# Production Calculation of Draw Frame with Formulas & Examples

Introduction
Drawing is a process by which carded slivers are make up form parallel, remove hook and ultimately converted into drawn sliver. In this process, the sliver is elongated, doubled, leveled when passing through pairs of rollers. The tasks of draw frame are equalizing, parallelizing, blending and dust removing. There are mainly three actions are involved in draw frame, which are drafting, doubling and drawing. Calculations play an important role during the drawing process. Some important production calculation (Draft, Sliver Hank, DCP, Machine Efficiency, Machine Production) of Draw Frame machine are discussed below.

Some Important Conversion Factors for Production Calculation of Draw Frame:

• 36 inch = 3 Feet = 1 Yard;
• 1 Meter = 1.0936 Yards;
• 1 Pound(lb) = 453.6 Gram = 16 Ounce (Oz);
• 1 Lea = 120 Yards;
• 840 Yard = 7 Lea = 1 Hank;
• 1 Pound (lb) = 7000 Grains;
• 1 Meter = 39.37 Inch;
• 1 Kg = 2.205 Pound (lb)

Hank or count means the number of 840 yards length that weight exactly 1 pound (lb)

Production Calculation of Draw Frame Machine with Formula and Examples:

……………..Draft Constant
1. Draft =————————-
…………………..DCP

……………….Feed Weight
2. Draft = —————————— x Doubling
…………….Delivery Weight

Example: Find out the DCP if,

• Feed Sliver weight = 62 grains/yd
• Delivery Sliver weight = 60 grains/yd sliver
• Delivery speed = 400 m/min
• No of doubling = 8
• Draft constant = 320

Solution:

………………Feed Weight
Draft =———————————x Doubling
…………..Delivery Weight

=   x 8 = 8.267 (Ans)

We know that,

…………..Draft Constant
Draft = ————————-
………………….DCP

…………………Draft Constant
Or, DCP = ————————
……………………..Draft

= 320/8.267
= 38.7≈ 39 T (Ans)

……………………….Sliver Length (L) X Weight Unit (w)
3. Sliver Hank = ———————————————————————
……………………….Length Unit (l) x Sliver Weight (W)

Example: If the sliver weight = 55.5 grains/yard, then what will be the sliver hank?

Solution:

Here, Sliver weight, W = 55.5 grains

….55.5
= ———–lbs/yard
7000

= 0.008 lbs/yard

So, Sliver Length, L = 1 Yard.

…………………………….1 x 1
Sliver Hank = ——————— = 0.15 (Ans)
……………………..840 x 0.008

….Present hank              Required DCP
4. —————————- = ————————-
….Required hank            Present DCP

Example: A drawing frame producing 0.19 hank sliver with DCP of 56 T. If we want to produce 0.18 hank sliver, then calculate the required DCP.

Solution:

Here given,
Present DCP of Drawing Frame = 56
Present Hank of Sliver = 0.19
Required Hank = 0.18

We Know,

Present hank            Required DCP
————————– = ———————–
Required hank          Present DCP

………………………………..Present Hank
Or, Required DCP = —————————– x Present DCP
……………………………….Required Hank

Required DCP = (0.19/018) x 56 = 59.11≈ 59 T (Ans)

….Required Draft              Present Hank
5. —————————– = —————————–
….Present Draft                Required Hank

Example: A drawing frame producing 0.18 hank sliver with Draft of 8. If we want to produce 0.17 hank sliver, then calculate the required Draft.

Solution:

Here given,
Present Draft of Drawing Frame = 8
Present Hank of Sliver = 0.18
Required Hank = 0.17

We Know,

Required Draft         Present Hank
————————– = ———————–
Present Draft           Required Hank

………………………………..Present Hank
Or, Required Hank = ————————— x Present Draft
………………………………Required Hank

………………………………..0.18
Required Draft = ————– x 8
……………………………….0.17

= 8.47 (Ans)

………………Deliver Sliver Hank
6. Draft = ————————————– x Doubling
………………Feed Sliver Hank

Example: To get 0.17 hank sliver from a drawing machine by feeding 0.14 hank carded sliver (No of carded sliver is 6), Calculate the Draft.

Solution:

Here given,
Doubling = 6
Feed or Carded Sliver Hank = 0.14
Delivery or Drawn Sliver Hank = 0.17

……………Delivery Sliver Hank
Draft = ———————————- x Doubling
……………..Feed Sliver Hank

…..0.17
= ———- x 6 = 7.29 (Ans)
….0.14

7. Surface Speed of Roller = π x Roller Dia x Roller Speed

Example: A conventional draw frame with a 1.25’’ diameterroller and running at 450 rpm, find the surface speed of that roller?

Solution:

Here given,
Roller Dia = 1.25”
Roller Speed = 450 RPM

Surface Speed of Roller = π x Roller Dia x Roller Speed
= 3.1416 x 1.25 x 450 inch/min
= 1767.15 inch/min
= 1767.15/36 yards/min
= 49.0875 yards/min (Ans)

……………………………………………Surface Speed of Front Roller x Effi. x 60 x 8
8. Machine Production Per Shift = ———————————————————————-
…………………………………………………………….36 x 840 x Sliver Hank

Example: A machine’s front roller dia is 11/10”, front roller speed = 480 rpm, sliver hank = 0.16 and efficiency is 90%. Then what will be the production per shift of the machine?

Solution:

Here given,
Front Roller Dia = 11/10”
Front Roller Speed = 480 RPM
Efficiency = 90%
Sliver Hank = 0.16

Surface Speed of Front Roller = π x Front Roller Dia x Front Roller Speed
= 3.1416 x (11/10) x 480 inch/min
= 1658.76 inch/min

……………………………………………………Surface Speed of Front Roller x Efficiency x 60 x 8
Machine Production Per Shift = —————————————————————————–
………………………………………………………………………….36 x 840 x Sliver Hank

1658.76 x 90 x 60 x 8
= ————————————- lbs
36 x 840 x 0.16 x 100

= 148.1 lbs (Ans)

……………………………Delivery Speed (m/min) x 1.0936 x Effi. x Wastage x 60
9. Production (kg/hr) = —————————————————————————————
……………………………………………………840 x Sliver Hank x 2.205

Example: If, Delivery speed = 600 m/min, Sliver hank = 0.11 Ne, Efficiency = 85%, Wastage = 5%, Then what will be the production per hour?

Solution:

Here given,
Delivery Speed = 600 m/min
Sliver Hank = 0.11 Ne
Efficiency = 85%
Wastage = 5% = 100-5/100 = 95/100

…………………………………..Delivery Speed (m/min) x 1.0936 x Efficiency x Wastage x 60
Production per hour = ——————————————————————————————
………………………………………………………………840 x Sliver Hank x 2.205

……600 x 1.0936 x 85 x 95 x 60
= ———————————————— kg
840 x 0.11 x 100 x 100 x 2.205

= 156.04 kg (Ans)

10. Production (lb/day) = Delivery Speed x Delivery Wt. x Effi(%) x No of Delivery/frame x No of Total Draw Frame

Example: If, delivery speed = 600 ft/min, Feed sliver weight = 72 grains/yard, Draft = 8, No. of delivery/frame = 2, No of doubling = 6, Efficiency = 90% and No. of total draw frame in the factory is 8, then what will be the production (lbs/day)?

Solution:

Here given,

Delivery Speed = 600 ft/min

600 x 60 x 24
= ———————– yards/day
…………3

= 288000 yards/day

Feed Sliver Weight = 72 grains/yard
Draft = 8
Doubling = 6
No of Delivery/Frame = 2
Efficiency = 90%
Total Draw Frame = 8

We Know, Feed wt. x Doubling = Draft x Delivery wt.

…………………………..Feed wt. x Doubling
Or, Delivery wt. = ———————————
…………………………………….Draft

…..72 x 6
= ———— = 54 grains/yard
…….8

= 54/7000 lbs/yard

Production (lbs/day) = Delivery Speed x Delivery Wt. x Effi(%) x No of Delivery/frame x No of Total Draw Frame
= 288000 x (54/7000) x (90/100) x 2 x 10 lbs/day
= 39990.85 lbs/day (Ans)

……………………………..S. Speed of Front Roller(m/min) x 60 x 8 x 0.59 x Effi.
11. Machine Prodn/Shift = ———————————————————————————
………………………………………………………Sliver Hank x 1000 x 100

Example: Calculate the machine production (in kgs) per shift, if the surface speed of front roller is 550 m/min; sliver hank is 0.12; efficiency is 75%. (Shift time = 8 hrs)

Solution:

Here Given,
S.S. of Front Roller = 550 m/min
Sliver Hank = 0.12
Efficiency = 75%

…………………………………………Surface Speed of Front Roller (m/min) x 60 x 8 x 0.59 x Effi.
Machine Production/Shift = ————————————————————————————–
………………………………………………………………………..Sliver Hank x 1000 x 100

550 x 60 x 8 x 0.59 x 75
= ————————————— kgs
……..0.12 x 1000 x 100

= 973.5 kgs (Ans)

………………………………..Total Shift Time – Total Stoppage Time
12. Machine Efficiency = —————————————————————– x 100
…………………………………………………Total Shift Time

Example: Calculate the machine efficiency using the following data-

• Shift Working Time = 8 hrs.
• Doffing Time = 90 mins.
• Sliver Breakage Time = 20 mins.
• Cleaning & Other Stoppage Time = 22 mins.

Solution:

Here, Total Shift Time = 8 hrs = 480 mins.

Total Stoppage Time = Doffing Time + Sliver Breakage Time + Cleaning & Other Stoppage Time
= 90 + 20 + 22 mins
= 132 mins.

…………………………………Total Shift Time – Total Stoppage Time
Machine Efficiency = ———————————————————– x 100
………………………………………………….Total Shift Time

480 – 132
= —————- x 100
…….480

= 72.5% (Ans)

Conclusion
I have tried to explain the production and other calculation formulas (such as Draft, Sliver hank, DCP, Machine efficiency, Machine Production etc.) with examples of Draw Frame (Drawing) machine through this article. Hope this article will be helpful for those who are new to the spinning mill or those who are students.