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Summary
Summary
From the ability to understand and use shop mathematics to the reading and interpreting of shop drawings, the editor's intent is to provide the information and know-how that students will need as they prepare themselves for jobs in metalworking industries. It includes material taken from Machinery's Handbook and other authoritative sources and is presented in as clear, accurate, and easy-to-follow form as possible. The reader will find a wide range of useful formulas and data together with extensive text. As a proven and affordable handbook covering those critical areas of interest commonly encountered by machinists, toolmakers, diemakers, drafters, and other shop and manufacturing personnel, it is an essential reference for students in vocational schools, technical institutes, and apprenticeship courses. Discusses those aspects of applied mathematics needed on the job and covers the proper use of measuring instruments and methods. Outlines the standard methods of presentation and the conventions used in preparing engineering drawings. Offers detailed information on inch and metric standard tolerances, allowances, limits and fits, preferred numbers and sizes, as well as in-depth descriptions of the sizes, forms, dimensions of standard machine elements commonly encountered in and around the shop. Provides machining methods and materials selection, recommended speeds and feeds for various kinds of machining operations on different materials, and the types and compositions of metals commonly used in machine construction. Includes an extensive index that will enable the user to quickly and conveniently find the information and data that he or she requires.
Table of Contents
Conversion Factors | |
Metric Conversion Factors | p. 1 |
Greek Letters and Standard Abbreviations | p. 7 |
Decimal Equivalents of Fractions of an Inch | p. 7 |
Use of Conversion Tables | p. 9 |
Fractional Inch to Millimeter | p. 10 |
Decimals of an Inch to Millimeters | p. 11 |
Millimeters to Inches | p. 13 |
Microinches to Micrometers | p. 15 |
Micrometers to Microinches | p. 16 |
Thermal Energy or Heat | p. 17 |
Thermometer Scales | p. 17 |
Absolute Temperature and Absolute Zero | p. 17 |
Thermal Energy | p. 17 |
Fahrenheit-Celsius Conversion | p. 17 |
Mathematics | |
Mathematical Signs and Commonly Used Abbreviations | p. 20 |
Arithmetic | p. 21 |
Common Fractions | p. 21 |
Adding Fractions and Mixed Numbers | p. 22 |
Subtracting Fractions and Mixed Numbers | p. 22 |
Multiplying Fraction and Mixed Numbers | p. 23 |
Dividing Fractions and Mixed Numbers | p. 23 |
Decimal Fractions | p. 24 |
Converting Common Fractions To Decimal Fractions | p. 25 |
Principal Algebraic Expressions and Formulas | p. 27 |
Solving First Degree Equations | p. 27 |
Solving Quadratic Equations | p. 28 |
Cubic Equations | p. 28 |
Rearrangement and Transposition Formulas | p. 29 |
Complex or Imaginary Numbers | p. 30 |
Operations on Complex Numbers | p. 31 |
Imaginary Quantities | p. 32 |
Squares and Cubes of Numbers | p. 33 |
Fractions of Pi | p. 39 |
Weights and Volumes | p. 40 |
Circumferences and Areas of Circles | p. 41 |
Lengths of Chords for Spacing Off the Circumferences of Circles | p. 53 |
Hole Coordinate Dimension Factors | p. 54 |
Spacing Off the Circumferences of Circles | p. 55 |
Diameters of Circles and Sides of Squares of Equal Area | p. 69 |
Distance Across Corners of Squares and Hexagons | p. 70 |
Formulas for Regular Polygons | p. 71 |
Areas and Dimensions of Figures | p. 72 |
Segments of Circles | p. 78 |
Volumes of Solids | p. 80 |
Ratio and Proportion | p. 86 |
Inverse Proportion | p. 87 |
Powers, Roots, and Reciprocals | p. 88 |
Powers of Ten Notation | p. 88 |
Solution of Triangles | p. 101 |
Trigonometric Relationships of Right Triangle Parts | p. 102 |
Angular/Linear Relationships | p. 102 |
Trigonometric Functions | p. 103 |
Solution of Triangles | p. 105 |
Degree to Radian Conversion Table | p. 110 |
Trigonometric Functions | p. 112 |
Laws of Sines and Cosines | p. 113 |
Trigonometric Identities | p. 113 |
Versed Sine and Versed Cosine | p. 118 |
Sevolute and Involute Functions | p. 118 |
Involute Functions Table | p. 119 |
Compound Angles | p. 123 |
Formulas for Compound Angles | p. 123 |
Engineering Drawings | |
Fundamental Rules | p. 126 |
Units of Measurement | p. 127 |
Types of Dimensioning | p. 127 |
Application of Dimensions | p. 128 |
Dimensioning Features | p. 133 |
Direct Tolerancing Methods | p. 145 |
Tolerance Expression | p. 146 |
Interpretation of Limits | p. 147 |
Single Limits | p. 147 |
Tolerance Accumulation | p. 147 |
Geometric Tolerance Symbols | p. 156 |
Feature Control Frame Placement | p. 159 |
Definition of Tolerance Zone | p. 160 |
Tabulated Tolerances | p. 160 |
Drafting Practices | p. 161 |
Sizes of Drawing Sheets | p. 161 |
Control and Production of Surface Texture | p. 161 |
Symbols for Section Lining | p. 163 |
Sampling Lengths | p. 167 |
Roughness Parameters | p. 168 |
Waviness Parameters | p. 168 |
Surface Roughness to Tolerances | p. 169 |
Roughness Measurements | p. 170 |
Surface Texture Symbols | p. 172 |
Roughness Average Values | p. 174 |
Lay Symbols | p. 174 |
Surface Texture of Castings | p. 177 |
Metric Dimensions on Drawings | p. 177 |
Checking Drawings | p. 177 |
Inspection | |
Measuring Instruments | p. 180 |
Steel Rules | p. 180 |
Micrometers | p. 182 |
Verniers | p. 185 |
Dial Calipers | p. 187 |
Protractors | p. 187 |
Sine-bar | p. 189 |
Tables for Sine-bar Constants | p. 191 |
Measuring Tapers | p. 198 |
Measuring Dovetail Slides | p. 198 |
Angles and Tapers | p. 199 |
Tapers per Foot | p. 200 |
Figuring Tapers | p. 201 |
Simplified Taper Calculations | p. 201 |
Measurement over Pins | p. 204 |
Allowances and Tolerances for Fits | |
Limits and Fits | p. 205 |
Basic Dimensions | p. 205 |
Tolerances | p. 205 |
Preferred Basic Sizes | p. 208 |
ANSI Standard Fits | p. 211 |
Running and Sliding Fits | p. 214 |
Clearance Locational Fits | p. 216 |
Transition Locational Fits | p. 218 |
Modified Standard Fits | p. 222 |
Tolerances Designation | p. 223 |
Preferred Metric Sizes | p. 225 |
Preferred Fits | p. 225 |
Hole Basis Metric Clearance Fits | p. 228 |
Hole Basis Metric Transition and Interference Fits | p. 230 |
Shaft Basis Metric Clearance Fits | p. 232 |
Shaft Basis Metric Transition and Interference Fits | p. 234 |
Gagemakers Tolerances | p. 236 |
Pins | |
ANSI Straight Pins | p. 238 |
ANSI Taper Pins | p. 238 |
Drilling Specifications | p. 239 |
Selection of Number and Sizes of Drills | p. 241 |
ANSI Grooved Pins | p. 242 |
Standard Tapers | |
Morse Taper | p. 245 |
Brown and Sharpe Taper | p. 245 |
Jarno Taper | p. 245 |
Morse Stub Taper Shanks | p. 246 |
Morse Taper Sleeves | p. 248 |
Brown and Sharpe Taper Shank | p. 249 |
Jarno Taper Shanks | p. 250 |
Machine Tool Spindles | p. 250 |
Tapers for Machine Tool Spindles | p. 250 |
Keys and Keyseats | |
Key Size Versus Shaft Diameter | p. 253 |
Depths for Milling Keyseats | p. 256 |
Cotters | p. 256 |
Plain and Gib Head Keys | p. 257 |
Fits for Parallel and Taper Keys | p. 258 |
Key Chamfer | p. 259 |
Keyseat Tolerances for Electric Motor | p. 259 |
Set Screws for Use Over Keys | p. 259 |
Woodruff Keys and Keyseats | p. 259 |
Keyseat Dimensions for Woodruff Keys | p. 262 |
Depth of Keyseat | p. 264 |
Preferred Lengths of Keys | p. 265 |
Screw Thread Systems | |
Screw Thread Forms | p. 266 |
Parts of a Screw Thread | p. 266 |
Thread Designations | p. 267 |
Cutting Screw Threads | p. 269 |
Tap Drill Sizes and Percentage of Thread | p. 271 |
Threading Formulas | p. 278 |
Internal Metric Thread | p. 278 |
External Metric Thread | p. 280 |
Standard Series Selected Combinations | p. 283 |
Measuring Screw Threads | p. 307 |
Pitch and Lead of Screw Threads | p. 307 |
Thread Micrometers | p. 307 |
Ball-point Micrometers | p. 308 |
Three-wire Method | p. 308 |
Classes of Formulas | p. 309 |
Screw Thread Profiles | p. 309 |
Checking Pitch Diameters | p. 309 |
Wire Sizes | p. 310 |
Diameters of Wires | p. 310 |
Measuring Wire Accuracy | p. 311 |
Measuring or Contact Pressure | p. 311 |
Formulas for Checking Pitch Diameters | p. 312 |
Common Hardware | |
Fastener Grade Marks | p. 313 |
Grade Identification Marks and Mechanical Properties of Bolts and Screws | p. 313 |
Hexagon and Spline Socket | p. 314 |
Drill and Counterbore Size | p. 315 |
Hexagon and Spline Keys and Bits | p. 316 |
Socket Head Cap Screws | p. 317 |
Drill and Counterbore Sizes | p. 320 |
Hardened Ground Machine Dowel Pins | p. 321 |
Gears and Gearing | |
Gears | p. 322 |
Definitions of Gear Terms | p. 323 |
Sizes and Shape of Gear Teeth | p. 327 |
Nomenclature of Gear Teeth | p. 327 |
Properties of the Involute Curve | p. 328 |
Diametral and Circular Pitch Systems | p. 329 |
Caliper Measurement of Gear Tooth | p. 329 |
Involute Gear Milling Cutter | p. 330 |
Chordal Thickness and Chordal Addenda of Milled and Gear Milling Cutter | p. 331 |
Finishing Gear Milling Cutters | p. 332 |
Module System Gear Design | p. 333 |
German Standard Tooth Form | p. 333 |
Rules for Module System of Gearing | p. 334 |
Tooth Dimensions Based Upon Module System | p. 335 |
Equivalent Diametral Pitches, Circular Pitches | p. 336 |
Spur Gear Calculations Formula | p. 337 |
Helical Gear Calculations Formula | p. 338 |
Bevel Gear Calculations Formula | p. 340 |
Milling Bevel Gears | p. 342 |
Indexing | |
Milling Machine Indexing | p. 346 |
Simple Indexing | p. 346 |
Indexing Movements for Standard Index Plate | p. 347 |
Angular Indexing | p. 348 |
B and S Index Plates | p. 350 |
Cutting Speeds and Feeds | |
Work Materials | p. 351 |
Cutting Speed, Feed, Depth of Cut, Tool Wear, and Tool Life | p. 354 |
Selecting Cutting Conditions | p. 354 |
Principal Feeds and Speeds Tables | p. 355 |
Cutting Speed Formulas | p. 355 |
Adjustment Factors for Turning with HSS Tools | p. 357 |
Cutting Speed for Tapping | p. 357 |
Cutting Speed for Broaching | p. 358 |
Cutting Speed for Thread Chasing | p. 359 |
Feed Rate for Milling | p. 360 |
Feed Rates for Drilling | p. 361 |
Cutting Speeds for Plain Carbon and Alloy Steels | p. 363 |
Cutting Speeds for Ferrous Cast Metals | p. 365 |
Cutting Speeds for Stainless Steels | p. 366 |
Cutting Speeds for Tool Steels | p. 367 |
Cutting Speeds for Light Metals | p. 368 |
Cutting Speeds for Titanium Alloys | p. 368 |
Cutting Speeds for Superalloys | p. 369 |
Feeds for Milling with HSS Cutters | p. 370 |
RPM for Various Cutting Speeds and Diameters | p. 375 |
Tapping and Threading | p. 379 |
Speeds for Metal-cutting Saws | p. 380 |
Speeds for Turning Unusual Materials | p. 381 |
Cutting Tools | |
Tool Contour | p. 382 |
Terms and Definitions | p. 382 |
Relief Angles | p. 386 |
Rake Angles | p. 386 |
Nose Radius | p. 388 |
Chipbreakers | p. 388 |
Planing Tools | p. 389 |
Indexable Inserts | p. 389 |
Insert Identification System | p. 390 |
Indexable Insert Tool Holders | p. 392 |
Standard Shank Sizes | p. 392 |
Indexable Insert Holders | p. 394 |
Single-Point Turning and Boring Tools | p. 398 |
Arbor-Mounted Side and Slot Mills | p. 401 |
High-Speed-Steel Peripheral and Slotting End Mills | p. 404 |
High-Speed-Steel Twist Drill Tool | p. 406 |
Length of Point on Twist Drills | p. 409 |
Tool Troubleshooting | p. 410 |
Machining Methods | p. 412 |
Tool Wear | |
Sharpening Twist Drills | p. 413 |
Relief Grinding of the Tool Flanks | p. 413 |
Drill Point Thinning | p. 414 |
Sharpening Carbide Tools | p. 414 |
Silicon Carbide Wheels | p. 415 |
Diamond Wheels | p. 415 |
Peripheral Versus Flat Side Grinding | p. 417 |
Lapping Carbide Tools | p. 417 |
Chip Breaker Grinding | p. 417 |
Summary of Miscellaneous Points | p. 418 |
Cutting Fluids for Machining | |
Types of Cutting and Grinding Fluids | p. 419 |
Cutting Oils | p. 419 |
Water-Miscible Fluids | p. 420 |
Cutting Fluids for Different Materials and Operations | p. 420 |
Cutting Fluids for Turning, Milling, Drilling and Tapping | p. 421 |
Cutting Fluids for Machining Operations | p. 422 |
Application of Cutting Fluids to Carbides | p. 423 |
Cutting Fluids for Machining Magnesium | p. 424 |
Coolants for Carbide Tool Grinding | p. 424 |
Machining Nonferrous Metals | |
Machining Magnesium | p. 425 |
Machining Aluminum | p. 426 |
Machining Plastics | p. 427 |
Machining Non-metallic Gear Blanks | p. 429 |
Zinc Alloy Die-Castings | p. 430 |
Monel and Nickel Alloys | p. 430 |
High Strength, Low Alloy Steel | p. 431 |
Materials | |
Carbon Steels | p. 433 |
Free Cutting Steels | p. 435 |
Carburizing of Steels | p. 435 |
Chromium Nickel Austenitic Steels | p. 438 |
Stainless Chromium Irons and Steels | p. 439 |
Unified Numbering System | p. 442 |
Standard Steel Numbering System | p. 444 |
Classification of Tool Steels | p. 445 |
Quick Reference Guide for Tool Steel Selection | p. 446 |
Molybdenum High-Speed Steels | p. 447 |
Tungsten High-Speed Tool Steels | p. 449 |
Hot-Work Tool Steels | p. 450 |
Cold-Work Tool Steels | p. 451 |
Shock-Resisting, Mold, and Special-Purpose Tool Steels | p. 452 |
Classification, Compositions, and Properties of Tool and Die Steels | p. 453 |
Heat Treatments for SAE Carbon Steels | p. 455 |
SAE Alloy Steels | p. 456 |
Composition and Physical Properties of Bronzes | p. 460 |
Wrought Copper and Copper Alloys | p. 461 |
Aluminum Bronze Rods, Bars, and Shapes | p. 461 |
Hardness and Ultimate Strength of Brass | p. 462 |
Copper-Silicon and Beryllium Copper Alloys | p. 465 |
Nominal Composition and Properties of Everdur | p. 465 |
Aluminum and Aluminum Alloys | p. 467 |
Temper Designations for Aluminum Alloys | p. 468 |
Designation Systems | p. 471 |
Composition of Casting Alloys | p. 473 |
Clad Aluminum Alloys | p. 474 |
Characteristics of Principal Aluminum Alloy Groups | p. 474 |
Cast Magnesium Alloys | p. 475 |
Wrought Magnesium Alloys | p. 475 |
Nickel and Nickel Alloys | p. 477 |
Inconel | p. 479 |
Titanium and Titanium Alloys | p. 479 |
Powder Metallurgy | p. 480 |
Hardness Testing | |
Brinell Hardness Test | p. 482 |
Rockwell Hardness Test | p. 482 |
Shore's Scleroscope | p. 483 |
Vickers Hardness Test | p. 483 |
Knoop Hardness Numbers | p. 483 |
Monotron Hardness Indicator | p. 484 |
Keep's Test | p. 484 |
Comparative Hardness Scales for Steel | p. 484 |
Creep | p. 489 |
Creep Rupture | p. 489 |
Identifying Metals | p. 489 |