## Experiment No. 5: Studying Ball Mill's Reduction Ratio and Residence Time

Sumedh Deshkar | 21MI3EP18

### Objective:
We want to understand how well a ball mill can crush a given material, and how the time it spends grinding affects this crushing process.

### Theory:

A ball mill is a machine used to crush materials. It does this by having balls inside that impact and rub against the material.
The ball mill looks like a rotating tube. It has two openings, one where you put the material in, and the other where the crushed material comes out.
The outer shell of the ball mill is made of strong steel. It can be horizontal or slightly tilted. Big ball mills are about 4 to 4.25 meters long and 3 meters wide. They use hard steel balls of different sizes (between 25 to 125 mm) to crush the material.
The inside of the ball mill is lined with special materials to resist wear and tear. These materials can be strong metals, stones, or rubber. Rubber liners are the best because they reduce wear. The friction between the steel balls and the liner is high, which helps lift the balls and drop them with more force to crush the material.
The balls used for grinding are usually made of cast steel, or sometimes flint. Their size can vary from 1 to 5 inches. The right ball size depends on the size of the material you're trying to crush.
The amount of wear on the balls and the liner usually ranges from 450 to 1250 grams per ton of material ground.
### Components of the Ball Mill:

* Cylindrical Shell: The outer rotating part of the ball mill. It's like a hollow tube where the material goes in at one end and comes out crushed at the other. It's made of strong steel.
* Inner Lining: The inside of the ball mill is covered with a special material to protect it from wearing out quickly. Rubber lining works best for this.
* Grinding Balls: These are the steel balls or flint used to crush the material. Their size depends on the material size.
* Drive: The ball mill spins thanks to electric motors connected to a gearbox and a ring gear system.

In simple terms, the ball mill is like a big rotating drum that crushes materials using steel balls and a special lining. The way it crushes stuff depends on how long the material stays inside and the size of the balls

* Ball Mill Operation: Ball mills may be continuous or batch type in which grinding media and the ore to be ground are rotated around the axis of the mill. Due to the friction between the liners–balls & liners–ore lumps, both the ore and balls are carried up along the inner wall of the shell nearly to the top from where the grinding media fall down on the ore particles below creating a heavy impact on them. This usually happens at the toe of the ball mill. The energy expanded in the lifting up the grinding media is thus utilized in reducing the size of the particles as the rotation of the mill is continued.

#### Fig: Schematic Diagram of Different forms of Deformation during Ball-powder Interaction

### Mill Specifications:
Circumference of the ball mill = 105 cm
Diameter of the Ball Mill = 33.5 cm
Length of the ball Mill = 33 cm
Diameter of the spherical ball = 3 cm, x cm, y cm
No. of balls used = 24
Total weight of balls = 2.74 kg
RPM of ball mill = 75 rpm
### Motor specifications:
H.P. = 1 / Single phase 220 volts
RPM – 1500 / Amp – 7
𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑖𝑜 = F(80)/P(80)

### Procedure:
1. Crush the given material of size -22mm + 9mm of 2 kg weight.
2. Place the given material and also the required spherical balls inside the Ball Mill.
3. Then tighten all the nuts of the flanges in the Ball Mill.
4. Now run the Ball Mill for 10 minutes.
5. After 10 minutes collect the crushed sample from the Ball Mill by opening the discharge flange.
6. After collecting all the crushed material remove the balls from the material and take the weight of the crushed material.
7. Now the material is put in sets of different mesh size for sieve analysis test.
8. After doing the sieve analysis test for 10 minutes, take a record of sieve analysis data.
9. Repeat the same process by feeding the product material of the previous cycle and follow steps 2 to steps 8 up to 3 cycles of time intervals of 10 minutes each.

### Observations:
* Weight of Sieves:
#### Note: A sieve of size 2 mm was excluded due to fitting issues with other sieves.
* Weight of Samples:
* Weight distribution of sample -1:


* Weight distribution of sample -2:
### Calculations:
* Size of the feed = -22mm + 9mm
Hence, 80% passing size of the feed (F80) = 18.8 mm
* Sample – 1:
80% passing size of product (P80) = 0.4 mm
Reduction ratio = F80 / P80 = 18.8/0.4 = 47

* Sample – 2:
80% passing size of product (P80) = 0.41 mm
Reduction ratio = F80 / P80 = 18.8/0.42 = 45.85

* **Critical speed of the ball mill:**
The diameter of the ball (d) = 2.85cm
The diameter of the Ball Mill (D) = 33.5 cm
RPM of ball mill = 75 rpm
Therefore, at the topmost point, for the balls to fall down,
Mv^2 /reff = mg
reff = Effective radius = R – r = (D – d)/2
m = mass of the ball
v = Critical speed of ball mill
g = Acceleration due to gravity = 9.81m/s2
Thus, v = √𝑔(𝑅 − 𝑟)
On calculating the angular velocity in r.p.m,
Nc = 42.3/ √𝐷 − 𝑑 rpm
On plugging in the values,
Nc = 148.40 rpm

### Result:
Reduction Ratio:
Sample 1: The reduction ratio for Sample 1 is calculated as 47.
Sample 2: The reduction ratio for Sample 2 is calculated as 45.85.
Critical Speed:
The critical speed of the ball mill is determined to be 148.40 rpm.

### Conclusions:

Impact of Mill Charge on Grinding Media: The reduction ratio, a pivotal metric assessed for both Sample 1 and Sample 2, underscores the role of the mill charge-to-grinding media ratio in shaping the grinding process. In essence, a higher reduction ratio signifies a more efficient reduction of material size. Sample 1 achieved a reduction ratio of 47.5, while Sample 2 attained 45.24, implying that Sample 1 accomplished a more substantial reduction of the input material.

Operational Ball Mill Speed: The ball mill was operated at a rotation speed of roughly 148.45 revolutions per minute (rpm), corresponding to 49.47% of the critical speed. Proximity to the critical speed is pivotal for optimizing the grinding process, ensuring that the grinding media within the mill reach an ideal elevation for enhanced impact and size reduction of the material.

Particle Size Reduction Mechanism: The results of the sieve analysis confirm the successful achievement of particle size reduction within the ball mill. The cumulative weight distribution of both Sample 1 and Sample 2 demonstrates the production of finer particles. These results point to a dominant particle size reduction mechanism inside the ball mill, stemming from a combination of impact and attrition. As the material and grinding media ascend along the inner wall of the mill and then descend, substantial impacts occur, leading to size reduction.

### Discussion:

* Reduction Ratio: The reduction ratio plays a critical role in ball mill operation, signifying the efficiency of size reduction. The higher reduction ratio observed in Sample 1 (47.5) compared to Sample 2 (45.24) indicates a more effective size reduction process in the former.
* Critical Speed: Operating the ball mill at a speed close to its critical speed is essential for efficient grinding. The experiment determined the critical speed to be approximately 148.45 RPM, and the operational speed was maintained at 49.47% of this critical speed, ensuring optimal grinding conditions.
* Particle Size Reduction Phenomenon: The primary particle size reduction mechanisms within the ball mill are a combination of impact and attrition. Impact forces occur as the material and grinding media are lifted and then fall, leading to significant energy transfer and size reduction. Simultaneously, attrition contributes to further particle size reduction through friction, scraping, and sliding actions.
* Material Feed Size: The initial feed size ranged from -22mm to +9mm, with an 80% passing size of 19 mm (F80). Understanding the initial feed size is crucial in assessing the effectiveness of the grinding process.

* Operating Parameters: The experiment involved running the ball mill for specified durations (10 minutes per cycle) to explore the impact of residence time on the reduction ratio. Residence time is a critical operational parameter influencing the grinding process's efficiency.

* Grinding Media: The choice of grinding media, both in terms of type and size, plays a pivotal role in the grinding process. In this experiment, spherical balls were utilized as the grinding media, contributing to the observed impact and attrition mechanisms.

* Impact and Attrition: The experimental results affirm that impact and attrition are the predominant mechanisms of size reduction inside the ball mill. As the material and grinding media are lifted and dropped within the mill, significant impact forces are generated, contributing to size reduction. Furthermore, the continuous abrasion due to attrition enhances the overall reduction process.

* Industrial Implications: The findings from this experiment hold significant value for industries engaged in size reduction processes, such as mining and materials processing. Understanding the key factors that influence the reduction ratio enables these industries to optimize their operations, enhancing efficiency and productivity.

### Questions:

**How does the ratio of mill charge to grinding media affect the grinding process?**

**Explanation:** The ratio of mill charge to grinding media directly influences the efficiency of the grinding process in a ball mill. A well-balanced ratio ensures several critical aspects:

Efficient Grinding: A proper ratio leads to effective size reduction as it ensures an adequate number of impacts and attrition.
Higher Reduction Ratio: A higher ratio results in a more substantial reduction in material size.
Uniform Impact Distribution: Proper balance ensures even impact across the material.
Reduced Wear and Tear: Balanced ratios minimize wear on mill components and grinding media.
Optimal Residence Time: It controls material residence time, crucial for efficient grinding.

**At what percentage of the critical speed was the ball mill being operated during the experiments?**

**Explanation:** The ball mill was operated at a speed of 75 RPM, while the critical speed of the ball mill was calculated to be approximately 148.45 RPM. Consequently, the Ball mill was operating at 49.47% of the critical speed.

**Comment on what you think were the dominating particle size reduction phenomena prevailing inside the ball mill, considering the ground product obtained in your experiments.**

**Explanation:** The dominating particle size reduction phenomena within the ball mill, as revealed by the experimental results, primarily involve a combination of impact and attrition. Here's a more detailed comment on these phenomena:

Impact: Impact forces occur as the material and grinding media (typically spherical balls) are carried up to the top of the mill and then descend under the influence of gravity. During their descent, they collide with one another and with the material being ground, imparting a significant amount of energy to break down the particles. The high kinetic energy generated during these impacts results in the fracturing of larger particles into smaller ones, contributing to size reduction.

Attrition: Attrition is another essential phenomenon where the material is worn down due to the rubbing, scraping, and sliding action between the particles and the grinding media. The coefficient of friction between the grinding media (usually steel balls) and the material is relatively high, which intensifies the attrition effect. This continuous abrasion between the material and grinding media contributes to further particle size reduction.

### References:
1. Lab Manual
2. Wikipedia