SURFACE QUALITY & MACHINIG SYMBOLS Introduction Types of surfaces Nomenclature of surface texture Surface roughness value Machining symbols Roughness

Size: px
Start display at page:

Download "SURFACE QUALITY & MACHINIG SYMBOLS Introduction Types of surfaces Nomenclature of surface texture Surface roughness value Machining symbols Roughness"

Transcription

1 1

2 SURFACE QUALITY & MACHINIG SYMBOLS Introduction Types of surfaces Nomenclature of surface texture Surface roughness value Machining symbols Roughness grades and symbols Surface roughness indication Direction of lay Roughness symbol on drawing Surface roughness for various machining processes 2

3 INTRODUCTION Engineering components are manufactured by casting, forging, welding etc These components are then subjected to various machining operations for getting required geometrical surfaces It is not practically possible to produce a component having a geometrically ideal surface The surface finish after machining depends upon the material, vibration, deflection, speed, feed and other working conditions The surface finish requirements depend upon the functional requirements of the components to be assembled 3

4 INTRODUCTION For high class of accuracy, surface finish requirements are high and hence it is more expensive Surface quality or surface texture or surface finish is the amount of geometric irregularity produced on the surface Surface texture notes on a drawing refer the required finish that must be machined on any particular surface 4

5 TYPES OF SUFRACES Surface of a body is its boundary which separates it from another body. Surface may be; (i) Normal surface (ii) Rough surface (iii) Wavy surface and (iv) Wavy surface roughness superimposed 5

6 NOMENCLATURE OF SURFACE TEXTURE (1) Profile: It is the contour of a surface in a plane which is perpendicular to the surface itself. (2) Surface roughness: It is the micro irregularities in a surface resulting from the action of production process. It is also called primary texture roughness. 6

7 NOMENCLATURE OF SURFACE TEXTURE (3) Roughness height: It is the arithmetic average of the roughness deviation and is measured in micrometers (4) Roughness width: It is the distance parallel to nominal surface between the adjacent peaks or ridges which constitute the predominant pattern of the roughness 7

8 NOMENCLATURE OF SURFACE TEXTURE (5) Roughness-width cut off: It is a particular length of the profile decided to evaluate the arithmetic average deviation. It is also called sampling length It is the greatest spacing of repetitive surface irregularities to be included in the measurement of average roughness height It must be greater than roughness width It may be taken as 0.8mm if not specified 8

9 NOMENCLATURE OF SURFACE TEXTURE (6) Waviness: It is the irregularities in a surface having wider spacing than the roughness-width cut off resulting from machine deflection, vibrations, heat treatment, warping etc (7) Waviness height: It is the distance from the peak to the valley of the wave and is measured in millimetres 9

10 NOMENCLATURE OF SURFACE TEXTURE (8) Waviness width: It is the distance between the adjacent peak or valley of the wave and is measured in milimetres. (9) Lay: It is the predominant direction of tool that makes the surface pattern on the machined surface. 10

11 NOMENCLATURE OF SURFACE TEXTURE (10) Flaw: It is an irregularity that occurs in a surface due to cracks, blow holes, ridges, scratches etc There are no finish symbols for flaws Special note should be included on the drawing where no flaw is permitted 11

12 SURFACE ROUGHNESS VALUE Figure shows hypothetical profile of a surface Centre line is a line about which the roughness is measured The roughness may be calculated by; (1) Centre Line Average (C.L.A.) method and (2) Root Mean Square (R.M.S.) method In both methods, surface roughness is measured as average deviation from the nominal surface 12

13 SURFACE ROUGHNESS VALUE In Centre Line Average (C.L.A.) method; y 1 +y 2 +y 3 +.+y n Centre Line Average = n In Root Mean Square(R.M.S.) method; Root Mean Square = y1 y2 y3... yn n As per BIS, the surface roughness is assessed in terms of C.L.A. value and is denoted by R a

14 MACHINIG SYMBOLS The quality of surface texture is indicated by certain symbols on technical drawings The basic symbol consists of two unequal legs at 60 0 included angle to the line representing the surface under consideration with vertex touching as shown in figure. Here, a = Surface may be produced by any method b = Removal of material is not permitted c = Removal of material by machining d = If special surface characteristic is to be indicated 14

15 ROUGHNESS GRADES & SYMBOLS The principal criterion of surface roughness, R a may be indicated by the corresponding roughness grade number, as shown in Table 15

16 SURFACE ROUGHNESS INDICATION The value or values defining the principal criterion of roughness are added to the symbol as shown in figure b (f) a e d a = Roughness value, R a in micrometres = Roughness limits or grade numbers N 1 to N 12 b = Production method/ treatment of coating c = Sampling length d = Direction of lay e = Machining allowance and f = Other roughness values 16

17 DIRECTION OF LAY The direction of lay is the direction of the predominant surface pattern ordinarily determined by the production method and is shown in table. 17

18 DIRECTION OF LAY 18

19 INDICATION OF ROUGHNESS SYMBOLS ON DRAWING The symbols should be oriented such that they may be read from the bottom or the right hand side of drawing Figure (a) If it is not practicable to adopt this general rule, the symbol may be drawn in any position provided that it does not carry any indications of special surface texture characteristics as in Figure (b). 19

20 INDICATION OF ROUGHNESS SYMBOLS ON DRAWING The symbol may be connected to the surface by a leader line, terminating in an arrow. The symbol or the arrow should point from outside the material of the piece, either to the line representing the surface, or to an extension of it as shown in Figure (a) 20

21 INDICATION OF ROUGHNESS SYMBOLS ON DRAWING In accordance with the general principles of dimensioning, the symbol is only used once for a given surface and, if possible, on the view which carries the dimension, defining the size or position of the surface. 21

22 INDICATION OF ROUGHNESS SYMBOLS ON DRAWING If the same surface roughness is required on all the surfaces of a part, it is specified, either by a note near a view of the part near the title block, or in the space devoted to general notes (as shown in figure), or following the part number on the drawing. 22

23 INDICATION OF ROUGHNESS SYMBOLS ON DRAWING If the same surface roughness is required on majority of the surfaces of a part, it is specified with the addition of the notation, except where otherwise stated (Figure a), or a basic symbol (in brackets) without any other indication (Figure b), or the symbol or symbols (in brackets) of the special surface roughness or roughnesses (Figure c). 23

24 INDICATION OF ROUGHNESS SYMBOLS ON DRAWING To avoid the necessity of repeating a complicated specification a number of times, or where space is limited, a simplified specification may be used on the surface, provided that its meaning is explained near the drawing of the part, near the title block or in the space devoted to general notes. 24

25 SURFACE ROUGHNESS FOR VARIOUS MACHINING PROCESSES 25

26 SURFACE ROUGHNESS FOR VARIOUS MACHINING PROCESSES 26

27 SURFACE ROUGHNESS FOR VARIOUS MACHINING PROCESSES 27

28 SURFACE QUALITY & MACHINING SYMBOLS 28

SURFACE TEXTURE *INTRODUCTION:

SURFACE TEXTURE *INTRODUCTION: SURFACE TEXTURE *INTRODUCTION: Surface topography is of great importance in specifying the function of a surface. A significant proportion of component failure starts at the surface due to either an isolated

More information

Predetermination of Surface Roughness by the Cutting Parameters Using Turning Center

Predetermination of Surface Roughness by the Cutting Parameters Using Turning Center Predetermination of Surface Roughness by the Cutting Parameters Using Turning Center 1 N.MANOJ, 2 A.DANIEL, 3 A.M.KRUBAKARA ADITHHYA, 4 P.BABU, 5 M.PRADEEP Assistant Professor, Dept. of Mechanical Engineering,

More information

Basic Components & Elements of Surface Topography

Basic Components & Elements of Surface Topography Basic Components & Elements of Surface Topography Skid and Skidless Measuring Equipment Surface Profile Measurement Lengths Sampling Length (l) Assessment (Evaluation) Length (L) Traversing Length Cutoff

More information

MetroPro Surface Texture Parameters

MetroPro Surface Texture Parameters MetroPro Surface Texture Parameters Contents ROUGHNESS PARAMETERS...1 R a, R q, R y, R t, R p, R v, R tm, R z, H, R ku, R 3z, SR z, SR z X, SR z Y, ISO Flatness WAVINESS PARAMETERS...4 W a, W q, W y HYBRID

More information

Surface Texture Measurement Fundamentals

Surface Texture Measurement Fundamentals Surface Texture Measurement Fundamentals Dave MacKenzie Slide 1 Presentation Scope Examples of Why We Measure Surface Texture Stylus Based Instruments Stylus Tracing Methods Filters and Cutoff Basic Parameters

More information

Section A Solids Grade E

Section A Solids Grade E Name: Teacher Assessment Section A Solids Grade E 1. Write down the name of each of these 3-D shapes, (i) (ii) (iii) Answer (i)... (ii)... (iii)... (Total 3 marks) 2. (a) On the isometric grid complete

More information

SURFACE TEXTURE PARAMETERS FOR FLAT GRINDED SURFACES

SURFACE TEXTURE PARAMETERS FOR FLAT GRINDED SURFACES ENGINEERING FOR RURAL DEVELOPMENT Jelgava, 20.2.05.2015. SURFACE TEXTURE PARAMETERS FOR FLAT GRINDED SURFACES Natalija Bulaha, Janis Rudzitis Riga Technical University, Latvia natalija.bulaha@rtu.lv, janis.rudzitis_1@rtu.lv

More information

Tropical Orthogonal Representations

Tropical Orthogonal Representations Tropical Orthogonal Representations Los Angeles Math Circle, May, 016 Bryant Mathews, Azusa Pacific University 1 Orthogonal Representations of Graphs A graph G consists of a set V of vertices and a set

More information

Test Report TRACEiT Mobile optical surface structure analysis

Test Report TRACEiT Mobile optical surface structure analysis Test Report TRACEiT Mobile optical surface structure analysis Würzburg, 2012-04-17 Customer: Samples: Filter plates Report no.: Test engineer: Report by: (sign) Table of contents 1. Principles of function

More information

MANUAL SURFACE ROUGHNESS TESTER TR-200 PARTNERS IN PRECISION

MANUAL SURFACE ROUGHNESS TESTER TR-200 PARTNERS IN PRECISION MANUAL SURFACE ROUGHNESS TESTER TR-200 PARTNERS IN PRECISION CONTENTS 1 Overview 5 1.1 Measurement principles 5 1.2 Standard configuration 6 1.3 Names of each part of the instrument 6 1.4 Basic connection

More information

Recognition and Measurement of Small Defects in ICT Testing

Recognition and Measurement of Small Defects in ICT Testing 19 th World Conference on Non-Destructive Testing 2016 Recognition and Measurement of Small Defects in ICT Testing Guo ZHIMIN, Ni PEIJUN, Zhang WEIGUO, Qi ZICHENG Inner Mongolia Metallic Materials Research

More information

Ch 22 Inspection Technologies

Ch 22 Inspection Technologies Ch 22 Inspection Technologies Sections: 1. Inspection Metrology 2. Contact vs. Noncontact Inspection Techniques 3. Conventional Measuring and Gaging Techniques 4. Coordinate Measuring Machines 5. Surface

More information

1. To condense data in a single value. 2. To facilitate comparisons between data.

1. To condense data in a single value. 2. To facilitate comparisons between data. The main objectives 1. To condense data in a single value. 2. To facilitate comparisons between data. Measures :- Locational (positional ) average Partition values Median Quartiles Deciles Percentiles

More information

SRT5000 Surface Roughness Tester. Instruction Manual

SRT5000 Surface Roughness Tester. Instruction Manual SRT5000 Surface Roughness Tester Instruction Manual Table of Content 1 General introduction... 3 2 Working principles... 5 3 Description of the gauge... 6 5 Entry into service... 8 5.1 Measurement preparation...

More information

This presentation focuses on 2D tactile roughness measurements. Three key points of the presentation are: 1. Profiles are simply a collection of

This presentation focuses on 2D tactile roughness measurements. Three key points of the presentation are: 1. Profiles are simply a collection of 1 This presentation focuses on 2D tactile roughness measurements. Three key points of the presentation are: 1. Profiles are simply a collection of relative heights. 2. Parameters are statistics, not dimensions.

More information

Reflection of Light. 1)Students will discover how light interacts with certain types of surfaces

Reflection of Light. 1)Students will discover how light interacts with certain types of surfaces Reflection of Light 1)Students will discover how light interacts with certain types of surfaces 2) Students will understand the laws governing the phenomenon of reflection 3) Discover how images are formed,

More information

QUICK GUIDE TO SURFACE ROUGHNESS MEASUREMENT

QUICK GUIDE TO SURFACE ROUGHNESS MEASUREMENT Bulletin No. 2229 QUICK GUIDE TO SURFACE ROUGHNESS MEASUREMENT Reference guide for laboratory and workshop SURFACE ROUGHNESS Surface profiles and filters (EN ISO 4287 and EN ISO 16610-21) 1 The actual

More information

An Experimental Analysis of Surface Roughness

An Experimental Analysis of Surface Roughness An Experimental Analysis of Surface Roughness P.Pravinkumar, M.Manikandan, C.Ravindiran Department of Mechanical Engineering, Sasurie college of engineering, Tirupur, Tamilnadu ABSTRACT The increase of

More information

25 METER - MIJ/LIKETER WAVE'TELESCOPE MEMO // 3 4

25 METER - MIJ/LIKETER WAVE'TELESCOPE MEMO // 3 4 25 METER - MIJ/LIKETER WAVE'TELESCOPE MEMO // 3 4 Specification for Prototype Surface Panels for 25 m Diameter mm Wave Radio Telescope October 20, 1975 I. General The National Radio Astronomy Observatory

More information

Surface Roughness Tester. Instruction Manual.

Surface Roughness Tester. Instruction Manual. YRT100 Surface Roughness Tester Instruction Manual Please visit for more details Content 1 General Introduction... 3 2 Work Principle... 4 3 Name of each components... 5 4 Technical Parameters... 5 5.

More information

ME 111: Engineering Drawing. Geometric Constructions

ME 111: Engineering Drawing. Geometric Constructions ME 111: Engineering Drawing Lecture 2 01-08-2011 Geometric Constructions Indian Institute of Technology Guwahati Guwahati 781039 Geometric Construction Construction of primitive geometric forms (points,

More information

Smarter Balanced Vocabulary (from the SBAC test/item specifications)

Smarter Balanced Vocabulary (from the SBAC test/item specifications) Example: Smarter Balanced Vocabulary (from the SBAC test/item specifications) Notes: Most terms area used in multiple grade levels. You should look at your grade level and all of the previous grade levels.

More information

Measures of Dispersion

Measures of Dispersion Lesson 7.6 Objectives Find the variance of a set of data. Calculate standard deviation for a set of data. Read data from a normal curve. Estimate the area under a curve. Variance Measures of Dispersion

More information

Abstract. Introduction

Abstract. Introduction The efficient calculation of the Cartesian geometry of non-cartesian structures J.M. Freeman and D.G. Ford Engineering Control and Metrology Research Group, The School of Engineering, University of Huddersfield.

More information

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET)

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 ISSN 0976 6340 (Print) ISSN 0976 6359 (Online) Volume

More information

Identify parallel lines, skew lines and perpendicular lines.

Identify parallel lines, skew lines and perpendicular lines. Learning Objectives Identify parallel lines, skew lines and perpendicular lines. Parallel Lines and Planes Parallel lines are coplanar (they lie in the same plane) and never intersect. Below is an example

More information

Student Outcomes. Lesson Notes. Classwork. Opening Exercise (3 minutes)

Student Outcomes. Lesson Notes. Classwork. Opening Exercise (3 minutes) Student Outcomes Students solve problems related to the distance between points that lie on the same horizontal or vertical line Students use the coordinate plane to graph points, line segments and geometric

More information

CARDSTOCK MODELING Math Manipulative Kit. Student Activity Book

CARDSTOCK MODELING Math Manipulative Kit. Student Activity Book CARDSTOCK MODELING Math Manipulative Kit Student Activity Book TABLE OF CONTENTS Activity Sheet for L.E. #1 - Getting Started...3-4 Activity Sheet for L.E. #2 - Squares and Cubes (Hexahedrons)...5-8 Activity

More information

From the SelectedWorks of Harish Chandra Rajpoot H.C. Rajpoot. Harish Chandra Rajpoot Rajpoot, HCR. Summer April 6, 2015

From the SelectedWorks of Harish Chandra Rajpoot H.C. Rajpoot. Harish Chandra Rajpoot Rajpoot, HCR. Summer April 6, 2015 From the SelectedWorks of Harish Chandra Rajpoot H.C. Rajpoot Summer April 6, 2015 Mathematical Analysis of Uniform Polyhedron Trapezohedron having 2n congruent right kite faces, 4n edges & 2n+2 vertices

More information

Properties of a Circle Diagram Source:

Properties of a Circle Diagram Source: Properties of a Circle Diagram Source: http://www.ricksmath.com/circles.html Definitions: Circumference (c): The perimeter of a circle is called its circumference Diameter (d): Any straight line drawn

More information

DATA MINING APPLICATION USING DECISION TREE AND ANN FOR PREDICTING SURFACE ROUGHNESS OF END MILLING MANUFACTURING PROCESS

DATA MINING APPLICATION USING DECISION TREE AND ANN FOR PREDICTING SURFACE ROUGHNESS OF END MILLING MANUFACTURING PROCESS International Journal of Computer Science Engineering and Information Technology Research (IJCSEITR) Vol.1, Issue 2 Dec 2011 61-68 TJPRC Pvt. Ltd., DATA MINING APPLICATION USING DECISION TREE AND ANN FOR

More information

Roughness measuring systems from Jenoptik Surface texture parameters in practice

Roughness measuring systems from Jenoptik Surface texture parameters in practice Roughness measuring systems from Jenoptik Surface texture parameters in practice Surface texture measurement Surface texture measurement with Jenoptik Surface texture is very important where it has a direct

More information

INFLUENCE OF THE HIGH SPEED PART POLISHING COATING TOOLS ON THE CHANGES SURFACE TEXTURE

INFLUENCE OF THE HIGH SPEED PART POLISHING COATING TOOLS ON THE CHANGES SURFACE TEXTURE INFLUENCE OF THE HIGH SPEED PART POLISHING COATING TOOLS ON THE CHANGES SURFACE TEXTURE Ondřej Klanica 1, David Dobrocký 2, Emil Svoboda 3, Jozef Sondor 4 1 Ing. Ondřej Klanica, Faculty of Military Technology,

More information

COMPRESSION SET IN SITU MEASUREMENT USING 3D PROFILOMETRY. Compression Set time: 1 min 10 min 30 min 60 min. Prepared by Duanjie Li, PhD

COMPRESSION SET IN SITU MEASUREMENT USING 3D PROFILOMETRY. Compression Set time: 1 min 10 min 30 min 60 min. Prepared by Duanjie Li, PhD COMPRESSION SET IN SITU MEASUREMENT USING 3D PROFILOMETRY Compression Set time: 1 min 10 min 30 min 60 min Recovered Height (um) 400 350 300 250 200 150 100 50 0-50 0 10 20 30 40 50 60 Time (min) Prepared

More information

Appendix 1: Manual for Fovea Software

Appendix 1: Manual for Fovea Software 1 Appendix 1: Manual for Fovea Software Fovea is a software to calculate foveal width and depth by detecting local maxima and minima from fovea images in order to estimate foveal depth and width. This

More information

DESIGN AND IMPLEMENTATION OF A CALCULATION PROGRAM IN MATLAB PLATFORM FOR EVALUATION OF ROUGHNESS

DESIGN AND IMPLEMENTATION OF A CALCULATION PROGRAM IN MATLAB PLATFORM FOR EVALUATION OF ROUGHNESS Master s Thesis Industrial Engineering DESIGN AND IMPLEMENTATION OF A CALCULATION PROGRAM IN MATLAB PLATFORM FOR EVALUATION OF ROUGHNESS JUNE 2015 Author: Advisor: Juan de Villanueva Jesús Álvarez Design

More information

16 SW Simulation design resources

16 SW Simulation design resources 16 SW Simulation design resources 16.1 Introduction This is simply a restatement of the SW Simulation online design scenarios tutorial with a little more visual detail supplied on the various menu picks

More information

SHAPE, SPACE and MEASUREMENT

SHAPE, SPACE and MEASUREMENT SHAPE, SPACE and MEASUREMENT Types of Angles Acute angles are angles of less than ninety degrees. For example: The angles below are acute angles. Obtuse angles are angles greater than 90 o and less than

More information

CHAPTER 3 SURFACE ROUGHNESS

CHAPTER 3 SURFACE ROUGHNESS 38 CHAPTER 3 SURFACE ROUGHNESS 3.1 SURFACE ROUGHNESS AND ITS IMPORTANCE The evaluation of surface roughness of machined parts using a direct contact method has limited flexibility in handling the different

More information

Advantages of 3D Optical Profiling Over Other Measurement Technologies

Advantages of 3D Optical Profiling Over Other Measurement Technologies Horizontal milling Ra (6.35 μm, 250 uin.) Vertical milling Ra (1.6 μm, 63 uin.) Flat lapping Ra (0.2 μm, 8 uin.) Application Note #558 Correlating Advanced 3D Optical Profiling Surface Measurements to

More information

CNC 8055 MC EXAMPLES MANUAL REF Ref. 0601

CNC 8055 MC EXAMPLES MANUAL REF Ref. 0601 EXAMPLES MANUAL Ref. 0601 All rights reserved. No part of this documentation may be copied, transcribed, stored in a data backup system or translated into any language without Fagor Automation's explicit

More information

WJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS

WJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS Surname Other Names Centre Number 0 Candidate Number WJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS A.M. MONDAY, 24 June 2013 2 1 hours 2 ADDITIONAL MATERIALS A calculator will be required for

More information

An objective method to measure and evaluate the quality of sanded wood surfaces

An objective method to measure and evaluate the quality of sanded wood surfaces An objective method to measure and evaluate the quality of sanded wood surfaces Abstract L. Gurau 1 No agreed guidelines exist in wood surface metrology about how to objectively measure and evaluate the

More information

Mathematics Curriculum

Mathematics Curriculum 6 G R A D E Mathematics Curriculum GRADE 6 5 Table of Contents 1... 1 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)... 11 Lesson 1: The Area of Parallelograms Through Rectangle Facts...

More information

Part 6 - Constructing Railroad Bridges

Part 6 - Constructing Railroad Bridges Part 6 - Constructing Railroad Bridges Bridges are a vital part of every railroad, and in Train Simulator we are fortunate to have a large variety of them, both in the game itself and available through

More information

Refraction & Concave Mirrors

Refraction & Concave Mirrors rev 05/2018 Equipment List Refraction & Concave Mirrors Qty Items Part Numbers 1 Light Source OS-8517 1 Ray Optics Set OS-8516 1 Optics Bench OS-8518 1 50 mm Concave Mirror, and Half Screen OS-8519 1 Viewing

More information

Unit 10 Study Guide: Plane Figures

Unit 10 Study Guide: Plane Figures Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece

More information

6. Find the equation of the plane that passes through the point (-1,2,1) and contains the line x = y = z.

6. Find the equation of the plane that passes through the point (-1,2,1) and contains the line x = y = z. Week 1 Worksheet Sections from Thomas 13 th edition: 12.4, 12.5, 12.6, 13.1 1. A plane is a set of points that satisfies an equation of the form c 1 x + c 2 y + c 3 z = c 4. (a) Find any three distinct

More information

1. Introduction to Constructive Solid Geometry (CSG)

1. Introduction to Constructive Solid Geometry (CSG) opyright@010, YZU Optimal Design Laboratory. All rights reserved. Last updated: Yeh-Liang Hsu (010-1-10). Note: This is the course material for ME550 Geometric modeling and computer graphics, Yuan Ze University.

More information

On Fig. 7.1, draw a ray diagram to show the formation of this image.

On Fig. 7.1, draw a ray diagram to show the formation of this image. 1- A small object is placed 30 cm from the centre of a convex lens of focal length 60 cm An enlarged image is observed from the other side of the lens (a) On Fig 71, draw a ray diagram to show the formation

More information

Ganado Unified School District 7 th Grade Mathematics

Ganado Unified School District 7 th Grade Mathematics Ganado Unified School District 7 th Grade Mathematics PACING Guide SY 2014-2015 Quarter 3 Week 1 Graphs Text Reference Concept : Use random sampling to draw inferences about population. 7.SP.A.1. Understand

More information

Fixed Perimeter Rectangles Geometry Creating a Document

Fixed Perimeter Rectangles Geometry Creating a Document Activity Overview: This activity provides the steps to create a TI-Nspire document that will be used to investigate side length and area in a rectangle with a fixed perimeter. An algebraic approach is

More information

Shippensburg Math & Computer Day 2013 Individual Math Contest Solutions

Shippensburg Math & Computer Day 2013 Individual Math Contest Solutions Shippensburg Math & Computer Day 2013 Individual Math Contest Solutions 1. Row n of Pascal s Triangle lists all the coefficients of the expansion of (1 + x) n. What is the smallest value of n for which

More information

Downloaded from

Downloaded from UNIT 2 WHAT IS STATISTICS? Researchers deal with a large amount of data and have to draw dependable conclusions on the basis of data collected for the purpose. Statistics help the researchers in making

More information

WORKSHOP EQUIPMENT. Engineers Stud. Flanged Nut. T-Slot Nut. Step Block. Extension Nut. Step Clamp

WORKSHOP EQUIPMENT. Engineers Stud. Flanged Nut. T-Slot Nut. Step Block. Extension Nut. Step Clamp GROUP Indexa T-Slot Clamping Kits Designed to save set up time and solve most T-Slot clamping problems. All components are manufactured from S45C (JIS)/CK45 (DIN) grade non-alloy carbon steel, heat treated

More information

MAC Rev.S Learning Objectives. Learning Objectives (Cont.) Module 4 Quadratic Functions and Equations

MAC Rev.S Learning Objectives. Learning Objectives (Cont.) Module 4 Quadratic Functions and Equations MAC 1140 Module 4 Quadratic Functions and Equations Learning Objectives Upon completing this module, you should be able to 1. understand basic concepts about quadratic functions and their graphs.. complete

More information

Grades 7 & 8 Pre-Algebra/Course 3,

Grades 7 & 8 Pre-Algebra/Course 3, Grades 7 & 8 Pre-Algebra/Course 3, TERM 1 - AUGUST/SEPTEMBER/OCTOBER Algebra Tools Solving Equations Integers Solving Multi-Step Equations and Inequalities TERM 2 NOVEMBER/DECEMBER/JANUARY Functions &

More information

Grade 6 Mathematics Item Specifications Florida Standards Assessments

Grade 6 Mathematics Item Specifications Florida Standards Assessments Content Standard MAFS.6.G Geometry MAFS.6.G.1 Solve real-world and mathematical problems involving area, surface area, and volume. Assessment Limits Calculator s Context A shape is shown. MAFS.6.G.1.1

More information

APPLICATION OF MACHINE VISION TECHNIQUES IN SURFACE FINISH MEASUREMENTS OF MACHINED COMPONENTS AND TO EVALUATE THE FUNCTIONING OF THE COMPONENT

APPLICATION OF MACHINE VISION TECHNIQUES IN SURFACE FINISH MEASUREMENTS OF MACHINED COMPONENTS AND TO EVALUATE THE FUNCTIONING OF THE COMPONENT Research Paper: Dhinesh Kumar and Rajaram, 2013: Pp.31-35 APPLICATION OF MACHINE VISION TECHNIQUES IN SURFACE FINISH MEASUREMENTS OF MACHINED COMPONENTS AND TO EVALUATE THE FUNCTIONING OF THE COMPONENT

More information

2 + (-2) = 0. Hinojosa 7 th. Math Vocabulary Words. Unit 1. Word Definition Picture. The opposite of a number. Additive Inverse

2 + (-2) = 0. Hinojosa 7 th. Math Vocabulary Words. Unit 1. Word Definition Picture. The opposite of a number. Additive Inverse Unit 1 Word Definition Picture Additive Inverse The opposite of a number 2 + (-2) = 0 Equal Amount The same in quantity = Fraction A number in the form a/b, where b 0. Half One of two equal parts of a

More information

Simulation based optimization on automated fibre placement process

Simulation based optimization on automated fibre placement process Simulation based optimization on automated fibre placement process Lei Shi Autodesk (China) Software Research and Development Co. Ltd., 399 Pudian Road, Pudong New District, Shanghai 200122, China forrest.shi@autodesk.com

More information

1. Use the Trapezium Rule with five ordinates to find an approximate value for the integral

1. Use the Trapezium Rule with five ordinates to find an approximate value for the integral 1. Use the Trapezium Rule with five ordinates to find an approximate value for the integral Show your working and give your answer correct to three decimal places. 2 2.5 3 3.5 4 When When When When When

More information

Mini-Project 1: The Library of Functions and Piecewise-Defined Functions

Mini-Project 1: The Library of Functions and Piecewise-Defined Functions Name Course Days/Start Time Mini-Project 1: The Library of Functions and Piecewise-Defined Functions Part A: The Library of Functions In your previous math class, you learned to graph equations containing

More information

KINETIC FRICTION TROUGH SURFACE MICRO ANALYSIS

KINETIC FRICTION TROUGH SURFACE MICRO ANALYSIS International Journal of Metallurgical & Materials Science and Engineering (IJMMSE) ISSN 2278-2516 Vol. 3, Issue 1, Mar 2013, 31-36 TJPRC Pvt. Ltd. KINETIC FRICTION TROUGH SURFACE MICRO ANALYSIS NIKOLA

More information

Advanced sensor for on-line topography in continuous lines

Advanced sensor for on-line topography in continuous lines Advanced sensor for on-line topography in continuous lines Moréas Geneviève (CRM) Van De Velde Frederik (Arcelor, Sidmar) Bilstein Wolfgang (Amepa) INTRODUCTION Complex metal forming, high quality in term

More information

Plate. Channels - Standard Structural* Conforms to ASTM A36 Lengths Available: 20 Ft. and 40 Ft. Stock items are highlighted in blue.

Plate. Channels - Standard Structural* Conforms to ASTM A36 Lengths Available: 20 Ft. and 40 Ft. Stock items are highlighted in blue. Channels - Standard Structural* Grades Conforms to ASTM A36 Lengths Available: 20 Ft. and 40 Ft. Stock items are highlighted in blue. A Depth B Flange Width C Web Thickness Estimated Weight - Lbs. Lbs/Foot

More information

Non-Contact Measurement for the Aluminum Industry WIDTH THICKNESS FLATNESS SURFACE.

Non-Contact Measurement for the Aluminum Industry WIDTH THICKNESS FLATNESS SURFACE. THE GLOBAL WORLD LEADER MARKET IN LEADER NON-CONTACT IN MEASURING MEASURING SYSTEMS SYSTEMS Non-Contact Measurement for the Aluminum Industry WIDTH THICKNESS FLATNESS SURFACE www.imssystemsinc.com Taking

More information

Subdivision Of Triangular Terrain Mesh Breckon, Chenney, Hobbs, Hoppe, Watts

Subdivision Of Triangular Terrain Mesh Breckon, Chenney, Hobbs, Hoppe, Watts Subdivision Of Triangular Terrain Mesh Breckon, Chenney, Hobbs, Hoppe, Watts MSc Computer Games and Entertainment Maths & Graphics II 2013 Lecturer(s): FFL (with Gareth Edwards) Fractal Terrain Based on

More information

CCM Unit 10 Angle Relationships

CCM Unit 10 Angle Relationships CCM6+7+ Unit 10 Angle Relationships ~ Page 1 CCM6+7+ 2015-16 Unit 10 Angle Relationships Name Teacher Projected Test Date Main Concepts Page(s) Unit 10 Vocabulary 2-6 Measuring Angles with Protractors

More information

Scalar Field Visualization I

Scalar Field Visualization I Scalar Field Visualization I What is a Scalar Field? The approximation of certain scalar function in space f(x,y,z). Image source: blimpyb.com f What is a Scalar Field? The approximation of certain scalar

More information

3D Surface Metrology on PV Solar Wafers

3D Surface Metrology on PV Solar Wafers 3D Surface Metrology on PV Solar Wafers Karl- Heinz Strass cybertechnologies USA 962 Terra Bella Ave San Jose CA 95125 P: 408-689-8144 www.cybertechnologies.com Introduction Solar photovoltaics is the

More information

Advanced Texture MetroPro Application

Advanced Texture MetroPro Application OMP-0362G Advanced Texture MetroPro Application AdvText.app This booklet is a quick reference; it assumes that you are familiar with MetroPro and the instrument. Information on MetroPro is provided in

More information

EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 1

EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 1 EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 1 TUTORIAL 4 AREAS AND VOLUMES Determine the fundamental algebraic laws and apply algebraic manipulation techniques to the solution

More information

INTERFERENCE. where, m = 0, 1, 2,... (1.2) otherwise, if it is half integral multiple of wavelength, the interference would be destructive.

INTERFERENCE. where, m = 0, 1, 2,... (1.2) otherwise, if it is half integral multiple of wavelength, the interference would be destructive. 1.1 INTERFERENCE When two (or more than two) waves of the same frequency travel almost in the same direction and have a phase difference that remains constant with time, the resultant intensity of light

More information

Name Date Class. When the bases are the same and you multiply, you add exponents. When the bases are the same and you divide, you subtract exponents.

Name Date Class. When the bases are the same and you multiply, you add exponents. When the bases are the same and you divide, you subtract exponents. 2-1 Integer Exponents A positive exponent tells you how many times to multiply the base as a factor. A negative exponent tells you how many times to divide by the base. Any number to the 0 power is equal

More information

CCSSM Curriculum Analysis Project Tool 1 Interpreting Functions in Grades 9-12

CCSSM Curriculum Analysis Project Tool 1 Interpreting Functions in Grades 9-12 Tool 1: Standards for Mathematical ent: Interpreting Functions CCSSM Curriculum Analysis Project Tool 1 Interpreting Functions in Grades 9-12 Name of Reviewer School/District Date Name of Curriculum Materials:

More information

Chinle USD CURRICULUM GUIDE. SUBJECT: MATH GRADE: 6th TIMELINE: 2 nd Quarter. Kid Friendly Learning Objective

Chinle USD CURRICULUM GUIDE. SUBJECT: MATH GRADE: 6th TIMELINE: 2 nd Quarter. Kid Friendly Learning Objective Concept 1: Numerical PO 1. Convert between expressions for positive rational numbers, including fractions, decimals, percents, and ratios. M I will convert between expressions for rational numbers; e.g.,

More information

Surface Texture Parameters

Surface Texture Parameters Mx TM Surface Texture Parameters Contents Standards... 2 Terminology... 3 Filtering... 4 Choosing Cutoffs (λc)... 4 Profile ISO Parameters... 5 Profile ISO Height Parameters... 5 Profile ISO Functional

More information

FDG SERIES LENSES for OSRAM GOLDEN DRAGON TM LEDs

FDG SERIES LENSES for OSRAM GOLDEN DRAGON TM LEDs FDG SERIES LENSES for OSRAM GOLDEN DRAGON TM LEDs High efficiency Available in 4 different s Patent pending The FDG Series offers a complete range of lenses especially designed for the Golden (1) LEDs

More information

FCP Lens series for Cree XP-E and XP-G LEDs

FCP Lens series for Cree XP-E and XP-G LEDs High efficiency 4 beams available Easy assembly The FCP lens offers low-profile lenses specifically designed for the XP-E and XP-G XLamp LEDs from Cree Corporation. A software-optimized aspheric profile

More information

Unit 1. Word Definition Picture. The number s distance from 0 on the number line. The symbol that means a number is greater than the second number.

Unit 1. Word Definition Picture. The number s distance from 0 on the number line. The symbol that means a number is greater than the second number. Unit 1 Word Definition Picture Absolute Value The number s distance from 0 on the number line. -3 =3 Greater Than The symbol that means a number is greater than the second number. > Greatest to Least To

More information

TA101 : Engineering Graphics Review of Lines. Dr. Ashish Dutta Professor Dept. of Mechanical Engineering IIT Kanpur Kanpur, INDIA

TA101 : Engineering Graphics Review of Lines. Dr. Ashish Dutta Professor Dept. of Mechanical Engineering IIT Kanpur Kanpur, INDIA TA101 : Engineering Graphics Review of Lines Dr. Ashish Dutta Professor Dept. of Mechanical Engineering IIT Kanpur Kanpur, INDIA Projection of a point in space A point is behind the frontal plane by d

More information

Click the mouse button or press the Space Bar to display the answers.

Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. 7-1 Objectives You will learn to: Find the geometric mean between two numbers. Solve problems involving relationships between parts

More information

Lesson 5: Identical Triangles

Lesson 5: Identical Triangles NS COMMON CORE MATHEMATICS CURRICULUM Lesson 5 7 6 Classwork Opening When studying triangles, it is essential to be able to communicate about the parts of a triangle without any confusion. The following

More information

Jenoptik twist measuring systems - Twist measurement in practice

Jenoptik twist measuring systems - Twist measurement in practice Jenoptik twist measuring systems - Twist measurement in practice Twist measurement Twist measurement with Jenoptik Dynamically stressed seals place high demands on the surface texture of a shaft at the

More information

ArmCAD 6. reinforced concrete detailing program [updated for Build 2028]

ArmCAD 6. reinforced concrete detailing program [updated for Build 2028] ArmCAD 6 reinforced concrete detailing program [updated for Build 2028] This user manual explains only new program features and commands that have not been included in ArmCAD 2005, so it is thus primarily

More information

Surface Roughness Tester SRTPro

Surface Roughness Tester SRTPro Surface Roughness Tester SRTPro Instruction manual 30 CONTENT 1 ROUGHNESS TESTER OVERVIEW... 3 1.1 FEATURES OF INSTRUMENT... 3 1.2 MEASUREMENT PRINCIPLE... 3 1.3 NAME OF EACH PART... 4 1.4 BUTTONS DEFINE...

More information

Geometry: Unit 1: Transformations. Chapter 14 (In Textbook)

Geometry: Unit 1: Transformations. Chapter 14 (In Textbook) Geometry: Unit 1: Transformations Chapter 14 (In Textbook) Transformations Objective: Students will be able to do the following, regarding geometric transformations. Write Transformations Symbolically

More information

Glossary Common Core Curriculum Maps Math/Grade 6 Grade 8

Glossary Common Core Curriculum Maps Math/Grade 6 Grade 8 Glossary Common Core Curriculum Maps Math/Grade 6 Grade 8 Grade 6 Grade 8 absolute value Distance of a number (x) from zero on a number line. Because absolute value represents distance, the absolute value

More information

5. Compare the volume of a three dimensional figure to surface area.

5. Compare the volume of a three dimensional figure to surface area. 5. Compare the volume of a three dimensional figure to surface area. 1. What are the inferences that can be drawn from sets of data points having a positive association and a negative association. 2. Why

More information

Oklahoma Learning Pathways

Oklahoma Learning Pathways BUI L F OKL ORT AHO MA 2015 2016 Oklahoma Learning Pathways Table of Contents Grade 3...3 Grade 4...5 Grade 5...8 Grade 6... 11 Grade 7... 15 Grade 8... 19 Algebra Readiness...22 Algebra I...25 Geometry...28

More information

Voltage Sag Simulator

Voltage Sag Simulator For use with all DPI s & VDC s 120/208/240V 50/60Hz LEADERS IN VOLTAGE-DIP PROOFING Contents Introduction to the DPI... 3 Theory of DPI operation... 3 Description -... 4 Operation... 5 Sag Simulation...

More information

Mini-Project 1: The Library of Functions and Piecewise-Defined Functions

Mini-Project 1: The Library of Functions and Piecewise-Defined Functions Name Course Days/Start Time Mini-Project 1: The Library of Functions and Piecewise-Defined Functions Part 2: Piecewise-Defined Functions A piecewise-defined function is two or more functions combined into

More information

CHAPTER 5 RANDOM VIBRATION TESTS ON DIP-PCB ASSEMBLY

CHAPTER 5 RANDOM VIBRATION TESTS ON DIP-PCB ASSEMBLY 117 CHAPTER 5 RANDOM VIBRATION TESTS ON DIP-PCB ASSEMBLY 5.1 INTRODUCTION Random vibration tests are usually specified as acceptance, screening and qualification tests by commercial, industrial, and military

More information

FPC connectors (0.2mm pitch) Back lock

FPC connectors (0.2mm pitch) Back lock 0.9 AYF21 For FPC FPC connectors (0.2mm pitch) Back lock Y2B Series New FEATURES 1. Slim and low profile design (Pitch: 0.2 mm) 0.2 mm pitch back lock design and the slim body with a 3.15 mm depth (with

More information

2D & 3D CAD SOFTWARE USER MANUAL. AutoQ3D CAD for ipad & iphone

2D & 3D CAD SOFTWARE USER MANUAL. AutoQ3D CAD for ipad & iphone Type to enter text 2D & 3D CAD SOFTWARE USER MANUAL AutoQ3D CAD for ipad & iphone AUTOQ3D TEAM FIRST EDITION AutoQ3D CAD for ipad & iphone 2D / 3D cad software user manual 2015 by AutoQ3D Team. All rights

More information

Eureka Math. Grade 7, Module 6. Student File_B Contains Exit Tickets, and Assessment Materials

Eureka Math. Grade 7, Module 6. Student File_B Contains Exit Tickets, and Assessment Materials A Story of Units Eureka Math Grade 7, Module 6 Student File_B Contains s, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. All rights reserved. No part of this

More information

Grade 9 Math Terminology

Grade 9 Math Terminology Unit 1 Basic Skills Review BEDMAS a way of remembering order of operations: Brackets, Exponents, Division, Multiplication, Addition, Subtraction Collect like terms gather all like terms and simplify as

More information

Overview. The Basics Equipment Measuring Conditions & Correlation Parameters Definitions Parameters and Function

Overview. The Basics Equipment Measuring Conditions & Correlation Parameters Definitions Parameters and Function MP1 MP2 Overview The Basics Equipment Measuring Conditions & Correlation Parameters Definitions Parameters and Function Slide 1 MP1 Miguel Portillo, 4/20/2016 MP2 Miguel Portillo, 4/20/2016 Measure What?

More information

Piping Design. Site Map Preface Getting Started Basic Tasks Advanced Tasks Customizing Workbench Description Index

Piping Design. Site Map Preface Getting Started Basic Tasks Advanced Tasks Customizing Workbench Description Index Piping Design Site Map Preface Getting Started Basic Tasks Advanced Tasks Customizing Workbench Description Index Dassault Systèmes 1994-2001. All rights reserved. Site Map Piping Design member member

More information