Design of Screw Conveyor

The size of screw conveyor depends on two factors

1. The capacity of the conveyor

2. The lump size of the material to be conveyed (Maximum dimensions of the particle)

Usually there are three ranges of lump sizes which are considered for selection of screw size. These are:

· A mixture of lumps and fines in which not more than 10% are lumps ranging from maximum size to one half of the maximum, and 90% are lumps smaller than one half of the maximum size.

· A mixture of lump and fines in which not more than 25% are lumps ranging from the maximum size to one half of the maximum, and 75% are lumps smaller than one half of the maximum size.

· A mixture of lump only in which 95% or more are lumps ranging from maximum size to one half of the maximum size and 5% or less are lumps less than one tenth of the maximum size.

The allowable size of a lump in a screw conveyor is a function of the radial clearance between the outside diameter of the central pipe and the radius of the inside of the screw trough, as well as the proportion of the lumps in the mixture.

The lump size of the material affects the selection of screw diameter which should be at least 12 times larger than the lump size of a sized material and four times larger than the largest lumps of an un-sized material.

Example, if screw diameter is 250mm means radial clearance is 105mm, & Maximum lump size is 60mm of 10% lumps.

Capacity of Screw Conveyor:

 

The capacity of a screw conveyor depends on the screw diameter, screw pitch, speed of the screw and the loading efficiency of the cross sectional area of the screw. The capacity of a screw conveyor with a continuous screw:

Q = V. ρ

Q = 60. (π/4).D².S.n.ψ.ρ.C

Where,

Q = capacity of a screw conveyor

V = Volumetric capacity in m³/Hr

ρ = Bulk density of the material, kg/m³

D = Nominal diameter of Screw in m

S = Screw pitch in m

N = RPM of screw

Ψ = Loading efficiency of the screw

C = Factor to take into account the inclination of the conveyor

 

Screw Pitch:

Commonly the screw pitch is taken equal to the diameter of the screw D. However it may range 0.75 – 1.0 times the diameter of the screw.

 

 

 

 

Screw Diameter:

 

Nominal Size D	Trough height from center of screw shaft to upper edge of the trough	Trough width C	Thickness of Tough	Tubular shaft (d1 * Thickness)	Outside diameter of solid shaft	Coupling diameter of shaft
Heavy Duty	Medium Duty	Light Duty
100	63	120	–	2	1.6	33.7*2.5	30	25
125	75	145	–	2	1.6	33.7*2.5	30	25
160	90	180	5	3.15	1.6	42.4*2.5	35	40
200	112	220	5	3.15	2	48.3*3.5	40	40
250	140	270	5	3.15	2	60.3*4	50	50
315	180	335	5	3.15	–	76.1*5	60	50
400	224	420	5	3.15	–	76.1*5	60	75
500	280	530	5	3.15	–	88.9*5	70	75

RPM of Screw:

The usual range of RPM of screw is 10 to 165. It depends on the diameter of screw and the type of material (Max RPM of screw conveyor is 165)

Loading efficiency:

The value of loading efficiency should be taken large for materials which are free flowing and non abrasive, while for materials which are not free flowing and or abrasive in nature, the value should be taken low:

Ψ = 0.12 to 0.15 for abrasive material

= 0.25 to 0.3 for mildly abrasive material

= 0.4 to 0.45 for non abrasive free flowing materials

Inclination Factor:

The inclination factor C is determined by the angle of screw conveyor with the horizontal.

 

Angle of screw with the horizontal	0°	5°	10°	15°	20°
Value of factor C	1	0.9	0.8	0.7	0.65

Types of screw flight:

The screw of the conveyor may be right hand or left hand, the right hand type being the usual design. The threads of the screw may be single, double or triple.

The flight of the screws may be made in either of the two ways:

1. As Helicoids

2. As Sectional flight

Helicoids Flight:

They are formed from a flat bar or strip into a continues helix. The threads are thinner at the outer edge and thicker at the inner edge.

Sectional flights:

Sectional flights are formed from a flat disc and the thickness of the thread is uniform throughout. A continuous helix is made by joining a number of sectional flights together on a piece of pipe and butt welded them. Various styles of screw flights are in use, depending on the service required.

Some of the typical configurations are:

1. Short pitch or continuous flight:

If the conveyor is required to handle dry granular or powdered materials that do not pack, this style of flight may be selected. It is of regular construction and recommended for inclined conveyors having a slope of 20 or more, including vertical conveyors. This style is extensively used as feeder screw.

2. Ribbon flight:

If the conveyor is to handle lumpy, clinging, sticky, gummy or viscous substances, this type flight may be selected. It consists of continuous helical flight formed from steel bar and secured to the pipe by supporting lugs.

3. Cut flight:

In this type of flight screws have notches cut in the periphery of the flight. These notches supplement the conveying with moderate mixing action. They are recommended for conveyors required to handle light, fine, granular or flaky materials.

4. Cut and folded flights:

This type of flight is characterized by notches as in cut flight, together with folded segments. This type of flight creates agitation and aeration resulting in better mixing. This type of flight is used to handle light or medium weight materials having fine, granular or flaky materials.

5. Some screw conveyors have cut flight with paddles mounted at regular intervals. The paddles counteract the flow of material past the flight resulting in greater agitation and mixing.

6. Sometimes screws are made of stainless steel to suit special requirements, like the sanitation requirements for handling food, drugs and other hygienic materials.

Vertical screw conveyors

A vertical screw conveyor conveys material upward in a vertical path. It requires less space than some other types of elevating conveyors. Vertical screw conveyor can handle most of the bulk materials provided there is no large lump. The maximum height is usually limited to 30m.

A vertical screw conveyor consists of a screw rotating in a vertical casing. The top bearing for the screw shaft must be designed to stand against radial and thrust loads. A suitable inlet port at the lower end and a discharge port at the upper end of the casing are provided. Feeding a vertical screw conveyor deserves careful consideration. Most materials are fed to the vertical conveyor by a straight or offset horizontal feeder conveyor. The ideal operation of a vertical screw conveyor is to have a controlled and uniform volume of material feeding.

Uneven feeding and start stop operation may adversely affect the performance of the vertical screw conveyor in terms of speed, capacity and horse power.

Average capacities and speeds of vertical conveyor

Nominal diameter of screw in mm	Capacities in m3/hr	Speed of screw
150	10	Up to 400 RPM
250	35	300 RPM
300	75	250 RPM
400	170	200 RPM

Vertical screw conveyors or some special design of vertical screw conveyor finds wide application in ship unloading.

Practical experience with these conveyors has shown that the resistance factor for vertical conveyors is higher than those of the horizontal conveyors. Resistance factor λ may be taken as 5.5 to 7.5 for grains. 6.5 to 8.3 for salt.

The driving power of the loaded screw conveyor is given by:

P = P_H + P_N + P_st

Where,

P_H = Power necessary for the progress of the material

P_N = Driving power of the screw conveyor at no load

P_st = Power requirement for the inclination of the conveyor

Power necessary for the progress of the material P_H:

For a length L of the screw conveyor (feeder), the power PH in kilo watts is the product of the mass flow rate of the material by the length L and an artificial friction coefficient λ, also called the progress resistance coefficient.

P_H = I_m.L. λ.g / 3600 (kilowatt)

= I_m.L. λ / 367 (kilowatt)

Where,

I_m = Mass flow rate in t/hr

λ = Progress resistance coefficient

Each material has its own coefficient λ. It is generally of the order of 2 to 4. For materials like rock salt etc, the mean value of λ is 2.5. For gypsum, lumpy or dry fine clay, foundry sand, cement, ash, lime, large grain ordinary sand, the mean value of λ is 4.0.

In this connection it should be noted that the sliding of the material particles against each other gives rise to internal friction. Other resistance due to grading or shape of the output discharge pattern contributes to the resistance factor. That is why the parameter λ is always higher than that due to pure friction.

Drive power of the screw conveyor at no load, P_N:

This power requirement is very low and is proportional to the nominal diameter and length of the screw.

P_N = D.L / 20 (Kilowatt)

Where,

D = Nominal diameter of screw in meter

L = Length of screw conveyor in meter

Power due to inclination: P_st

This power requirement will be the product of the mass flow rate by the height H and the acceleration due to gravity g.

P_st = I_m.H.g / 3600

= I_m.H / 367

H should be taken positive for ascending screws and will be negative for descending screws.

Total power requirement:

The total power requirement is the sum total of the above items

P = (I_m (λ.L + H) / 367) + (D.L /20) (Kilowatt)

Oscillating Conveyor System

Selection of vibratory conveyor:

The oscillating motion of the trough is achieved via specially designed inclined arms and an eccentric shaft driven by a motor through V-belts. The eccentric shaft is mounted on anti friction bearings and has V-pulleys at both ends with weights on them to counteract the unbalancing force. The rotation of the eccentric shaft provides a forward and backward motion to a connecting arm attached to the trough through a rubberized pin. The trough motion is predominantly horizontal with some vertical component, which causes it to oscillate with a pattern conductive to conveying material. A retaining spring assembly at the back of the trough absorbs shock load. All components including drive motor are mounted on a rigidly constructed base frame.

Advantages:

· Hot and abrasive materials can be handled

· Cooling, drying and de-watering operation can be done during transport

· Scalping, screening or picking can be done

· Units can be covered and made dust tight

· Simple construction and low head room

· Can be made leak proof

Disadvantages:

· Relatively short length of conveying ( about 50m Maximum)

· Limited capacity, about 350 tons per hour for length of conveying of 30 m.

· Some degradation of material takes place.

Applications:

Vibratory conveyors find wide spread application in the transportation of dusty, hot, toxic, and chemically aggressive bulk material through a closed trough or pipe in chemical, metallurgical, mining industries and manufacturing of building materials.

Vibratory conveyors are also employed for transportation of steel chips in machine shop, hot knocked out sand, wastes and small castings in foundry shop. Vibratory feeders are also in use for delivery of small machine parts like screws, rivets etc.

Sticky materials like wet clay or sand are unsuitable for vibratory conveyors. In handling finely pulverized materials, like cement etc., the performance of such conveyors are reported to be poor.

Vibratory conveyors are hardly employed for handling common bulk loads, such as sand, gravel, coal etc as the same can be done more efficiency by belt conveyors.

Red Marbles, Blue Marbles

Problem: you have two jars, 50 red marbles, 50 blue marbles. you need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. (when picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar) you can arrange the marbles however you like, but each marble must be in a jar.

Solution

Chance! chance is easy if you know how to do the formula. we know that we have two choices to make. first we’ll pick a jar, and each jar will have a 1/2 chance of being picked. then we’ll pick a marble, and depending how we stack the marbles, we’ll have a (# of red marbles in jar)/(# of total marbles in jar) chance of getting a red one.

for example, say we put all the red marbles into JAR A and all the blue ones into JAR B. then our chances for picking a red one are:

1/2 chance we pick JAR A * 50/50 chance we pick a red marble
1/2 chance we pick JAR B * 0/50 chance we pick a red marble

do the math and you get 1/2 chance for a red marble from JAR A and a 0/2 chance for a red marble from JAR B. add ‘em up and you get the result = 1/2 chance for picking a red marble.

think about it for awhile and see if you can figure out the right combination. we had a 50/50 (guaranteed) chance in picking a red marble from JAR A, but we didn’t have to have 50 red marbles in there to guarantee those fantastic odds, did we? we could’ve just left 1 red marble in there and the odds are still 1/1. then we can take all those other marbles and throw them in JAR B to help the odds out there.

let’s look at those chances:

1/2 we pick JAR A * 1/1 we pick a red marble
1/2 we pick JAR B * 49/99 we pick a red marble

do the math and add them up to get 1/2 + 49/198 = 148/198, which is almost 3/4.

we can prove these are the best odds in a somewhat non-formal way as follows. our goal is to maximize the odds of picking a red marble. therefore we can subdivide this goal into maximizing the odds of picking a red marble in JAR A and maximizing the odds of picking a red marble in JAR B. if we do that, then we will have achieved our goal. it is true that by placing more red marbles into a jar we will increase the chances of picking a red marble. it is also true that by reducing the number of blue marbles in a jar we will increase the odds also. we’ve maximized the odds in JAR A since 1/1 is the maximum odds by reducing the number of blue marbles to 0 (the minimum). we’ve also maximized the number of red marbles in JAR B. if we added any more red marbles to JAR B we would have to take them out of JAR A which reduce the odds there to 0 (very bad). if we took any more blue ones out of JAR B we would have to put them inJAR A which reduce the odds there by 50% (very bad).

it wasn’t really a good proof, but QED anyway 😛