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Module 2

Milling calculations,

coordinates and program preparing

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Module Objectives:

1. Calculate the cutting speed, feed rate and depth of cut

2. Recognize coordinate

3. Differentiate between Cartesian and Polar coordinate systems.

4. Recognize the milling machine axes

5. Recognize positive and negative directions on milling machines.

6. Know the program procedure and zero points.

Module Contents

1. Cutting speed, feed rate and depth of cut

2. Coordinate systems

3. CNC machines coordinates

4. Conventional and CNC machining

5. Programming procedure

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2.1: Milling cutting values

2.1.1: Cutting speed (CS)

The cutting speed is the speed at which the circumference of the work part

moves along the cutter. The magnitude of cutting speed is determined by the:

1. Material of the work part.

2. Material of the cutter.

3. Infeed (surface quality roughing, finishing).

4. Life of the tool.

Note: The cutting speed is chosen from tabulated values.

2.1.2: Rotational speed (n):

Once the cutting speed is chosen, the rotational speed has to be calculated.

The following formula can be used to calculate the rotational speed:

Where:

CS: the cutting speed in (m/min).

d: the cutting tool diameter in

(m).

n: the rotational speed in revolution per minute (RPM)

(Rev/min).

Example 1:

Calculate the cutting speed for milling if the milling tool diameter

(d) = 50 mm and the number of rotations (n) = 520 rev. /min?

Solution:

=

≈ 82 m/min

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Example 2:

Calculate the number of rotations (n) if the milling tool diameter = 12 mm and

the cutting speed Vc = 120 m/min.

Solution:

=

≈ 3185 rev/min

Example 3:

Calculate the cutting speed for turning if the cutting is done on 60 mm

diameter workpiece and at rotational speed of 1500 RPM?

Solution:

=

= 283 m/min

2.1.3: Feed speed (Vf)

Together with the cutting movement, infeed allows a continuous chip removal

during several rotations. The infeed speed (Vf) is indicated in mm/min.

The following formula is used to calculate the infeed speed:

Vf = n f

Where,

Vf: the infeed speed in mm/min

n: revolution per minute (RPM).

f: the feed in mm/rev; chosen from tabulated values.

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Example:

A plate is to be milled in one cut using an end-face mill with indexable inserts.

The spindle speed = 1500 rev/min, and the feed in mm/rev is 0.40. How high is

the infeed speed Vf?

Known: 1. n = 1500 rev /min 2. f = 0.40 mm/rev

Unknown: Vf in mm/min

Solution:

Vf = n f

= 1500 x 0.40 = 600 mm/min

3.1.4: Cutting depth is the difference in height between machined

surface and the work surface.

Example:

When roughing a bar of aluminum we want to reduce the diameter in a bar

from 25mm to 23 mm diameter in one cut.

What is the depth of cut?

depth of cut =

Depth of cut =

D =

= 1.0 mm

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2.2: Coordinate systems

The cutting tool should move in contact with the workpiece at certain specific

points, in order to shape metal by machine tools while the workpiece or cutting

tool is rotating.

Coordinate system is required to define the movement on the milling machine.

2.2.1: Types of coordinates systems

To know the current and target positions of the cutting tool we need a

coordinate system.

There are two common coordinate systems:

A. Cartesian coordinate system.

It is used to describe the position of a point

in the space.

1. When dealing with 2 dimensions

(2D), the two-dimensional coordinate

system is used; Fig. 1

Fig. 1 Cartesian coordinate system

2. When dealing with three dimensions

(3D), the three-dimensional coordinate

system is used; Fig. 2

Fig. 2 Cartesian coordinate system

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Example 1:

Locate points P1 through P4 on the coordinate system

shown in Fig. 3. A

Point X Z

P1 70 60

P2 80 20

P3 -40 -50

P4 50 -70

Fig. 3. A

Example 2:

Locate points P1 and P2 on the coordinate system shown in Fig. 3. B

Point X Y Z

P1 20 30 0

P2 -30 -20 25

P3 30 0 -10

Fig. 3. B

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B. Polar Coordinate system.

The point is located by its distance (radius r) to the point of origin and its angle

(alpha α) to a specified axis.

1. The angle is positive if it is measured in

Counter clockwise direction starting from

positive X-axis; Fig. 4. A

Fig. 4. A

2. The angle is negative if it is measured in

the clockwise direction starting from

positive X-axis; Fig 4. B

Fig. 4. B

2.2.2: CNC Machines' coordinates:

The machine tool has its own "coordinate system", to indicate the position of

the workpiece and read the specified coordinates correctly;

The following points are part of this system.

A. Machine Zero Point (M):

It is the origin of the coordinate system,

and defined by the manufacturer and cannot

be changed. Fig. 5

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Fig. 5

B. Workpiece Zero Point:

Defined by the programmer and can be

changed. The workpiece zero point "W",

can be specified as desired; Fig. 6

Fig. 6

2.2.3: Milling machine axes:

A milling machine has at least 3 controllable

feed axes marked as X, Y and Z, Fig. 7

1. The Spindle axis is Z axis.

2. X axis is the axis of left and right movement

of the machine table.

3. Y axis is the axis for in and out movement on

the vertical milling machine or up and down

movement on horizontal milling machine.

Fig. 7

Notes:

1.The X axis and the Y axis are usually parallel to the clamping

plane of the work part.

2. When standing in front of the machine the positive X direction

runs to the right and the Y axis away from the viewer.

3. For an easier calculation of the points needed for programming

it is advisable to use the outer edges of the upper or the lower

area.

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Types of zero and reference points

2.2.4: Dimensioning

To machine a workpiece we need a technical drawing on which we should

illustrate the required dimensions (information) to make the required shape.

To dimension the workpiece we need to specify a certain point on it, from which

we should take the measurement.

There are two types of dimensioning:

1. Absolute Dimensioning:

All measurements are taken from

the workpiece zero point. See Fig. 8

Fig. 7

Absolute dimensioning

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2. Incremental Dimensioning:

Uses incremental values that are always

measured from the current point to the

next point. See Fig. 8

Fig. 8

Incremental dimensioning

2.2.5: Conventional and CNC machining

CNC-manufacturing has advantages over manufacturing with conventional

machine tools, e.g. shorter production times.

Advantages of CNC

1. Increased productivity

2. Constant quality of the work part

3. Less waste (scrap)

4. Increased dimension accuracy (up to 1/1000 mm)

5. Producing complex parts

Disadvantages of CNC

1. High initial cost (capital cost)

2. Need high qualified operator.

CNC machine tools use special NC tools. These tools meet the following criteria:

1. Better milling performance

2. Short changing and setup times

3. Standardized tools

4. Improved tool management

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2.2.6: Quality assurance during CNC production

The quality of parts manufactured on conventional machine tools is especially

dependent upon the machine operator’s training and constancy.

The following factors can affect the quality of the manufactured work part:

1. The created NC-program

2. Tool cutting-edge life)

3. The work part material

4. The CNC-machine precision

Programming standards (ISO)

The ISO-Norm 6983 strives for standardizing the NC-programming of machines

in the production area. This is however limited to standardizing certain

commands as well the general structure of a NC-program

2.3: Programming procedure

Generating NC-programs in the workshop is known as machine-based

programming. The NC-programs can either be directly created on a machine or

at a programming terminal near the machines.

The NC-programs written in the workshop and in production planning are

directly controlled and optimized on the CNC-machine tool by the operator

during set-up.

A skilled worker on a milling machine must defined by the programmer in

advance.

The programming steps are:

1. Definition of machining steps

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Specifying the machining sequence structures and individual

operations based on the production drawing.

2. Definition of necessary tools

The programmer specifies the tools needed for each machining step.

3. Calculations of technological data

The cutting data with respect to the material and the used tool must

be specified for each machining step.

4. Calculation of geometric data

The coordinates needed are taken from the production drawing or are

specified by calculating known coordinates.

5. Generating NC programs

With respect to the previously determined geometric and technological

data, the programming steps are registered on a programming sheet.

6. Control of NC programs

The travel movements are simulated on a CNC-machine tool in order

to detect and control programming errors.

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Student's Notes

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Student's Notes

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