fall 1433h (2012g) saturday, monday & wednesday...
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Metrology & Quality Control
Fall 1433H (2012G)
Saturday, Monday & Wednesday 11:00am -
11:50am and Saturday 13:00am - 14:50pm
MENG 436 Class FA
Dr. Walid A. AissaDr. Walid A. Aissa
Associate Professor, Mech. Engg. Dept.
Faculty of Engineering at Rabigh, KAU, KSA
Chapter #4
September XX, 2012
Announcements:
Dr. Walid’s e-mail and Office Hours
Office hours for Metrology & Quality Control will be
every Sunday and Tuesday from 11:00 – 13:00 am in Dr.
Walid’s office (Room 5-109).
Text book:Text book:
1-Metrology for Engineers, J.F.W. Galyer & C. R.
Shotbolt, 4th Edition, Cassell Ltd., London, ISBN-0-
304 30612 6, 1980.
2-Essentials of Quality With Cases and
Experimental Exercises, Victor E. Sower, John Wiley
& Sons Inc., London, ISBN-978-0-470-50959-3, 2011.
Chapter 4ANGULAR MEASUREMENTS
Objectives of CH4: To
• Recognize
- Plate Protractor.
- Combination Squares.
- Universal Bevel Protractor.- Universal Bevel Protractor.
- Sine Bar.
4. ANGULAR MEASUREMENTS
4.1. General :
Chapter 4
It is well known that the quality of workpieces
depends greatly on precise measurement of
workpieces and cutting tools.workpieces and cutting tools.
Angles are considered one of most important
characteristics of workpieces and cutting tools.
Hence, knowledge of angle measurement is an
important task for workshop and quality
personnel.
Angle ACB is defined as the intersection between
the lines AC and BC.
4.2. Some of General Concepts:
Unit of angle is degrees (°°°°).
1 degree (°°°°) = 60 minutes (′′′′), 1 minute (′′′′) = 60
seconds (′′′′′′′′)
Hence,
1 degree (°°°°) = 60 minutes (′′′′) = 3600 seconds (′′′′′′′′)
Circle is divided to 360 division. Closed circle is
defined as complete angle and it equals 360°°°°.
If the angle equals 90°°°°, it is called right angle.
If the angle is lower than 90°°°°, it is called acute angle.
If the angle is bigger than 90°°°°, it is called obtuse angle.
4.3. Some Techniques for Angle Measurement:
4.3.1. Plate Protractor
Protractor is the simplest device used to measure
the angles of workpieces and cutting tools. It
is graded from 0 to 180 degrees, provided
with measuring arm which rotates relative to
protractor pivot. Pointer; at the end of the
Plate Protractor for Angle Measurement
protractor pivot. Pointer; at the end of the
arm, is used to specify the protractor reading.
Plate protractor is used for measurement of angles of
workpieces, external angles, slopes, drill angles, marking,
….etc.
4.3.2. Combination Squares (used for marking
angles, square and level)
Combination Squares
The blade (steel rule) is designed to allow the different
heads to slide along the blade and be clamped at any
desired location. By removing all the heads, the blade may
be used alone as a rule or a straight edge. This tool, with its
attachments, may be used for a great many purposes in
framing and general work.
The blade can be used as a rule or a straight edge by itself The blade can be used as a rule or a straight edge by itself
or with any one of the following components.
It is usually twelve inches long (though sometimes
combination squares have rules up to twenty-four inches in
length), with a headpiece that slides along its length.
A knurled nut and set screw are used to fix the headpiece to
the rule at any point along its length, depending upon the
The square head is designed with a 45 and 90 edge, which
makes it possible to be used as a try square and miter
square. It may also be used as a height or depth gage. The
square head is also fitted with a level vial and a removable
scriber
the rule at any point along its length, depending upon the
purpose to be served
There is a spirit (bubble) level in its handle, so the
combination square can be used for leveling. Some
models even have a scribe in the handle.
1/4
Various uses of
the combination
square:
2/4
Laying out parallel lines with
a combination square
3/4
The center head can be used to locate and
lay out the exact center of round stock
The protractor head
can be used to mark
off or measure any
angle through 180.
Angular graduations
4/4
Angular graduations
usually read from 0
to 180 degrees both
ways, permitting the
supplement of the
angle to be read.
4.3.3. Universal Bevel Protractor:
(a) Schematic illustration of a bevel protractor for
measuring angles.
Universal Bevel Protractor is the most accurate device
for angle measurement of workpieces and cutting
tools in workshops and labs.
Its accuracy reaches 1/12 °°°° (= 5′′′′).
The angle to be measured is put between blade and
acute angle attachment in the case of acute angle
measurement or and fixed surface in the case of
obtuse angle measurement.
Obtuse angle measurement.Acute angle
measurement.
Example 4-1:
Vernier for angular measurement, indicating 15°.
Example 4-2:
4.3.4. Sine Bar (Angle Measurement)
Setup showing the use of a sine bar for precision measurement of workpiece angles.
Example 4-3:
Calculate the angle of taper if the sine bar length is 120 mm and the required slip gage pile is 57.567 mm and 12.545. The radius of balls is 10 mm.
57.5
67+
10.0
-
10.0
+12.5
45=
70.1
12 m
m
Solution:
57
10
Sin θ = 70.112 mm/140.0 mm = 0.5008
Hence, θ = 30.0 °
θ
Example 4-4:
Find the cone taper angle; α (= 2θ )
S1= 5 mm, S2= 30 mm, M1= 55.4174 mm, M2= 75.3086 mm.
(α)
Tan (θ) = (M2-M1)/[2*(S2-S1)] = (75.3086 - 55.4174)
/[2*(30 - 5)]= 0.397824
Hence, θ = 21.685 °
Hence, α = 2θ = 43.37 °= 43° 22′
q
Experiment (2): Evaluation of semi-taper angle; q:
C1 C1
C2AC2A
AC1 = S - r + r = S
AC2 = [(M1 + 2r)- (M2 + 2r)]/2= (M1-M2)/2
Tan q = AC2/AC1= [(M1- M2)/2]/S= (M1-M2)/2S
Hence, Semi-taper angle; q = Tan-1 (M1-M2)/2s
Example 4-5:
Find the cone taper angle; α (= 2q )
S= 50 mm, M1= 29.3086 mm, M2= 15.4174 mm.
Solution:
Semi-taper angle; q = Tan-1 (M1-M2)/2s
= Tan-1 (29.3086 - 15.4174)/(2* 50)
=Tan-1 (0.138912) = 7.9°
Hence; αααα = 2*q = 2* 7.9°= 15.8° = 15° 48′
M1
; θ :-
M2
θ
r1
r2
M2
r1
r1-r2
M1
M2
θ L
r2
L = (M2-M1)- r1+r2= (M2-M1)-
(r1-r2)
θ
Sin θ = (r1-r2)/L
Hence, Sin θ = (r1-r2)/[(M2-M1)-(r1-r2)]
i.e., Sin θ = 1/ (k-1)
where, k = (M2-M1)/(r1-r2)
Example 4-6:
Find the cone taper angle; α (= 2θ )
r1= 7.5 mm, r2= 5.0 mm, M1= 13.4174 mm, M2= 38.3086 mm.
Solution:
Semi-taper angle; θ = Sin-1 1/ (k-1)
where, k = (M2-M1)/(r1-r2)
k = (38.3086-13.4174)/(7.5-5.0) = 9.95648
θ = Sin-1 [1/ (k-1)] = Sin-1 1/ (k-1)=
Hence; αααα = 2* θ = 2* 6.4° = 12.8°
θ = Sin-1 [1/ (k-1)] = Sin-1 1/ (k-1)=
Sin-1 1/ ( 9.95648 -1)= 6.4°
β
C2
r2
r1β
L2
C1
L1
r1
θ
C2
C1 A
[(L2-2*r2)-(L1-2*r1)]/2
θ
A
(r2-r1)
βθ
(r2-r1)
C2
C1 A
[(L2-2*r2)-(L1-2*r1)]/2
θ
Hence, Tan θ = (r2-r1)/[(L2-2r2)-(L1-2r1)]
i.e., Tan θ = (r2-r1)/[(L2-L1)-2(r2-r1)]
But, β + 2θ = 90°
Hence, β = (90°-2θ )
Example 4-7:
Find ; β (° )
r1= 5.0 mm, r2= 12.5 mm, L1= 45.4134 mm, L2= 70.2084 mm.
Solution:
Tan θ = (r2-r1)/[(L2-L1)-2(r2-r1)]
Hence, Tan θ = (12.5 -5.0)/[(70.2084- 45.4134)
- 2(12.5 -5.0)]
Hence, θ = 37.44°
But, β + 2θ = 90°
β = (90°-2θ )
Hence, θ = 37.44°
Hence, β = (90°-2θ) = [90°-(2* 37.44] =15.11°=
15° 6′ 36′′
Problem 4–1: Find Universal Bevel Protractor reading?.
Sheet #4
Problem 4–2: Find Universal Bevel Protractor reading?.
Problem 4-3:
37.567
Calculate the angle of taper if the sine bar length is 120 mm and the required slip gage pile is 37.567 mm and 12.545. The radius of balls is 10 mm.
37.567
Problem 4-4:
Find the cone taper angle; α (= 2θ )
S1= 5 mm, S2= 40 mm, M1= 55.4174 mm, M2= 75.3086 mm.
(α)
Problem 4-5:
Find the cone taper angle; α (= 2q )
S= 60 mm, M1= 29.3086 mm, M2= 15.4174 mm.
Problem 4-6:
Find the cone taper angle; α (= 2θ )
r1= 7.5 mm, r2= 5.0 mm, M1= 13.4174 mm, M2= 48.3086 mm.
Problem 4-7:
Find ; β (° )
r1= 5.0 mm, r2= 12.5 mm, L1= 50.4134 mm, L2= 75.2084 mm.