7c. DFA Exercise for High Speed Automatic Assembly

Contact Information

• Dr. Arfauz A Rahman: arfauz.arahman@qub.ac.uk, Ashby Room 6.18
• Prof. Yan Jin (Coordinator): y.jin@qub.ac.uk, Ashby Room 5.18

Module Information

• Module: MEE3014 Module 07C
• Topic: DFA (Design for Assembly) Exercise for High Speed Automatic Assembly

Key Concepts

• Design for Assembly (DFA)
• High Speed Automatic Assembly
• Feeding and Insertion Costs

Equations

Cycle Time

• Cycle time (s) = $\frac{60}{F}$
  • Where:
    • $F$ = Feed rate (parts / min), can be required ($F<em>r$) or maximum ($F</em>m$)

Feeding Cost - Standard Feeder

• $C<em>f = \frac{60}{F</em>r} R_r$
  • Where:
    • $C_f$ = Feeding cost
    • $F_r$ = Required feed rate (part / min)
    • $R_r$ = Cost of using feeding equipment (cent / s), e.g., 0.03 cent / s for a standard feeder

Feeding Cost - Specific Feeder

• $C<em>f = \frac{60}{F</em>r} C<em>r R</em>r$
  • Where:
    • $C_r$ = Relative cost factor for feeding
      • $C_r$ = 1 for a standard feeder
      • $C_r$ = determined by using classification tables for a specific feeder

Maximum Feed Rate

• $F_m = \frac{1500 E}{I}$
  • Where:
    • $E$ = Orienting efficiency for a part (determined by using classification tables)
    • $I$ = Length (mm) of a part

Insertion Cost

• $C<em>i = \frac{60}{F</em>r} W<em>r R</em>i$
  • Where:
    • $C_i$ = Insertion cost
    • $F_r$ = Required feed rate for insertion (part / min)
    • $R_i$ = Cost of using automatic workhead (cent / s), e.g., 0.06 cent / s for a standard workhead
    • $W_r$ = Relative cost factor for insertion
      • $W_r$ = 1 for a standard workhead
      • $W_r$ = determined by using classification tables for a specific workhead

Total Cost for a Part

• Total Cost = Feeding cost ($C<em>f$) + Insertion cost ($C</em>i$)

Exercise A: Feeding

Objective

• Determine $E$, $C<em>r$, and $C</em>f$ for feeding a part.

Given Information

• Working cycle time: 5 seconds
• Cost of using a standard feeder: $R_f$ = 0.03 cent/s

Steps

1. Determine the 3-digit code:
   • Use "dimension ratio" to determine the 1st digit.
   • Use "rotational symmetry" to determine the 2nd digit.
   • Use "orientation" to determine the 3rd digit.
2. Determine Orienting Efficiency (E) and Relative Feeder Factor (Cr) using classification tables.
3. Calculate Fr and Fm:
   • $F_r = \frac{60}{\text{cycle time}}$
   • $F_m = \frac{1500 E}{I}$
   • Compare $F<em>r$ and $F</em>m$ to decide which to use.
4. Determine Cf:
   • $\frac{R<em>f \cdot 60}{F</em>r} C_r$
   • $\frac{R<em>f \cdot 60}{F</em>m} C_r$

Part Dimensions (Example)

• A = 30 mm, B = 20 mm, C = 15 mm

Step/Groove Heights (Example)

• Height of step and grooves in X direction = 4 mm
• Height of grooves in Y direction = 4 mm
• Height of step in Z direction = 10 mm

3rd Digit Note

• If the part has main features in X, Y, Z axis simultaneously, select the feature that gives the "smallest third digit".

Exercise B: Insertion and Total Cost

Objective

• Determine $W<em>r$ and $C</em>i$ for insertion and the total cost (sum of feeding and insertion costs).

Given Information

• Part is inserted horizontally in the direction of arrow Y.
• Cycle time is 5 s.

Steps

1. Determine the 2-digit code:
   • 1st digit: straight line insertion or not, vertically or horizontally?
   • 2nd digit: Is it easy to align and position; is there any resistance to insertion?
2. Calculate Total Cost:
   • Feeding cost ($C<em>f$) + Insertion cost ($C</em>i$)

Contact Details

• DR ARFAUZ A RAHMAN
• Room 06.018, Ashby Building
• Stranmillis Road Belfast
• Northern Ireland BT9 5AH
• Tel: +44 (0) 28 9097 5495
• Email: arfauz.arahman@qub.ac.uk