Connecting Math Science to the Manufacturing Process MM

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

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.

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

Cartesian Coordinate System The Cartesian Coordinate System (3 D) 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.

Plotting Data Points for Manufacturing Process Control & Material Characteristics Testing

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?

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

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

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 = 54. 2611 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

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

Trigonometry for X Y Z Coordinates Y X

Machine Motion

---Metrology--The Science of Measurement The CMM Machine Coordinate Measuring Machine Can Measure a component to. 00005” Fifty Millionth of an inch

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

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

Sample CNC Program % O 12345 (Basic start to a program) N 10 G 20 N 11 G 0 G 17 G 40 G 49 G 80 G 90 N 12 T 1 M 6 N 13 G 0 G 90 G 54 X 0. 0 Y-1. 00 N 14 S 2500 M 3 N 15 G 43 H 1 Z 1. N 16 G 1 Z-. 1045 F 20. 0 N 17 M 98 P 1001 L 6 (Sub program call with a loop command of 6 passes) N 18 G 1 G 91 Z-. 1045 (Incremental Z move, . 625” / 6 ) N 19 G 1 G 90 Z-. 625 (Sub program call with FINISH PASS) N 20 M 98 P 1002 N 21 G 90 Z. 2 F 20. (Basic end to a program) N 22 G 0 Z 1. N 23 G 91 G 28 Z 0. N 24 G 28 X 0. Y 0. A 0. N 25 M 30 O 01001 Sub Program Finish Pass N 180 G 1 G 41 D 1 X 0. 0 Y-1. 0 F 10. 0 (Enter a tool diameter +. 010”) N 190 G 1 X 0. 0 Y 0. 0 N 200 G 1 X 0. 0 Y 2. 0 N 210 G 1 X. 500 Y 2. 0 N 220 G 3 X. 750 Y 2. 250 R. 250 N 230 G 1 X. 750 Y 2. 750 N 240 G 3 X. 500 Y 3. 000 R. 250 N 250 G 1 X 0. 0 Y 3. 000 N 260 G 1 X 0. 0 Y 4. 250 N 270 G 1 X. 750 Y 5. 000 N 280 G 1 X 2. 000 Y 5. 000 N 290 G 1 X 2. 000 Y 4. 500 N 300 G 3 X 2. 250 Y 4. 250 R. 250 N 310 G 1 X 2. 750 Y 4. 250 N 320 G 3 X 2. 750 Y 4. 500 R. 250 N 330 G 1 X 2. 750 Y 5. 000 N 340 G 1 X 4. 250 Y 5. 000 N 350 G 1 X 5. 000 Y 4. 250 N 360 G 1 X 5. 000 Y 3. 000 N 380 G 1 X 4. 500 Y 3. 000 N 390 G 3 X 4. 250 Y 2. 750 R. 250 N 400 G 1 X 4. 250 Y 2. 250 N 410 G 3 X 4. 500 Y 2. 000 R. 250 N 420 G 1 X 5. 000 Y 2. 000 N 430 G 1 X 5. 000 Y. 750 N 440 G 1 X 4. 250 Y 0. 0 N 450 G 1 X 3. 000 Y 0. 0 N 460 G 1 X 3. 000 Y. 500 N 470 G 3 X 2. 750 Y. 750 R. 250 N 480 G 1 X 2. 250 Y. 750 N 490 G 3 X 2. 000 Y. 500 R. 250 N 500 G 1 X 2. 000 Y 0. 0 N 510 G 1 X. 750 Y 0. 0 N 520 G 1 X-. 750 Y 1. 500 N 530 G 1 G 40 X-1. 000 N 540 G 0 Y 1. 0 N 550 G 0 X 0. 0 N 560 M 99

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

Motion requires 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? https: //www. youtube. com/watch? v=Iv. UU 8 jo. Bb 1 Q&index=1&list=PLbg. Wd. O 9 ys. ZSEzmh. QBb. H 5 q_R 2 g. PQW 0 R 2 KQ https: //www. youtube. com/watch? v=b. Adqazixu. RY&index=2&list=PLbg. Wd. O 9 ys. ZSEzmh. QBb. H 5 q_R 2 g. PQW 0 R 2 KQ

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