Calculation Formulas

View: 813  From: HONG'S BELT  Date: 2013-01-06

Units Conversion

 English (USA) Unit X

Multiply by

 = Metric Unit

X Multiply by

= English (USA) Unit

 Linear Measure

in

25.40

 mm

0.0394

in

Linear Measure

in

0.0254

 m

39.37

in

ft

304.8

mm

0.0033

ft

ft

0.3048

m

3.281

ft

Square Measure

in2

645.2

 mm2

0.00155

 in2

Square Measure

in2

0.000645

 m2

1550.0

in2

ft2

92.903

mm2

0.00001

ft2

ft2

0.0929

m2

10.764

ft2

 Cubic Measure

ft3

0.0283

m3

35.31

ft3

 Cubic Measure

ft3

28.32

L

0.0353

ft3

Speed Rate

ft / s

18.29

m / min

0.0547

ft / s

Speed Rate

ft / min

0.3048

m / min

3.281

ft / min

Avoirdupois

Weight

lb

0.4536

kg

2.205

lb

Avoirdupois

Weight

lb / ft3

16.02

kg / m3

0.0624

lb / ft3

Bearing Capacity

lb

0.4536

kg

2.205

lb

Bearing Capacity

lb

4.448

 Newton (N)

0.225

lb

kg

9.807

 Newton (N)

0.102

kg

lb / ft

1.488

kg / m

0.672

lb / ft

lb / ft

14.59

N / m

0.0685

lb / ft

kg - m

9.807

N / m

0.102

kg - m

 Torque

in - lb

11.52

kg - mm

0.0868

in - lb

 Torque

in - lb

0.113

N - m

8.85

in - lb

kg - mm

9.81

N - mm

0.102

kg - mm

Rotate Inertia

in4

416.231

mm4

0.0000024

in4

Rotate Inertia

in4

41.62

cm4

0.024

in4

Pressure /Stress

lb / in2

0.0007

kg / mm2

1422

lb / in2

Pressure / Stress

lb / in2

0.0703

kg / cm2

14.22

lb / in2

lb / in2

0.00689

N / mm2

145.0

lb / in2

lb / in2

0.689

N / cm2

1.450

lb / in2

lb / ft2

4.882

kg / m2

0.205

lb / ft2

lb / ft2

47.88

 N / m2

0.0209

 lb / ft2

 Power

HP

745.7

watt

0.00134

HP

Power

ft - lb / min

0.0226

watt

44.25

ft - lb / min

Temperature

°F

T C = ( °F - 32 ) / 1.8

Temperature

Symbol of B D E F

Symbol

 Unit

BS

Conveyor Belt Tensile Strength

Kg/M

BW

Belt Width

M

 C  Symbol Definition


Symbol

 Unit

Ca

See the Table FC

----

Cb

See the Table FC

----

  Symbol Definition


Symbol

 Unit

 DS

Shaft Deflection Ratio

mm

  Symbol Definition


Symbol

  Unit

 E

Shaft Elongation Rate

Gpa

  Symbol Definition


Symbol

  Unit

FC

Friction Coefficient Between Belt Edge and Hold Down Strip

----

FBP

Friction Coefficient Between Carry Product and Belt Surface

----

FBW

Friction Coefficient of Belt Support Material

----

FA

Coefficient Amended

----

FS

Tensile Strength Coefficient Amended

----

FT

Conveyor Belt Temperature Coefficient Amended

---

 

Symbol of H I L M

Symbol

  Unit

H

Elevation Conveyor incline altitude.

m

HP

Horsepower

HP

 I   Symbol Definition


Symbol

  Unit

I

Moment Of Inertia

mm4

  Symbol Definition


Symbol

 Unit

L

Conveyance Distance (Center Point From Drive Shaft To Idler  Shaft)

M

LR

Return Way Straight Run Section Length

M

LP

Carry Way Straight  Run Section Length

M

  Symbol Definition


Symbol

 Unit

M

Spiral Conveyor Layer Level

----

MHP

Motor Horsepower

HP

 

Symbol of P R S

Symbol

  Unit

PP

Product Accumulated Measure Area Percentage of Carry Way

----

  Symbol Definition


Symbol

  Unit

R

Sprocket Radius

mm

RO

Outside Radius

mm

rpm

Revolutions Per Minute

rpm

  Symbol Definition


Symbol

  Unit

SB

Interval Between Bearing

mm

SL

Shaft Total Loading

Kg

SW

Shaft Weight

Kg/M

 

Symbol of T V W

Symbol

  Unit

TA

Conveyor Belt Unit Allowable Tension

Kg/M

TB

Conveyor Belt Unit Theory Tension

Kg/M

TL

Conveyor Belt Unit Catenary's Sag tension.

Kg/M

TN

Tension Of Section

kg/M

TS

Torque

Kg.mm

TW

Conveyor Belt Unit Total Tension

Kg/M

TWS

Particular Type Conveyor Belt Unit Total Tension

Kg/M

  Symbol Definition


Symbol

  Unit

V

Conveyance Speed

M/min

VS

Theory Speed

M/min

  Symbol Definition


Symbol

  Unit

WB

Conveyor Belt Unit Weight

Kg/M2

Wf

Accumulated Conveyance Friction Stress

Kg/M2

WP

Conveyor Belt Carry Product Unit Weight

 

Pusher And Bidirectional

For the pusher or bidirectional conveyor, the belt tension will be higher than the ordinary horizontal conveyor; therefore, the shafts at two ends are necessary to be considered as drive shafts and subsumed in the calculation. In general, it is approximate 2.2 times the experience factor to get the total belt tension.

FORMULA :

TWS = 2.2 TW = 2.2 TB X FA

  TWS in this unit means the tension calculation of the bidirectional or pusher conveyor.

 

Turning Calculation

The tension calculation TWS of the turning conveyor is to calculate the accumulated tension. Therefore, the tension in every carrying section will affect the value of total tension. That means, the total tension is accumulated from the the beginning of the drive section in return way, along the return way to the idler section, and then pass through the carrying section to the drive section.

The design point in this unit is T0 that under the drive shaft. The value of T0 is equal to zero; we calculate every section from T0. For example, the first straight section in return way is from T0 to T1, and that means the accumulated tension of T1.

T2 is the accumulated tension of the turning position in the return way; in another word, it is the accumulated tension of T0, T1 and T2. Please according to the illustration above and figure out the accumulated tension of the latter sections.

FORMULA :

TWS = ( T6 )

 

Total tension of the drive section in the carrying way.

TWS in this unit means the tension calculation of the turning conveyor.

 

 

FORMULA :

T0 = 0

 

T1 = WB + FBW X LR  X WB

 

Tension of catenary sag at the drive position.

 

 

FORMULA :

TN = ( Ca X TN-1 ) + ( Cb X FBW X RO ) X WB

 

Tension of the turning section in the return way.

 

For the value Ca and Cb, please refer to Table Fc.

 

T2 = ( Ca X T2-1 ) + ( Cb X FBW X RO ) X WB

 

TN = ( Ca X T1 ) + ( Cb X FBW X RO ) X WB

 

 

FORMULA :

TN = TN-1 + FBW X LR X WB

 

Tension of the straight section in the return way.

 

T3 = T3-1 + FBW X LR X WB

 

T3 = T2 + FBW X LR X WB

 

 

FORMULA :

TN = TN-1 + FBW X LP X ( WB + WP )

 

Tension of the straight section in the carrying way.

 

T4 = T4-1 + FBW X LP X ( WB + WP )

 

T4 = T3 + FBW X LP X ( WB + WP )

 

 

FORMULA :

TN = ( Ca X TN-1 ) + ( Cb X FBW X RO ) X ( WB + WP )

 

Tension of the turning section in the carrying way.

For the value Ca and Cb, please refer to Table Fc.

 

T5 = ( Ca X T5-1 ) + ( Cb X FBW X RO ) X ( WB + WP )

 

T5 = ( Ca X T4 ) + ( Cb X FBW X RO ) X ( WB + WP )

 

Spiral Conveyor

FORMULA :

TWS = TB × FA

  TWS in this unit means the tension calculation of spiral conveyor.

FORMULA :

TB = [ 2 × RO × M + ( L1 + L2 ) ] ( WP + 2WB ) × FBW + ( WP × H )

FORMULA :

TA = BS × FS × FT

 

Please refer to Table FT and Table FS.

Practical Example


The comparison of TA and TB, and other related calculations are the same as other types of conveyors. There are certain restrictions and regulations on the design and construction of the spiral conveyor. Therefore, while applying HONGSBELT spiral or turning belts to spiral conveyor system, we recommend you to refer to HONGSBELT Engineering manual and contact with our technical service department for further information and details.

 

Unit Tension

FORMULA :

TB = [ ( WP + 2WB ) X FBW ] X L + ( WP X H )

If carrying products are with the characteristic of piling up, the friction force Wf  that increases during the piling up conveyance should be subsume to the calculation.

FORMULA :

TB = [ ( WP + 2WB ) X FBW + Wf ] X L + ( WP X H )

FORMULA :

Wf = WP X FBP X PP

 

 

Allowable Tension

Due to the different material of belt has different tensile strength that will be affected by temperature variation. Therefore, the calculation of unit allowable tension TA can be used to contrast with the belt total tension TW. This calculation result will help you to make the right choice of belt selection and match the demands of the conveyor. Please refer to Table FS and Table Ts in left menu.

FORMULA :

TA = BS X FS X FT

 

BS = Conveyor Belt Tensile Strength ( Kg / M )

 

FS and FT Refer to Table FS and Table FT

 

Table Fs

Series HS-100


Series HS-200


Series HS-300


Series HS-400


Series HS-500


 

Table Ts

Acetal


Nylon


Polyethylene


Polypropylene


 

Shaft Selection

FORMULA :

SL = ( TW + SW ) ?BW

Driven / Idler Shaft Weight Table - SW


Shaft Dimensions 

Shaft Weight ( Kg/M )

 Carbon Steel 

Stainless Steel

 Aluminum Alloy 

Square shaft

38mm

11.33

11.48

3.94

50mm

19.62

19.87

6.82

Round Shaft 

30mm?/FONT>

5.54

5.62

1.93

45mm?/FONT>

12.48

12.64

4.34

Deflection of Drive / Idler Shaft - DS


Without Intermediate Bearing

FORMULA :

DS = 5 ?10-4 ( SL ?SB3 / E ?/FONT> I )

With Intermediate Bearing

FORMULA :

DS = 1 ?10-4 ( SL ?SB3 / E ?I )

Elasticity of Drive Shaft  - E


 Unit : Kg/mm2

 Material  

 Stainless Steel 

Carbon Steel

 Aluminum  Alloy

 Drive Shaft Elastic Rate

19700

21100

7000

 Inertia Moment  - I


Bore diameter of drive sprocket 

Inertia moment of shaft  ( mm4 )

 Square Shaft 

38mm

174817

50mm

1352750

 Round Shaft 

30mm?/FONT>

40791

45mm?/FONT>

326741

Drive Shaft Torque Calculation - TS


FORMULA :

TS = TW ?BW ?R

For the calculation value above, please compare with the table below for selecting the best drive shaft. If the torque of the drive shaft is still too strong, the smaller sprocket can be used to reduce the torque, and also economize the prime cost of shaft and bearing.

Using the smaller sprocket to fit the drive shaft that with the bigger diameter to reduce the torque, or using the bigger sprocket to fit the drive shaft that with  the smaller diameter to increase torque.

Maximum Torque Factor for Drive Shaft


 Torque

 Material 

Journal Diameter (mm)

50

45

40

35

30

25

20

Kg-mm

x

1000

 Stainless Steel 

180

135

90

68

45

28

12

 Carbon Steel 

127

85

58

45

28

17

10

 Aluminum Alloy 

--

--

--

28

17

12

5

 

Horsepower

 

If the drive motor is selected for a gear reducer motor, the horsepower ratio should be greater than the carrying products and the total tensile force that generates during the belt running.

Horse Power (HP)


FORMULA :

= 2.2 × 10-4 × TW × BW × V

 

= 2.2 × 10-4 ( TS × V / R )

 

= Watts × 0.00134

Watts


FORMULA :

= ( TW × BW × V ) / ( 6.12 × R )

 

= ( TS × V ) / ( 6.12 × R )

 

= HP × 745.7

Table FC

Rail Material

Temperature

FC

 Belt Material 

 Dry

Wet

HDPE / UHMW

-10°C ~ 80°C

P.P.

0.10

0.10

P.E.

0.30

0.20

Actel

0.10

0.10

Nylon

0.35

0.25

Acetal

-10°C ~ 100°C

P.P.

0.10

0.10

P.E.

0.10

0.10

Actel

0.10

0.10

Nylon

0.20

0.20

Please contrast the rails material and belt material of the conveyor with the transporting procedure in dry or wet environment to get value FC.

 

Ca, Cb Value

Conveyor Belt Turning Angle

Friction Coefficient Between Conveyor  Belt Edge & Rail Strip

FC ≤ 0.15

FC ≤ 0.2

FC ≤ 0.3

Ca

Cb

Ca

Cb

Ca

Cb

≥ 15 °

1.04

0.023

1.05

0.021

1.00

0.023

≥ 30 °

1.08

0.044

1.11

0.046

1.17

0.048

≥ 45 °

1.13

0.073

1.17

0.071

1.27

0.075

≥ 60 °

1.17

0.094

1.23

0.096

1.37

0.10

≥ 90 °

1.27

0.15

1.37

0.15

1.6

0.17

≥ 180 °

1.6

0.33

1.88

0.37

2.57

0.44

After getting value FC from Table FC, please contrast it with the curved angle of the conveyor, and you can get value Ca and value Cb.

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