7b. DFA Calculations 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 7B
• Topic: DFA Calculations for High Speed Automatic Assembly

Learning Outcomes

• Understand calculations of DFA for automatic assembly.
• Familiarize with calculation concepts through sample exercises.

Design for Automatic Assembly - General Design Rules (1)

• Minimize the number of parts.
• Ensure:
  • The product has a suitable base part for building the assembly.
  • The base part has features for stable location in the horizontal plane.
  • The product can be built up in layers, with each part assembled from above.
• Provide chamfers or tapers to guide and position parts correctly.
• Avoid expensive and time-consuming fastening operations like screw fastening and soldering.

Design for Automatic Assembly - General Design Rules (2)

• Avoid projections, holes, or slots that cause tangling when parts are in bulk.
• Attempt to make parts symmetrical.
• If symmetry is not achievable, provide asymmetrical features for part orientation.
• Use self-centering screws whenever possible.

High Speed Automatic Assembly - Calculations of Feeding Cost (Cf)

• Feeding cost depends on:
  • Cost of the equipment required.
  • Time interval between delivery of successive parts.
• Time between delivery of parts:
  • Reciprocal of the delivery rate (higher delivery rate means shorter delivery time).
  • Equal to the cycle time of the machine or system.
• Feeding cost for each part $C<em>f$ (in cents) is given by: $C</em>f = (60/F<em>r) R</em>f = 0.03 (60/F_r)$
  • $F_r$: Required feed rate (parts/minute).
  • $R_f$: Cost of using feeding equipment (cents/second), i.e., 0.03 cent/second.

Feeding Cost with Specific Feeder

• A relative cost factor, $C_r$, is assigned if a specific feeder is needed.
• The feeding cost for each part, $C<em>f$, becomes: $C</em>f = 0.03 (60/F<em>r) C</em>r$
  • For a standard feeder: $C<em>r = 1$, $C</em>f = 0.03 (60/F_r)$
  • For a specific feeder: $C_r$ is determined using a classification table.

Factors Affecting Feeding Cost

• From $C<em>f = (60/F</em>r) R<em>f$, feeding cost per part $C</em>f$ is:
  • Proportional to the cost of using feeding equipment ($R_f$).
  • Inversely proportional to the required feed rate ($F_r$).
• Compared with the feeding cost for a machine with a 3s cycle (20 parts/min), a machine with a 6s cycle (10 parts/min) would double the cost to feed identical parts.
• It's preferable to use feeding equipment with a short cycle time.

Feed Rate and Part Size Considerations

• The faster the parts are required, the lower the feeding cost.
• There is an upper limit to the feed rate obtainable from a particular feeder.
• $F_m$ = Maximum feed rate = $1500 E / I$
  • $E$: Orienting efficiency for the part (determined by classification table).
  • $I$: Length (mm) of the part (the longest dimension of the part).
• Automatic feeding methods are applicable to small parts.
• Parts larger than about 8” in their major dimension cannot be fed economically.

Using Required Feed Rate (Fr) or Max Feed Rate (Fm) to Calculate Feeding Cost (Cf)

• Selection of $F<em>r$ or $F</em>m$ depends on the situation.

Case 1: Fr < Fm

• Suppose $F_m$ of a feeder is 10 parts/min (cycle time 6s).
• $F_r$ is 5 parts/min (cycle time 12s).
• Since $F<em>r$ (5 parts/min) < $F</em>m$ (10 parts/min), use $F_r$.
• $C<em>f = (60/F</em>r) R<em>f C</em>r$
  • $R_f$: Cost of using feeding equipment (cent/second), i.e., 0.03 cent/second.
  • $C_r$: 1 (for a standard feeder) or determined by classification table (for a specific feeder).
  • $F_r$: Required feed rate (part/minute).
• This leads to feeding cost increases because it does not reach the full capacity of the feeder.

Case 2: Fr = Fm

• $F_r$ is 10 parts/min (cycle time 6s).
• Since $F<em>r$ (10 parts/min) = $F</em>m$ (10 parts/min), use $F_m$.
• $C<em>f = (60/F</em>m) R<em>f C</em>r$
  • $R_f$: Cost of using feeding equipment (cent/second), i.e. 0.03 cent/second.
  • $C_r$: 1 (for a standard feeder) or determined by classification table (for a specific feeder).
  • $F<em>m$: Max feed rate (part/minute) where $F</em>m = 1500 E / I$
    • $E$ is the orienting efficiency of the part (determined by classification table).
    • $I$ is the length (mm) of the part.
• Feeding cost reaches the minimum (ideal case).

Case 3: Fr > Fm

• $F_r$ is 20 parts/min (cycle time 3s).
• Since $F<em>r$ (20 parts/min) > $F</em>m$ (10 parts/min), use $F_m$.
• $C<em>f = (60/F</em>m) R<em>f C</em>r$
  • $R_f$: Cost of using feeding equipment (cent/second), i.e. 0.03 cent/second.
  • $C_r$: 1 (for a standard feeder) or determined by classification table (for a specific feeder).
  • $F<em>m$: Max feed rate (part/minute) where $F</em>m = 1500 E / I$
    • $E$ is the orienting efficiency of the part (determined by classification table).
    • $I$ is the length (mm) of the part.
• Cannot be achieved by one feeder (consider using more feeders).

Summary of the 3 Cases

• Suppose $F_m$ of a feeder is “10 parts/min (cycle time is 6s)”
  • Case 1: $F<em>r$ = 5 parts/min (required cycle time of 12s) results in higher feeding cost ($C</em>f$)
  • Case 2: $F<em>r$ = 10 parts/min (required cycle time of 6s) Feeding cost ($C</em>f$) reaches to the minimum
  • Case 3: $F<em>r$ = 20 parts/min (required cycle time of 3s) Cannot be achieved by one feeder (i.e. need to use more feeders to fulfil the required feed rate of $F</em>r$ > 10)

Determining Max Feed Rate (Fm) When Not Known

• In most situations, $F_m$ is not known.
• It needs to be determined by following logical steps and using classification tables.

Feeding Cost Calculation at Max Feed Rate (Fm)

• Feeding cost for each part ($C<em>f$) working at max feed rate ($F</em>m$): $C<em>f = 0.03 (60/F</em>m) C<em>r$ where $F</em>m = 1500 E/I$
  1. The cost of using feeding equipment ($R_f$ or 0.03 cent/s) and length of part ($I$) are already known by the designer / engineer.
  2. Determine the orienting efficiency E and relative feeder factor $C_r$ using standard classification table.
  3. When E and I are both known, $F_m$ can be determined.
  4. When $C<em>r$ and $F</em>m$ are both known, $C_f$ can finally be determined.

Use of Classification Table to Determine Orienting Efficiency (E) and Relative Feeder Factor (Cr)

• Use the classification table to determine $E$ and $C_r$

Determining E and Cr Using Classification Table

• Determine orienting efficiency ($E$) and relative feeder factor ($C_r$) using classification table (three-digit code).
  • Use dimension ratio to determine the 1st digit.
  • Use rotational symmetry to determine the 2nd digit.
  • Use orientation to determine the 3rd digits.
• 1st digit, 2nd digit, 3rd digit -> E, Cr
• 1st Digit:
  • Oriented by length oriented by main feature
• 2nd Digit:
  • Symmetry about all axes Symmetry about one axis No symmetry

1st Digit Determination

• The 1st Digit Tables are different for “rotational” and “non-rotational parts”.

Rotational Parts

• $L$ is the length
• $D$ is the diameter of the smallest cylinder (that can completely enclose the part).

Non-Rotational Parts

• $A$ is the length of the longest side
• $C$ is the length of the shortest side
• $B$ is the length of the intermediate side of the smallest rectangular prism (that can completely enclose the part).
• $X$, $Y$ and $Z$ are the three axis directions

Example of Using Classification Table - Rotational Parts

• If the three-digit code for a rotational part is “100”, then:
  • $E = 0.7$
  • $C_r = 1$

Example of Using Classification Table - Non-Rotational Parts

• If the three-digit code for a non-rotational part is “610”, then:
  • $E = 0.4$
  • $C_r = 1$

Working Example (Non-Rotational Parts)

• Determine the 1st digit (based on dimension ratio).
• Determine the 2nd digit (based on rotational symmetry):
  • If the part has rotational symmetry of 180 degrees about one axis => digit 1, 2, 3 for x, y, z axis
  • If the part has no rotational symmetry => digit 4

Working Example (Non-Rotational Parts) - Determining the 3rd Digit

• Orientation of the part is defined by the main feature (steps / chamfers / grooves).
• Size of which must be larger than 0.1B or 0.1C, depending on the axis parallel to:
  • 0.1C for X and Y axis, 0.1B for Z axis
• If the part has:
  • Steps / chambers parallel to axis => digit 0, 1, 2 for X, Y, Z axis
  • Grooves parallel to axis => digit 3, 4, 5 for X, Y, Z axis
• Example Measurements: A = 30 mm, B = 20 mm, C = 15 mm. Step/groove heights: X=4mm, Y=4mm, Z = 10mm

Part Orientation & 3rd Digit Selection

• Part can be fed in only one orientation.
• If the part has main features in X, Y, Z axis at the same time, select the feature to give the smallest third digit (i.e. X-direction in the example).

Calculations of Insertion Cost (Ci)

• Automatic workhead can be operated on a cycle less than 1 second.
• The automatic insertion cost for each part ($C<em>i$) is given by: $C</em>i = (60/F<em>r) R</em>i W<em>r = 0.06 (60/F</em>r) W_r$
  • $F_r$ is the required feed rate for insertion (part/minute)
  • $R_f$ is the cost of using the automatic workhead (cent/second), i.e. 0.06 cent/second
  • $W<em>r$ is the relative cost factor to specific work head (i.e. $W</em>r$ is 1 for a standard work head)

Determining Wr Using Classification Table

• Determine the relative cost factor ($W_r$) using classification table (2-digit code).
  • Determine the 1st digit: based on the motion and axis of insertion (row of the table).
    • For a straight line motion, go for “digit 0 (vertical) or 1 (not vertical)”
    • If “not” a straight line motion, go for “digit 2”
  • Determine the 2nd digit: based on the difficulty of alignment (column of the table).
    • If easy to align and position, go for “digit 0 (no resistance) or 1 (has resistance)”
    • If “not” easy to align or position, go for “digit 2 (no resistance) or 3 (has resistance)”