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Discussion on grinding process of thermal paper coating (Ⅱ)

Discussion on grinding process of thermal paper coating (Ⅱ)

  • May 13,2020.

Discussion on grinding process of thermal paper coating (Ⅱ)

Author: LiMeng, Lei

(Puhler International Holding Group-PUHLER (Guangdong) Smart Nano Technology Co.,Ltd - General Manager)


2 - Questions

A certain output of thermal sensitive coatings, after determining the corresponding properties such as the feeding fineness, the discharge fineness (or particle distribution), then a certain amount of Bead Mill is needed to complete the grinding task.

After the type of Bead Mill is determined, the output of a single Bead Mill can be estimated through experiments, so that the number of Bead Mill needed to produce this output of paint can be roughly calculated. The number of Bead Mill required also varies according to the grinding process and the structure of the Bead Mill.

Generally speaking, the choice of grinding process (Bead Mill arrangement, layout) is based on the principle of maximizing the grinding capacity of the Bead Mill.

For example, if two Bead Mills are connected in series, the question is: how fine the paint should be grinded by the former Bead Mill before entering the following Bead Mill, to maximize the function of the two Bead Mills, and reach a balanced state. It has practical significance to discuss this question.

The following is a discussion of some possible states in the grinding process from the perspective of energy, so as to find some common laws.

2.1 Energy requirements in the grinding process (Energy consumption of the Bead Mill)

In the process of grinding, motor transfer electricity to grinding disk or grinding peg, grinding disk or grinding peg pass kinetic energy to zirconia beads (and grinding media), movements of the grinding media will grind the solid particles fine, the energy that solid particles gained is stored in the form of increasing surface energy and surface area. This is the energy change during the grinding process.

To discuss this question, we can start with a simple model and deduce it according to some physical and chemical theorems.

Assumed that the material is initially a cube, and the side length of the cube is 1 unit. And assumed that the energy used for grinding material by the Bead Mill is converted to the newly increased surface area of the cube.


The cube continuously grinds (cuts) a smaller cube with half of the side length of the previous cube, and the grinding (cuts) process continues to the required grinding fineness.


Number of Grind (Cut) 1 2 3 4 5 ...n
Newly increased surface area 6 12 24 48 96 ...3*2n
Reduced length of cube 1/2 1/4 1/8 1/16 1/21 ...1/2n
Increase of cube particles 8 8*8 8*8*8 ... ... ...8n
Remark: n is positive integer

2.1.1 Input Energy

The input energy is provided by the 355KW main motor. The power conversion relationship of the three-phase motor is analyzed, the motor current is calculated, then determine its operating current value.

Three-phase motor power conversion relationship:

P = η * 1.732 * U * I * Cosφ

η - The ordinary motor efficiency, the average is about 0.8 or above. Let's take 0.8

Cosφ -- Generally it is 0.8-0.85. Let's take 0.8

U - Industrial voltage, generally 380V

By calculating the main motor current 830A. Take the efficiency of 40%~45%, so the operating current of the Bead Mill should be 320-370A.

2.1.2 System Energy Relationship

Through energy balance, we know that:

Q =E1+E2+E3+Q1

According to the kinetic energy theorem:

E = 1/2mv2

Through system analysis, the input energy Q is mainly related to the input power. Can be expressed as:

Q =ξ×P×s

Analyze the power conversion relastionship of three-phase motor:P = η * 1.732 * U * I * cosφ


ξ * η * 1.732 * U * I * cosφ * s = m1v2 / 2 + m2v2 / 2 + m3v2 / 2 + Q1

m1—Quality of main shaft and dispersing disk. According to the model of bead mill, it is fixed value.

m2—Quality of grinding media

m3—Quality of griding slurry

ξ—Efficiency of the bead mill


η—Ordinary motor efficiency, generally around 0.8 (Take 0.9) or above

cosφ—Generally, it is 0.8-0.85

U—Industry voltage, generally 380V

v—Linear velocity

Q1—Thermal energy

Ideally, based on the above relationship, we use a constant θ instead of all constants, to get the relationship as below:

I = θ (m2+m3) +Q1

It can be seen from the above formula that the running current of Bead Mill is proportional to the grinding medium and the grinding slurry.

Q: In actual production, how to ensure the running current of Bead Mill?

A: Through the study of grinding medium and grinding slurry.

There are many factors influencing the slurry, here we discuss about the slurry feeding quantity and slurry viscosity...

Here are some useful conclusions:

  • In the thermal paper coating grinding process, if two Bead Mills are connected in series, if the model, capacity and particle size of the beads are the same, the final fineness is D50≤0.65µm, and the former bead mill should grind the coating to about D50≤ 1.30µm, in this way, from the perspective of energy, the two Bead Mills are in a big balance state, which can better play their respective functions.
  • If there are 4 same Bead Mills, grind in series with 1+3. In the grinding process of thermal paper coating, the first Bead Mill should grind the thermal paper coating to D50≈2.60µm, then the next 3 Nano Bead Mills circulate grind the thermal coating which come from the previous Bead Mill to D50≈0.65µm.
  • If the final fineness of the thermal paper coating is reduced from D50≤0.65µm to D50≤0.35µm, from the perspective of energy, the quantity of Bead Mill should be increased by about 1 times.

2.2 The reaggregate state of materials during grinding

According to the second law of heat, the energy of the system always tends to be minimal. Therefore, with the increase of grinding process, the particles are finer and finer, the increased surface area is larger and larger, and the total surface energy of the system becomes larger and larger. The materials (the system being grinded) have a tendency to reaggregate to reduce the total surface energy by reducing the newly added area. This phenomenon is more obvious in the finer particles. This is also the reason why nano-materials are difficult to grind and surfactants are needed.

If this factor and the energy factor are taken into consideration, it is easier to understand that in the sub-micron and nano grinding process, the grinding time for the final particle size to be reduced by half is longer than the previous total grinding time.

Some of the above conclusions or inferences are based on the ideal model, mathematical derivation, laws of physical chemistry and some phenomena in the actual grinding process. Although not exactly equal to the actual state of the grinding process, but it still has certain guiding significance in the production process and the experimental process .

(To be continued)

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