阅读说明：本技术 一种基于钢球与矿石碰撞能量确定钢球尺寸的方法 (Method for determining size of steel ball based on collision energy of steel ball and ore ) 是由 肖庆飞 杨森 高玉和 韩增强 林玉明 赵华科 朱林 徐志勇 于 2020-10-30 设计创作，主要内容包括：本发明涉及一种基于钢球与矿石碰撞能量确定钢球尺寸的方法,属于选矿中的磨矿技术领域。本发明测定了矿石的最大单轴抗压强度、球磨机给矿95%过筛粒度值、钢球在矿浆中的有效密度、球磨机转速率、磨机内有效半径R、衬板高度r、钢球在磨机内与矿石碰撞作用的接触时间t、代入钢球直径计算公式,计算精确确定的钢球直径D；最后将计算确定的D直径与其它大小的钢球在同等条件下进行磨矿对比试验,以最佳磨矿效果来验证D的精确性。本发明考虑了矿石性质以及多个影响钢球运动状态的因素,从钢球在磨机内运动状态出发,建立了基于钢球运动能量与矿石破碎能量相匹配的计算钢球直径方程,为提高磨矿产品质量和节能降耗提供了技术支撑。(The invention relates to a method for determining the size of a steel ball based on collision energy of the steel ball and ore, and belongs to the technical field of ore grinding in ore dressing. The invention determines the maximum uniaxial compressive strength of the ore Feeding 95% sieving granularity value of ball mill Effective density of steel balls in ore pulp Rotation rate of ball mill)

1. A method for determining the size of a steel ball based on collision energy of the steel ball and ore is characterized by comprising the following specific steps:

(1) determination of the diameter of the steel ball:

feeding the determined ball mill with 95% sieving granularity valueEffective density of steel balls in ore pulpMaximum uniaxial compressive strength of oreRotation rate of ball millEffective radius R in the mill, the height R of a lining plate, the contact time t of a steel ball in the mill and the collision action of ore, substitution steel ball diameter calculation formula, and calculation of the steel ball diameter D determined accurately:

(2) and (3) verifying a steel ball grinding ore comparison test:

and (4) performing ore grinding comparison test on the diameter of the D determined by calculation and steel balls with other sizes under the same condition, and verifying the accuracy of the D by using the optimal ore grinding effect.

2. The method of determining a size of a steel ball based on steel ball and ore collision energy of claim 1, wherein: the optimal ore grinding effect is that the granularity characteristic and unit ball consumption of the ore grinding product are used as the judgment basis, and the granularity is determined by the fineness requirement of one-section and two-section ore grinding of specific ore.

Technical Field

The invention relates to a method for determining the size of a steel ball based on collision energy of the steel ball and ore, and belongs to the technical field of ore grinding in ore dressing.

Background

The ore grinding medium is not only an implementation body for ore crushing, but also a transmission body of energy required by ore crushing, and the motion rule of the ore grinding medium determines the energy of the steel ball impacting the ore in the grinding machine. On the one hand, it determines the crushing behaviour of the ore and even whether this crushing process can take place; on the other hand, it has decisive influence on the size of the production capacity of the mill, the quality of the ground ore products (including the granularity characteristic and the monomer dissociation characteristic of the ground ore products), the steel consumption and the energy consumption in the grinding process, and the like. Therefore, the impact kinetic energy of the steel ball on the ore in the mill is matched with the energy required by ore crushing to obtain the steel ball size suitable for the ore with specific properties, and the steel ball size can be used for improving the quality of the ore grinding product, reducing the energy loss and further achieving the purposes of improving the quality and reducing the consumption.

The motion states of the medium in the ball mill are mainly three types: cascading, throwing, and circular motions. When the rotating speed of the ball mill is lower, the steel balls in the ball mill move along with the cylinder body, the steel balls reach the upper end of the steel ball stack and slide downwards along the surface layer, and a strong grinding force is shown among the steel balls, and the moving state is called a cascading type movement; when the rotating speed of the ball mill is higher but not higher than the critical rotating speed, the steel balls in the ball mill are lifted along with the movement of the cylinder body and fall downwards in a parabola shape after reaching a certain height, the steel balls mainly show impact force, and the movement state is called falling movement; when the rotating speed of the ball mill exceeds the critical rotating speed, the steel balls in the ball mill move tightly on the inner wall of the cylinder body, no acting force exists between the steel balls basically, and the moving state is called circular motion. Generally, the impact of the falling steel ball on ore is the main way of applying work on ore by the steel ball in the mill.

Many researchers at home and abroad have different starting points for considering problems and experience of each person is different, so that a plurality of sphere diameter empirical formulas are provided, and the sphere diameter empirical formulas mainly comprise: (1) rasomoff formulaAnd its simple formula(ii) a Oltves' formula(ii) a Davis formula(ii) a Simple empirical formula of bond(ii) a The above empirical formula takes too few factors into consideration, and one empirical coefficient is difficult to include the rest of the factors. The empirical formulas, which are widely used in europe and america, include a number of influencing factors, most typically the aries charmmers formula and the nocks lode formula:，however, the two ball diameter formulas are not convenient to apply to factories and mines in China, the empirical coefficients are summarized under the condition that the specifications of foreign mills are large, the falling height of a steel ball in a mill with a large diameter is large, the defect of the ball diameter can be overcome, the diameter of the mill in China is generally small, and the summarized empirical coefficients in foreign countries are not necessarily applicable. The segmental auspicious professor starts from the national conditions of China and deduces a segmental sphere radius semi-theoretical formula:the formula considers a plurality of factors and establishes a coefficient K aiming at different ores and ore grinding conditions_cThe calculation result is more accurate, and is a semi-theoretical formula which is more applied in China at present. However, the formula does not consider the influence of different lining plate heights and other factors influencing the motion state of the steel ball on the motion state of the steel ball in the mill, and the following conditions are easily caused: the excessive crushing and energy loss increase when the steel ball impacts the ore with excessive energy. And the impact kinetic energy of the steel ball is too small, so that the impact kinetic energy of the steel ball is smaller than the energy required by ore crushing, and the ore cannot be effectively ground.

Disclosure of Invention

Aiming at the problems and the defects in the prior art, the invention provides a method for determining the size of a steel ball based on the collision energy of the steel ball and ore. The invention aims to establish a steel ball diameter calculation formula for matching the steel ball motion energy with the energy required by ore crushing, and provides a new method for accurately calculating the steel ball diameter by measuring ore properties and ore grinding condition parameters. The invention is realized by the following technical scheme.

A method for determining the size of a steel ball based on collision energy of the steel ball and ore comprises the following specific steps:

(1) determination of the diameter of the steel ball:

feeding the determined ball mill with 95% sieving granularity valueEffective density of steel balls in ore pulpMaximum uniaxial compressive strength of oreRotation rate of ball millEffective radius R in the mill, the height R of a lining plate, the contact time t of a steel ball in the mill and the collision action of ore, substitution steel ball diameter calculation formula, and calculation of the steel ball diameter D determined accurately:

whereinIs the acceleration of gravity;

(2) and (3) verifying a steel ball grinding ore comparison test:

and (4) performing ore grinding comparison test on the diameter of the D determined by calculation and steel balls with other sizes under the same condition, and verifying the accuracy of the D by using the optimal ore grinding effect.

The optimal ore grinding effect is that the granularity characteristic and unit ball consumption of the ore grinding product are used as the judgment basis, and the granularity is determined by the fineness requirement of one-section and two-section ore grinding of specific ore.

The working principle of the invention is as follows:

according to the Davis steel ball motion theory, the steel ball mainly drops in the mill and the radial component velocity of the steel ball is used for impacting ore to do work, the invention can determine the steel ball diameter calculation formula by the following modes:

assuming an effective density in the slurry ofThe dense steel balls moving in the mill at a radially divided speedThe component velocities for impacting the ore are:

linear velocity of ball millAngle of separation from steel ballThe following relationships exist:

due to the fact thatAnd the rotating speed rate of the ball mill and the separation angle of the steel ballExistence relationshipThe radius of the mill is R, the height of the lining plate is R, the method

When the steel ball impacts the kinetic energyEqual to the impact kinetic energy corresponding to the crushing energy needed by the steel ballThe ore can just break:

the minimum impact momentum required for the ore to undergo a crushing action; t is the contact time of the steel ball and the ore;

the ore is regarded as a sphere with a diameter d and an ore surface area of：

Minimum impact momentum required for ore breaking actionImpact strength with oreThe following relations are provided:

the formula is arranged and simplified to obtain:

。

symbols not specifically described in all of the above formulas are symbols well known to those skilled in the art and can be found within the common general knowledge.

The invention has the beneficial effects that: the invention matches the motion energy of the steel ball with the energy required by ore crushing to calculate the optimal steel ball diameter. The method fully considers the motion influence factors of the steel ball in the mill, including the rotation speed rate of the mill, the radius of the mill, the height of the lining plate and the like, and combines the properties of ore, the size of the steel ball calculated by the method not only reduces energy loss, but also enables the granularity of the ore grinding product to be more reasonable, and provides favorable conditions for subsequent flotation operation. The invention has stronger applicability and universality than an empirical formula and a semi-theoretical formula and has extremely good application value.

Detailed Description

The present invention will be further described with reference to the following embodiments.

Example 1

In order to make the objects, technical solutions and benefits of the present invention more clear and intuitive, the present invention will be further described in detail below with reference to a specific example of a 3.2 × 3.1-meter format ball mill from the german Sicheng Mill.

The method for determining the size of the steel ball based on the collision energy of the steel ball and the ore comprises the following specific implementation steps:

(1) determination of the diameter of a steel ball

Determination of maximum uniaxial compressive strength of oresIs 800kg/cm²Feeding 95% sieving granularity value of ball millThe effective density of the steel ball in the ore pulp is 12mmIs 5.82g/cm³Rotation rate of ball mill75 percent, the inner radius R of the mill is 1.6m, the height R of the lining plate is 0.1m, the contact time t of the steel ball in the mill and the ore under the collision action is 0.01s, the steel ball is substituted into a steel ball diameter calculation formula, the size D of the steel ball based on the matching of the crushing energy of the steel ball and the ore is calculated,d =66.1mm is obtained, and D is 70mm which is consistent with the specification of the steel ball produced at present, and is used as the determined steel ball size.

(2) Verification of steel ball grinding ore comparison test

A comparative test is carried out on steel balls with the calculated ball diameter phi of 70mm and steel balls with different sizes, wherein the comparative test comprises that phi 100mm (the ball diameter is adopted on site), phi 90mm, phi 80mm and phi 60mm, a Sizhou ore dressing plant is a section of grinding ore, the-200-mesh is required to be 65%, the excessive coarse fraction plus 80-mesh and the excessive fine fraction minus 400-mesh are both excessive, and the unit ball consumption is high, so that the-200-mesh, plus 80-400-mesh and the unit ball consumption are taken as indexes to be used as the judgment standard for verifying the accuracy of the ball diameter.

Table 1: ore grinding contrast test with different ball diameters

The comparison test result shows that (1) when the diameter of the steel ball is too large, the collision probability of the steel ball and the ore is reduced because the number of the steel balls with the same mass is reduced due to the too large diameter of the steel ball, the fineness of minus 200 meshes and the coarse fraction of plus 80 meshes are lower than those of the steel ball with the accurate calculated size, and meanwhile, the steel consumption is increased; when the diameter of the steel ball is too small, the impact force of the steel ball is insufficient, so that the plus 80-mesh coarse grade is too high. The energy steel ball loss is reduced compared with a field scheme by accurately calculating that the steel ball with the diameter phi of 70mm has the lowest coarse fraction and higher fineness and grinding uniformity. (2) Compared with an on-site scheme, the steel ball size scheme calculated based on the collision energy of the steel balls and the ore improves the fineness by 3.17 percent, reduces the fineness of a coarse grade of +80 meshes by 1.83 percent, improves the intermediate easy-to-select grade by 3.47 percent, and reduces the loss of the steel balls by 0.032 kg/t.

In conclusion, the optimal size of the grinding steel ball of the grinder with the model is phi 70 mm.

While the present invention has been described in detail with reference to the specific embodiments thereof, the present invention is not limited to the embodiments described above, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.