 − 0.11
= −0.112
5
− 0.05 − 0.06 − 0.04 − 0.05 − 0.05
𝐵=
= −0.05
5
− 0.26 − 0.25 − 0.24 − 0.25 − 0.26
𝐶=
= −0.252
5
VI. REVIEW AND COMMENT THE RESULT
𝐴=
Specimen 8
Average error at A: −0.112 mm
17
Average error at B: −0.05 mm
Average error at C: −0.252 mm
We have level of accuracy of size 𝐴±0.04 , 𝐵±0.05 , 𝐶±0.06
=> Specimen 8 has only dimension B which is belong to allowable limit for deviation,
and dimensions A, C which is not belong to allowable limit for deviation.
Causes of errors:
- Measurement process: Due to the erection of the patterns, incorrect adjustment of
the meter,…
- Error due to tools.
18
LAB 5: MEASURING THE TAPER HOLE BY INDIRECT METHOD
I. OBJECTIVES
- Learn about the structure of the machine based on the principle of photo mechanics,
know how to apply external dimension measurement.
- Understand the principle of using ball bearings to measure tapered holes
II. MEASURING INSTRUMENTS
As a mechanical-optical gauge, it is used to measure straight dimensions (diameter,
length). The size of the measured part is equal to the difference between the two
readings corresponding to the position of the measuring head when in contact with the
work piece and the measuring table.
Figure 5.1
Structures according to the principle: ruler and size to be measured consecutively on
a straight axis. The structure of the machine includes transparent glass ruler 1 is clamped
hard along the measuring axis and covered with glass plate 2. The scale of the ruler
coincides with the direction of the measuring head. The scale interval is 1mm.
Figure 5.2
19
Ruler 1 is illuminated by light source 3 through light filter 4 and condenser 5. Light
from the ruler through objective lenses 6, prisms 7 and 8, focuses at the focal plane of
the objective lens for image of millimeter ruler. When measuring the measuring axis,
the ruler moves according to the dimensions to be measured. When the ruler moves, the
image also moves. Read the measurement results according to the main ruler 1 thanks
to the eyepiece microscope including the eyepiece 9 and the flat plate 10, 11 placed
close together. Flat plate 10 is fixed and carries a ruler 2 with 10 divisions, the value of
each line is 0.1mm. Flat plate 11 has a 3 rounds ruler with 100 divisions, the value of
each line is 0.001mm.
Figure 5.3 & 5.4
How to read the results:
After the measuring head is in contact with detail, through the eyepiece we see an
image of ruler 1, of which 1 line will be in the area of ruler 2, part of the ruler 3. The
vertical line corresponds to the value of the ruler.
The ruler value in the arc region is the whole millimeter part. Adjust the knob so that
the line is between the two lines corresponding to the measurement closest to it, which
is the tenth value. The measuring needle is located at one mark on the ruler, which is
the percentage and the thousandth value.
III. MEASURING TAPERED HOLE WITH SPHERICAL BALL
To determine the angle of the tapered hole, we can use the indirect method according
to the following picture.
20
Figure 5.5 Taper bore measurement diagram
In which:
ℎ1 , ℎ2 – size value from the top of ball to the standard face
𝐷, 𝑑 – diameter of the big and small ball
𝐿 – center distance of two balls
𝛼 – the tapered angle of details Formula of indirect method is:
𝛼 = arcsin
= arcsin
̅ − 𝑑̅
𝐷
2𝐿
̅ − 𝑑̅
𝐷
̅ − 𝑑̅
𝐷
2[(ℎ̅2 − ℎ̅1 ) − (
)]
2
̅ − 𝑑̅
𝐷
= arcsin
̅ − 𝑑̅ )
2(ℎ̅2 − ℎ̅1 ) − (𝐷
IV. PROCEDURE
1.Measure the size of each marble, determine D, d, (Each ball is measured 5 times)
𝜎𝐷 = √
̅)
∑5𝑖−1(𝐷𝑖 − 𝐷
𝑛−1
2. Place the part with the taper hole to be checked on the detail table of the gauge. Put
marble 1 in, drop the measuring head, read h1 (measured 5 times like that)
3. The same applies to the second marble.
4. Calculation of taper angle, data processing to calculate measurement method error.
𝛼 = arcsin
𝜎𝛼̅ = √𝜎𝐷2 (
̅ − 𝑑̅
𝐷
̅ − 𝑑̅
𝐷
2[(ℎ̅2 − ℎ̅1 ) − (
)]
2
𝜕𝛼 2
𝜕𝛼 2
𝜕𝛼 2
𝜕𝛼 2
2
2
2
) + 𝜎𝑑 ( ) + 𝜎ℎ1 (
) + 𝜎ℎ2 (
)
𝜕𝐷
𝜕𝑑
𝜕ℎ1
𝜕ℎ2
21
With:
ℎ̅2 − ℎ̅1
𝜕𝛼 1
= ×
𝜕𝐷 𝐿
𝜕𝛼
1
= ×
𝜕ℎ1 𝐿
𝜕𝛼
1
=− ×
𝜕𝑑
𝐿
̅ − 𝑑̅ )2
√4𝐿2 − (𝐷
̅ − 𝑑̅
𝐷
̅ − 𝑑̅ )
√4𝐿2 − (𝐷
ℎ̅2 − ℎ̅1
̅ − 𝑑̅ )2
√4𝐿2 − (𝐷
𝜕𝛼
1
=− ×
𝜕ℎ2
𝐿
2
̅ − 𝑑̅
𝐷
̅ − 𝑑̅ )
√4𝐿2 − (𝐷
2
Table 5.1
Parameters 1st
𝐷
𝑑
ℎ1
ℎ2
30.14
23.78
37.121
62.882
2nd
3rd
4th
5th
Average
30.14
23.77
37.071
62.837
30.15
23.77
37.111
62.846
30.15
23.77
37.091
62.857
30.14
23.78
37.123
62.861
30.144
23.774
37.1034
62.8566
̅ − 𝑑̅
𝐷
30.144 − 23.774
) = (62.8566 − 37.1034) − (
) = 22.5682
2
2
𝜕𝛼
𝜎𝐷 = 0.0055
= 0.0255
𝜕𝐷
𝜕𝛼
𝜎𝑑 = 0.0055
= −0.0255
𝜕𝑑
𝜕𝛼
𝜎ℎ1 = 0.0221
= 0.0063
𝜕ℎ1
𝐿 = (ℎ̅2 − ℎ̅1 ) − (
𝜕𝛼
= −0.0063
𝜕ℎ2
𝜎ℎ2 = 0.0170
̅ − 𝑑̅
𝐷
𝛼̅ = arcsin
̅ − 𝑑̅
𝐷
2[(ℎ̅2 − ℎ̅1 ) − (
)]
2
30.144 − 23.774
=
= 8.1131°
30.144 − 23.774
2[(62.8566 − 37.1034) − (
)]
2
𝜎𝛼̅ = √𝜎𝐷2 (
𝜕𝛼 2
𝜕𝛼 2
𝜕𝛼 2
𝜕𝛼 2
2
2
2
) + 𝜎𝑑 ( ) + 𝜎ℎ1 (
) + 𝜎ℎ2 (
) = 0.0003°
𝜕𝐷
𝜕𝑑
𝜕ℎ1
𝜕ℎ2
22
V. RESULT OF THE EXPERIMENT
𝛼 = 𝛼̅ ± 𝜎𝛼̅ = 8.1131° ± 0.0003°
VI. COMMENT
The measurement results are relatively accurate due to the following factors:
- The ball’s diameter is measured using a micrometer with a precision of 0.01 mm.
- A dynamometer with an accuracy of 0.001 mm is used, and the dimensions ℎ1 and
ℎ2 are measured accurately to the nearest millimeter.
However, some errors arise from the indirect method used to determine the hole’s
inclined angle. This method relies on direct measurements of the parameters 𝐷, 𝑑, ℎ1,
and ℎ2, which introduces potential errors during the measurement process. Additionally,
rounding errors in the calculation formulas also contribute to the overall measurement
error.
23
LAB 6: MEASURE THE GEAR RUNOUT
I. OBJECTIVE
- Know how to measure the radial runout in general on the basis of measuring the
gear run.
- It is one of the important factors in the kinematic accuracy of the gears.
- Know how to handle the measuring head when encountering complex surfaces.
II. APPARATUS
- Gear m=2÷3, z=20÷25.
- Round type dial gauge 0.01 mm.
- Clock fixture.
- Table top.
- Center jig.
- A grinding mandrel has an ovality of 0.005 and is fitted with a gear hole.
- An appropriately sized roller.
III. PROCEDURE
1. Diagram Measurement
Figure 6.1 Diagram measurement of gear runout
2. Method
- Select the roller with a diameter such that its contact with the tooth profile is at the
engagement line. Roller length is about 3 times its diameter for stability when placed in
tooth groove.
- Place the roller in any slot.
- Place the meter relative to the blade gauge (easier to measure) at the center of the
mandrel.
24
- Gently rotate the mandrel around the gauge head and record the highest reading as
𝑅𝑖 .
- Repeat for each track to the end of the gear circumference.
Table 6.1
Order
R
Order
R
1
0
14
0
2
-0.03
15
0.02
3
-0.04
16
0.05
4
-0.07
17
0.04
5
0.02
18
0.06
6
-0.08
19
0.07
7
-0.06
20
0.06
8
-0.03
21
0.07
9
-0.01
22
0.06
10
-0.02
23
0.07
11
0
24
0.07
12
0.02
25
0.03
13
0.01
26
0.03
IV. EVALUATE
The gear runout:
V. COMMENT
𝑅𝑚𝑎𝑥 = 0.07𝑚𝑚
𝑅𝑚𝑖𝑛 = −0.08 𝑚𝑚
𝑅𝑚𝑎𝑥 − 𝑅𝑚𝑖𝑛 = 0.07 − (−0.08) = 0.15
- The gear radial runout is used to evaluate the kinematic accuracy of the gear.
- The accuracy of the measurement depends on the selection of the roller. The center
of the roller needs to be on the gear ring to be accurate.
- The gear runout error is not significant. Half of the gear error is half up, the other
half down.
25
LAB 7: MEASURE GENERAL NORMAL LENGTH
I. OBJECTIVE
- Know how to use the micrometer to measure the length of normal.
- Know how to determine the length of normal.
II. GENERAL INTRODUCTION OF PRINCIPLES
The oscillation of the normal length Δ0 L is the difference between the biggest and the
smallest length of general normal on different positions of the tooth ring.
Figure 7.1 Structural diagram of the tooth ring
Based on the definition of the general normal length, its value is equal to AB arc
length, which is L = AB.
If we call n is the gear tooth in the 𝐿 length, the formula to calculate the general
normal length is:
L = m × cos α [(n − 0.5)π + Zθ + 2ξtgα]
With:
𝑚 – gear module; 𝛼 – pressure angle (𝛼 = 20°) Z – quantity of teeth
𝜃 = 𝑡𝑔𝛼 – choose 𝛼 = 20°
𝜉 – the coefficient of correction, generally choose 𝜉 = 0
𝑛 – quantity of teeth in general normal length base on approximate formula:
𝑛 = 0.111𝑍 + 0.5
III. PROCEDURE
Choose one of the gears in the table 7.1:
Table 7.1 (Choose No.4)
No.
Number
Module
1
1
1
2
2,4,8
2
3
3
3
26
Note
4
26
1,5
5
7
1,8
6
65
2,5
Number
1
2
3
4
5
11.61
11.57
11.62
11.54
11.58
Average value:
11.61 + 11.57 + 11.62 + 11.54 + 11.58
= 11.584 𝑚𝑚
5
IV. EVALUATE AND REVIEW THE RESULT
𝐿𝑎𝑐𝑡𝑢𝑎𝑙 =
The real general normal length:
𝐿 = 𝑚 × 𝑐𝑜𝑠 𝛼 [(𝑛 − 0.5)𝜋 + 𝑍𝜃 + 2𝜉𝑡𝑔𝛼]
With:
𝑚 = 1.5
𝑍 = 26
𝜃 = 𝑡𝑔𝛼 − 𝛼(𝑐ℎ𝑜𝑜𝑠𝑒 𝛼 = 20°) → 𝜃 = 𝑡𝑔20 −
20𝜋
= 0.0149
180
𝜉 = 0
𝑛 = 0.111𝑍 + 0.5 = 0.111 × 26 + 0.5 = 3.386 ≈ 3 𝑡𝑒𝑒𝑡ℎ
Therefore:
𝐿 = 1.5 × 𝑐𝑜𝑠20 [(3 − 0.5)𝜋 + 26𝜃 + 26 × 0.0149 + 2 × 1 × 𝑡𝑔20] = 11.6165
Difference between the titular and the real general normal length after the
measurement
𝛥𝐿 = 𝐿 − 𝐿
𝑎𝑐𝑡𝑢𝑎𝑙
= 11.6165 − 11.584 = 0.0325 𝑚𝑚
V. COMMENT
The result is approximately correct because:
- Using the proper micrometer which has high precision.
- The measurement is conducted based on Abbe rule.
Tolerance of general normal length oscillation is used to review the precision of gear
kinematics.
27
LAB 8: SURVEY THE CHARACTERISTICS OF DYNAMOMETER BASED
ON PRINCIPLE OF DEFORMATION
I. OBJECTIVE
- Understand the characteristics and structure of the ring dynamometer type strain
measuring instrument.
- Construct a reversible characteristic curve and the relationship between load and
displacement of the tool.
II. APPARATUS
- 0.01mm type dial indicator attached to strain gauge.
- Deformable ring type 50 kg.
- Scale force to load (0 - 160) kg.
Figure 8.1 Structural diagram of the ring dynamometer type strain gauge
III. PROCEDURE
- Place the dial indicator in the bracket of the dynamometer ring, install the support
so that the measuring head contacts the measuring head of the meter. Adjust and create
initial force.
- Place the strain gauge on the force scale, use the crank to create a preliminary
stabilizing force, and adjust the dial indicator to 0.
Slowly increase the applied force by 10kg, 20kg, ...100kg. At each level, stop reading
the displacement results of the dial indicator, then slowly reduce the force in the opposite
direction at each level of 100kg, 90kg, ...10kg.
The values are recorded in table 8.1.
28
Table 8.1
Direction of force increase
No.
Force
level
Direction of force decrease
Dial indicator (0.01mm)
Force
level
Dial indicator (0.01mm)
(Kg)
1st
2nd
3rd
(Kg)
1st
2nd
3rd
1
10
0
0
0
10
0
0
0
2
20
0.03
0.03
0.03
20
0.03
0.03
0.03
3
30
0.05
0.05
0.05
30
0.05
0.05
0.05
4
40
0.07
0.07
0.08
40
0.08
0.08
0.08
5
50
0.1
0.1
0.1
50
0.1
0.1
0.1
6
60
0.12
0.12
0.12
60
0.12
0.12
0.12
7
70
0.14
0.14
0.14
70
0.14
0.15
0.15
8
80
0.16
0.17
0.17
80
0.17
0.17
0.17
9
90
0.19
0.19
0.19
90
0.19
0.19
0.19
10
100
0.21
0.21
0.21
100
0.21
0.21
0.21
Which:
- P is the force (N)
- J is stiffness of the system (Deformation ring) (N/mm)
- y is the displacement (Elasticity) (mm)
We have the formula related to the hypothesis of working within the proportional
limit is as follows:
𝑦=
𝑃
𝐽
or
𝐽=
𝑃
𝑦
IV. REPORT
Constructing the forward and reverse deformation curves
29
Figure 8.1 Graph of forward and reverse deformation curves
Comment
- The forward curve appears to be approximately linear and can be considered as a
first-order relationship. This indicates that the deformation is proportional to the applied
force — as the force increases, the deformation increases correspondingly.
- Similarly, the reverse curve also follows an approximately linear trend, showing that
as the applied force decreases, the deformation reduces accordingly.
- However, the two curves do not overlap, which means there is a deviation between
the increasing force and decreasing force processes. This suggests that the deformation
behavior during the increase and decrease of force is not identical.
Reason
- During the force increasing phase, this deviation is not observed because the
deformation occurs in sequence — the front part (smaller deformation) reacts first,
followed by the rear part. There is no additional deformation margin introduced in this
process.
- In contrast, during the force decreasing phase, to minimize the deviation, it is
recommended to pause briefly before taking a reading on the dial indicator. This waiting
period allows the object to recover elastically, eliminating the influence of residual
deformation from the previous loading.
- Hardness of the deformation ring:
𝑃
𝑦
- In this experiment, the actual deformation of the deformation ring has been
𝐽=
amplified by a mechanical amplification system before being measured with the dial
30
indicator. As a result, in order to accurately calculate the stiffness (hardness) using the
formula above, it is necessary to know the amplification factor of the mechanism. Since
this factor is unknown, it is not possible to determine the exact stiffness of the
deformation ring.
31
LAB 10: MEARSURE DEFORMATION USING STRAIN GAUGE
Figure 10.1 Experimental model
I. OBJECTIVE
- Learn how to use strain gages to measure strain.
- Learn about the Wheatstone bridge circuit used with strain gages.
II. INSTRUMENTS
- Aluminum cantilever beam (Figure 10.1) with strain gages mounted at fixed
positions to simulate load-bearing structure.
- Weights (with marked values), rulers, calipers.
- Test board, resistors, DC power supply.
- Multimeter.
III. WHEATSTONE BRIDGE CIRCUIT
Since dR/R is very small and hard to measure directly, we use the Wheatstone bridge
to detect resistance changes.
Figure 10.2 Wheatstone Bridge Circuit
The potential difference 𝑉0 is calculated as follow:
𝑅 𝑅 −𝑅 𝑅
𝑉0 = 𝑉𝑠 (𝑅 3 1)(𝑅4 2 )
2 +𝑅3
(10.1)
1 +𝑅3
32
When the circuit is balanced (𝑉0 = 0) from (10.7), we have:
𝑅
𝑅4
𝑅2
𝑅3
𝑅3 𝑅1 = 𝑅4 𝑅2 or 1 =
For simplicity, assume 𝑅1 = 𝑅2 = 𝑅3 = 𝑅4
Relationship between change value in resistance 𝑑𝑅𝑖 and potential difference 𝑉𝑜:
𝑑𝑉0 =
𝜕𝑉0
𝜕𝑅1
𝑑𝑅1 +
𝜕𝑉0
𝜕𝑉0
𝑑𝑅2 +
𝜕𝑅2
𝜕𝑅3
𝑑𝑅3 +
𝜕𝑉0
𝜕𝑅4
(10.2)
𝑑𝑅4
Taking partial derivatives of equation (10.2) , we have:
𝑅 𝑅
𝑑𝑅1
1 +𝑅2
𝑅1
𝑑𝑉0 = [(𝑅 1 2 )2 (
−
𝑑𝑅2
𝑅2
𝑅 𝑅
𝑑𝑅3
3 +𝑅4
𝑅3
) + (𝑅 3 4 )2 (
−
𝑑𝑅4
𝑅4
)] 𝑉𝑠
(10.3)
With the condition for a balanced circuit, the equation (10.3) is rewritten as:
1 𝑑𝑅1
𝑑𝑉0 = [
4
𝑅1
−
𝑑𝑅2
𝑅2
+
𝑑𝑅3
𝑅3
−
𝑑𝑅4
𝑅4
] 𝑉𝑠
(10.4)
From (10.4), we have:
𝑆
(10.5)
𝑑𝑉0 = [𝜀1 − 𝜀2 + 𝜀3 − 𝜀4 ]𝑉𝑠
4
Because the Wheatstone bridge is balanced at the start, (10.5) is equivalent to:
𝑆
(10.6)
𝑉0 = [𝜀1 − 𝜀2 + 𝜀3 − 𝜀4 ]𝑉𝑠
4
This is the basic equation showing the relationship between the potential difference
of the Wheatstone bridge and the deformation of the strain gauge.
Using strain gauge and Wheatstone bridge to measure the deformation.
a. Bridge circuit with 1 strain gauge
Strain gauge is put at any branch in the bridge circuit, the other 3 resistors are fixed.
In figure 10.3, strain gauge replaces by 𝑅3.
Figure 10.3 Bridge circuit with 1 strain gauge
From (10.6), we can consider:
33
𝑆
(10.7)
𝑉0 = [𝜀𝑎 ]𝑉𝑠
4
b. Bridge circuit with two strain gauge
In a bridge circuit with two strain gauges, the two strain gauge is put at 2 branches of
the circuit, the other resistors are fixed. In figure 10.4, two strain gauges replacing 𝑅1,
𝑅3(𝑎) 𝑜𝑟 𝑅1, 𝑅2(𝑏).
Figure 10.4 Bridge circuit with 2 strain gauge
𝑆
(10.8a)
𝑉0 = [𝜀1 + 𝜀3 ]𝑉𝑠
4
𝑆
(10.8b)
𝑉0 = [𝜀1 − 𝜀2 ]𝑉𝑠
4
IV. BAR WITH ONE FIXED END
1. Relationship between force, stress, and deformation
𝜎𝑎 =
𝐹
(10.9)
𝐴
From the formula (10.9) we can know the force from the stress value, but it very hard
to measure directly so we have to use the relative deformation 𝜀𝑎
(10.10)
𝜎𝑎 = 𝐸𝜀𝑎
One way to find relative deformation is using the strain gauge.
2. Experimental model
The model is build based upon the problem of a fixed end beam. Two strain gauges
are put on top and bottom surface of the beam. When there is a force the strain gauge on
top will be stretched and the bottom strain gauge will be compressed.
34
Figure 10.5
Following strength:
𝑀.𝑐
𝜎𝑎 =
𝐼
=
𝐹.𝐿.𝑐
𝐼
(10.11)
= 𝐸𝜀𝑎
With c is the distance of strain gauge to the neutral plane) and I is moment of inertia:
𝑐=
𝐼=
ℎ
(10.12)
2
𝐵.ℎ 3
(10.13)
12
3. Strain gauge (tension variable resistor)
Resistor of the strain gauge change when the strain gage is deformed, the relationship
can be written as:
𝑑𝑅
𝑅
(10.14)
= 𝑆𝜀𝑎
S – Variation coefficient
In the experiment strain gauge has 𝑅 = 120,0 ± 0.3% (𝑂ℎ𝑚)
V. HOLLOW TUBE WITH ONE FIXED END
Theory
Normal stress caused by bending moment:
𝜎=
𝑀𝑐
(10.15)
𝐼
In which:
M: Bending moment where stress need to be identified.
c: The distance from the neutral axis to where stress needs to be identified.
I: Moment of inertia (=
𝜋𝑟04
4
−
𝜋𝑟𝑖4
4
)
Shear stress caused by shear force:
35
𝜏=
𝑄𝑦 𝑆 𝑐
(10.16)
𝐼𝑥 𝑏𝑐
In which:
𝑄𝑦: shear force
𝑆𝑐: static moment of area of the cross section
𝑏𝑐: Thickness of cross section
Torsional stress:
𝜏=
𝑇
(10.17)
𝑊
In which :
T: torque where stress need to be identified
W: Polar modulus of section (=
𝜋
16
𝑑
𝐷 3 (1 − η4 )) với (η = )
𝐷
The pair Pl causes torsional stress at every point on the surface of the hollow shaft.
(H.10.6a)
Load P causes maximum normal stress at B and compression stress at any points
symmetrical to B.
Load P also causes maximum shear stress on the yz plane.
Figure 10.6 Installed position of strain gauge A,B
36
Any of the above stress is maximum at some points on the area of the surface of the
fixed end. So, we need to identify the position of the cross sections of the tube. Figure
10.7 show the state of the stress at A and B.
Figure 10.7 Stress distribution diagram at locations A and B
Shear and torsional stress will be in the same direction on the right of the shaft and
opposite direction on the left of the shaft. Normal stress at is 0 because it is on the neutral
plane. As a result, at A will cause the maximum stress is the combination of the two
stresses. Consequently, the maximum stress at A is the total 2 of the above stresses.
𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛 & 𝑠ℎ𝑒𝑎𝑟 =
𝑇
𝑊
+
𝑄𝑦 𝑆 𝑐
(10.18)
𝐼𝑥 𝑏𝑐
At point B normal stress is maximum because of equation 1.
The SG rosette at point A and B of the sample.
With the SG structure like 10.6c we can see the relationship between stress and
deformation like this:
Figure 10.8 Strain gauge rosette
The relationship between stress and force of the middle SG:
The relationship between stress and force of the side SG:
𝜀𝑎 = 𝜀45 =
𝜀𝑎 = 𝜀45 =
𝜀𝑥 +𝜀𝑦
2
𝜀𝑥 +𝜀𝑦
2
+
+
𝛾𝑥𝑦
2
𝛾𝑥𝑦
2
sin(2 × 45𝑜 ) =
𝜀𝑥 +𝜀𝑦
2
sin(2 × (−45𝑜 )) =
+
𝜀𝑥 +𝜀𝑦
2
Relationship between stress and deformation at B:
37
𝛾𝑥𝑦
(10.19)
2
+
𝛾𝑥𝑦
2
(10.20)
𝛾𝑥𝑦 =
𝜏𝑥𝑦
𝐺
=
𝑇
(10.21)
𝑊𝐺
At A we also stick the same SG but because there is no normal stress so the
deformation along the x axis value is equal to 0. The other two SG also give out the
value like the 2 equations above.
Relationship between the stress and shear deformation at A:
𝛾𝑥𝑦 =
𝜏𝑥𝑦
𝐺
=
𝑐
𝑇 𝑄𝑦 𝑆
+
𝑐
𝑊 𝐼𝑥 𝑏
(10.22)
𝐺
When we know the shear stress, we will calculate the shear deformation from Hooke’s
equation:
(10.23)
𝜏𝑥𝑦 = 𝛾𝑥𝑦 . 𝐺
And normal stress will be identified as follow:
𝜎𝑥 =
𝜎𝑦 =
𝐸
1−𝑣 2
𝐸
1−𝑣 2
(𝜀𝑥 + 𝑣𝜀𝑦 )
(10.24)
(𝜀𝑦 + 𝑣𝜀𝑥 )
(10.25)
With single shaft normal stress, we have: 𝜀𝑦 = −𝑣𝜀𝑥
VI. PROCEDURE
Figure 10.9 Circuit due to deformation using strain gauge
Using the resistors, test board, and DC power source, the aluminum bar with strain
gauge, students build the Wheatstone bridge.
38
Figure 10.10 Diagram due to deformation using strain gauge
Write down the value of potential difference when there is no weight 𝑉𝑟𝑒𝑓 = 0.46
(𝑚𝑉)
Put the weight on the structure and read the value of potential difference 𝑉𝑟𝑒𝑎𝑑 and
write them in the table:
VII. RESULT TABLE
Table 10.1
Bridge circuit with 2 strain gauge
No.
Potential difference
Mass
𝑉𝑟𝑒𝑎𝑑 (mV)
M (kg)
1
0.56 (mV)
0.1 (kg)
2
0.71 (mV)
0.25 (kg)
3
1.02 (mV)
0.58 (kg)
4
1.36 (mV)
0.93 (kg)
5
0.9 (mV)
0.45 (kg)
6
1.04 (mV)
0.6 (kg)
7
1.99 (mV)
1.58 (kg)
8
2.41 (mV)
2.01 (kg)
VIII. REPORT
1. Describe the relationship between the mass applied to the free end and the voltage
𝑉0 = 𝑉𝑟𝑒𝑎𝑑 − 𝑉𝑟𝑒𝑓
39
Answer:
There is a nearly linear relationship between the applied mass and the output voltage
𝑉0. As the mass increases, the strain in the beam increases proportionally, which changes
the resistance in the strain gauge. This causes a change in the bridge output voltage that
is proportional to the applied load.
2. Comment on the relationship between mass and output voltage
Answer:
The voltage increases with the mass in a relatively linear manner, indicating good
sensitivity and responsiveness of the system. However, small deviations may occur due
to equipment errors, environmental disturbances, or resolution limits of the measuring
device.
3. Explain the instability (if any) of the Wheatstone bridge output voltage during the
experiment. Suggest ways to reduce the instability.
Answer:
Instability may arise from:
- Fluctuations in power supply voltage.
- Temperature effects on resistance.
- Mechanical vibration.
- Poor contact in the circuit.
Solutions:
- Use a stabilized DC power source.
- Ensure proper wiring and tight connections.
- Perform experiments in a stable temperature environment.
- Use shielding to reduce noise.
40
4. Explain the operating principle of the deformation measurement circuit using strain
gauge in Figure 10.5
Answer:
When a load is applied to the cantilever beam, it bends, causing strain on the surface.
Strain gauges mounted on the top and bottom measure tensile and compressive strains,
respectively. These strains change the resistance of the strain gauges, which unbalances
the Wheatstone bridge and causes a measurable output voltage.
41
LAB 11: MAKING A DRAWING FROM A SAMPLE
I. OBJECTIVE
- Know how to make a drawing from the available sample.
- Know how to use measuring instruments.
II. APPARATUS
- Vernier caliper with a precision of 0.02 mm
- Height gauge.
- Each student measure only one of the three available details: piston, connecting rod,
cube.
III. PROCEDURE
- Check if the available measurements are enough to draw the detail? (There is a
chance the required measurements are missing).
- Measure all the required measurements to show them in the drawing
Figure 11.1 Connecting rod structure
Figure 11.2 Piston structure
42
Figure 11.3 Cube structure
IV. REPORT
Figure 11.4 Specimen dimension
In the measurements, which one is important, why?
43
In the set of measurements taken, the diameter of the holes is the most critical
dimension. This is because it directly affects the fit tolerance of the joint and ensures the
correct positioning of the hole’s center, which is essential for mechanical alignment and
assembly precision.
Which measurements is identified through indirect ways, talk about how to do
Among the measured values, one dimension is determined indirectlythat is, the
distance from the edge of the cube to the center of the hole. To obtain this value, the
following method is used:
First, the diameter of hole (d₁) is measured. Then, the distance from the edge of the
cube to the nearest edge of the hole is measured (d₂). Using these two measurements,
the final required distance (d₃) from the cube’s edge to the hole center is calculated using
the formula:
𝑑3 =
𝑑1
+ 𝑑2
2
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LAB 13: SURVEY THE HEAT MEASUREMENT SYSTEM
I. OBJECTIVE
- Learn about the element of heat measurement system.
- Know some calculation content about heat measurement system.
II. APPARATUS
- Temperature control system.
- Liquid-in-glass thermometer.
- Heating ring.
- Metal block evenly heats and places thermocouple, liquid thermometer.
- Oscilloscope.
Figure 13.1 The temperature measurement and control system
III. PROCEDURE
- Turn on the heat ring power switch to heat.
- As the temperature of the metal block increases, record the temperature by reading
the value on the liquid thermometer and record the voltage value of the thermocouple
by Oscilloscope. Numerical values are recorded in Table 13.1.
- When the temperature rises to about 300 oC, stop heating, the temperature of the
metal block will gradually decrease, recording the temperature and voltage of the
temperature reduction process.
IV. EXPERIMENT RESULTS
45
Table 13.1
Voltage
Voltage
in ↑
in ↓
direction
direction
(mV)
(mV)
153
4.87
165
162
3
175
4
Time
Time
in ↑
in ↓
direction
direction
5.13
0
917s
5.29
5.55
60s
718s
173
5.65
5.93
123s
560s
185
183
6.06
6.36
193s
406s
5
195
193
6.44
6.76
261s
288s
6
205
202
6.84
7.14
333s
186s
7
215
212
7.24
7.54
411s
88s
8
225
223
7.66
7.83
496s
0
Thermal
Metal
resistor
core
(oC)
(oC)
1
155
2
No.
V. REVIEW AND COMMENT THE RESULTS
Figure 13.2 The temperature versus voltage graph
Comment:
2 curves are almost straight lines.
46
The value of voltage when the increased temperature is difference from the value of
voltage when the decreased temperature.
Characteristic curve equation:
When temperature increases:
∆𝑇 = 3.9 − 0.18𝑣 + 0.0039𝑣2 − 3.7𝑒 − 0.5𝑣3 + 2.03𝑒 − 0.7𝑣4 − 6.5𝑒 − 10𝑣5
+ 1.13𝑒 − 12𝑣6 − 8.3𝑒 − 16𝑣7
When temperature decreases:
∆𝑇 = 1.01 − 0.07𝑣 + 0.0022𝑣2 − 2.43𝑒 − 0.5𝑣3 + 1.5𝑒 − 0.7𝑣4 − 6.5𝑒 − 10𝑣5 +
1.1𝑒 − 12𝑣6 − 8.5𝑒 − 16𝑣7
47
REFERENCES
1. T.T.Thu Hà (2010), “Hướng dẫn thí nghiệm kỹ thuật đo lường cơ khí”, NXB Đại
học Quốc gia TP Hồ Chí Minh, Hồ Chí Minh.
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