THE EFFECT OF ROLL DIAMETER ON MILL CAPACITY CA GARSON

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1 THE EFFECT OF ROLL DIAMETER ON MILL CAPACITY By CA GARSON Bundaberg Walkers Engineering Ltd, Bundaberg KEYWORDS: Mill, Capacity, Roll, Diameter, Speed. Abstract THE THROUGHPUT of a mill is related to the size of its rollers and the required level of performance. The effect of roll length and roll diameter on capacity (throughput at a given level of performance) is of interest because the size of the rollers strongly influences the installed cost of a mill. The effect of roll diameter on the capacity of a mill is not well established. It is complicated by a likely interaction with mill speed. A rudimentary, theoretical approach is used to advance the thesis that mill capacity is fundamentally proportional to the diameter of the mill rolls. Introduction The term throughput is used here to mean the mass rate at which a mill processes a given material supplied from a given feed arrangement. Performance is taken to be the proportion of the liquid phase separated from the feed. Capacity is used to mean the throughput possible at a specified level of performance. The throughput of a mill can often be increased, without changing the size of the rolls, by raising the speed of the mill and/or increasing the mill settings. Both approaches, however, would probably reduce the extraction performance of the mill. The effect of a given parameter on the capacity of a mill is defined in this paper as the effect on throughput while maintaining the same level of performance. For a given material and feeding conditions, the capacity of a mill is thought to depend on the size of the mill rolls, their speed and the mill settings. The exact nature of this dependence is important because the size of the mill rolls has a substantial influence on installed cost of a mill. This paper considers the likely effect of roll diameter on the capacity of a mill. The diameter of the grooved mill rolls is taken to be the mean diameter of the rolls throughout this paper. A two roll mill as sketched in Figure 1 is considered for simplicity. However, the same arguments are thought to apply to the case of more complex arrangements of three or more rolls. Geometric considerations and the effect on mill throughput The throughput of the mill in Figure 1 could be raised by increasing the work opening of the mill, W O, alone but this approach would also reduce the compaction at the nip of the mill and so reduce the performance of the mill. 510

2 h D W O Fig. 1 Arrangement of a two roll mill. Other things being equal, the exit of the feed chute, h, and the work opening at the nip of the mill, W O, must be varied in proportion to the diameter of the mill rolls, D, to maintain feeding conditions (as characterised by the contact angle at the exit of the feed chute, α) and keep the nip compaction similar. Murry and Holt (1967) present a more formal derivation of this same equivalency. The simpler, intuitive argument of geometric similitude is used in the cases considered here. Given that the exit of the feed chute and the work opening at the nip of the mill are varied in proportion to the diameter of the mill rolls, geometric considerations predict that the throughput of the mill for a given material and feeding conditions will be proportional to: the length of the mill rolls the diameter of the mill rolls the lineal surface speed of the mill rolls. Throughput is considered fundamentally proportional to the length of the mill rolls for a given diameter and speed. Except as noted, the arguments used in this paper are on the basis of per unit length and assume no significant end effects. The effect of roll diameter on throughput cannot be considered in isolation. There is an interaction between roll diameter and rotational mill speed. Geometric considerations on their own predict that doubling the diameter of the rolls will give a four fold increase in throughput if the rotational speed of the mill rolls is maintained. This quadrupling of theoretical throughput comes about from a general, two fold increase in size to maintain geometric similitude when the diameter of the rolls is doubled plus a general, two fold increase in lineal speeds due to the larger rolls operating at the same speed of rotation. However, it is generally understood that the performance of a mill with rolls of given size decreases with increasing mill speed. If this was not so, the effect of roll diameter on capacity would be relatively unimportant as it would be most economical to have small mills 511

3 running at high speed. What is not known is whether the decline in the performance of a given mill with increasing speed is a function of the rotational speed of the rolls or a function of the lineal surface speed of the rolls. Roll diameter and roll speed and the effect on mill capacity Batstone et al. (2001), Munro (1964) and Kent and Delfini (2000) all reported a decline in mill performance at higher mill speed but the precise mechanism by which this occurs is not known. Bullock and Murry (1957) found that the coefficient of friction between the surface of a roll and a mat of bagasse decreased as the surface speed increased. This reduction in the coefficient of friction could conceivably cause feeding problems at high surface speeds. Kent and Delfini (2000) noted the use of a special roll roughening technique to enhance feeding and reduce the wear of mills operating at high speeds. Severe feeding difficulties were reported to occur if the special roughening was lost. This experience indicates that mill feeding becomes more difficult at high mill speeds and, along with slip and roll wear, may be responsible for the decline in mill performance with increased mill speed. Work by Williams et al. (2001) suggested that impaired feeding due to high juice drainage rates might contribute to declining performance at high speeds in the case of two roll mills operating at large specific throughputs. De Boer (1972) recognised the importance of both roll diameter and roll speed stating that a two-roll mill, equipped with large rollers running at a low speed, has the advantage over a two-roller mill equipped with small rollers running at high speed. Hugot (1986) acknowledged the interaction between roll diameter and mill speed and introduced the concept of a limiting mill speed and whether that limiting speed should be a rotational speed or a lineal surface speed. He concluded that surface speed is the more fundamental limit because the juice must flow back against the feed to be extracted on the feed side of the nip and avoid flowing forward through the nip. Hugot (1986) cited Murry (1960) as coming to the same conclusion. However, Hugot (1986) suggested that for reasons of economics, some compromise between surface speed and rotational speed was necessary. Hugot (1986) reported several formulae for maximum mill speed from various sources. As seen in Figure 2, the form of most of these relations differs substantially from Hugot s own assertion that surface speed, independent of roll diameter, is the fundamental parameter of importance. Murry and Holt (1967) also noted the importance of the interaction of roll diameter with mill speed. They suggested three logical speeds for consideration: the speed to maintain crushing rate, the same surface speed, and the same rotational speed. Murry and Holt (1967) reported that experimental evidence suggested extraction was the same at the same surface speed if roll diameter was varied. This statement supports the existence of a limiting surface speed but Murry and Holt (1967) did not present the experimental results in any detail. Nor did they advance an explanation for the dependence of mill performance on surface speed independent of roll diameter. 512

4 Surface speed (mm/s) Cail FCB Hugot Tromp Louisiana Roll diameter (m) Fig. 2 Limiting milling speeds as a function of roll diameter from various sources (after Hugot, 1986). Long standing Australian practice has been to regard speeds around 300 mm/s as the maximum top roll surface speed to achieve good performance with a six roll mill (Cullen and McKay, 1993). Evidently, there is uncertainty about the effects of roll diameter and its interaction with roll speed. No precise experiments at industrial scale are known. Hugot (1986) gave the following reasons for this lack of experimentation: tandems can only operate over a limited speed range making conclusions difficult to draw with certainty performance depends significantly on factors other than mill speed which cannot be eliminated mill designs do not allow significant variation in speed without an associated change in crushing rate. Fundamentally, the uncertainty is because roll diameter cannot be varied substantially in a practical manner at industrial scale. Theoretical consideration of roll diameter and roll speed and the effect on mill capacity. The effect of speed on mill performance is fundamental to the effect of roll diameter on the capacity of a mill. Some insight is possible from consideration of the underlying theory. Liquid flow through a rigid, porous medium typically obeys Darcy s law (Darcy, 1856). In one dimensional form, Darcy s law may be written as: P = V L / K where: P = pressure drop between the sections of interest V = Q / A (superficial, specific velocity of the liquid phase relative to the solid phase) 513

5 superficial refers to the gross cross-section and not the actual area available for flow Q = volume flow rate of the liquid phase relative to the solid phase A = superficial area through which the liquid flows (actual area through which the liquid phase flows divided by the areal porosity) L = length of the flow path = dynamic viscosity of the liquid phase K = intrinsic permeability of the rigid medium The three dimensional nature of the flows in a mill, deformation of the porous medium, complex and ill defined boundary conditions and probable anisotropy mean the situation in a mill is too involved for an analytical solution or hand calculation. However, some progress may be possible if one is willing to accept the notion of a typical flow path for the juice. That is, a single flow path of definite length flowing through a rigid medium of specified permeability that is representative of the bulk flow. The concept of representative parameters is used routinely in fields such as heat transfer to consider complex phenomena on a scale that is relatively coarse but much easier to comprehend. Given the concept of a typical flow path, Darcy s law can be applied to that flow path to consider the effects of changes in roll diameter. Consider the case where roll length is fixed, the diameter of the mill rolls is doubled and the rotational speed of the rolls is maintained (Figure 3b). Mill throughput will increase with the square of roll diameter given the assumptions of no slip and uniform feed velocity. On this basis, a doubling of diameter means a four fold increase in throughput and a four fold increase in juice flow if mill performance is maintained. The relative superficial velocity, V, will double because the superficial volume flow rate quadruples with the increased throughput while the superficial area available for the flow only doubles due to geometric similitude and the doubling of roll diameter. In addition, doubling the roll diameter causes the length of the flow path to double due to geometric similitude. By Darcy s law then, the peak pressure needed to drive this juice flow will quadruple. It is the gradient of the pressure, P/ L, that gives rise to the juice flow and shearing forces that must be resisted by the feed blanket. In this instance, the overall pressure drop has gone up by a factor of four but the associated typical length has only doubled so that the typical pressure gradient also doubles. This increase in the relative, superficial velocity and associated pressure gradients may have an adverse effect on mill feeding and hence on throughput and performance. Fig. 3 General effect of doubling roll diameter, D, on lineal speeds, S, widths, W and lengths, L while maintaining (b) rotational speed and (c) surface speed. 514

6 Consider a second case where roll length is fixed, the diameter of the mill rolls doubles and the rotational speed of the rolls is halved to maintain the surface speed of the rolls (Figure 3c). In this case, idealised mill throughput increases in proportion with the diameter of the mill rolls. If a doubling of diameter means a doubling in throughput, then the juice flow must double if mill performance is maintained. The area available for flow is doubled so the relative superficial velocity of the juice, V, is unchanged. However, the length of the flow path will have doubled. By Darcy s law then, the peak pressure needed to drive this juice flow will have to double but the gradient of the pressure, P/ L, is unchanged. Mill feeding and thus mill throughput and performance are less likely to be changed. By the foregoing argument, the capacity of a mill of given length is more likely to be proportional to roll diameter rather than the square of roll diameter, other things being equal. Other matters for consideration Applicability of Darcy s law The form of the Darcy equation used here is the original form determined empirically by Darcy. This formulation ignores the effect of gravity. This original form is thought reasonable in a general sense for cane mills given the potential juice pressures and the cohesion of the fibre blanket. The original Darcy equation used here ignores the effect of viscous drag which is always present but becomes more important at higher Reynolds numbers. The Hazen-Dupuit-Darcy model (Arunn, 2007a) is capable of representing the viscous drag which is dependant on the square of the relative fluid velocity. Arunn (2007b) suggests that departure from linear Darcy flow occurs at Reynolds numbers of the order of 10 or higher. Substitution of a characteristic permeability and juice velocity from Loughran and Adam (1998) and Loughran and Kannapiran (2002) respectively, into the expression for Reynolds number (Arunn, 2007b) indicates that linear Darcy flow will represent the situation adequately but an experiment to confirm this assumption would be worthwhile. Computer modelling The theoretical approach considered here is not amenable to analytical solution or hand calculations. Over the last 15 years or so in Australia, effort has gone into the development of a finite element model and the associated material properties (Loughran and Kannapiran, 2002). This computer modelling approach could be used to investigate the effect of roll diameter without the need to resort to the gross assumptions and simplifications used in the foregoing theoretical considerations. Practical constraints At some point as roll diameter decreases, the capacity of a mill is anticipated to decline faster than the product of roll diameter and roll length. This expectation relates to practical limits on the ratio of the length of the rolls to their diameter and end effects. Rolls with a length large relative to their diameter are unlikely to have sufficient strength to withstand the forces necessary to achieve good performance. Very short rolls are unlikely to perform well because of feeding problems associated with end effects. There is anecdotal evidence to support this assertion. Conclusions For existing mills, the size of the rolls cannot be varied significantly but roll size is an important consideration in the selection of new milling units. 515

7 The underlying theory of flow through porous media suggests that it is the surface speed of the mill rolls rather than their rotational speed that will determine the capacity of a mill, other things being equal. For the same level of performance then, mill throughput is thought to be proportional to roll diameter (and roll length). This reasoning supports the argument of Hugot (1986) and others by providing an elementary theoretical basis for it. Acknowledgement The support of Bundaberg Walkers Engineering Ltd in allowing time to prepare this paper and permission for its publication is gratefully acknowledged. REFERENCES Arunn N (2007a) Arunn N (2007b) Batstone DB, Hatt RJ, Evans BD, Mitchell GE (2001) Development of the Bundaberg tworoll mill. Proceedings of the International Society of Sugar Cane Technologists 24, Bullock KJ, Murry CR (1957) The pressure required to feed cane mills, part 1 theoretical considerations. Proceedings of the Queensland Society of Sugar Cane Technologists 24, Cullen RN, McKay BR (1993) A review of the influence of mill size on milling capacity. International Sugar Journal 95, Darcy HPG (1856) Les fontaiones publiques de la Ville de Dijon. (Victor Dalmont: Paris). De Boer AT (1972) Two-roll cane mills: a reappraisal in the light of value engineering of milling (parts I, II and III). International Sugar Journal 74, , , Hugot E (1986) A handbook of cane sugar engineering. 3 rd edn (Elsevier: New York) Kent GA, Delfini P (2000) High-speed milling a low cost avenue for increasing milling capacity. Proceedings of the Australian Society of Sugar Cane Technologists 22, Loughran JG, Adam CJ (1998) Properties of prepared cane for computational crushing models. Proceedings of the Australian Society of Sugar Cane Technologists 20, Loughran JG, Kannapiran A (2002) Finite element modelling of the crushing of prepared cane and bagasse. Proceedings of the Australian Society of Sugar Cane Technologists 24, Munro BM (1964) An investigation into crushing bagasse and the influence of imbibition on extraction. PhD thesis, University of Queensland, Brisbane. Murry CR (1960) The mechanics of crushing sugar cane. PhD thesis, University of Queensland, Brisbane. Murry CR, Holt JE (1967) The mechanics of crushing sugar cane. (Elsevier Publishing Company: London). Williams LJ, Garson CA, Adam CJ (2001) Identification of mill feeding parameters. Proceedings of the Australian Society of Sugar Cane Technologists 23,

MILL SETTINGS AND REABSORPTION

MILL SETTINGS AND REABSORPTION A WIENESE and M A GOOCH Sugar Milling Research Institute, Durban, 4041, South Africa E-mail: awienese@smri.org Abstract This paper describes the Natal Method for the calculation