Heidenhain iTNC 530 (340 420) User Manual Page 409
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10.4 Trigonometric Functions
10.4 Trigonometric Functions
Definitions
Sine, cosine and tangent are terms designating the ratios of sides of
right triangles. For a right triangle, the trigonometric functions of the
angle a are defined by the following equations:
where
n c is the side opposite the right angle
n a is the side opposite the angle a
n b is the third side.
The TNC can find the angle from the tangent
a = arctan (a / b) = arctan (sin a / cos a)
Example:
a = 25 mm
b = 50 mm
a = arctan (a / b) = arctan 0.5 = 26.57°
Furthermore:
a² + b² = c² (where a² = a x a)
Sine: sin a = a / c
Cosine: cos a = b / c
Tangent: tan a = a / b = sin a / cos a
b
c
a
α
c (a² + b²)=
- User’s Manual 1
- HEIDENHAIN Conversational 1
- Contents 11
- 1 Introduction ..... 1 13
- 12 MOD Functions ..... 441 26
- Introduction 29
- 1.1 The iTNC 530 30
- Keyboard 31
- 1.2 Visual Display Unit and 31
- Screen layout 32
- 1.3 Modes of Operation 34
- 1.4 Status Displays 37
- Touch Probes and Electronic 41
- Handwheels 41
- HR electronic handwheels 42
- Manual Operation and Setup 43
- 2.1 Switch-on, Switch-O ff 44
- 2.1 Switch-on, Switch-Off 44
- 2.2 Moving the Machine Axes 46
- Function 49
- Entering values 49
- Touch Probe) 50
- Datum setting 51
- 2.5 Tilting the Working Plane 52
- Positioning with Manual Data 57
- Input (MDI) 57
- Simple Machining Operations 58
- Fundamentals of NC 61
- File Management 61
- Programming Aids, Pallet 61
- Management 61
- 4.1 Fundamentals 62
- 4.1 Fundamentals 62
- 4.2 File Management: 67
- Data backup 68
- 4.3 Standard File Management 69
- 4.4 Advanced File Management 76
- Creating a new part program 91
- Actual position capture 94
- Editing a program 95
- The TNC search function 98
- 4.6 Interactive Programming 100
- Graphics 100
- Block number display ON/OFF 101
- To erase the graphic: 101
- 4.7 Structuring Programs 102
- 4.8 Adding Comments 103
- 4.9 Creating Text Files 104
- Operation 108
- Messages 109
- 4.12 Pallet Management 110
- Oriented Machining 114
- Selecting a pallet file 119
- To leave the pallet file: 124
- Executing the pallet file 124
- Programming: Tools 127
- Feed rate F 128
- Spindle speed S 129
- 5.2 Tool Data 130
- 5.3 Tool Compensation 142
- 5.4 Three-Dimensional Tool 146
- Compensation 146
- DR2>0 148
- Ta b l e s 152
- Table for workpiece materials 153
- Table for cutting data 154
- Changing the table structure 156
- Configuration file TNC.SYS 158
- Programming: 159
- Programming Contours 159
- 6.1 Tool Movements 160
- 6.2 Fundamentals of Path 161
- Functions 161
- 6.3 Contour Approach and 165
- Departure 165
- 6.4 Path Contours—Cartesian 172
- Coordinates 172
- Straight line L 173
- Corner rounding RND 175
- Circle center CC 176
- 6.5 Path Contours—Polar 184
- Straight line LP 186
- Helical interpolation 187
- Example: Helix 190
- 6.6 Path Contours—FK Free 192
- Contour Programming 192
- Initiating the FK dialog 194
- Input possibilities 196
- Auxiliary points 199
- Relative data 200
- Example: FK programming 1 202
- Example: FK programming 2 203
- Example: FK programming 3 205
- 6.7 Path Contours—Spline 207
- Interpolation 207
- Miscellaneous-Functions 209
- 7.1 Entering Miscellaneous 210
- Functions M and STOP 210
- Program Run Control, Spindle 211
- Coordinate Data 212
- Contouring Behavior 215
- Machining open contours: M98 218
- Delete basic rotation: M143 225
- Rotary Axes 226
- Selecting tilting axes: M138 231
- Laser Cutting Machines 233
- Programming: Cycles 235
- 8.1 Working with Cycles 236
- 8.2 Point Tables 240
- Thread Milling 243
- PECKING (Cycle 1) 245
- DRILLING (Cycle 200) 246
- REAMING (Cycle 201) 248
- BORING (Cycle 202) 250
- BACK BORING (Cycle 204) 254
- UNIVERSAL PECKING (Cycle 205) 256
- BORE MILLING (Cycle 208) 258
- (Cycle 206) 261
- RIGID TAPPING (Cycle 17) 263
- THREAD CUTTING (Cycle 18) 266
- THREAD MILLING (Cycle 262) 271
- Q355, multiplied by the pitch 272
- (Cycle 263) 273
- Q359 (incremental 275
- (Cycle 265) 280
- Example: Drilling cycles 287
- (dependent 290
- Studs and Slots 294
- POCKET MILLING (Cycle 4) 295
- POCKET FINISHING (Cycle 212) 297
- STUD FINISHING (Cycle 213) 299
- SLOT MILLING (Cycle 3) 307
- Patterns 315
- CIRCULAR PATTERN (Cycle 220) 316
- N = Q242 318
- N = Q243 318
- 8.6 SL Cycles 322
- Fundamentals 349
- Defining contour descriptions 350
- Entering a contour formula 351
- Overlapping contours 351
- Overview 357
- RUN 3-D DATA (Cycle 30) 358
- MULTIPASS MILLING (Cycle 230) 359
- RULED SURFACE (Cycle 231) 361
- Example: Multipass milling 364
- DATUM SHIFT (Cycle 7) 367
- DATUM SETTING (Cycle 247) 371
- MIRROR IMAGE (Cycle 8) 372
- ROTATION (Cycle 10) 374
- SCALING FACTOR (Cycle 11) 375
- WORKING PLANE (Cycle 19) 377
- 8.10 Special Cycles 384
- Programming: Subprograms 389
- 9.1 Labeling Subprograms and 390
- Program Section Repeats 390
- 9.2 Subprograms 391
- 9.3 Program Section Repeats 392
- 9.4 Separate Program as 393
- Subprogram 393
- 9.5 Nesting 394
- 9.6 Programming Examples 397
- Programming: Q Parameters 403
- 10.1 Principle and Overview 404
- Place of Numerical Values 406
- Mathematical Operations 407
- 10.4 Trigonometric Functions 409
- 10.5 Calculating Circles 411
- Parameters 412
- Abbreviations used: 413
- 10.7 Checking and Changing Q 414
- 10.8 Additional Functions 415
- 10.8 Additional Functions 415
- Entering formulas 432
- Rules for formulas 434
- Programming example 435
- Active tool radius: Q108 436
- Tool axis: Q109 436
- Spindle status: Q110 437
- Coolant on/off: Q111 437
- Overlap factor: Q112 437
- 10.11 Programming Examples 441
- Test Run and Program Run 449
- 11.1 Graphics 450
- 11.3 Test Run 458
- 11.4 Program Run 460
- 11.5 Automatic Program Start 466
- 11.6 Optional block skip 467
- 11.7 Optional Program Run 468
- Interruption 468
- MOD Functions 469
- 12.1 MOD functions 470
- 12.2 Software Numbers and 472
- Option Numbers 472
- 12.3 Code Numbers 473
- Software for data transfer 476
- 12.5 Ethernet Interface 478
- 12.6 Configuring PGM MGT 485
- 12.7 Machine-Specific User 486
- Working Space 487
- 12.9 Position Display Types 489
- 12.10 Unit of Measurement 490
- 12.10 Unit of Measurement 490
- 12.11 Select the Programming 491
- Language for $MDI 491
- 12.12 Selecting the Axes for 492
- Generating L Blocks 492
- Datum Display 493
- 12.14 Displaying HELP Files 494
- 12.15 Display operating times 495
- 12.16 External Access 496
- Tables and Overviews 497
- 13.1 General User Parameters 498
- Cable for the Data Interfaces 512
- Non-HEIDENHAIN devices 513
- RS-422/V.11 interface 514
- 13.3 Technical Information 515
- Ta b l e o f C yc l es 527
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