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IHT400 Calculation

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Description

CONVERSION FACTORS 1 HP = 1 HP = 1 HP =

33,000 ft

4 BTU/Min

Electric HP =

H2O = 62

4 lb/ft3

34 # / gal

Gal = 4

BASIS WEIGHT CONVERSIONS Offset (3300 ft2) x 1

GSM GSM GSM GSM

CONVERSION FACTORS FROM lb in in in ft/min (fpm) cfm cfm/in cfm/in2 cfm/in2/1000 fpm oz oz/ft2

TO OBTAIN kg mm cm m m/min (mpm) m3/hr m3/hr/cm m3/hr/cm2 3 m /hr/cm2/100 mpm g g/m2

MULTIPLY BY 0

M/c M/c

SPEED x DECKLE x GSM x 60 2 (mt/min) (mt) (Gm/mt ) (min/hr) M/C PROD =

M/C PROD (Tons/hr)

Speed x Deckle x GSM x 60

EXAMPLE Let

M/c Speed Deckle GSM

2 mt 50

M/C PROD =

200 x 3

92 Tons/hr

M/C Production in kg units Speed x Deckle x GSM x 60 M/C Prod

REAM WEIGHT CALCULATION REAM WEIGHT = PAPER SIZE x GSM x NO

OF SHEETS (Gm) = Length x Width x GSM x 500 (Let) (Mt) (Mt) GM (

Paper size GSM No

Ream Weight

60000000 =

10000 x W

Weight of paper in gms

Length of paper in cms

Width of paper in cms

EXAMPLE : Let a paper sample of dimensions 10 cm x 15 cm That means

l = 10 cm B = 15 cm Weight of this sample,

10000 x 0

Second Expression 10 cm x 15 cm size of paper has 0

-----150

0048 gms

0048 gms

0048 gms

Area of templet size sample = 2 x 25 cm x 20 cm = 1000 cm2 Let

1 cm2 1

0058 gms

0058 gms

----100

Theoretical Head =

V K Head K

Spouting velocity (fpm) Constant (see table)

In of H2O 1

Ft of H2O 23

In of Hg 26

Pressure PSIG 53

In of Hg 513

Pressure PSIG 732

SPOUTING VELOCITY V Where,

V h k Head K

h Spouting velocity (fpm) Theoretical head Constant (see table)

In of H2O 139

Ft of H2O 481

HEAD CALCULATION V2

h = Height of stock in head box V = Velocity (M/c speed in m/min) g = Acceleration due to gravity (9

81 m/sec2)

EXAMPLE Let M/c speed V = 200 m/min V2 h =

-----min 2

-------

62 min2

5663 m 56

= 1 min x 1 min = 60 sec x 60 sec 3600 sec2

Short Method 200 x 200

200 x 200

200 x 200

------m

81 x 3600

200 x 200

32 2 x 9

81 x 3600

QUICK FORMULA Speed x Speed h =

Where h in cms Speed = in m/min

EXAMPLE M/c Speed 1) 180 M/min ,

87 cms 706

200 x 200

63 cms 706

250 x 250

49 cms 706

Wire speed < 12 fpm : 1

5 – 2

Wire speed > 1200 fpm : 1

0 seconds

Multiply forming length by 60 to obtain M/c speed potential

Liner : 1

25 seconds

Multiply forming length by 48 to obtain M/c speed potential

Foodboard : 2 seconds

Multiply forming length by 30 to obtain M/c speed potential

V Cv g h

Stock speed at slice Coefficient of velocity discharge Acceleration due to gravity Head of stock

If h is measured close to the slice and V is measured at the vena-contracta of the Jet,

Cv is approximately 1

______ V =  2 gh Friction losses will reduce Cv possibly to around 0

EXAMPLE Let head of stock

Then Jet Velocity V

______________________ =  2 x 9

-----Sec2

____________________________ =  57 x 2 x 9

1 1 cm =

Similarly 3600 sec2 = 1 min2 1 Sec2 =

______________________ =  57 x 2 x 9

81 x 36 M2

-----Min

QUICK FORMULA

Jet Velocity (In m/min)

EXAMPLE 1) h = 46 cms,

72 = 180

48 = 250

72 M/min

12 x 106 x

= Critical speed (fpm) Ro = Outside radius (inches) Ri = Inside radius (inches) L'= Centerline to centerline bearing (inches) (assume L'= face + 40 inches)

Net consistency Retention % =

Head box consistency

Filler in sheet

Filler in Sheet 4) First – Pass Retention =

Where Av = Area of cross section at Vena-contracta Av = Ca As Ca = Coefficient of contraction As = Areas of cross section at the Slice opening

_____ Ca As Cv  2 g h _____ Ca Cv As  2 g h _____ Cq As  2 g h where,

Cq = Coefficient of volume discharge

______ Q = Cq As  2 g h 11 SANTOSH SWAR

GPM x 0

Velocity in fps A = Area in (inches 2) NOTE : This formula is for savealls and general paper flow,

since there is no orifice Coefficient included

82 ( V )

RPM = V = Do =

revolutions per minute Speed (fpm) Roll outside diameter (inches)

- V Sin A)

X V A g h

Distance of slice to lead forming board blade Initial Jet Velocity Jet angle 32

Water removed by a table roll per unit time & width Diameter of roll Wire speed A drainage factor (proportional to basis weight) determined by the Sag of wire,

thickness and porosity of mat,

degree of flocculation and evenness of formation

Exponent defining the effect of speed on drainage,

characteristics of type and quality of pulp (varies between 0

3 – 1

Second Method STOCK

Extracted water

Table Roll (mechanism of water extraction) According to Mr

the quantity of water that is being removed from the wire from A to B is equal to 4 K2 R gh =

R g h V

Drainage coefficient (dependent on the sheet weight & type of wire) Radious of the roll Acceleration due to gravity Head of stock suspension above the wire Velocity of the wire

VACUUM PUMP CAPACITY (CFM) PV

P V n T R

Absolute pressure,

lbs Absolute temperature  R = F + 460 Gas constant,

lbf x ft / (lbn x  R ) Ra (air) = 53

or for temperature cooling effects : P1V1

------T1

------T2

the following empirical formula can be used for obtaining a rough value of dryer surface required

(Exact value will depend on the quality of paper and constructional details etc

SWd = K

Peripherial length in meters of dryers in contact with paper During drying

Constant value around 0

EXAMPLE Let

M/c speed S = 180 M/Min GSM W = 50 Dryer shell thickness d'= 2

-----50

Spouting velocity (fpm) Slice opening (inches) Orifice coefficient (see table for approximate values)

Type Nozzle A B

A) Low angle,

Converflo

Type B) High angle

ß Type C) Straight

Sheet width,

Dryer diameter) Production Rate = 40 TPD Sheet width (to dryer) in inches W = 200 inches

----- = 16

Dryer diameter,

Hourly production

-----24

Tons/hr

Now water to be removed 94 33333 x (

Dryer surface required @ 2

-------2

Now Area of single dryer surface,

67 = 261

-------262

PI = PLI = Speed =

Press impulse (Psi – Sec) Nip pressure (Pli) Nip speed (fpm)

Torque (inch – pounds) in pounds in inches

WR2 W L'Do Di

in (lbs – ft2) Density (pounds/inches 3) Length (inches) Outside diameter (inches) Inside diameter (inches)

Vrc Q d

---- d2

Velocity of flow Total quantity Pipe diameter

IDEAL DRAINAGE IN WIRE PART a) Theoritically after forming board the drainage should be 80 to 85 % of stock thickness ( i

Slice opening)

b) At half of the forming zone,

it should be 40 % of slice stock thickness c) Before dandy it should be 20 to 25 % of slice stock thickness

Thickness of stock on table in cm

Basis weight in g/cm2 % Consistency in

Jet/Wire ratio = 1

overall retention of a machine with slice opening of ½  making 50 gsm at 0

0060 ) x 1

Ls l'D1 D2 K EXAMPLE L'D1

Length of wire (in mm) Distance between center of breast roll to couch roll (in mm) Diameter of breast roll (in mm) Diameter of couch roll (in mm) A constant,

Then Ls

75 mm 27

093 mtr

The term drag load resulted from the necessity of fabric manufacturers to monitor the power used to drive the fabric

It is a measure of the increase in tension ( T) of the fabric as a result of the suction forces pulling the fabric against the foil surfaces,

the iovac surfaces & the hivac surfaces

Suction Couch Drive Power = VOLT x AMP

DRAG LOAD =

------UW

Kilonewtons

Where V A U W

Volt AMP Fabric speed (M/S) Fabric width (M)

------ ,

DL in Pli

Drive volts (V) 20 SANTOSH SWAR

Drive AMPs (AMPS) Nominal fabric speed (fpm) Nominal fabric width (inches)

DRAG LOAD CALCULATION Safe drag load is 10 – 12 HP/Meter width of the wire/100 m/min wire speed If it is beyond 15 HP then it is alarming

VOLT x AMP x 49 (Constant) DRAG LOAD =

(EM + Ts)

DL Vn Vs EM

Drag load (Pli) Fabric speed at point n in fabric run (fpm) Fabric speed on slack side of fabric run (fpm) Fabric elastic modulus (young) at temperature

T ~ EMr – KT Elastic modulus at reference temperature r (Pli)

Modulus

Slack side tension (Pli)

Pli (----- ) ºF

Below 240 m/min dandy of diameter equal to 10 % wire width may be used

At higher speed the diameters should be more because with very high number of revolutions it throws water causing damage to the web

For Wove Dandy M/C Speed

Dia of Dandy =

Diameter in mm M/c speed in m/min Maximum number of revolution for a wove Dandy & it should be taken as 150 rev/min

------477

EXAMPLE Let M/c speed 400 D'=

V = 400 m/min

150 400

250 500

300 600

Web Speed (fpm)

Maximum 250 rpm

TONS PER DAY (T/D)

Capacity (gpm) x % Bone dry consistency

9 kg/min

Bs factor = 1

------68

Bs factor x prod

No of legs required

Primary legs Secondary legs Tertiary legs

Pressure drop = 1

4 kg/cm2

WEIR FLOW – CONTRACTIONS

RECTANGULAR

Q (ft2 H2O/Sec) = 3

2 H) H 1

5 Where,

Length of weir opening in feet (should be 4 – 8 times H) Head on weir in feet ( ~ 6 ft back of weir opening) at least 3 H (end contraction)

WEIR FLOW – TRIANGULAR NOTCH WEIR WITH END CONTRACTIONS 24 SANTOSH SWAR

Width of notch in ft at H distance above apex Head of water above apex of notch in feet 0

For 90 notch the formula is : Q

438 H 5/2

For 60 notch the formula is : Q

4076 H 5/2

Wv DA DW U t ∆P P

Wasted volume (in ft3/min

or m3/sec) Drilled Area (in %) Drilled width (in inch or M) Machine speed (in ft/min

or M/minute) Shell Thickness (in inch or cm) Suction Pressure (couch vacuum) in inch Hg) Pressure (in inch Hg)

EXAMPLE

DA DW U t ∆P P

= 50 % = 286 inch = 300 fit/min = 2

DA x DW x U x t

50/100 = 0

26 M 914

6 M/min 6

0635 M 81

3 K Pa 101

5 inch x

30 inch Hg

26 M x 914

35 cm x

6 M = 0

81 m3/S

V b S E

M/c speed,

feet % Open area of shell P2 Expansion factor,

-----P1

 Hg absolute Suction box vacuum, Hg absolute 26 SANTOSH SWAR

FORMATION – BLADE PULSE FREQUENCY F

------5x

= Formation – blade pulse frequency (in cycle/sec) = Wire speed (fpm) = blade spacing,

Optimum frequency for formation improvement “ F > 60 cycle/sec

SF – S1

Final Speed,

SLICE JET SPEED

Efflex ratio should be 0

9 – 1

EXAMPLE : Let M/c speed Head in the head box

Slice jet speed

Slice Jet Speed

JET VELOCITY VS WIRE SPEED IF IF IF

Jet velocity > Wire speed Jet velocity < Wire speed Jet velocity = Wire speed

Floading problem GSM drastically changed Real fiber orientation not occur

So Jet velocity is kept slightly less than M/c speed for real fiber orientation

ID and Caliper in inches

Example : 30 lb/3000 ft2 Area (ft2) Density (lbs/in3),

see table below Average paper density Grade Coated & supered Coated only News print

Density lb/ in3 0

Fine paper Liner board Board (coated)

------ (D

-d ) x W x

D = Parent roll dia (in m) d'= Empty spool dia (in m) W = Reel width (deckle) (in m) Thickness in mm

UNIT CALCULATION  GSM 2 2

------ (D

-d ) x W x

EXAMPLE Let a parent roll of deckle 3 meter

GSM = 50 Thickness = 0

67 kg/m3 0

(Apparent density) Parent roll circumference  D'= 3

2157 m 3

142 D2 = 1

3533 m 3

142 d2 = 0

------ (D

-d ) x W x

478 – 0

67 4 = 0

7857 x 1

67 = 2126

torque (inch – pounds) speed (rpm)

Vacuum box width x Vacuum

Vacuum box width (inches) Vacuum (inches of Hg)

By taking 80 % efficiency 2

By Amp reading method 1st Method Motor capacity = 10 KW 80 % efficiency,

V = I = COS  =

Input voltage (in volt) Current (in Amp) Power factor

EXAMPLE If 10 KW motor taking load 12 Amp Input voltage V = 410 V COS  = 0

95 KWH =

In centrifugal pumps or blowers A) Capacity varies directly with speed B) Head varies as the square of speed C) Horse power varies as the cube of speed

Ton/24 hr/in) (16

Net consistency = Head box consistency

Throat opening (inches) Spouting velocity (fpm)

If the belt is tight the pulley will also run tightly

Its bush bearings shall also worn out easily

On the other hand if length of a belt is in excess of the need,

it will slip frequently and result in loss of power

In order to determine the right length of belt,

the following formula are applied

Indications L= C= D= d=

Requisite length of the belt Distance from the center Diameter of the larger pulley Diameter of the smaller pulley

Length of Open Belt 32 SANTOSH SWAR

- d'2 2

-------2

6 x 2000

Volume = 3200 x # tons/% B

US Gallons = Volume / 7

Weight of dry stock at % consistency Volume of tank in cubic feet 2

inches Percent consistency of stock

------b

Ph F b L

Production of paper/hr (in kg/hr) Working surface of paper m/c wire Working width of paper web on the wire (in m) Distance from the axis of breast roll to the axis of couch roll (in m) (working length of Wire)

C Ne Nc D1 D2 OR

Change in total crown of two rolls (inches) Nip width at the ends (inches) Nip width at the center (inches) Top roll diameter (inches) Bottom roll diameter (inches)

NOTE : If C is minus,

EXAMPLE Let us assume that we have two 30 inch (762 mm) diameter rolls and we find that the nip widths are 0

Then Nc Ne D

8 mm) 0

7)2 C =

-----30

0915 x C 1

89 x Q 0

06 Where,

H = Head loss in feet of water / feet of pipe K = A constant depending of the type of stock (for bleached sulphite = 0

Q = Flow of stock L'= Pipe length D'= Pipe diameter (in inch) For pipes made of 2 or more section of different diameter and length,

H = K x 0

0915 x C

This can be addressed either by increasing the PLI KN/M to compensate for the vacuum or by sealing off the section box area with plastic and applying an amount of vacuum equal to that normally run in the roll

If the increased PLI KN/M method is used,

the original equipment supplier should be contacted to obtain the correct amount to be used

If this information is not readily available,

the incremental PLI KN/M addition can be approximated by using the following formula : 35 SANTOSH SWAR

Vacuum PLI KN/M = 0

The width,

in inches (mm) of the vacuum box

The vacuum level,

Box seal efficiency factor ( F = 0

Only 70-75 % of the vacuum PLI KN/M is used as an addition to the applied loading

C3 = FUN = V

P x C2 x C3 x 1000

(For cone pulley C3 is not required)

% WEAROUT OF WIRE 1) For single layer synthetic wire Original caliper

For Metal wire Original caliper

NOTE :- Synthetic wire is weft runner so weft  is taken for calculation & metal wire is wrap runner so wrap  is taken for calculation

EXAMPLE Single layer synthetic wire Original caliper Average used caliper Weft 

565 mm 0

565 – 0

4 % Wear =

28 = 84 %

Grade Liner board Bond Cover Index Bristol Offset Manuscript Wrapper News print

Production Factor Speed Deckle Basis weight

lbs/hour From table Feet/minute inches at reel lbs/ream

Ream size

Ft2/Ream 1000 1300 1805 2700 2110 3300 1948 2880 3000

Factor 0

00385 0

00277 0

00185 0

00225 0

00152 0

00258 0

00174 0

M/C Efficiency = (%)

Total Actual Prod

(MT) Actual Production (MT) x 106

Actual Production (MT) x 108 M/C Efficiency =

EXAMPLE

Actual Production (T) 2T 11

Total Running Efficiency Time (in min

of  Roll weight Cylinder x pressure x sides (kg) (cm2) (kg/cm2) Nip Load on Press =

Area of Cylinder   2 2 This is D

----4 4 2

Fulcrum Air for Loading  Here Area of cylinder is (D2 – d2)

Air for

Here Area of

Loading

Air for Loading  Here Area of cylinder is (D2 – d2) =

Intensity Pressure Intensity pressure can be found from pressure gauge reading

Lever Edge

(It is only ratio)

Y ( 1000) = X (500)

X 1000 =

------ =

X 14

X (26) 40

----26

Roll Weight If the loading role is lower side then the role weight to be subtracted & if it is on upper side the role weight to be added

Here loading roll is on lower side,

So roll weight is

Here loading roll is on upper side,

So roll weight is +ve

EXAMPLE

X (14 + 26)

Given Data Roll weight = 2 T = 2000 kg Intensity pressure = 5 kg/cm2 Face length = 220 cms Cylinder bore (in cms) D'= 25 cm Piston rod dia (in cms) d'= 5 cm Distance from roll center to fulcrum = 26  Distance from loading edge to fulcrum = 40

Area of cylinder is  2 2 (D – d')

----4 3

7855 = 471

Lever edge Y (14 + 26) X

---26

Unit load on roll 42 SANTOSH SWAR

Area of x Intensity x Lever x No

of  Roll weight Cylinder pressure edge sides

538 x 2

- 2000 kg

- 2000 kg

-----220

8 kg/cm

Given Data Roll weight = 2 T (2000 kg) Face length = 320 cms Intensity pressure = 6 kg/cm2 Cylinder bore = 10 inch = 25

Distance between fulcrum to roll center = 500 cms  Are of cylinder D2

----4 3

4 cm) x

X (500)

-----500

Nip load on press

Area of x Intensity x Lever x No

of  Roll weight Cylinder pressure edge sides

2 + 2000

26 kg/cm

Dia of couch (d) (in metres) Couch gear box teeth details (ratio) Couch gear box pulley  ( Max

(in mm) Line shaft couch cone pulley  ( Max

(in mm) Main motor pulley  (in mm) Main motor RPM Line shaft pulley  ( in mm)

EXAMPLE Main motor pulley  = Main motor RPM = Line shaft pulley  =

360 x 1500

Line shaft pulley RPM =

Ratio =

Mean = 735 mm

Mean = 435 mm

263 19 378

66 metres

Speed of couch =  d'x RPM 45 SANTOSH SWAR

142 x 0

Final Dryness

EXAMPLE Let Final dryness = 95 % Paper web entering the dryer Section of dryness = 38 % Production = 1200 kg/hr 95 Water evaporated at = (

Amplitude x (Frequency)2

Amplitude in inches Frequency in strokes/minute Wire speed in feet/minute

Optimum shake number is generally over 30 – 60

Stock flow (gpm)

Acceptable Range 7 – 14 fps

Paper / ft2 dryer surface /hour) SW “ L” Factor =

L S W N

# paper /ft2 dryer surface/hr M/c speed (fpm) Basis weight (lbs

Evaporation = # H2O /ft2 dryer surface / hr BD = Percent bone dry

deflection (inches) overface Resultant unit load of shell (pounds/inch) Shell face (inches) Centerline to centerline bearings (inches) Modulus of elasticity (lb/in2) Moment of inertia (inches 4) 0

0491 ( Do4

37 Do (0

Critical speed (fpm) Out side diameter of roll (inches) Roll deflection (inches) over face due to roll weight only (not to include externally applied forces) (See previous formula)

RIMMING SPEED (5’ & 6’ dryers) 2160 Remming speed (fpm) = ( 5720

Inside diameter of roll (feet) Condensate film thickness (feet)

127 F =

Natural frequency (cycles/second) Static deflection due only to weight of body (No externally applied forces)

of dry material 72) Consistency =