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机械工程学院届本科生毕业设计题目任务书指导教师姓名年龄职称毕业院校所学专业题目名称立式行星球磨机的设计题目类别工程题目来源科研生产拟指导的人数题目内容及要求:(5)立式行星球磨机的设计行星球磨机是混合、细磨、小样制备、纳米材料分散、新产品研制和小批量生产高新技术材料的必备装置,本课题旨在设计一种实验室用立式行星球磨机。参数如下:1、电源及功率:AC380V/550W;2、球磨罐容积:500ml4;3、球磨罐:配四个尼龙罐(硬质合金、不锈钢)及氧化锆球;4、转速: 340 r/min;5、进料粒度:5mm 出料粒度:0.1um具体内容及进度:1、课题调研:资料检索、调研。(1周)2、毛坯设计、工艺路线拟定。(2周)3、工艺设计。(2周)4、夹具设计。(2周)5、夹具零件图纸绘制;(2周)6、产品设计使用说明书;(1周)7、与课题相关的外文资料翻译3000字。(1周)8、其他要求:学生在教师指导下独立完成;一组学生的技术参数或结构方案不得相同;参考资料:1、工艺设计课程设计指导书2、金属切削机床夹具设计手册3、机械工艺师杂志4、相关专业教材题目所涉及的知识面:机械设计、材料、工艺、电气控制、环保学院审核意见 院长签字: 年 月 日注:1、题目类型:工程设计、实验、理论计算、其他; 2、题目来源:科研生产、实验室建设、其他。球磨机磨损的推断模型摘要:球磨机,典型矿物加工业,被用于将大小分布的矿石磨成别的。磨损与影响研磨性能的钢球电荷方面的细碎机械学的建立联系在一起。在本研究中,球磨机磨损与研磨工作参数有关,决定使用一种数学磨损模型。这种磨损模型联合在压碎过程中能量的消散和填装层的磨损区段同粘着力和磨损描述。这种模型已经被加到钢球装填层运动模型,球磨机磨损率的模拟实验以及球磨机的元件磨损和它的对研磨性能的影响。现有模拟结果显示了在磨损和研磨性能之间的交互作用。更深入的研究是用工业日期确认装填层和磨损模型的答案。1997年,加拿大采矿和冶金学会。由Elsevier Science Ltd出版。引言粉碎,磨碎到微粒,磨成粉都是用于该矿产加工工业的水磨程序的同义名词。与这些过程有关联的是金属磨损,加拿大和美国的年度消耗钢铁量达300 000吨。磨损也影响着研磨性能和品质。在这一篇论文中,磨损的推断模型的预测对减少工序磨损、保持研磨性能和品质最理想的磨损状况的决定是必需的。磨损和它与磨损有关机械学原理已经被广泛的应用在2-4期实验数据上,有用的模型对磨损现象的理解在5-9期实验数据上,理论研究在10-12期实验数据上。这篇论文的目的是根据球磨机水磨工序理论的发展而做出的磨损模型的推测。背景球磨机(图1所示)是由许多相互联系和相互作用的零件组合成的一个体系,这些零件组合起来是为了磨碎矿石。这种机械粉碎法的工序是由一些特殊的钢球组成的球磨机的零件用来磨碎矿石的过程。同时,这些球在球磨机工作期间能够很好地建成球磨机的填装层的轮廓,如图2所示。填装层的轮廓标志描绘为三个有典型破碎特性的区域。研磨区段是由彼此滑动球层数描述,磨碎它们之间的矿石;翻滚的区域是在低能量的冲击下对钢球相互的滚动和磨碎矿石的描述。击碎的区域是在高能量的冲击下对钢球的飞行和击碎矿石的描述。填装层的轮廓的形成是直接地依靠存在填装层和球磨机滚筒壁之间的摩擦力。通过用不同的衬板轮廓,摩擦力也可改变由此而生的影响球磨机轮廓的形式。轮廓运动模型如上述所提。球磨机磨损是能量转移的作用在衬板和球轮廓之间以及在二个碰撞的球之间。因此,塑造轮廓运动模型是预测球磨机磨损和对研磨的影响的作用第一步。模型的发展开始以单个的球的运动为对象(如图4)。如所描述由Mclvor和Powell 15、16,在球磨机中单个球飞行的问题是由转动速度,滚筒半径,静摩擦因子和轮廓的角度决定: (1)无论如何,Hukki 17 提及球轮廓的运动不是全部依靠一个的单点飞行如假设上述等式。它也是依靠描述球轮廓和衬板类型相互联系的有效的摩擦因子是否和我的差不多。所以,如果我们描述动力传递损耗在二球层数之间作为静态和运动摩擦因子17之间的一个关系; (2)旋转的动力传递损耗速度为: (3)使用这个结果,我们可以区分球飞行和点稳定的动力传递损耗之间如下:1. 飞行的问题 (1.0) (4)2. 稳定的动力传递损耗问题(1.0) (5)有效的摩擦因子被定义为; (6)用这些关系与被描述的那些一起18-20和应用于他们描述离散的球填充层的质点系,它变得可能模仿球填充运动(如图5所示)。因而被定义为填充层运动,我们在各种各样的粉碎区域在填充外形可以通过确定被消耗的运动和分布能量(如图2),使用下式18-21: (7) (8) (9)在球磨机中这种能量轮廓(如图6)现在被确定为Hardinge磨机(如图1)。这个轮廓运动模型确定显示能量怎么在研磨,击碎和翻滚时被消耗后分布作为磨机转动速度、滚筒直径、填充层和衬板表示法功能。磨损率的估计如前面所提到,在球磨机的球轮廓的运动外形有三个粉碎区域。虽然有别的磨损机械学的存在,只有胶粘剂和磨蚀是与这些粉碎区域有联系。同翻筋斗和击碎区域联系在一起,当球在这些区域碰撞,当黏着性磨损联系到研磨区域时,球滑过另一个球或越过另一个球。这些机制可以被表达,根据在23-24磨损的能量率而做黏着性磨损 (10)腐蚀磨损 (11)运用这些磨损模型于球磨机的情况,我们可以得出: (12) (13) (14)比较最初和最后的衬板磨损外形,衬板磨损率可以被估计使用: (15)我们可以通过比较公式(15)和公式(12)确定磨蚀因素,因而得到: (16)进一步,使用公式(13)和公式(14)以及(16)的结果,我们可以尽可能地确定黏着力的大小: (17)以磨蚀因素并且为特定球磨机操作的上下文确定的黏附力可能性,现在我们从这个上下文可以确定球磨机的磨损率的影响是怎么改变的。保持和P为常数,变化的参量例如磨房转动速度和轮廓边界,我们可以推出对球磨机磨损率24的有关的变动。然而,推测球磨机磨损率是有限的,在球磨机研磨时,考虑到我们的确定球的磨损的影响的目标时的表现。衬板磨损在球磨机研磨的表现取决于主要能量怎样被分布在球轮廓外形的各种各样的粉碎区域。如被提及,轮廓外形的形式,和每个粉碎区域的重要特性,是直接地依靠存在球轮廓和球磨机桶壁之间的摩擦力。不同的衬板轮廓类型(图3) 在球轮廓和球磨机筒壁以及研磨的表现之间影响这中摩擦力。由于有特定的上下文,所以使用被认为优选的衬板类型的轮廓是可能的。然而,以时间,球磨机磨损将修改最初的衬板轮廓外形和随后碾碎研磨。在球磨机轮廓的力量下塑造运动形式成为推断球磨机磨损和它对研磨性能的影响的下一个步骤。在球磨机运转期间,整个轮廓大厅由重心和离心力然后施加力场组成衬板轮廓(图7)23-25。用这种描述,平均的组成力可以被确定作为展示在图8中;(i)平均组成的离心力 (18)(ii)平均组成的重力 (19)进一步,在球磨机衬板上面作为球磨机轮廓,球磨机轮廓的衬板部分的位移会产生一个压缩力(图9)。 这力量被定义如下: (20)这里通常表示为: (21)在衬板表面总的平均作用力可以成为: (22)衬板磨损,作为球磨机球轮廓创造的力场的位置和强度功能以及磨蚀因素,成为: (23)那里 (24)指出在衬板的滑动速度由早先的公式(2)重新整理。在衬板离散化到的区别,定时乘,这种仿真算法可以被开发之后成为23-25,包括衬板齿廓磨损的模拟实验。举例来说,图10中图解的一种波形衬板的轮廓磨损的模拟实验和在图11中现实的衬板的轮廓磨损差不多。球磨机磨损和研磨性能虽然工业上的研究需要更多这样的磨损模型,但是想象出一种弹性衬板的进化磨损的推断模型是有可能的。当然,这将计算怎样的磨损影响对研磨性能的决定,这里解释为在颗粒测定的生产能力的变化。由图1.的Hardinge情况得,消逝在倾斜的衬板的现象由这里转化为模拟如图12所示。进一步,该图6的能量率曲线是怎么随这种衬板磨损而变化的,推断球磨机的输出同输入的变化一样,是有可能的。从表格1可以看出,使用一种已经被开发的破碎模型,可以解释衬板的寿命期限是有可能的。这里,球磨机生产能力将提高而衬板磨损下降。与这种现象相联系,球磨机能源消耗的减少如所显示。这两种现象说明最佳化球磨机的性能作为一种推断磨损影响的函数是可能的。表1.球磨机的输出量作为衬板曲线的一个函数。颗粒大小(m)最初通过量%1/2通过量 %最后通过量%741001503008301170165058.0868.2578.5492.1299.4599.96100.0058.2568.4478.6892.1599.4599.96100.0060.1370.3880.2593.9699.6199.97100.00讨论在结束这篇论文之前应该对球磨机填装层运动、衬板磨损和球磨机输出的产品做几点评论。如所示,球磨机的填装层运动依靠许多物理和操作因素;它也依靠矿浆的流变特性。当然这些矿浆的流变特性是百分比固体的作用并且矿石的性质。在填装层运动的模型中,这些因素的影响被包括在(2)滑动速度的关系中,如所描述的静态和动摩擦因素。摩擦因素的变化,如矿浆的流变特性的一个可能的变化造成的,可以增加或减少在钢球层之间和衬板磨损之间的相当数量的动力传递损耗。在球磨机的磨损模型和两种磨损机械学中,它只是一种假设,球磨机不是空转的或者运转状况不直接地把钢球放到球磨机衬板里。在这样的情况下,衬板磨损同磨损机械学一样(表面,破裂,磨损),都增加了衬板的磨损率。球磨机产品的变化的重要性与衬板的磨损有关,是从属与一种特殊的矿石的破碎特性。同样地,检验使用的工业数据为了确定这个模型精确度是必要的。然而,假设,整体模型的一个充分检验是可能的,这里被提出的初步结果表示,考虑使用这个模型为球磨机优化作为能源消耗和球磨机衬板磨损功能变得可能。结论这篇论文根据球磨机的一个理论描述提出了一个有预测性的衬板磨损模型。当包括一个简单的胶粘剂和磨损模型的应用对一个复杂的钢球填装层模型时,不仅能确定必要的磨损参数,而且推断衬板和研磨性能是可能的。无论如何,进一步的研究对模型的检验和参数确定是必要的。尽管这是必要的,但在将来,球磨机在设计和操作方面的优化也有了可能性。鸣谢-本文的出版物由加拿大研究经费自然和工程研究委员会使成为可能。PREDICTIVE MODEL FOR BALL MILL WEARAbstract-ball mills, characteristic of the mineral processing industry, are used to reduce ore from one size distribution to another. Wear is associated with comminution mechanisms found in the ball charge which in turn affects grinding performance. In this work, ball mill wear, as a function of mill operating variables, is determined using a mathematical wear model. The wear model incorporates the energy dissipated in crushing, tumbling and grinding zones of the charge profile with adhesive and abrasive wear descriptions. This model has been added to a ball charge motion model allowing the simulation of mill wear rates as well as ball mill element wear and its affect on grinding performance. Simulation results presented show the interaction between wear and grinding performance. Further work is necessary to validate charge and wear model results using industrial date.1997 Canadian Institute of Mining and Metallurgy. Published by Elsevier Science Ltd.INTRODUCTIONTo comminute, to reduce to minute particles, to pulverize, are all synonyms of grinding processes used in the mineral processing industry. Associated with these processes is metal wear which in Canada and the United States represents an annual consumption of some 300 000 tons of iron and steel 1. Wear also affects grinding performance and quality. In such a context, predictive wear models become a necessity to determine optimal grinding conditions that reduce process wear while maintaining grinding performance and quality. Wear and its mechanisms related to grinding has been studied extensively using experimental data 2-4, models useful to understanding of wear phenomena 5-9 and theoretical studies 10-12.The goal of this paper is the presentation of a predictive wear model based on a theoretical development for one such grinding process, the ball mill.BACKGROUND The ball mill (Fig.1) is a system composed of a number of interrelated and interactive elements that work together in order to grind a given ore. This comminution process is achieved by the individual balls which constitute the actual ball mill element that brings about ore breakage. Together, these balls form the mill ball charge which, during ball mill operation, typically has a charge profile as found in Fig.2. Note that the charge profile shows three zones that are characterized by the type of breakage occurring there. The grinding zone is described by ball layers sliding over one another, breaking the material trapped between them; the tumbling zone is described by balls rolling over one another and breaking the material in low-energy impact; the crushing zone is described by balls in flight re-entering the ball charge and crushing the material in high-energy impact. The form of the charge profile is directly dependant on the friction force existing between the charge and the ball mill wall. By the use of different liner profile (Fig.3), the friction force can be changed subsequently affecting the form of the mill charge as well.Charge motion model As mentioned. Mill wear is a function of the energy transferred between liner and ball charge as well as between two colliding balls. Therefore, modelling charge motion is a first step to predicting mill wear and its effect on grinding. Model development starts with defining single ball motion (Fig.4). As described by Mclvor and Powell 15、16, the point of flight of a single ball in a ball mill can be determined as a function of rotation speed, mill radius, static friction factor and the liner lifer angle: (1) However, Hukki 17 mentions that ball charge motion is not entirely dependant on a single point of flight as assumed with the above equation. It is also dependant on whether the effective friction factor describing the interrelationship between ball charge and type of liner used is greater or less than I. Therefore, if we describe slippage between two ball layers as a relationship between static and kinetic friction factors 17; (2) Rotational slippage speed becomes: (3)Using this result, we can differentiate between ball flight and the point of stable slippage as:1. point of flight (1.0) (4)2. point of stable slippage (1.0) (5)Where the effective friction factor is defined as; (6) Using these relationships along with those described in 18-20 and applying them to a system of particles that describe a discretized ball charge, it becomes possible to simulate ball charge motion (Fig. 5). Having thus defined charge motion, we can further this development by determining energy consumed and distributed in the various comminution zones on the charge profile (Fig, 2) using the following equations 18, 21: (7) (8) (9) The energy profile (Fig. 6) in a ball mill can now be determined as for the Hardinge mill of Fig. 1. Note that this charge motion model determines how energy is consumed and then distributed in grinding, crushing and tumbling as a function of mill rotation speed, mill diameter, ball charge and liner representation.Wear rate estimation As mentioned earlier, there are three comminution zones in the ball charge motion profile. Although other wear mechanisms exist, only adhesive and abrasive wear are associated here with these comminution zones. Adhesive wear is associated with the tumbling and crushing zone as balls in these zones collide while abrasive wear is associated to the grinding zone where balls slide pass one another or over the null liner. These mechanisms can be expressed in terms of energy rate used in wear as 23-24:adhesive wear (10)abrasive wear (11)Applying these wear models to the ball mill case, we write; (12) (13) (14)Comparing initial and final liner wear profiles, liner wear rate can be estimated using: (15)We can determine the abrasion factor by equating eqn (15) with eqn (12), thus getting: (16)Further, using eqn (13) and eqn (14) with the result of eqn(16),we can determine the adhesion probability: (17)With the abrasion factor and adhesion probability P determined for a given mill operating context, we can now determine how changes from this context affect mill wear rates. Keeping and P constant, and varying parameters such as mill rotation speed and charge column, we can predict the associated changes to mill wear rates 24. However, predicting wear rates is only of limited use when considering our goal of determining the effect of wear on ball mill grinding performance.Liner wear Grinding performance in a ball mill is determined primarily by how energy is distributed into the various comminution zone found in the ball charge profile. As mentioned, the form of the charge profile, and consequently the importance of each comminution zone, is directly dependant on the friction force existing between the ball charge and the mill wall. Different liner types (Fig.3) affect this friction force between the ball charge and the mill wall and the mill grinding performance. For a given grinding context, it is possible to use a liner type that is considered optimal. However, with time, mill wear will modify the initial liner profile and subsequently mill grinding. Modelling the forces acting on the mill liners becomes the next step to predicting mill wear and its effect on grinding. During mill operation, the hall charge exerts a force field composed of gravitational and centrifugal components on the mil liner (Fig.7) 23, 25.Using this description, normal force component can be determined as show in Fig.8, giving: (i) centrifugal normal component (18)(ii) gravitational normal component (19)Further, as the ball charge slip over the mill liner, a compression force is created with the local displacement of the mill charge by the liner (Fig.9). This force is defined as: (20)Where The normal compression component as: (21)The total normal force acting on the liner surface becomes: (22)Liner wear, as a function of the position and intensity of the force field created by the ball charge as well as the abrasion factor 0, become: (23)Where (24)Note that slippage speed on the liner is defined previously by rearrangement of eqn (2).After liner discretization into differences ,and time into , a simulation algorithm can be developed 23, 25 which allows liner profile wear simulation.As an example, Fig. 10 illustrates a wave liner profile wear simulation which is comparable to the real liner profile wear presented in Fig.11.MILL WEAR AND GRINDING PERFORMANCEEven though industrial studies are needed to further validate these wear models, it is possible envisage the prediction of wear evolution of a given liner type. This, of course, wou1d allow the determination of how wear affects grinding performance here defined as variations in output granulometry. For the Hardinge case of Fig.1, this translates into simulating the effect of wear on the bevel liner as shown in Fig.12.Further, simulating how the energy rate profile of Fig.6 changes with this liner wear, it is possible to predict the changes in mill output granulometry for the same input granulometry. Table 1 shows how, using a breakage model developed in 22,23, it is possible to illustrate output variation over the life period of the liner. Here, mill output becomes finer with liner wear.Associated with this phenomenon, mill energy consumption decreases as shown in Fig.13. Both these phenomena illustrate the possibility of optimizing ball mill performance as a function of the predetermined effect of wear.Table 1. Ball mill output granulometries as a function of worn liner profileParticle size(m)Initial %passing1/2 life %passingFinal %passing741001503008301170165058.0868.2578.5492.1299.4599.96100.0058.2568.4478.6892.1599.4599.96100.0060.1370.3880.2593.9699.6199.97100.00DISCUSSIONBefore concluding this work a few remarks should be made concerning charge motion, liner wear and associated mill output product.As shown, ba11 charge motion is dependant on a number of physical and operating factors; it is also dependant on the rheological characteristics of a given slurry. These rheological characteristics are of course a function of percentage solids as well as ore properties. In the model of charge motion the effect of these factors is included in the relationship (2) for slippage speed as escribed using static and kineticd friction factors. A variation in the friction factors, as caused by a possible change in rheological characteristics of a given slurry, can increase or decrease the amount of slippage between ball layers and thus increase or decrease liner wear. In modelling ball mill wear with only two wear mechanisms, it is assumed that a mill is not run empty or that operating conditions do not send mill balls crashing directly into the mill liner. Under such conditions, liner wear increases considerably with added wear mechanisms (surface fatigue, fracture, cratering) gaining importance.The importance of ball mill product variations as a function of liner wear is dependant on the breakage characteristics of a particular ore. As such, validation using industrial data is necessary in order to determine the precision of this model. However, assuming that an adequate validation of the whole model is possible, the preliminary results presented here show that it becomes possible to consider using this model for ball mill optimization as a function of energy consumption and mill wear.CONCLUSIONSThis work has presented a predictive wear model based on a theoretical description of the ball mill. While covering the application of a simple adhesive and abrasive wear model to a complex ball charge model, it was possible not only to identify the required wear parameters, but also to predict liner wear and grinding performance.However, further work is required particularly in model validation and parameter identification. Notwithstanding this need, ball mill optimization, in design and operation, becomes a future possibility.Acknowledgement-The publication of this paper has been made possible by a Natural and Engineering Research Council of Canada research grant.
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