Determination of thrust forces and useful power consumption.
During rolling, forces arise in the working gap that try to push the rolls apart. These forces are called expansion forces. They must be taken into account when calculating, otherwise, if excessive forces are applied, the rollers may break.
The complexity of the rolling phenomenon and insufficient theoretical knowledge make it difficult to calculate thrust forces and power consumption. These values can be determined by two methods:
1. Processing of experimental data based on the theory of similarity
2. Mathematical analysis of the process with the introduction of certain assumptions.
For the first method, experiments are carried out on a model machine, thrust forces and power consumption are obtained.
where: - diameter of the rolls; - gap size; - friction value; - specific gravity of the mixture; L - roll length; - angular speed of the high-speed roll; - final plasticity of the material 
- experimental coefficients, which for some materials are given in reference books.
According to the second method, simple mathematical dependencies are obtained by introducing the following assumptions:
1. The effective viscosity (average) of the mixture does not change
2. The minimum flow regime of the mixture in the gap is laminar
3. The material sticks to the surface of the rolls and the speed of the layers at the surface is equal to the speed of the roll (U=V)
4. Inertial forces are small
5. Material flow is one-dimensional (into the gap)
6. The speed of the mixture does not change vertically
7. The pressure at the inlet and outlet of the material into the rolls is zero
8. The pressure in planes parallel to the axes of the rolls does not change.
Then the equation of motion of a viscous fluid (Navier-Stokes) has the form:
, (6.3)
By integrating this equation and taking into account the assumptions, an expression for the thrust force was obtained:
, (6.4)
where: - friction value; - effective viscosity; - speed of the front roll; - roll radius; - roll length; - gap between rollers.
The moment consumed by the rolls is equal to the sum of the torques:
, (6.5)
- torques of high-speed and low-speed rolls.
Total power consumed by the rolls.
It is calculated using the formula:
(6.8)
where: is the required total torque.
where: - idle speed; - moment of additional friction forces.
, (6.10)
where: - radial load on the axle; - bearing friction coefficient; - journal diameter; - gear ratio of the transmission and friction pair; - overall efficiency transmission and friction pair;
The moment of additional forces is equal to:
, (6.11)
where: is the thrust force on the rolls.
Performance calculation.
Roller machines operate according to the schemes of single and multiple passage of the processed material through the gap. For a single passage of material through the rollers, productivity is determined by the formula:
, (6.12)
where: - one-time download; - machine utilization rate (0.85 - 0.9). - specific gravity of the material; - cycle duration;
where: - diameter of the front roll; - length of the roll barrel.
The cycle time is determined by the formula:
, (6.14)
where: - loading and unloading time; - technological operating time. This time is determined experimentally.
It should be noted that there are other calculations of dependence when determining the productivity of rollers.
Thermal calculation of rollers.
When processing material in the roll gap, a large amount of heat is released and, as a result, the temperature of both the working surface of the rolls and the processed mixture increases. To prevent unwanted temperature changes (scorching, etc.), special cooling of the rolls is provided. The amount of heat generated during processing can be determined by the power consumed by the rollers, taking into account the efficiency of all gears and axles.
This heat is spent on heating the mixture being processed Q 1, on losses to the environment Q 2 and on heating by cooling water Q 3.
, (6.16)
where: G - roll productivity; c - specific heat capacity; t k, t n - final and initial temperature of the mixture.
Heat loss to the environment consists of heat loss by convection and radiation.
, (6.18)
where: - temperature of the roll and ambient air, ° C; - absolute temperature of the roll and air, ° K; - total emissivity (depends on the radiation of the roll, the environment and the black body); - surface of heat transfer and radiation; - heat transfer coefficient (for still air).
, (6.19)
4.2 Stamping on forging rollers (rolling).
This stamping resembles longitudinal rolling in one working stand, on two rolls which are secured with sector dies having corresponding grooves.
The heated workpiece 1 is fed to the stop 2 at the moment when the sector dies 3 diverge. When the rolls turn, the workpiece is captured and compressed to the shape of the cavity; simultaneously with compression, the workpiece is pushed towards the feed.
Rollers are used to produce forgings of relatively simple configurations, such as chain links, levers, wrenches, etc. In addition, blanks are shaped on rollers for subsequent stamping, most often on crank hot stamping presses.
They are profiled and stamped on rollers in one or more streams. The initial cross-section of the workpiece is taken equal to the maximum cross-section of the forging, since during rolling, mainly broaching occurs.
4.3 Design and principle of operation of deforming equipment and stamping equipment.
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Kinematic diagram of the CGShP
Picture 1
1- Slider;
4- Electric motor
5- Reception shaft
6- Small gear
7- Large gear
8- Pneumatic functional disc clutch
9- Crank shaft
11- Press table
Stamping on crank hot stamping presses KGShP is produced with a force of 5-10 mm. They successfully replace and in many cases surpass in technological capabilities steam-air stamping hammers with feed parts weighing up to 10 tons. KGSHP is characterized by the fact that the force generated during stamping is perceived by a massive frame. An electric motor is installed on the press bed. A pulley is attached to its shaft, from which the torque is transmitted through a V-belt transmission to a flywheel mounted on the receiving shaft. At the other end of this shaft there is a small gear mounted, which meshes with a large gear with a pneumatic engagement clutch built into it. A large gear with a clutch is located on the crankshaft, which, when rotated, drives the connecting rod with the slider in the guide directions.
A brake is used to stop the rotation of the crank shaft after the clutch is engaged. The press table, installed on an inclined surface, can be moved by a wedge and thereby adjust the height of the stamping space within small limits. To ensure removal of the forging from the press die, there are switches in the table and slide. The ejectors are activated when the slide moves upward. The flywheel is stopped using a brake when the electric motor is turned on.
Unlike hammers, presses have a rigid movement schedule for the slider, the full stroke of which up and down is the same and is equal to twice the radius of the crank. In this regard, when multi-strand stamping it is impossible to use lingering, rolling, or cutting strands. Forgings that require the use of the specified strands are stamped at a CGSP from periodically rolled or pre-shaped blanks on forging pins. The speed of the slider at the moment of contact of the upper part of the die with the workpiece is 0.3 - 0.8 m/s, that is, several times less than the speed of the hammer base at the moment of impact. Since deformation is carried out in each strand in one press stroke, the workpieces must be clean of scale to avoid damage to the package surface.
Constancy of the stroke of the slider, greater accuracy of its movement in powerful adjustable guides of the press frame, the use of dies with guide columns and ejectors for forced removal of forgings ensures greater precision in the manufacture of forgings, with smaller stamping slopes, allowances, tolerances and metal consumption than when stamping with hammers . Ejectors are placed in the vertical holes of the groove inserts of the stamp. During stamping, the working surface of the ejectors forms part of the surface of the streams. During the reverse stroke of the slide, a special mechanism in the die, driven by the press ejector, raises the stream ejectors, which eject the forging from the stream.
To avoid jamming and breakage of the press, the open dies on the CGSP do not close to the size of the burr due to the lack of impacts, they serve longer than the hammer ones. At KGShP they use dies of a prefabricated design with grooved inserts, which are replaced when worn out. The presence of ejectors ensures the convenience of stamping in closed dies by extrusion and piercing. When extruding, the workpiece is installed in the die cavity and is deposited in this cavity with the simultaneous flow of part of the metal beyond its limits. The efficiency of presses is approximately 2 times higher than the efficiency of hammers. The presses make 35-90 strokes per minute, that is, approximately as much as 4 hammers of equivalent power. Stamping on a press is 1.5 - 3 times more productive than on a hammer, and it is easier to mechanize and automate.
For closed stamping without a burr, the force values obtained from the above formula are reduced by 2.0 – 2.5%. P = k F, where P is the projection area of the stamped package with a barbed toe, cm sq; k – coefficient taking into account the complexity of the forgings’ shape (k = 6.4 / 7.3).
Recently, I have received several requests from blog readers for help in solving the same problem: how to determine the final location of the middle roller (roll) when working on three-roll sheet bending rolls and profile benders...
Regarding the position of the outer rollers (rolls), which will ensure bending (rolling) of the workpiece with a certain specified required radius? The answer to this question will increase labor productivity when bending metal by reducing the number of runs of the workpiece until a suitable part is obtained.
In this article you will find theoretical solving the problem. Let me make a reservation right away: I did not apply this calculation in practice and, accordingly, did not check the effectiveness of the proposed method. However, I am confident that in certain cases metal bending can be done much faster using this technique than usual.
Most often, in normal practice, the final location of the movable central roller (roll) and the number of passes until a suitable part is obtained is determined by the “poke method”. After a long (or not so long) development of the technological process on a test part, the coordinate of the position of the central roller (roll) is determined, which is used for further reconfiguration of the rollers, producing a batch of these parts.
The method is convenient, simple and good for a significant number of identical parts - that is, for mass production. In single or “very small-scale” production, when it is necessary to bend different profiles or sheets of different thicknesses with different radii, the loss of time for adjustment “at random” becomes catastrophically huge. These losses are especially noticeable when bending long (8...11 m) workpieces! While you make a pass..., while you take measurements..., while you rearrange the position of the roller (roller)... - and all over again! And so a dozen times.
Calculation in Excel of the location of the moving middle roller.
Launch MS Excel or OOo Calc and get started!
General rules for formatting spreadsheets that are used in blog articles can be found here .
First of all, I would like to note that sheet bending rollers and profile benders of different models may have movable outer rollers (rollers), or they may have a movable middle roller (roller). However, for our task this is not of fundamental importance.
The figure below shows the calculation diagram for the problem.
At the beginning of the process, the part to be rolled lies on two outer rollers (rolls) having a diameter D. Middle roller (roller) diameter d summed up until it touches the top of the workpiece. Next, the middle roller (roller) moves down to a distance equal to the calculated size H, the roller rotation drive is turned on, the workpiece is rolled, the metal is bent, and the output is a part with a given bending radius R! All that's left to do is to learn how to calculate the size correctly, quickly and accurately. H. This is what we will do.
Initial data:
1. Diameter of the movable upper roller (roll) /for reference/ d write in mm
to cell D3: 120
2. Diameter of support rollers (rollers) with rotation drive D we write in mm
to cell D4: 150
3. Distance between the axes of the support outer rollers (rolls) A in mm enter
to cell D5: 500
4. Height of the section of the part h enter in mm
to cell D6: 36
5. Internal bending radius of the part according to the drawing R enter in mm
to cell D7: 600
Calculations and actions:
6. We calculate the estimated vertical feed of the upper roller (roll) Hcalculation in mm excluding springing
in cell D9: =D4/2+D6+D7- ((D4/2+D6+D7)^2- (D5/2)^2)^(½)=45,4
Hcalculation =D /2+h +R - ((D /2+h +R )^2- (A /2)^2)^(½)
7. We adjust the rollers to this size Hcalculation and make the first run of the workpiece. We measure or calculate the resulting internal radius from the chord and height of the segment, which we denote R 0 and write down the resulting value in mm
to cell D10: 655
8. We calculate what the calculated theoretical vertical feed of the upper roller (roll) should be. H0calc in mm for the manufacture of parts with a radius R 0 excluding springing
in cell D11: =D4/2+D6+D10- ((D4/2+D6+D10)^2- (D5/2)^2)^(½)=41,9
H 0calc =D /2+h +R0 — ((D /2+h +R0 )^2- (A /2)^2)^(½)
9. But a part with an internal bend radiusR 0 turned out with the top roll lowered by sizeHcalculation, but notH0calc!!! We calculate the correction for back springing x in mm
in cell D12: =D9-D11 =3,5
x = Hcalculation — H0calc
10. Since the radii R And R 0 have similar dimensions, then it is possible to accept the same correction value with a sufficient degree of accuracy x to determine the final actual distance H, onto which the upper roller (roller) must be fed down to obtain an internal radius on the rolled part R .
We calculate the final calculated vertical feed of the upper roller (roll) H in mm taking into account springing
in cell D13: =D9+D12 =48,9
H = Hcalculation+ x
Problem solved! The first part from the batch was made in 2 passes! The location of the middle roller (roller) has been found.
Features and problems of metal bending on rollers.
Yes, how beautiful and simple everything would be - pressed, pushed, the part was ready, but there are a few “buts”...
1. When rolling parts with small radii, in a number of cases it is impossible to obtain the required radius R in one pass due to the possibility of deformations, corrugations and tears in the upper (compressible) and lower (tensile) layers of the workpiece section. In such cases, the appointment of several passes by the technologist is determined by the technological feature of a particular part. And these are not exceptional cases, but very common ones!
2. Single-stage feeding of the middle roller (roll) over a long distance without rolling H may be unacceptable due to the occurrence of significant forces that overload the mechanism of vertical movement of the rollers beyond the permissible norm. This may cause machine damage. The rotation drive of the rollers (rolls) may also find itself in a similar overload situation!
3. The ends of the workpiece, if they are not bent first, for example, on a press, will remain straight sections when bending on three-roll rollers! Length of straight sections L slightly more than half the distance between the lower rollers A /2.
4. When the middle roller (roller) moves downwards in the section of the workpiece subject to bending, normal stresses gradually increase, which initially cause spring deformation. As soon as the stresses in the outermost and lower fibers of the section reach the yield strength of the part material σт, plastic deformation will begin - that is, the bending process will begin. If the middle roller (roller) is pulled back up before plastic deformation begins, the workpiece will spring back and retain its original straight state! It is the effect of reverse springing that forces you to increase the size of the vertical feed Hcalculation by the amount x, since sections of the workpiece spring back and partially straighten, leaving the bending zone located between the rollers (rolls).
We found this fix x empirically. The springback or residual curvature of a part can be calculated, but this is not an easy task. In addition to the yield strength of the material σт a significant role in solving this issue is played by the moment of resistance to bending of the cross section of the rolled element Wx. And since often profiles, especially those made of aluminum alloys, have a very intricate cross-section, then the calculation of the moment of resistance Wx turns into a separate difficult task. In addition, the actual value of the yield strength σт often varies significantly even for samples cut for testing from the same sheet or the same piece of profile.
In the proposed methodology, an attempt is made to avoid defining reverse springing using the “scientific poking method”. For ductile materials, such as aluminum alloys, the value
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Emergency device
Gap adjustment mechanism
The front roll moves when the bearing housing moves in the openings of the machine frame. The gap adjustment mechanism is a screw pair: the nut is fixedly fixed in the frame, and the screw is rotated by an electric motor through worm gears.
The screw rests against a safety washer, which is located in the bearing housing. This washer is destroyed if the rollers are overloaded with the thrust force.
Roller machines are equipment with increased maintenance hazards. The roller emergency device includes cables located above the rollers. One end of the cable is rigidly connected to the traverse of the left frame, and the other to the switch lever. When you press the cable, the lever turns off the electric motor.
Determination of thrust forces and useful power consumption
Total power consumed by the rolls
Performance calculation
Determination of thrust forces and useful power consumption.
During rolling, forces arise in the working gap that try to push the rolls apart. These forces are called expansion forces. They must be taken into account when calculating, otherwise, if excessive forces are applied, the rollers may break.
The complexity of the rolling phenomenon and insufficient theoretical knowledge make it difficult to calculate thrust forces and power consumption. These values can be determined by two methods:
1. Processing of experimental data based on the theory of similarity
2. Mathematical analysis of the process with the introduction of certain assumptions.
For the first method, experiments are carried out on a model machine, thrust forces and power consumption are obtained.
where: - diameter of the rolls; - gap size; - friction value; - specific gravity of the mixture; L - roll length; - angular speed of the high-speed roll; - final plasticity of the material 
- experimental coefficients, which for some materials are given in reference books.
According to the second method, simple mathematical dependencies are obtained by introducing the following assumptions:
1. The effective viscosity (average) of the mixture does not change
2. The minimum flow regime of the mixture in the gap is laminar
3. The material sticks to the surface of the rolls and the speed of the layers at the surface is equal to the speed of the roll (U=V)
4. Inertial forces are small
5. Material flow is one-dimensional (into the gap)
6. The speed of the mixture does not change vertically
7. The pressure at the inlet and outlet of the material into the rolls is zero
8. The pressure in planes parallel to the axes of the rolls does not change.
Then the equation of motion of a viscous fluid (Navier-Stokes) has the form:
, (6.3)
By integrating this equation and taking into account the assumptions, an expression for the thrust force was obtained:
, (6.4)
where: - friction value; - effective viscosity; - speed of the front roll; - roll radius; - roll length; - gap between rollers.
The moment consumed by the rolls is equal to the sum of the torques:
, (6.5)
- torques of high-speed and low-speed rolls.
Total power consumed by the rolls.
It is calculated using the formula:
(6.8)
where: is the required total torque.
where: - idle speed; - moment of additional friction forces.
, (6.10)
where: - radial load on the axle; - bearing friction coefficient; - journal diameter; - gear ratio of the transmission and friction pair; - overall efficiency transmission and friction pair;
The moment of additional forces is equal to:
, (6.11)
where: is the thrust force on the rolls.
Performance calculation.
Roller machines operate according to the schemes of single and multiple passage of the processed material through the gap. For a single passage of material through the rollers, productivity is determined by the formula:
, (6.12)
where: - one-time download; - machine utilization rate (0.85 - 0.9). - specific gravity of the material; - cycle duration;
where: - diameter of the front roll; - length of the roll barrel.
The cycle time is determined by the formula:
, (6.14)
where: - loading and unloading time; - technological operating time. This time is determined experimentally.
It should be noted that there are other calculations of dependence when determining the productivity of rollers.
Thermal calculation of rollers.
When processing material in the roll gap, a large amount of heat is released and, as a result, the temperature of both the working surface of the rolls and the processed mixture increases. To prevent unwanted temperature changes (scorching, etc.), special cooling of the rolls is provided. The amount of heat generated during processing can be determined by the power consumed by the rollers, taking into account the efficiency of all gears and axles.
This heat is spent on heating the mixture being processed, on losses to the environment and on heating by cooling water.
, (6.16)
where: - roll productivity; - specific heat capacity; - final and initial temperature of the mixture.
Heat loss to the environment consists of heat loss by convection and radiation.
, (6.18)
where: - temperature of the roll and ambient air, ° C; - absolute temperature of the roll and air, ° K; - total emissivity (depends on the radiation of the roll, the environment and the black body); - surface of heat transfer and radiation; - heat transfer coefficient (for still air).
, (6.19)
where: - roll diameter.
Amount of heat carried away by cooling water:
, (6.20)
- The rollers consist of 2 or 3 parallel hollow rolls rotating towards each other.
- Apply for plasticizing rubber, preparing rubber mixtures, heating them before calendering or extrusion, as well as in the production of reclaimed material.
Modern rollers have measuring instruments and auxiliary devices, but they also have serious disadvantages: low productivity, lack of tightness, and danger during maintenance. Rollers are displaced by closed machines.
- Classification according to functional purpose.
Crushing rollers (Other) – for crushing old rubber. Heating rollers (Hd.) – to increase the plasticity and heating of rubber compounds. Washing rollers (Ex.) – for washing rubber with water. Grinding rollers (Rz.) – for grinding rubber waste. Refining rollers (Russian Federation) – for cleaning reclaimed material and rubber mixtures from foreign inclusions. Mixing rollers (See) - for mixing rubber with various ingredients, for preparing and sheeting rubber compounds. Mixing and heating rollers (Sm.-Pd.) – for plasticizing rubber, mixing it with various ingredients and heating rubber compounds. Laboratory rollers (Lb.) – for laboratory work.
- Classification by design characteristics
According to the size of the rolls and their rotation speed: production - light type D / L : 300/800; 500/800, medium type D / L : 550/1500, heavy type D / L : 660/2100; laboratory
By the number of rolls: 2 and 3 (Russian Federation).
By type of drive: individual, dual and group (3, 4, less often 5).
By the amount of friction (the ratio of the rotation speed of the rear roller to the front): Dr. – 2.55, 3.08, 3.25; Pd. – 1.22, 1.25, 1.27, 1.28, 1.29; Etc. – 1.39; Rz. – 4.00; Russia – 2.55; See – 1.07, 1.08, 1.11, 1.27; See-Pd. – 1.14; Forehead – 1-4. Friction designation: 1:1.22.
- Symbol contains the name, length and diameters of the rolls (front and rear), drive location (right - P, middle - S, left - L) and GOST. Rollers Lb 100 50/50 P GOST…; Rollers Lb 200 100/100 GOST... with individual drive for each roll; Rollers Sm 2100 660/660 L GOST…; Rollers Sm 2100 660/660 L with friction switching GOST...; Roller unit RF 800 490/610 S 2 GOST…
1.3.2. Roller operation diagram.
The material to be processed (rubber or rubber compound) in the form of pieces or plates is loaded and repeatedly passed through the gap between the rolls.
The material is drawn into the gap under the influence of frictional forces and as a result of adhesion between the material and the surface of the awls.
The degree of deformation and the degree of material capture is determined by the capture angle =10-45 o. The arc subtending this angle is called the capture arc. Pull-in force P>0 , If > ; – friction angle; = tg – friction coefficient.
During operation, shear and shear deformations are realized; There is always a supply of material in the gap area.
After leaving the gap, the mixture is deflected towards the front roller, because it rotates slower than the rear one; This is also due to safety reasons. The layer of mixture formed on the front roller is called skin or fur coat.
The gap is adjustable within 10-12 mm.
The greater the friction, the more intense the mixing and the higher the temperature.
The same applies to the speed, which is in the range of 35-40 m/min. The increase in speed is limited by safety considerations.
1.3.3. Roller device.
Two hollow rolls rotate towards each other in rolling bearings installed in frames, which are pulled together by traverses.
The crossheads form rectangular windows in which the roller bearing housings are installed.
The frames are installed on a foundation slab.
To measure the gap between the rollers, the front shaft bearing housings can be moved along guides along the frame. The movement is carried out by a pressure screw using a gap adjustment mechanism.
– The mechanism is operated manually by a handwheel or handle or by an electric motor.
The pressure screw rests against the front roller bearing housing through a safety washer, which breaks through as the spacer forces increase.
When the rolls move or move too far, the limit switches are triggered.
The beds have discs that indicate the amount of clearance.
There are limit arrows to avoid clogging the bearings.
The engine transmits force through drive and friction gears.
Lubrication is carried out manually or with a pump from an oil station, which is easier.
There is an emergency stop that stops the flow of electricity to the engine. After it is triggered, the rollers go through a quarter of a revolution when the rollers are unloaded and stop instantly when the rollers are loaded.
1.3.4. Main nodes.
- Foundation slab – cast iron with reinforcement with stiffeners, 3.5 t.
Can be made of reinforced concrete with a frame made of reinforcing steel (10-12% by weight).
- bed – steel, consists of two parts – the frame itself and the crossbar – the upper part, 800-1350 kg. Must be designed for a thrust force of 14 kN per 1 cm of the length of the working part of the roll.
- Rolls – the main unit is cast into a cast iron mold, and the surface is bleached to a depth of 8-25 mm.
The barrels are mainly cylindrical; the refining rollers are bombarded. Front (diameter 490 mm) – 0.151 mm, rear (diameter 610 mm) – 0.075 mm.
Crushing and washing rollers have a corrugated surface (corrugation at an angle of 4-15 o to the longitudinal axis).
Cooling the rolls - usually the temperature of the rolls should be ~60 o C. The water temperature should not exceed 12-14 o C. In summer, tap water must be cooled.
When plasticizing NK and when processing mixtures based on it, the temperature of the front roll should be 5-10 degrees. Less than the rear temperature - then the mixture will go to the front roller.
When processing mixtures from SC, the temperature of the front roll should be 5-10 degrees. More rear temperature.
Two cooling methods are filling the roller with water and periodically replacing it - an open method. Using spray devices at a distance of 150-200 mm from each other.
Water consumption 1.2-2.5 m 3 /hour - small, 5-12 - medium, 8-18 - large.
There are designs with bearing cooling.
- Gap adjustment mechanism. Gap 0.05-12 mm. The pressure screw rotates in a steel nut fixed in the frame. The reverse stroke can be carried out by an electric motor or due to spacer forces.
- Knives (there are two of them) are mounted in a carriage and can be moved along the roller.
- Devices for mixing and cooling the mixture. The mixture is cut off from the front roller and tucked into the gap between the cooling drum and the pressure roller and again sent into the gap - it is mixed, moving intensively along its length with the help of special rollers and a carriage - a stock blender. This system is used to refine rubber compounds after RS.
- Features of different types of rollers. RF (refining) breaker rollers – for preliminary cleaning, refiner rollers – for final cleaning. The mixture is removed from the rear roller and rolled into rolls. The surface is smooth, barrel-shaped, inclusions extend to the edges. Various roll diameters. Friction 1:2.55. Dr (crushing) – barrel sizes and friction are the same as in Russia. Pr (washing) - corrugated surface, but the same diameters of the rolls.
1.3.5. Stress distribution in the material in the gap between the rolls.
- Assumptions: laminar flow regime, no-slip condition, Newtonian fluid.
Navier-Stokes equation.
There are 2 fundamentally different flow areas . Up to the boundary of the two zones (above), forward and counter flow takes place; below – only progressive. Between this boundary and the narrowest section there is a plug flow regime - the forces arising due to hydrostatic pressure and acting on one side of the section are balanced by the forces acting on the other side of the section.
The shear stress in this section is zero, and the pressure is maximum - the material moves like a solid plug without deformation.
- Temperature distribution in the roll gap. Two peaks near the surfaces due to the presence of cooling.
1.3.6. Expansion forces.
- Based on the patterns of plastic deformation of the material between the rolls.
Expansion force is the magnitude of the force tending to push the rolls apart when deformable material passes between them.
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,Where – relative broadening of the material, = b To / b n (it could be considered =1), b n – initial width, b To – final width, k – empirical coefficient, T – yield strength of the rolled material, h ns – thickness of the neutral layer, h ns ( h n h To ) ½ , h n And h To – material thickness before and after rolling, = / lg ( /2) , – friction coefficient, – grip angle, R – roll radius, cm, h =2 R (1- cos ) – linear compression.
- Based on the laws of elastic deformation.
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,Where E - elastic modulus.
In this case, friction forces are not taken into account; after passing through the gap, the thickness is restored.
- Based on the hydrodynamic theory of rolling.
The thrust force is divided into two components: 1) directed against the rotation speed vector (horizontal component), 2) directed towards the speed vector (vertical component)
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Where T - friction force, l – grip arc length, f – friction, v 1 , v 2 – linear speed of the front and rear rolls, L – roll length, IN 1,2 – coefficients, n – rheological coefficient/
If P 1 And P 2 are known, then the coordinate of the point of application of the resultant can be determined as
Where ef – coefficient of effective viscosity, h To – minimum clearance.
For approximate calculations P = qL , q = 400 kN/m (for NK), for filled mixtures q = 600-1100 kN/m.
A technique based on the theory of similarity.
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N
N
NWhere B=( h n – h 2 )/( h n - h 1 ) – recoverability, M=( h n – h 1 )/( h n + h 1 ) – softness, h n – initial height of the sample, h 1 – height under load, h 2 – height after unloading, Pl To – final plasticity
Coefficient values:
For example, for SKN-40:
P=18059860.66 1.4 2.1 0.7 0.002 0.1 0.48 –0.4 =1.22 MN=122 t.
1.3.7. Power consumption.
- A technique based on the theory of plastic or elastic deformation.
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kWWhere M – moment of resistance to roll rotation, Nm, M=M R +M tr, M R – the moment to overcome the resistance to deformation of the material, M R = PDsin ( /2) , P – thrust force, – grip angle, M tr – moment of resistance to friction in bearings, taking into account the gravity of the rolls and spacer forces, M tr = ( P + G V ) d , – coefficient of friction in bearings, G V – shaft gravity, d – diameter of the roll journal, n – average speed of rotation of the rolls, – Efficiency of the gear pair.
- A technique based on the hydrodynamic theory of rolling.
Where – peripheral speed of the high-speed roll, s –1.
Coefficient values:
For example, for SKN-40:
N=0.069861.8750.66 2 2.1 0. 6 0.002 0.1 0.48 –0. 7 1.22 –0.25 =65 kW.
1.3.8. Drive unit.
The rollers can have an individual, paired or group drive.
The drive can be located on the right or left side of the workplace.
At the beginning of the processing cycle, the power is 1.5-2 times more than the power consumed by the rollers. Therefore, the power of the electric motor must be selected taking into account this peak load.
With an individual drive, a synchronous motor is installed, which, when underloaded, can act as a compensator and improve cos.
There may be a separate motor for each roll (in laboratory rolls).
To connect the gearbox output shaft to the transmission shaft, couplings , they allow some distortion of the connected shafts and ensure elasticity of the transmission. A Fast gear coupling, a Franke pin coupling, and a Bibi spring coupling are used.
There can be either rubber or rubber-pneumatic couplings, which ensure smooth operation of the drive and some misalignment of the axes.
For rollers with a large spread of the rolls and with large expansion forces, a block gearbox is used (up to 20 kN/cm). It houses the drive and friction gears. The gearbox unit is connected by two output shafts through universal joint devices with roller rollers.
The cost of a block gearbox is much higher, but it has many advantages - gears and bearings operate in more favorable conditions.
1.3.9. Installation features.
Previously, rollers were installed on a special foundation and secured with foundation bolts.
Vibrations are transmitted to the structural elements of the building.
Transferring rollers from one place to another is associated with a large volume of construction work
Vibration-isolating supports are used - without a special foundation and bolts.
1.3.10. Selection of rollers.
Individually designed heating rollers have a motor power of 180 kW and a unit power of 320 kW. Saving 40 kW.
In a group drive, the load on the rollers can be made more uniform. Any overload is undesirable.
You cannot load several rollers at once with a group drive.
Engines must be dustproof.
To reduce peak loads, preheating (in hot water) is used for hard mixtures (treads, rollers, etc.).
1.3.11. Roller performance.
- Periodic mode.
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kg/hour,Where V –liter capacity or volume of one-time loading, in liters: V =(0.0065-0.0085) D 1 L , D 1 – diameter of the front roller, cm, L – its length, cm, – density kg/dm 3, – coefficient of computer time use (0.85-0.9), t ts = t 1 + t 2 + t 3 – cycle time (loading, plasticizing, unloading) in min.
When plasticizing rubber:
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min,Where Pl – change in plasticity according to Carrer, i – gap, cm, u – peripheral speed of the high-speed roll, m/min, f – friction, A , n , m – coefficients.
Coefficient values:
There is approximately the same amount of mixture in reserve during rolling as on the roller.
- Continuous mode.
Where 0.75 – coefficient of filling of corrugation grooves with the processed material, F – cross-sectional area of the groove, m2, l – corrugation step, i.e. distance between adjacent grooves, m, k =1 or 2 depending on how many rolls are with grooves.
1.3.12. Cooling system.
The cooling system can be closed (not currently used) or open. The advantage of the latter is the high values of the heat transfer coefficient in thin jets from nozzles (small jet diameter, high speed, high value of the Reynolds criterion) and due to the partial evaporation of water upon contact with hot walls.
- Heat balance.
Where Q 1 = N t ts – heat released due to internal friction in the material, kJ, N – engine power, kW; – drive efficiency, t ts – cycle time, s; Q 2 – additional heat input, kJ; Q 2 = m h t ts - with steam, m – steam consumption, kg/s, h – change in steam enthalpy, kJ/kg; Q 3 = G.C. Tt ts – heat used to heat the rubber mixture, kJ, G – roller productivity, kg/s, WITH – heat capacity of the rubber mixture, kJ/(kgK), T – change in mixture temperature, K; Q 4 = F ( T pov – T V )+s 0 F (( T pov /100) 4 –( T V /100) 4 ) – heat loss to the environment, consisting of convective and radiant (calculated for each roll), kJ, – heat transfer coefficient during natural convection from the roller wall to the air, kW/(m 2 K), F – heat exchange surface, m2, T pov And T V – temperature of the roll surface and ambient air, respectively, K, With 0 – black body emissivity, With 0 =5.6710 -3 kW/(m 2 K 4), – degree of blackness; Q 5 = m V WITH V T V t ts – heat carried away by cooling water, kJ, m V – water consumption, kg/s, WITH V =4.2 kJ/(kgK) – heat capacity of water, T V – change in water temperature, K.
1.3.13. Installations for receiving and cooling a strip of rubber mixture.
- Scalloped type. The tape is cut from rollers or FM with a sheeting head, passes through a bath of kaolin suspension and is fed into the scallop former. The scallop is obtained as a result of pressing the rubber mixture belt against the conveyor bar with a lever that is driven by a pneumatic cylinder. As soon as the scallop is formed, the lever moves one step. Next, the mixture enters a chamber cooled by air using a fan. The chamber size is designed for 4 beams. Cooled festoons are fed to the laying unit, where the tape is cut into sheets of a given length, which are fed onto pallets mounted on scales.
The disadvantage of this system is that it is cumbersome; there is no way to roll the mixture into drums for subsequent delivery to the World Cup. The last drawback has been eliminated in some designs (by Pirelli).
In the new systems, a 0.6 m wide strip is cut from the rollers, treated with an aqueous kaolin suspension, then cut in half lengthwise with a circular knife. Then it is cooled by fans. Movement speed – 8-38 m/min, number of fans 4-7. It takes longer to cut into strips or roll into reels. There are such installations of a partially vertical type, very compact
- Tape type. In continuous production, the tape from the rollers goes to the calenders or FM along a conveyor belt without additional cooling. First, it is cut into a narrow strip lengthwise or crosswise (not completely).