The roll mill is the simplest batch mixing equipment. The principal design consists of two horizontal rolls, usually of equal size, arranged side by side and rotating toward each other at different speeds. The ratio of the peripheral speeds of the rolls, known as friction ratio, ranges from 1 to 2 but is usually around 1.2. The higher friction ratio leads to a higher heat generation in the processed material. Friction, speed, and the sizes of the rolls influence the cooling of the material mass and the intensity of its treatment. Depending on the properties of the process material and its desired temperature, the rolls may be internally cooled or heated by using circulating cooling water or a suitable heating medium.
The basic mixing operation is illustrated in Fig.4.5. The material is charged between the rolls in the form of lumps, pellets, chunks, or powder. As a result of rotation, adhesion, and friction, the material is entrained into the gap between the rolls, and upon discharge it sticks to one of the rolls, depending on their temperature difference and velocities. Another factor is the gap between the rolls. In batch mixing the material after loading passes through the gap between the rolls several times, and the mixing action is due to the different speeds of the rolls. Both the shearing action and entrainment of the material into the gap are very important in the mixing process and transporting of the material through the unit. The gap between the rolls can be adjusted by a massive screw mechanism.
Figure4.5. Operation of mixing rolls. (A) Batch operation ((1) loading; (2) rolling; (3) end of rolling; (4) mass shear; (5) knife). (B) Continuous operation (1knife, 2continuous removal of the material).
During the operation, cutting of the sheet of the material (blanket), folding, and rolling are carried out, which increases the uniformity of the composition. If additives, often in the powder, liquid, or paste form, are to be incorporated, they are added into a rolling bank formed between the rolls.
Roll mills are also used for warming up materials for calendering or extrusion. In such cases the warm material is cut into strips that are fed into the calender or extruder often continuously. Another application of roll mills is to cool materials discharged from an internal batch mixer in a form of large lumps (see Section 126.96.36.199.2). The resulting blanket is then transported in the form of strips to the calender or extruder or removed from the rolls as thick sheets.
The two-roll mill was used in industrial operations of various types well into the dimmest past. It was, however, only with the 1836 patent of Chaffee31 that roll mills began to be used in the polymer industry. Chaffee32 sought to use roll mills and calenders in place of the solution processing and coating technologies current at the time.7 The two-roll mill has been with the industry ever since.
Mixing actions of different materials and additives occur in flow through the nip. In mill mixing, one generally slices the polymer banded on the rolls to make the initial circumferential direction enter the nip at a skew angle. This yields enhanced mixing.
The stress fields in two-roll mills were first carefully discussed by Bergen.33 Flow processes and material characteristic problems associated with rubber on mills were later described by Tokita and White.34 These latter authors35 also discussed how material characteristics, specifically the tearing and crumbling of elastomers, affect mixing. Tearing and crumbling prevent the development of good dispersion.
Mixing is accomplished using two roll mills, internal mixers, and continuous mixers. The resulting compound is then further processed through extrusion, calendaring, etc. The objective of the mixing process is to incorporate compounding ingredients uniformly in the rubber matrix. The mix quality of the rubber compound depends on the processing parameter, such as viscosity, cure characteristics, etc. ASTM D 3182 specifies the mixing equipment, general mixing procedures, vulcanization equipment, and procedures.
A two roll mill consists of two horizontally placed hollow metal rolls rotating towards each other. The distance between the mill rolls can be varied and this gap is known as nip. The speed difference between the rolls is called friction ratio and it allows the shearing action. The back roll moves faster than the front roll; a common friction ratio is 1:1.25. Two roll mill mixing is also known as open mill mixing.
Two different types of internal mixers are generally usedBanbury and intermix. The advantages of internal mixers are they are faster, need fewer operators, need less floor space, etc. The rolls of internal mixers are known as rotors. The various processing parameters in internal mixing are batch size, sequence of loading, ram pressure, rotor speed, mixing time, and temperature of mixing.
There are mainly two types of continuous mixersFarrel continuous mixers (FCM) and Long continuous mixers (LCM). They provide processing efficiency, extreme versatility, dependability, and profitability.
FCM All ingredients can be fed into the mixer separately and liquids can be injected directly into the mixing chamber. Intensive material shear is applied to melt the polymer and to mix all of the ingredients by kneading between the rotors and chamber wall as well as by the rolling action within the material itself.
Some of the most important features are: counter-rotating, non intermeshing rotors at synchronous speed; the unique rotor geometry enables superior dispersive mixing; large rotor tip-to-wall clearance minimizes the effect of wear; large feed opening allows for high filler loadings; and they are energy efficient with low operating costs.
LCM The LCM design includes a two-stage mixing chamber in combination with 10L/D long rotors. The primary mixing stage features include: dry blending of the polymer with all other ingredients followed by preheating of dry blend, and subsequently there is a breakdown of larger agglomerates by friction between polymer particles, the ball mill effect.
Secondary mixing stage features include: the intensive shear between the rotor tips and chamber wall melts the polymer and provides dispersive mixing to incorporate the other ingredients; back mixing via longitudinal cut-back pushes the material back and forth along rotor axes for distributive mixing; uniformity is achieved in the final kneading step by the rolling action between the two rotors. After this step, the material leaves the mixing chamber.
A paper roll mill in Paperie du Rhin in France installed an MBR process based on hollow-fiber membranes (Table 19.2). The mill uses recycled (not de-inked) paper as the raw material for the production of 40,000tons of paper rolls annually. The bioreactor (1500m3) is operated at an MLSS content of 1216g/L. The wastewater from the mill is first prescreened with drum screens; then it is sent to an equalization basin, from which it is pumped directly into the bioreactor. The MBR process decreased the COD from 4000mg/L to less than 200mg/L and the BOD from 1700mg/L to less than 5mg/L. Permeate is partly recycled as process water. The main reasons for choosing MBR treatment were on-site space limitations and the need to recirculate the purified water (Ramaekers etal., 2001).
Two-roll mills have been used for rubber compounding since the middle of the 19th century. Originally, they were also used for mastication of natural rubber, to break down high-molecular-weight fractions. However, such breakdown is generally not desirable for synthetic elastomers, including fluoroelastomers, which are designed to have molecular weight distributions optimized for various processing methods and end uses. Mills are suited to low-volume production of specialty fluoroelastomer compounds, but have been largely replaced with internal mixers. In many production operations, mills are used for sheeting off stock from internal mixers or for warm-up of compounds for sheet feed to extruders or calanders.
A typical rubber mill is shown in Fig. 7.1.5 The mill consists of two closely spaced parallel, horizontal rolls made from hard castings supported by strong bearings in a mill frame. The counterrotating rolls are driven at different speeds to maintain a friction ratio of 1.051.25, transporting the rubber over the top of the roll to the nip area, then through the nip with small adjustable clearance (usually 26mm or 0.080in.0.240in.) to subject the stock to high shear stresses. To get good mixing, the amount of stock and mill clearances used should result in the formation of a smooth band on one roll, with a rolling bank of stock in the nip. The surface speed of the slow roll is about 50cm/s, allowing the mill operator to cut the band diagonally and fold the cut portion over the remaining band for blending. The mill rolls are hollow to allow flow of coolant (most commonly water) for control of roll and stock temperatures. A number of safety features are incorporated into mill design, including shutoff switches and brakes to stop the rolls quickly, means to move the rolls apart, and guards to keep hands and tools away from the nip area. Stringent operator training and adherence to safe procedures are necessary to avoid the inherent hazards involved in mill operation.
A typical mill mixing procedure is given in a 1975 DuPont product bulletin.6 The fluoroelastomer described is a VDF/HFP copolymer precompound, based on Viton E-60C, containing about 2phr BpAF and 0.55phr BTPPC accelerator. The medium-viscosity polymer was designed with a considerable high-molecular-weight fraction to impart enough cohesive strength for good mill mixing. A batch size of about 40kg (approximately 90lbs.) is recommended for a production-scale mill with dimensions about 500mm (20in.) diameter and 1500mm (60in.) length. The complete compound recipe contains 100phr E-60C precompound, 30phr MT black, 6phr calcium hydroxide, and 3phr magnesium oxide. The clean mill is cooled to about 25C (77F) and the nip is adjusted to about 3mm (0.12in.). The polymer is added to the mill for banding. Ordinarily, the fluoroelastomer bands on the fast roll, but may be forced to the slow roll by increasing the temperature slightly on the slow roll. The nip is adjusted to about 5mm (0.20in.) to get a rolling bank in the nip. The banded polymer is cut about three times from each side to get a uniform sheet on the roll. The powdered ingredients are preblended and added at a rapid uniform rate across the width of the nip. Loose filler that falls through the nip is swept from the pan and added to the batch before cutting the sheet. Further mixing is carried out by cutting and blending the sheet about four times from each side. The mixed sheet is cut off from the mill and cooled. About 15min of milling time is usually adequate for the total operation described. Cooling of the slab is accomplished by dipping in a water tank, or by water spray or forced air. If water cooling is used, it is important to dry the stock with forced air before storing it.
Mill mixing is difficult, especially on a production scale, for a number of gum fluoroelastomers. Polymers with narrow molecular weight distribution and low ionic end group levels may not have adequate cohesive strength to form a smooth, hole-free band on a single roll. When the addition of powdered ingredients is attempted, the stock and loose fillers may drop off the rolls into the pan. Subsequent consolidation of such a batch is time consuming and messy at best. Very high-molecular-weight fluoroelastomers undergo significant breakdown during initial passes through a tight nip of a cold mill, with resultant deterioration of vulcanizate physical properties. On the other hand, bimodal blends (formed by latex mixing before isolation) have excellent milling characteristics, with negligible breakdown of high-molecular-weight fractions. High-viscosity elastomers with considerable long-chain branching and gel fractions may also break down during milling, possibly improving subsequent processing characteristics (eg, extrusion).
Mixing was performed by two-roll mill, on which the surface temperature was kept at 180C. After melting PP, 5wt% of SiO2 was added and blended for 10min. Then, the obtained mixture was pressed into a flat sheet at 230C under a pressure of 100kg/cm2 for 5min using a compression-molding machine. Two kinds of PP/SiO2 nanocomposites were prepared at the different cooling conditions ; (I) quenched at 100C (Sample-I), (II) quenched at 0C then annealed at 100C for 24h under N2 (Sample-II).
Rubber compounding was performed on a two-roll mill (Lab Walzwerk MT 613, Rubicon, Germany) in a three-stage process. In the first stage, the rubber was mixed with zinc oxide, stearic acid, CB, and Struktol or IPPD. Then the rubber/MLG masterbatch was added to the rubber compound in the second stage. For the M-MLG route, the MLG was added directly at this stage of compounding. Finally, the curatives (sulfur and MBTS) were added in the third stage. For all compounds, the rolls were set to a temperature of 50C at a speed of 19rpm with a friction ratio of 1.1:1 and a mixing time of 20min. For the reference compounds without MLG the second stage was not performed.
The same procedure was applied for the CIIR-based compounds containing CB . CB was added in the second processing stage on the two-roll mill, with or without MLG masterbatch added at the same time.
Vulcanization was performed at 300bar with curing temperatures of 180C for CIIR and 150C for the other materials. The curing times were determined beforehand by a dynamic moving die rheometer (D-MDR 300, MontechWerkstoffprfmaschinen, Germany), as the time of maximum torque (t100). For CIIR and NBR, the curing time was 20min, for NR 18min, and for SBR 60min.
Two major types of mixing equipment are used in rubber processing: roll mills and internal mixers.1 Figure 14.29 shows a modernized roll mixer which allows for dust-free processing.2 The rubber mixer (1) comprises of the rubber mixing section (2) and the driving section (3). In the rubber mixing section (2), the rubber mixing rolls (4) (usually comprising two rolls, i.e., a drive roll (4a) and a counter roll (4b)) and the rotation shafts (5) of the rolls are supported by the bearings (6). The driving section (3) is composed of the motor (7), emergency shutdown mechanism (8) and speed reduction mechanism (9). The speed reduction mechanism (9) and the drive roll (4a) are connected by means of a chain or belt (10). The whole parts of the rubber mixer except the rubber mixing rolls (4) are covered with the casing (11) and the casing (11) is a covering of the rubber mixer. The casing (11) (outer casing) is provided with the air intakes (12) in a periphery of the rotation shafts (5) of the rubber mixing rolls (4) and also the exhaust duct (13) at the bottom of the driving section (3). The exhaust duct (13) is connected to the outside of the working room (14). Also the exhaust duct (13) is provided with air suction means (15) such as a suction pump.2
Figure 14.30 shows the example of the internal mixer. Internal mixer assembly (10) is shown having a mixer body (12) with a mixing chamber (14) having a capacity of 8.36 cubic feet (237 liters). A door (16) (shown in the closed condition) is provided to close a discharge opening (18) in the mixer body (12). A throat (20) is provided in an upper wall (22) of the mixer body for receiving the ingredients to be mixed from a hopper (24) mounted on the upper wall (22) of the mixer body (12). A piston-cylinder assembly (26) is mounted on the hopper (24) with a piston (28) fastened to a piston rod (30) connected to a ram weight (32) located in the hopper (24).3
Figure 14.31 shows a rubber kneading line which makes use of both internal and two-roll mixers. A Banbury mixer (1) has a pair of rotors (4) and (5) for kneading rubber alone or together with additives in the chamber (2). A first roll mechanism (8) consisting of a pair of parallel rolls (6) and (7) is installed under the kneading mixer (1). It operates to deform the rubber coming out of the kneading mixer (1) into a rubber sheet (9) having a thickness of about 8 mm. A first conveyor (11) is arranged below the first roll mechanism (8). The first conveyor (11) is adapted to convey the rubber sheet (9) to a second roll mechanism (14) consisting of a pair of rolls (12) and (13). The second roll mechanism (14) deforms material into a rubber sheet (15) of thickness of 3 mm or less.4 Further sets of two similar units form a continuous rubber sheet of required thickness and width.
In any of the above systems plasticizers are added manually or automatically directly into a rubber mass according to the adapted technological process. Some rubber products are manufactured from emulsion. These products also need the incorporation of the plasticizer as shown in Figure 14.32. Plasticizer may be premixed with other additives and added in any mixing order required.5
The mixing process in the rubber industry usually begins with mastication which is to obtain suitable viscoelastic properties. The next step is frequently called masterbatching in which all additives with the exception of curative are added.22 Plasticizer is usually added at this point either alone or premixed with other additives. The order of addition is usually very important. Frequently, plasticizers (and/or process oils) are added following mastication.6 This is essential in the case of some rubbers, which are very difficult to process without liquid additions because of their very high molecular weight (e.g., EPDM13). In some cases, fillers need to form associations with rubber molecules. Addition of such fillers after premixing them with the plasticizer will delay the process or make it less efficient.1 In some technological processes7 fillers are added before addition of the plasticizer.
Addition of fragile components of the mixture (e.g., fibers or microballoons) or components which are likely to be affected by moisture (e.g., desiccant)8 requires predispersion of the additive in the plasticizer. The plasticizer frequently helps to wet powdery raw materials.8
Plasticizers affect many properties in rubber. They improve low temperature properties,9 help to increase rate of surface plasticization acting partially as surfactants,10 increase modulus of side wall of tire insert by compatibilizing starch with rubber,11 or increase heat resistance of the rubber compound.12
Action of the plasticizer depends also on the structure of the rubber. For example, a low amount of chlorine in chlorinated rubber decreases compatibility of chlorinated rubber with the plasticizer and the other resins.13
In many products produced by rubber compounding, plasticizer affects properties of material by outgassing, fogging, and degrading mechanical properties as was the case of pressure sensitive adhesive in which problems were solved by elimination of plasticizer.14 Blooming is a frequent problem encountered in rubber goods. It was solved by the selection of an appropriate plasticizer (naphthenic oil) and an organic sulfur vulcanizing agent.15
During vulcanization, materials, such as sulfur, zinc salts, oils, and waxes tend to migrate from the rubber compound and deposit on the mold. Repeated vulcanization of rubber compounds in the mold causes the material to build up on the mold. This buildup of material is commonly referred to as mold fouling.16 Starch is used as a fouling inhibitor.
The type of selected plasticizer affects staining, extraction and migration.17 The selection of adequate plasticizer is composition sensitive and especially dependent on the properties of rubber. Migration of plasticizer and bleeding problems may be remedied by addition of an intermediate layer in the material which will prevent or slow down such processes.18 It is also possible to reduce blooming by selection of suitable plasticizer, designed for this purpose.17
The interphase transfer of a plasticizer occurs between immiscible rubbers residing in different layers of products.24 The difference in the interaction parameters is the driving force of the transfer.24 The plasticizer transfer affects the glass transition temperature of each rubber involved in the transfer.24 The transfer phenomenon is applicable for an allseason tire among many other products which can be involved.24
Accumulation of large quantities of rubber waste leads to studies in different direction to process these materials to useful components. One such attempt aims at the manufacture of plasticizer by pyrolysis of rubber wastes.19 Road bitumen and styrenebutadiene-styrene-modified bitumen were applied as reactive plasticizers to enhance reclaiming of ground tire rubber.25 The application of bitumen in ground tire rubber improves processing and prevents oxidation of reclaimed ground tire rubber through enhancement of physical and chemical interactions between ground tire rubber and bitumen.25 Liquid reclaimed rubber was produced from ground tire rubber in a continuous operation by using a co-rotating twin-screw extruder.26 The liquid reclaimed rubber had many unique properties, such as low viscosity, good compatibility with natural rubber, and possibility to be vulcanized again.26 It can be used as reactive polymeric plasticizer in natural rubber to replace the conventional oils such as the environmental aromatic oil.26
E54 epoxy resin was first mixed with a certain proportion of CNTs in a three-roll mill. The black mixture was degassed at 130C in vacuum for 1.5h, then cast in mold, and finally followed by a curing process at 180C for 3h to produce CNT/epoxy composites.
The density of E54 epoxy was 1.21gcm3 and the density of the produced composites was about 1.201.30gcm3. Figure 10.4 shows the morphology of the fracture. No big pores in the surface verified a successful curing process. While it can be noted that the CNTs have been pulled out for several hundreds of nanometers to nearly 1m, it inferred that interfacial bonding between CNTs and the resin was weak. In fact, there is no difference in infrared adsorption spectra of the epoxy resin and CNT/epoxy composites, which indicates that there is no chemical bonding between CNTs and the epoxy resin.
Roller mills accomplish size reduction through a combination of forces and design features. If the rolls rotate at the same speed, compression is the primary force used. If the rolls rotate at different speeds, shearing and compression are the primary forces used. If the rolls are grooved, a tearing or grinding component is introduced. There is little noise or dust pollution associated with properly designed and maintained roller mills. Their slower operating speeds do not generate heat, and there is very little moisture loss. Particles produced tend to be uniform in size; that is, very little fine material is generated. The shape of the particles tends to be irregular, more cubic or rectangular than spherical. The irregular shape of the particles means they do not pack as well. For similar-sized particles, bulk density of material ground on a roller mill will be about 5 to 15 percent less than material ground by a hammermill.
Disadvantages: - little or no effect on fiber - particles tend to be irregular in shape and dimension - may have high initial cost (depends on system design) - when required, maintenance can be expensive
General Design There are many manufacturers of roller mills, but they all share the following design features shown adjacent picture: - a delivery device to supply a constant and uniform amount of the material to be ground - a pair of rolls mounted horizontally in a rigid frame - one roll is fixed in position and the other can be moved closer to or further from the fixed roll - the rolls counter rotate either at the same speed or one may rotate faster; roll surface may be smooth or have various grooves or corrugations - bar; pairs of rolls may be placed on top of one another in a frame.
To ensure optimum operation, material must be introduced between the rolls in a uniform and constant manner. The simplest feeder is a bin hopper with an agitator located inside it and a manually set discharge gate. This type of feeder is best suited for coarse processing. For grinding operations, a roll feeder is suggested. In this type of feeder, the roll is located below the bin hopper and has a manually set or automatic adjustable discharge gate. If the gate is adjusted automatically, it will be slaved to the amperage load of the main motor of the roller mill.
The rolls that make up a pair will be 9 to 12 inches (23 to 30.5 cm) in diameter, and their ratio of length to diameter can be as great as 4:1. It is very important to maintain the alignment between the roll pairs. Sizing of the material is dependent upon the gap between the rolls along their length. If this gap is not uniform, mill performance will suffer, leading to increased maintenance costs, reduced throughput, and overall increased operation costs. The gap may be adjusted manually or automatically through the use of pneumatic or hydraulic cylinders operated through a computer or programmable controller.
Each pair of rolls is counter rotating. For improved size reduction one of the rolls rotates faster. This results in a differential in speed between the roll pair. Typical differentials range from 1.2:1 to 2.0:1 (fast to slow). Typical roll speeds would be 1,300 feet per minute (~ 395 m/min) for a 9-inch (~23 cm) roll to 3,140 feet per minute (~957 m/min) for a 12-inch (~30.5 cm) roll. Usually a single motor is used to power a two high roll pair, with either belt or chain reduction supplying the differential. In a three high roll pair, the bottom pair will have a separate drive motor. In addition, the roll faces can be grooved to further take advantage of the speed differential and improve size reduction.
By placing (stacking) pairs of rolls on top of one another, two or three high, it is possible to reduce particle sizes down to 500 microns, duplicating the size-reducing capability of a hammermill for grain. For coarse reduction of grain, a roller mill may have a significant advantage (perhaps as high as 85 percent) over a hammermill in terms of throughput/kwh of energy. For cereal grains processed to typical sizes (600 to 900 microns) for the feed industry, the advantage is about 30 to 50 percent. This translates into reduced operating expense.
Since for granulation processes the crusher operation has a decisive influence on the system stability, a reliable mathematical model to represent an industrial double-roll crusher of a urea granulation circuit is provided in this work. The crusher was described by the model given by Austin et al. [Austin L.G., Van Orden D.R., Perez J.W. A Preliminary Analysis of Smooth Roll Crushers, International Journal of Mineral Processing, 6 (1980), 321336.] for mineral processing. The breakage parameters estimation was based on industrial data. The experimental particle size distributions of the feed, intermediate and product streams were obtained from large-scale crushers belonging to a urea granulation plant with a nominal capacity of 1million tons/year. The results indicate that the model reproduces in a very accurate way the performance of this type of crushers, being a useful tool to: a) optimize the gap setting to meet specific crushed particle size distribution requirements and b) be included as a mathematical module in a plant simulator of the whole urea granulation circuit.
Since for granulation processes the crusher operation has a decisive influence on the system stability, a reliable mathematical model to represent an industrial double-roll crusher of a urea granulation circuit is provided in this work. The proposed model is a useful tool to optimize the gap setting to meet specific product requirements and to be included as a module in a simulator of the urea granulation circuit.Download : Download full-size image
Rongrong Peng, Xingzhong Zhang, Peiming Shi, "Coupled Vibration Behavior of Hot Rolling Mill Rolls under Multinonlinear Effects", Shock and Vibration, vol. 2020, Article ID 6104028, 14 pages, 2020. https://doi.org/10.1155/2020/6104028
A coupled vibration model of hot rolling mill rolls under multiple nonlinear effects is established by considering the nonlinear spring force produced by the hydraulic cylinder, the nonlinear friction between the work rolls, the dynamic variation of rolling force, and the effect of external excitation as well as according to the structural constraints of a four-high hot rolling mill in the vertical and horizontal directions. The amplitude-frequency response equation of rolling mill rolls is determined by using a multiple-scale approximation method. Furthermore, use of actual data for simulation indicates that the internal resonance is the main cause of coupling vibration of the rolling mill rolls. In addition, changes in the movement displacement of the hydraulic cylinder and the coupling parameters strongly affect the coupling system of the rolling mill rolls. Finally, the study of the dynamic bifurcation characteristics of the rolling mill rolls indicates that, with varying external excitation amplitude, the vibration of rolls alternates between periodic motion, period-doubling motion, and chaotic motion in both vertical and horizontal directions. This is one of the reasons for the appearance of periodic light and dark stripes on the strip surface. Furthermore, the range of the external excitation amplitude (F0) at which the rolling mill roll system vibrates violently, that is, 5.68e5 N
Hot rolling is an important process in the manufacturing and processing of steel strips. It is a high-temperature and large-reduction process, which imparts large fluidity in the workpiece. In addition, with the application of various new processing technologies, rolling mill vibration is an inevitable problem, which potentially loosens and wears out the mechanical parts, shortens the rolling mill life, and causes vibration of steel strips, thereby reducing the overall product quality and accuracy .
Most studies on rolling mill vibration focus on a single vibration system, such as vertical, horizontal, or torsional vibration. For instance, Sun et al. considered the interaction between strip tension and thickness and analyzed the effect of multiple-source external disturbance on rolling mill vibration; they established a vertical vibration model of the rolling mill and further improved the control accuracy of tension and thickness of the hot rolling mill through optimization design . Fan et al. analyzed and calculated the structural stability of hot rolling mill rolls and revealed that the gap between the framework and rolling mill rolls can cause the phenomenon of vibration jump, which destroys the balance of a rolling mill system . Shi et al. studied the nonlinear torsional vibration characteristics of the main drive system of a rolling mill under different connection angles, damping coefficients, and friction force [6, 7]. Under continuous and high-speed rolling, different forms of coupled chatter are generated [8, 9]. This coupled vibration contributes to the low accuracy of a vibration model established on the basis of a single vibration system. Moreover, the research conclusions derived from such models cannot fully explain the complex nonlinear characteristics of rolling mill vibration. To address this problem, some research has been conducted on the chatter mechanism and behavior of coupled vibration . Yun et al. established a 2-degree-of-freedom (DOF) linear coupling vibration model by considering the coupling effect of longitudinal and transverse movements of the roll and the effect of rolling speed on the rolling process [13, 14]. Yang et al. established a rolling mill model, including a rolling process model, a mill stand model, and a hydraulic servo system model, and they analyzed the effect of different working conditions on the coupling model . Liu et al. considered the interaction between rolling mill structure vibration and workpiece vibration, proposed a model of workpiece-roll coupling vibration, studied the transition and bifurcation characteristics of vibration under the main resonance conditions, and introduced time-delay feedback control to suppress rolling mill vibration . Wang et al. considered the friction force due to the roughness between rolls and the work roll movement on the basis of the rolling theory and lubrication theory. They established a coupling vibration model of the rolling interface under unsteady lubrication and the effect of multiple factors . In addition, Lu et al. established a coupling vibration model of the dynamic rolling process and nonlinear vibration parameters and analyzed the bifurcation characteristics and stability of the vibration system using the Hopf bifurcation theorem . In conclusion, although some achievements have been realized in the exploration of the coupling vibration mechanism of rolling mill rolls, there are still some limitations or problems with existing models and studies. Therefore, the complex vibration behavior of a rolling mill itself needs to be further explored and verified from different perspectives.
In this study, we consider the effects of the nonlinear spring force of the hydraulic cylinder of a rolling mill, the nonlinear friction force between rolls, the nonlinear rolling force, and the structural constraints of the rolling mill and establish a coupling vibration model of a four-high hot rolling mill. We investigate the effects of tuning parameters, nonlinear stiffness, and coupling parameters on the amplitude-frequency characteristics of the vibration system. The simulation results show that a process of energy exchange occurs between the vertical and horizontal directions of the rolling mill vibration system. When the vibration parameters change, a jumping phenomenon occurs in both directions, causing instability of the coupling vibration system of the rolling mill. A change in the nonlinear spring force coefficient of the hydraulic cylinder considerably affects the vibration state of the rolling mill rolls, and changes in the coupling parameters lead to the complex nonlinear phenomenon of the vibration system. Thus, the coupling vibration model of a hot rolling mill established in this paper is confirmed to be effective. Finally, the bifurcation and chaos behavior of the coupled vibration system of the rolling mill under dynamic external excitation are studied. It is found that different periodic motions exist and the vibration alternates among different forms, which is one of the reasons for the appearance of periodic light and dark stripes on the strip surface. The results of this study can provide certain theoretical reference and technical support for reducing or restraining rolling mill vibration.
The mechanical structure of a hot rolling mill can be simply illustrated as shown in Figure 1. In a rolling mill, the cylindrical block of the hydraulic cylinder is placed on the bearing bracket of the upper backup roll, and the piston is placed against the heel block under the mill stand. Therefore, the force is transmitted to the strip through the backup rolls and the upper and lower work rolls; then, the gap between the two work rolls is varied to enable rolling of strips to different thickness and specifications. Hence, the effect of nonlinear forces of the hydraulic system in the vertical direction cannot be ignored in the vibration model of rolling mill rolls.
Furthermore, because the diameter and rotation speed of the backup rolls and work rolls differ, when the rolling speed changes, the friction force on the strip changes, and the rolling force of the roll system is not in the vertical direction. In other words, during tension rolling, the impact load of the hot rolling mill is extremely large when it bites into the strip, and the bearing bracket will impact the mill housing, which will degrade the stability of the rolling mill system, and the rolling force of the rolling mill rolls does not act in the vertical direction. Therefore, to improve the accuracy of a vibration model of the hot rolling mill, the nonlinear vibration factors of the rolling mill rolls in the horizontal direction must be considered. Consequently, by considering the effect of the nonlinear force of the rolling mill in the vertical and horizontal directions and combining it with rolling mill vibration, we can better explore the chatter mechanism and vibration behavior of a hot rolling mill.
A hydraulic cylinder has many advantages in practical application and is widely used in the hydraulic screwdown device of a rolling mill. In this study, we consider a double-acting single-piston servo hydraulic cylinder in a hot rolling mill as an example for the analysis; its structure diagram is presented in Figure 2.
As Figure 2 shows, A1 and A2 are the effective areas of piston rodless cavity and rod cavity of the hydraulic cylinder, respectively. VL1 and VL2 are the volumes of oil in the pipeline between the valve and the rodless cavity and between the valve and the rod cavity, respectively. L is the total stroke of the hydraulic cylinder, L0 is the initial position of the piston, y is the piston displacement, which is also the vibration displacement in the vertical direction of the rolling mill rolls, and k (y) is the total hydraulic spring stiffness of the hydraulic cylinder.
During the working of the hydraulic cylinder, the piston can be regarded as a rigid body. The change in the piston displacement changes the pressure and oil volume in the two oil cavities, changing the oil stiffness accordingly. Therefore, k (y) is equivalent to the parallel stiffness of the two chambers hydraulic spring :where e is the elastic modulus of the oil volume and V1 and V2 are the volumes of the rodless cavity and rod cavity, respectively.
The calculation accuracy of rolling force greatly affects the distribution of friction force and strip quality in the deformation zone. Many expressions for rolling force under different working conditions have been proposed by analyzing, simplifying, and regressing the characteristics of nonlinear coupling vibration of the rolling mill and dynamic components of rolling force based on actual tests [18, 20]. Of them, we adopt the AlexanderFord formula for hot rolling . The dynamic rolling process in the deformation zone is shown in Figure 4.
As Figure 4 shows, b and f are the tension at the entrance and exit of the rolling, respectively. h0 and h1 are the thickness at the entrance and exit of the workpiece in steady state, respectively. h2 is the thickness at the exit of the workpiece in dynamic rolling, h2=h1+y, is the rotation speed of the roll, and F is the friction force on the work rolls:where P is the rolling force, K is the strip deformation resistance, B is the average width of the workpiece, Qp is the influence coefficient of the stress state, and lc is the horizontal projection length of the roll contact arc in the deformation area:where h is the reduction, h=h0h1y, R is the roll radius, and is the friction coefficient between rolls. is the reduction rate, =h/h0, T is the deformation temperature, T=(t0+273)/1000, and e is the deformation degree, e=ln[1/(1)]. Regression coefficients 0 and a1a6 have a set of coefficients for different steel grades. In this study, the regression coefficient of the deformation resistance of ordinary carbon steel is taken  as follows:
Considering that the friction coefficient between roll gaps varies with the fluctuation of rolling speed during rolling, Roberts formula for friction coefficient is adopted :where G1 and G2 are the friction characteristic coefficients, whose values are determined by specific friction model parameters; generally, G1=0.51 and G2=0.001. is the vibration speed in the horizontal direction. Because , equation (9) can be changed to and yh0h1; hence, equation (9) can be further expressed aswhere 0 is the friction coefficient of the roll gap in the steady state and (, y) is the dynamic values of the friction coefficient.
Here is the rolling force in the steady state of the vibration system of the hot rolling mill; is the dynamic value of the rolling force in the unsteady state. Therefore, equation (12) is the nonlinear rolling force, which is affected by the coupling of vertical vibration displacement and horizontal vibration speed, as shown in Figure 5.
According to the structure diagram of the four-high hot rolling mill shown in Figure 1, we consider the structural constraints on the roll and the effect of dynamic rolling force, the nonlinear spring force exerted by the hydraulic cylinder in the vertical direction, and the friction force change caused by the rolling speed fluctuation in the horizontal direction. Then, the mass concentration method is adopted, wherein the upper backup and work rolls are equivalent to a mass block, while the lower backup and work rolls are equivalent to a mass block. At the same time, in the experiment, the vibration displacement of the upper and lower rolls of the rolling mill is the same, but in the opposite directions. For the convenience of calculation and analysis, owing to the symmetry of rolling mill vibration, the rolling mill can be simplified as an effective and reliable 2-DOF vibration system . The coupling vibration model of the upper rolls of the hot rolling mill under multiple nonlinear effects is established, as shown in Figure 6.
As Figure 6 shows, m is the equivalent mass of the upper roll system of the rolling mill, is the rotation speed of the work roll, F0cost is the external excitation of the roll system, F0 is the external excitation amplitude, and is the external excitation frequency. k1 and c1 are the equivalent stiffness and damping between the upper roll system and the frame and the archway column, respectively, and k2 and c2 are the equivalent stiffness and damping between the upper roll system and the steel strip, respectively.
The friction on the roll is small in the vertical direction and can be neglected. Therefore, from equations (10) and (12), the nonlinear friction on the roll in the horizontal direction can be obtained as follows:where F (, y) is the dynamic change of friction.
According to the Lagrange theory, the coupled vibration dynamic equation of the hot rolling mill rolls can be obtained as follows:where and are the vibration accelerations in the horizontal and vertical directions, respectively. and are the vibration velocities in the horizontal and vertical directions, respectively. x and y are the vibration displacements in the horizontal and vertical directions, respectively, and is the constraint coefficient of the nonlinear spring force. Therefore, equation (15) can be simplified as
The multiscale method has strong problem-solving ability and good computing ability, and considering that it is widely used in solving coupled vibration system problems, we use the multiscale method to solve the dynamic response of the system . The nonlinear term in equation (16) is assigned a small parameter , and the fast and slow time scales T0=t and T1=t, respectively, are introduced to obtainwhere Dn (n=0, 1) is the partial differential sign, and Dn=/Tn. The solution for equation (16) is set as follows:
The solution of equation (20) is set as follows:where A and B are the undetermined complex functions and cc is the complex conjugate of the left side items. By substituting equation (22) in equation (21), we obtain
Considering the internal resonance of the system, =2+ and 1=2+1 are set, where and 1 are the tuning parameters; can better describe the change between and 2 and represent the value range between them. To avoid the duration term, A and B must satisfy the following:
We set and , where a and b are the amplitudes of rolling mill rolls in the horizontal and vertical directions, respectively. Substituting A and B into equation (24) and separating the real and imaging parts, the average equation of the coupling system can be obtained as follows:where 1=211T1 and 2=T12. Considering the occurrence of a periodic movement in the coupling system of the hot rolling mill rolls, holds. Then, substituting this value into equation (25) and eliminating 1 and 2, the amplitude-frequency response equation of the coupling vibration system can be written aswhere .
Figure 7 shows the amplitude-frequency diagram of the coupling vibration rolls of the hot rolling mill as a function of tuning parameter . Set initial value =1.05e12 (N/m3) and 1=3.3. An energy exchange process is observed between the vertical and the horizontal direction, which is a special phenomenon that occurs in response to internal resonance. When tuning parameter >10Hz, amplitude a in the horizontal direction basically remains constant, while amplitude b in the vertical direction increases rapidly and then decreases after reaching the maximum. When 16.5Hz<<21.5Hz, a increases and b decreases gradually. When 8.40Hz<<6.87Hz, there are multiple solutions in the two directions and a jump phenomenon exists, causing instability of the coupling vibration system of the rolling mill in this range. Due to external disturbance, 12 and 2, which imply that the external excitation frequency is close to the natural frequency in both directions and that resonance occurs. In addition, Figure 7 indicates a large linear frequency in the horizontal direction. This is because of the energy exchange to the horizontal direction when the vibration in the vertical direction is weakened. Moreover, the external excitation frequency is similar to the natural frequency in the horizontal direction; therefore, the amplitude in the horizontal direction increases rapidly. The resonance can be avoided by changing the external excitation amplitude or the linear stiffness between the rolls to maintain each frequency separated from each other.
Figure 8 shows the amplitude-frequency curve of the coupling vibration of the hot rolling mill rolls under varying nonlinear spring force coefficient of the hydraulic cylinder for tuning parameter =14.5Hz. In the figure, stable branches are plotted with solid lines, while unstable branches are plotted with dotted lines. When =0, that is, when the hydraulic cylinder piston is at the initial position, the vertical vibration of the rolling mill is only affected by the linear stiffness between the stands, and the amplitude of the vibration system is small. At this point, the rolling mill is in a steady state. With the increase in the piston movement displacement of the hydraulic cylinder, the corresponding nonlinear stiffness increases. For 2.605e12 (N/m3), there are multiple solutions, the amplitude increases, and the resonance region expands. This indicates that the change in the piston position of the hydraulic cylinder greatly affects the vibration state of the rolling mill rolls. In actual rolling, hydraulic oil with good temperature characteristics and large bulk modulus of elasticity should be used as much as possible. Moreover, seals with good performance should be selected to prevent an increase in the level of impurities due to the long-term use of oil. However, the change in nonlinear stiffness is caused by the change in viscosity, leading to abnormal vibration.
Figure 9 shows the amplitude-frequency curve of the coupling vibration of the hot rolling mill rolls under varying coupling term parameter 1, which is composed of horizontal vibration speed and vertical vibration displacement y. In the plot, the stable branches are indicated with solid lines, and the unstable branches are indicated with dotted lines. For tuning parameter =14.5Hz, when 12<1<3, there are multiple solutions and the vibration amplitude increases gradually, causing severe vibration of rolling mill rolls. The vibration form of the rolling mill in this range of coupling parameter is complex and variable. As 1 increases, the vibration state of the rolling mill gradually stabilizes. This further indicates that the study of the coupling vibration of the hot rolling mill rolls is meaningful and would provide some guiding significance to explain the vibration phenomenon of rolling mills.
In this study, using the bifurcation and chaos theory, we determine the critical value and parameter range from the bifurcation solution of the coupling vibration system of the hot rolling mill rolls, so as to restrain and avoid rolling mill vibration.
Figure 10 shows the dynamic bifurcation diagram of the vertical coupling vibration of the hot rolling mill rolls. Figures 11 and 12 show the phase path and the Poincare section under different external excitation amplitude F0.
Figure 10 indicates that when the external excitation amplitude F0<5.54e5 N, the vibration is period-1 motion, the corresponding phase path is a closed curve (Figure 11(a)), and the corresponding Poincare section is a fixed point (Figure 12(a)). This implies that the vertical vibration of the rolling mill has a stable solution and the vibration displacement is small. With increasing F0, the steady-state vibration becomes period-2 motion, the corresponding phase path is a closed curve formed after two circles (Figure 11(b)), and the Poincare section is two fixed points (Figure 12(b)). In this status, the vibration displacement of the rolling mill in the vertical direction increases gradually, resulting in an increase in the roll gap and the increase in the rolling workpiece reduction, causing uneven oscillation marks on the strip surface. With further increase in F0, the vibration displacement will also increase. As shown in Figure 10, the system will enter into paroxysmal chaos, resulting in up and down vibration disorder of the rolling mill rolls, seriously affecting strip quality and aggravating oscillation marks. Therefore, the range 5.68e5 N
Figure 13 shows the dynamic bifurcation diagram of the horizontal vibration of the hot rolling mill rolls. Its specific vibration form is periodic-1 motionperiodic-2 motionchaos motiondegeneration to period-2 motionparoxysmal chaoschaos motion. The phase path and Poincare sections corresponding to different external excitation amplitudes F0 are shown in Figures 14 and 15.
When F0<5.31e5N, the horizontal vibration of the hot rolling mill is stable; the corresponding phase path is shown in Figure 14(a), and the Poincare section is shown in Figure 15(a). As F0 gradually increases, the horizontal vibration system directly enters chaotic motion after period-2 motion, and when F0>5.95e5N, the system gradually degenerates into period-2 motion. The corresponding Poincare sections of the phase path are, respectively, shown in Figures 14(b) and 15(b). Then, the system passes through paroxysmal chaos when F0>6.20e5N, and it finally enters chaotic motion. The corresponding phase trajectory is shown in Figure 14(c). The trajectory is a set of unclosed curves, indicating that the system does not have periodicity at this time; the corresponding Poincare section is shown in Figure 15(c). Note that the system undergoes a periodic motion, period-doubling motion, and chaotic motion in the horizontal direction, and the movement alternates among these forms. Thus, different forms of chatter marks are caused on the steel strip.
Figures 10 and 13 indicate that changes in the external excitation amplitude will cause changes in the vibration displacement in both vertical and horizontal directions. Therefore, fluctuation of the speed of the rolls is caused, which in turn leads to changes in nonlinear friction force and dynamic rolling force, resulting in abnormal vibration of the coupling system of the rolling mill rolls. Comparison of Figures 10 and 13 indicates that the two ranges of F0, namely, 5.68e5N
In this study, a coupled vibration model of hot rolling mill rolls under the effect of multiple nonlinear forces was established. Below is the summary of the analysis and steps involved in establishing the model.(1)By analyzing the actual structure and working principle of a double-acting single-piston servo hydraulic cylinder, the nonlinear spring force produced by it was obtained. Considering the velocity fluctuation at the entry of the strip workpiece in the horizontal direction and the changes in the vibration displacement in the vertical direction, the nonlinear friction force between the rolls was obtained. Finally, by considering the dynamic variation of the rolling force, the coupling vibration model of a four-high hot rolling mill under the effect of multiple nonlinearity was established.(2)Based on the amplitude-frequency response equation, and by using the actual rolling parameters of the 1780 four-high hot rolling mill, the main reason for the severe resonance of the rolling mill was found to be the occurrence of the internal resonance when the external excitation frequency is close to the derived frequency in the vertical and horizontal directions. This results in the instability of the system and occurrence of the jump phenomenon. Further, changes in the movement displacement of the hydraulic cylinder and the coupling term parameters considerably contribute to the changes in the amplitude and resonance range of the coupling vibration system of the hot rolling mill rolls.(3)From the study of the bifurcation characteristics of the coupled vibration system of the hot rolling mill under varying external excitation amplitude, it was found that period and period-doubling motions exist in both vertical and horizontal directions, and the vibration alternates between different forms. Therefore, periodic light and dark stripes appear on the strip. The results indicate that the abnormal vibration of rolling mill rolls can be mitigated if the external excitation amplitude is maintained below the critical value.
This research was supported by National Natural Science Foundation of China (Grant no. 61973262) and Hebei Province Natural Science Funds for the Joint Research of Iron and Steel (Grant no. E2019203146).
Copyright 2020 Rongrong Peng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.