1. Connecting Math & Science to the Manufacturing Process
M&M Summer Institute
Platt Technical High School
July 25, 2018

2. Manufacturing is 100% Dependent on Math & Science
Engineering Designs
Materials (What stuff is made from & why)
Expected Forces, Loads, Strengths, Environments, etc.
Life expectancy of a component.

3. Real World Mathematics Applied Everyday in Manufacturing
Fractional – Decimal conversions.
Percentage calculations – chemical, motion, time, costs
Ratios – mechanical, chemical
Time & cost – Everything has a cost
Geometry for areas, volume. Engineering needs
Trigonometry - Polar coordinates
Rotational - circumference, radians, angular
Weights – What does it weigh, What will it weigh?
Dimensions – Dictates all engineering designs
Imperial & Metric conversions – Global Economy
Cartesian Coordinates – All machines are driven from

4. Cartesian Coordinate System
The Cartesian Coordinate
System (3D) is the entire motion basis for all manufacturing processes, machine tools and measurement
Machines can achieve axial position increments of .0001” within a cubic work envelope. One Ten Thousandths of an Inch.

5. Plotting Data Points for Manufacturing Process Control & Material Characteristics Testing

6. Mathematical Calculations in Manufacturing
Rotational Speeds = RPM to Surface feet per minute.
Controls product costs and quality
The materials used in the manufacturing process dictate all speeds and subsequently cost and pricing
Cutting tools rotate and create friction. Rotation impacts temperature.
Feed Rates = Distance over time
Controls product cost, quality and tool life
The materials used in the manufacturing process dictate allowable feeds.
How deep and aggressive of a bite can the machine or cutting tool take?

7. Mathematical Calculations in Manufacturing
Distance per revolution & per cutting tooth
Controls product cost, quality and tool life
Controls thermal factors which can affect material microstructures
Materials control chip load (feed per tooth)
Geometry
Area-Perimeter-Cubic-Circumference
Material removal rates in volume & weight
Surface area for speed control
Material costs by volume

8. Mathematical Calculations in Manufacturing
Percentages
Incremental changes in cutting rates
Time and cost savings
Salary increases
Cost & Time
Cost of manufacturing over time
Cost of labor over time
Inch & Metric
Manufacturing is GLOBAL. America works every day within a dual measurement
system and within dual Cartesian Coordinate systems

9. Calculations in Manufacturing
Angular
Manufacturing Equipment runs from Decimal Degrees
Conversion to Decimal I.e. Degrees, minutes & seconds to decimal
54 degrees, 15 minutes, 40 seconds = degrees
How many seconds are in 360 degrees???
1,296,000
Manufacturing Equipment positions in 6 Axial locations
X Y Z locations within a cube
Rotational --A B C Axial positions
Combined --XYZABC positions

10. Calculations in Manufacturing
Weights
Volume calculations per cubic inch to determine materials cost, materials removal weight and recycling savings
Ratios
Chemical solutions in machining coolants, adhesives, paints
Production rates of machine time vs. labor hours
Overhead, overtime, labor

11. Trigonometry for X Y Z Coordinates

12. Machine Motion

13. ---Metrology--- The Science of Measurement
The CMM Machine
Coordinate Measuring Machine
Can Measure a component to ”
Fifty Millionth of an inch

14. Computer Numerical Control --CNC--
CNC Machines operate from a computer program that automates a machining or motion processes.
The program contains codes and coordinates which is a list of motion commands for the machine to execute.
The coordinates are determined by dimensional information on the engineering drawings.
The final result of an executed CNC program should be the precision manufactured or measured component

15. The CNC Programmer must be able to interpret the design and with
a background in precision machining write a list of robotic commands
which will result in the intended design

16. Sample CNC Program
N250 G1 X0.0 Y3.000
N260 G1 X0.0 Y4.250
N270 G1 X.750 Y5.000
N280 G1 X2.000 Y5.000
N290 G1 X2.000 Y4.500
N300 G3 X2.250 Y4.250 R.250
N310 G1 X2.750 Y4.250
N320 G3 X2.750 Y4.500 R.250
N330 G1 X2.750 Y5.000
N340 G1 X4.250 Y5.000
N350 G1 X5.000 Y4.250
N360 G1 X5.000 Y3.000
N380 G1 X4.500 Y3.000
N390 G3 X4.250 Y2.750 R.250
N400 G1 X4.250 Y2.250
N410 G3 X4.500 Y2.000 R.250
N420 G1 X5.000 Y2.000
N430 G1 X5.000 Y.750
N440 G1 X4.250 Y0.0
N450 G1 X3.000 Y0.0
N460 G1 X3.000 Y.500
N470 G3 X2.750 Y.750 R.250
N480 G1 X2.250 Y.750
N490 G3 X2.000 Y.500 R.250
N500 G1 X2.000 Y0.0
N510 G1 X.750 Y0.0
N520 G1 X-.750 Y1.500
N530 G1 G40 X-1.000
N540 G0 Y1.0
N550 G0 X0.0
N560 M99 %
O (Basic start to a program)
N10 G20
N11 G0 G17 G40 G49 G80 G90
N12 T1 M6
N13 G0 G90 G54 X0.0 Y-1.00
N14 S2500 M3
N15 G43 H1 Z1.
N16 G1 Z F20.0
N17 M98 P1001 L6 (Sub program call with a loop command of 6 passes)
N18 G1 G91 Z (Incremental Z move, .625” / 6 )
N19 G1 G90 Z (Sub program call with FINISH PASS)
N20 M98 P1002
N21 G90 Z.2 F20. (Basic end to a program)
N22 G0 Z1.
N23 G91 G28 Z0.
N24 G28 X0. Y0. A0.
N25 M30
O01001 Sub Program Finish Pass
N180 G1 G41 D1 X0.0 Y-1.0 F (Enter a tool diameter +.010”)
N190 G1 X0.0 Y0.0
N200 G1 X0.0 Y2.0
N210 G1 X.500 Y2.0
N220 G3 X.750 Y2.250 R.250
N230 G1 X.750 Y2.750
N240 G3 X.500 Y3.000 R.250

17. What could we teach with this image?
What about math conversions?
Fraction to decimal?
Fraction to percentage?
Rotational motion to linear motion?
Motion?
Ratios?
Circumference?
Rotation?

18. Motion requires Math Does Music require math?
All mechanical devices utilize hardware to provide motion from the sum of the parts.
All of the moving parts must interact with the others to ensure smooth operations.
The engineered designs of the components must be dimensionally accurate otherwise the result of the final assembly will not function to desired expectations.
Does Music require math?

24. Green
Grey
Clear
Grey
Clear
Grey