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BASIC INTRODUCTION TO CONVEYORS


SECTION EIGHT
USEFUL FORMULAS

BELT CONVEYOR - HORSEPOWER CALCULATIONS

To determine the horsepower required for a belt conveyor, it is first necessary to determine the total belt pull. The belt pull, in turn, is based upon the live load plus the weight of all moving parts, multiplied by the coefficient of friction. The information required is listed as follows:
1. Size and weight of each package.
2. Belt speed.
3. Number of bed rollers times the weight of each roller.
4. Number of return idlers times the weight of each roller.
5. Total weight of all of the belting.
6. Total weight of all pulleys.
7. On inclines (or declines), the additional belt pull is required for that portion of weight on the conveyor on the incline (or decline). This is equal to the weight of all packages on the incline (or decline) times the sine of the angle.

COEFFICIENT OF FRICTION

Type of Conveyor

Friction Factor

Multiplier

Roller Bed - Ball Brgs.

5%

0.05

Roller Bed - Wood Sleeve Brgs.

10%

0.1

Steel Slider Bed with Return Idlers

30%

0.35

Steel Slider Bed with Steel Return

35%

0.35

Belt Driven Live Roller

7.50%

0.075


A. Live Load

The live load is the actual load on the conveyor at a given time. First we multiply the weight of each package times the number of packages per minute; we divide this total by the belt speed in feet per minute. This gives us the live load per foot which when multiplied by the total length of conveyor results in the total live load.

B. Weight of Belt

This includes the actual weight of both the TDP and bottom runs, in other words, the belt on top of the slider bed or carrying rollers and the return strand. See attached belt length formulas

WEIGHTS OF COMMONLY USED BELTS

Belt Description

Weights per inch width x 12" long

3 Ply Solid Woven Cotton

.040 lb.

Black PVC - 90

.040 lb.

Balck PVC - 120

.060 lb.

Black or White IWP-3

.047 lb.

Black Hilltopper

.100 lb.

Brown - 3 Ply Neoprene - Ruff tip

.120 lb.

 

How To Obtain Approximate Belt Lengths For Various Conveyors
NOTE: These formulas are for calculating horsepower only, not for determining replacement lengths of belts. *OAL = Overall Length

MODEL

TYPE OF DRIVE

FORMULA

TA

4" or 8" Dia. End Drive
4" or 8" Dia. Center Drive

2 x OAL + 1' - 0"
2 x OAL + 3' - 6"

TR

Same as for "TA"

 

TL

8" End Drive, 4" or 6" Dia. Tail Pulleys
8" Center Drive, 4" or 6" Dia. Tail Pulleys

2 x OAL + 1' - 0"
2 x OAL + 3' - 6"

190 RB

8" End Drive, 4" or 6" Dia. Tail Pulleys
8" Center Drive, 4" or 6" Dia. Tail Pulleys

2 x OAL + 6"
2 x OAL + 3' - 0"

25 RB

12" or 16" End Drive
12" or 16" Center Drive

2 x OAL + 3' - 0"
2 x OAL + 6' - 0"

190 LR

8" Center Drive

2 x OAL + 3' - 6"

25 LR

12" or 16" Center Drive

2 x OAL + 6' - 0"

Notes:1. Add 2 0 for double nose over on incline belts.2. Add 2 6 for underside take-ups for all above, except 25 RB.3. Add 6 6 for underside take-up for 25 RB.4. Add 2 x OAL + 6 for chain driven power feeders.5. Add 2 x OAL + 2 6 for integral type power feeders.

 

C. Weight of Rollers: Include the total weight of all bed rollers and return idlers. When slider bed construction is use, include only the weight of the return idlers.

ROLLER WEIGHTS (IN POUNDS)

Roller Length

6"

12"

18"

24"

30"

36"

42"

48"

Roller Diameter

 

 

 

 

 

 

 

1  3/89

0.7

1.2

1.8

2.6

-

-

-

-

1.9 x 16 Ga.

1

1.8

2.7

3.6

4.5

5.4

6.3

7.2

1.9 x 9 Ga.

2.1

3.8

5.4

7.1

8.8

10.5

12.1

13.8

2

1.6

2.8

4.3

5.7

7.2

8.6

10

11.5

2 1/8

2

3.2

4.9

6.5

8.1

9.7

11.3

12.9

2.5

2.4

4.1

6.1

8.2

10.2

12.2

14.3

16.3

2 5/8

3.5

5.9

8.8

11.8

14.7

17.6

20.6

23.5

 

D. Coefficient of Friction: Use the coefficient of friction which corresponds to one of the sketches pictured below. The percentages shown are for all types of belting on roller conveyor. Rubber covered belting is not normally recommended for slider bed construction, except for short lengths and light loads.

1. Roller bed with return idlers Coef. of friction
a. Ball bearings 5%
b. Wood burning 10%

2. Roller bed with steel slider return Coef. of friction
a. Roller bed with slider return & F.S. x F.S. belt 30%
b. With PVC belt 25%

3. Steel slider bed with return idlers Coef. of friction
a. With F.S. x F.S. belt 30%
b. With PVC belt 25%

4. Steel slider bed with steel slider return Coef. of friction
a. With F.S. x F.S. belt 35%
b. With PVC belt 30%

E. Weights of All Pulleys: Include total weight of all drive and idler pulleys, snub rollers, end and take-up pulleys.

PULLEY WEIGHTS (IN POUNDS)

 

 

 

 

 

 

Pulley Diameter

6"

12"

24"

30"

36"

42"

48"

4"

6

12

24

30

36

42

48

6"

9

16

33

42

50

58

67

8"

13

27

54

68

81

95

108

12"

-

-

108

135

162

189

216

 

F. Inclines or Declines: When all or any part of a conveyor is inclined or declined, an added belt pull is applied. This additional belt pull is obtained by multiplying the total live load on the inclined (or declined) portion by the sine of the angle.

SINE OF ANGLES

 

 

 

 

 

 

Angle

Sine

Angle

Sine

Angle

Sine

Angle

Sine

2

0.03

12

0.21

22

0.37

32

0.53

4

0.07

14

0.24

24

0.41

34

0.56

6

0.1

16

0.28

26

0.44

36

0.59

8

0.14

18

0.31

28

0.47

38

0.62

 

Belt pull for inclined portion = Live Load on incline times sine of angle or incline.

G. Two and Three Pulley Device: Add 5% of the Live Load preceding the device.

H. Deflectors: To accurately determine the total belt pull, add 30% of the weight of the heaviest package being diverted. We normally do not recommend diverting from belt conveyors except for light weight packages.

Belt pull equals weight of heaviest package times coefficient of friction for specific belting being used. Use only a smooth top belting.

I. Mechanical Traffic Cop: Add 30% of the weight of the maximum number of packages which will be held back by the traffic cop arm. The maximum weight of the total number of packages should never exceed 250 lbs.

J. Formula:
Horsepower = Effective belt pull x conveyor speed (feet per minute)
33,000 x .85 x .95
1. One horsepower is defined as the power required to move 33,000 lbs. A distance of one
foot in one minute.
2. .85 allows for 85% for worm gear efficiency. Hytrol gear boxes use worm gears.
3. .95 allows for the roller chain drive efficiency.

Example (Level RB Belt Conveyor)
1. Package weight = 45 lbs.
2. No. of packages per minute = 20
3. Belt speed = 65 FPM
4. Bed rollers = 12" CTRS. (Ball bearings)
5. Return idlers = 10' - 0" CTRS.
6. Belt width = 12" PVC 120
7. Conveyor width = 15" BR
8. Conveyor length = 100'= 0"
9. Drive 8" pulley = Center drive and take-up
Live load per foot = 45 x 20 = 14 lbs. Per foot
65
Live load = 100 ft. x 14 lbs. Per foot = 1400 lbs.
Bed rollers = 100 x 1.5 lbs = 150 lbs
Return idlers = 10 x 1.5 lbs. = 15 lbs.
Belting = 206 ft x .060 x 12 = 150 lbs.
Center drive and end pulleys = 77 lbs.

TOTAL WEIGHT TO MOVE 1792 lbs
Coef. of Friction 5% x .05
EFFECTIVE BELT PULL 90 lbs.

HP = 90 lbs. X 65 FPM = .20
33,000 x .85 x .95
Summary: Use the minimum horsepower offered by Hytrol: 1/3 hp (1/3 more than required).

LIVE ROLLER - HORSEPOWER CALCULATIONS
The same method for belt conveyors can be used for belt driven live roller conveyors. If the live roller is to accumulate a blocked load, simply calculate as though it were a moving load then double the horsepower.
Horsepower for single strand chain driven live roller as well as roller-to-roller chain driven live roller is calculated as follows:
A. Determine the live load in the same manner as for belt conveyor.
B. Add the weight of the rollers (See chart under belt conveyor).
C. Add the weight of sprockets and roller chain.

Conveyor Type

WEIGHT OF SPROCKETS

2 Dia. #50 CH

2 Dia. #60 CH

3 Dia. #80 CH

Single strand

.9#

 

 

Roller to roller

1.8#

3.0#

6.6#

WEIGHT OF CHAINS

Single strand

1.5#

 

 

Roller to roller

2.1#

3.0#

5.7#

 

D. Determine chain pull in the same manner as for belt pull under belt conveyor.

Chain Number

Allowable Chain Pull

Conveyor Speed F.P.M

to 65

65 to 80

80 to 100

100 to 150

RC 50

875#

800#

750#

650#

RC 60

1200#

1075#

1000#

850#

RC 80

2100#

1950#

1800#

1550#

 

SERVICE FACTORS
Operation up to 24 hours
Continuous single strand: 1.0
Roller to roller: 1.2
Sudden stopping or reversing: 1.4
Dirty conditions: 1.4

COEFFICIENT OF FRICTION
Single strand 6%
Roller to roller 5%

The formula to use is:
HP = Effective chain pull x speed in FPM
33,000 x .85 x .95
Multiply the effective chain pull service factor to determine if it is higher or lower than the allowable chain pull.
Horsepower calculations for chain conveyors are more complex in that shaft torque and bending moments farther the picture. Suggest checking with your Master Hytrol Distributor on applications which require chain conveyor.

Below is a formula for determining sprocket ratio, motor RPM, or belt speed:
No. of teeth (motor spkt.) x Pulley Dia. (inches) x TT x Reducer shaft RPM = Belt speed (ft. per min)
No. of teeth (pulley spkt.) 12
Substitute known values and solve for unknown.
EXAMPLE:
Wanted number of teeth on motor sprocket:
Known values:
1. Drive pulley dia. = 8 inches.
2. Reducer output shaft = 48 RPM
3. Belt speed = 65 FPM
4. Number of teeth (pulley sprocket) = 32
Then: 65 x 32 x 12 = 21 teeth
8 P x 48
MORE MISCELLANEOUS USEFUL FORMULAS
RPM (pulley) = FPM (belt) x 12
Pulley dia. (in inches) x P
RPM (roller) = FPM belt x 12
Roller dia. (in inches) x P
RPM (pulley) = Motor sprocket (no. of teeth)
RPM (motor) Pulley sprocket (no. of teeth)
FPM = RPM (motor) x no. teeth (motor spkt.) x pulley (or roller) dia. x P
No. of teeth (pulley sprocket x 12)
HP = Torque (lb. -ft.) x RPM = Torque (lb - inch) x RPM
2552 63,025
Torque = Effective belt pull x dia. of drive pulley.

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1996 FloStor Engineering