## Class Details

- Class Name:
- Calculations for Programming the Lathe 311
- Difficulty:
- Advanced
- Number of Lessons:
- 16

## Class Outline

- Calculating Toolpaths and Coordinates for the Lathe
- Trigonometric Ratios
- Sine, Cosine, and Tangent
- Drilling Calculations
- Trigonometry Review
- Tool Nose Radius Compensation
- Chamfering Coordinates
- Tool Nose Radius and Chamfers Review
- Arc Programming
- Calculating a Full Arc
- Programming an Arc Motion
- Arcs and Tool Nose Radius Review
- Partial Arcs
- Partial Arc Start Calculations
- Partial Arc End Calculations
- Partial Arc Review

## Objectives

- Describe CNC toolpaths. Describe coordinates for the lathe.
- Describe the three trigonometric ratios.
- Describe sine, cosine, and tangent.
- Explain how to use right triangles to calculate drilling dimensions.
- Describe tool nose radius compensation.
- Describe calculations for chamfering.
- Describe programming for partial or full arcs.
- Explain how to find the coordinates for the center of a full arc.
- Describe the G codes required to program an arc motion.
- Explain how to calculate the X axis coordinates for turning the start of a partial arc. Explain how to calculate the Z axis coordinates for turning the start of a partial arc.
- Explain how to calculate the X axis coordinates for turning the end of a partial arc. Explain how to calculate the Z axis coordinates for turning the end of a partial arc.

## Job Roles

## Glossary

Vocabulary Term | Definition |
---|---|

adjacent | The side next to the reference angle in a right triangle. The adjacent side cannot be the hypotenuse. |

approach | A small distance that the cutting tool travels before engaging the workpiece. The approach distance is added for safety reasons. |

axes | Imaginary lines that pass through the center of a point or object. Axes are used to describe the positions of objects on the Cartesian coordinate system. |

CAD/CAM | Computer-aided design/computer-aided manufacturing. CAD/CAM software helps programmers to efficiently design parts and generate part programs. |

Cartesian coordinate system | A system of numerically locating points in three-dimensional space. CNC machines use the Cartesian coordinate system to locate the tool tip and map the dimensions of a workpiece. |

centerline | An imaginary line that bisects an object into two equal halves. The centerline of a drill is used to divide its tip into two equal right triangles. |

chamfering | Machining an angled edge around the end of a cylindrical workpiece to remove sharp corners. Chamfering generally produces a 45° angle. |

chuck | A device that holds a workpiece in place as it rotates on a CNC lathe. A chuck commonly has three or four jaws that can be adjusted to fit variously sized parts. |

circular interpolation | The toolpath required to create a circular or partially circular part. Circular interpolation necessitates simultaneous movement on at least two axes. |

CNC | Computer numerical control. A computerized system used to control a mill, lathe, or turning center. CNC machines are much more precise than their manual counterparts. |

CNC lathe | A lathe that is controlled by a computer running programs driven by numerical data. CNC lathes are much more precise than their manual counterparts. |

complementary | Two angles that, when added together, measure exactly 90 degrees. For example, angles measuring 52° and 38° are complementary angles. |

computer numerical control | CNC. A computerized system used to control a mill, lathe, or turning center. Computer numerical control machines are much more precise than their manual counterparts. |

cosine | The ratio of the length of the side adjacent to the angle divided by the hypotenuse. Cosine is often written as cos. |

diameter | The measurement of a circle or cylinder at its widest point. The diameter of a drill can be used to find the length of its tip. |

drill | A fluted tool designed to drill holes. Drills used for CNC lathes typically have a 118° tip. |

drilling | A machining operation designed to create a circular hole in a workpiece. Drilling to the correct depth requires using trigonometry to calculate the length of the drill tip. |

facing | An operation in which an operator uses a lathe to feed a cutting tool across an end of a cylindrical workpiece to create a flat surface. Facing is usually completed before setting program zero. |

full arcs | A portion of a circle that forms an angle measuring exactly 90 degrees. Cutting full arcs requires circular interpolation. |

G40 | The G code to turn off tool nose radius compensation. G40 should be used for any part program in which G41 or G42 has been activated, either before a toolchange or at the end of the program. |

G41 | The G code to turn on tool nose radius compensation. G41 compensates to the left of the toolpath. |

G42 | A G code to turn on tool nose radius compensation. G42 compensates to the right of the toolpath. |

hypotenuse | In a right triangle, the side located opposite the right angle. The hypotenuse is always the longest side. |

I and K method | A method for programming circular interpolation that uses an I code and a K code to indicate the coordinate locations of the arc center. The I and K method cannot be used with the R method. |

linear interpolation | The toolpath required to create a straight line that does not travel parallel to any axis. Linear interpolation necessitates simultaneous movement on at least two axes. |

offset | In CNC programming, a mathematical, spatial value that compensates for a variable that would otherwise result in an improperly sized workpiece. Offsets for the lathe include tool nose radius compensation. |

origin | The fixed center point of the Cartesian coordinate system. The origin has a numerical value of zero for any axis. |

part program | Instructions used by a CNC machine to perform the necessary sequence of operations to machine a specific workpiece. Part programs are composed of G code. |

partial arcs | A portion of a machined circular part. Every partial arc measures less than 90 degrees. |

perpendicular | An object or plane that exists at a right angle to another object or plane. Three perpendicular axes are used to define the Cartesian coordinate system. |

program zero | A position that acts as the origin for the part program of each particular workpiece. Program zero is selected by the part programmer. |

R method | A method for programming circular interpolation that uses an R code to indicate the size of the radius that forms the arc. The R method cannot be used with the I and K method. |

right triangles | A triangle containing one right angle, which is an angle that measures exactly 90 degrees. Right triangles are useful for calculating tool positions. |

shoulder | On a workpiece with different diameters, the area where it transitions from one diameter to the other. Shoulders may be curved, requiring partial arc calculations. |

sine | The ratio of the length of the side opposite the angle divided by the hypotenuse. Sine is often written as sin. |

symmetrical | An object that is identical on each side of its centerline, or for which each half is a mirror image of the other. Symmetrical parts can be machined on lathes or turning centers. |

tangent | The ratio of the length of the side opposite the angle divided by the adjacent side. Tangent is often written as tan. |

taper angle | The degree at which a cylindrical part changes diameters along its length. Taper angles are used in programming calculations for turning tapered workpieces. |

theoretical tool tip | TTT. The location from which the CNC lathe calculates the position of the tool. The theoretical tool tip may or may not be located at the actual tip of the tool. |

tool nose radius | TNR. Describes the rounded tip of some tools. TNR must be compensated for with TNRC. |

tool nose radius compensation | TNRC. An offset feature that adjusts the toolpath to accommodate the rounded tip of an insert during contouring, chamfering, and other multi-axis operations. Tool nose radius compensation may be calculated either automatically by the lathe, turning center, or CAD/CAM software or manually by the part programmer. |

toolpath | A series of coordinate positions that determine the movement of a tool during a machining operation. Toolpaths are expressed in G code. |

trigonometric ratios | Mathematical ratios from which the sides or angles of a right triangle can be calculated. Trigonometric ratios are used often in CNC lathe programming. |

trigonometry | The branch of mathematics that addresses the measurements and relationships of a triangle and its parts. Trigonometry is used extensively in CNC machining. |

turning centers | CNC lathes that are also capable of milling operations. A turning center requires calculations in all three Cartesian axes. |

X axis | The linear axis representing the longest distance of travel perpendicular to the spindle. The X axis typically describes forward-and-away movement on the CNC lathe or turning center. |

Y axis | A linear axis that is rarely used on CNC lathes. The Y axis typically describes up-and-down travel on a turning center. |

Z axis | The linear axis that runs parallel to the spindle, or around which the spindle rotates. The Z axis typically describes right-to-left or left-to-right travel on the CNC lathe or turning center. |