American Journal of Technology and Applied Sciences 
ISSN (E): 2832-1766        Volume 41, October - 2025                              

 

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DEVELOPMENT OF AN ENERGY-SAVING OPERATING MODE 

FOR MILLING INSTALLATIONS, TAKING INTO ACCOUNT THE 

VARIABILITY OF INCOMING ORE PARAMETERS  
Mavlonov Jonibek Ashurovich 

Navoi State Mining and Technologies University 

 

A B S T R A C T K E Y W O R D S 

Globally, particular attention is being paid to ensuring the energy 

efficiency of large-scale equipment in the mining and metallurgical 

industry by optimizing its operating modes to reduce energy costs and 

improve production efficiency. Currently, in developed countries, 

"...global energy consumption in the mining and metallurgical industry 

accounts for approximately 3.5% of global energy annually, with crushing 

processes accounting for 30-40%. By 2060, energy consumption is 

projected to increase by 2-8 times due to declining ore quality and 

growing demand for metals." 

 

Synchronous motor, 

mill, grinding, ball 

loading, rotation 

speed, power. 

 

Introduction 

Research Objective 

Improving methods for ensuring energy efficiency of energy-intensive equipment in the mining and 

metallurgical industry based on an analysis of the influence of technological factors on the operation 

of ball mills. 

 

Materials and Methods 

A ball mill's adjustable synchronous electric drive must ensure optimal operation, taking into account 

the variability of incoming ore parameters (weight, moisture, hardness, and particle size distribution). 

This paper presents a mathematical model that accounts for the dynamics of the electric drive and 

mechanical system, taking into account the impact of changing ore characteristics.  

 

Results and Discussion 

Model of a synchronous motor in the d-q coordinate system: 

𝑈𝑑 = 𝑅𝑠𝐼𝑑 + 𝐿𝑑

𝑑𝐼𝑑

𝑑𝑡
− 𝜔𝐿𝑞𝐼𝑞 

𝑈𝑞 = 𝑅𝑠𝐼𝑞 + 𝐿𝑞
𝑑𝐼𝑑

𝑑𝑡
− 𝜔𝐿𝑞𝐼𝑞 + 𝐸𝑓   (1) 



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41, October - 2025 

 

 
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where: 𝑈𝑑  𝑈𝑞 − voltage components in the d- and q-axes; 𝐼𝑑 𝐼𝑞– current components; 𝐿𝑑𝐿𝑞– 

inductances; are the stator winding resistance; 𝜔 – rotor angular velocity; 𝐸𝑓 − excitation EDF. Motor 

torque: ѱ 

 
Fig. 1. With fixed ore variability W ≈ 0.5. 

𝑀𝑒 =
3

2
𝑝[ѱ𝑑𝐼𝑞 − ѱ𝑞𝐼𝑑] 

where p - number of pole pairs, ѱ𝑑ѱ𝑑 −flux linkage. 

Differential equation of motion of a mechanical system: 

𝐽
𝑑𝜔

𝑑𝑡
= 𝑀𝑒 − 𝑀𝑐 − 𝑀𝑓     (2) 

where: J - moment of inertia of the system; 𝑀𝑒 − electromagnetic torque of the engine; 

𝑀𝑐– moment of resistance to ore crushing; 𝑀𝑓 – moment of mechanical losses. 

The moment of resistance to ore crushing is described by the empirical relationship: 

𝑀𝑐 = 𝑘1 ∙ 𝑚𝑟
𝛼 ∙ 𝑑𝑟

𝛽
∙ 𝜔𝛾 

𝑚𝑟– mass of loaded ore; – average particle size; 𝑑𝑟𝑘1, 𝛼, 𝛽, 𝛾 – experimentally determined coefficients. 

The control system includes a PID speed controller, implemented by the equation: 

𝑈𝑟𝑒𝑔 = 𝐾𝑝(𝜔𝑟𝑒𝑔 − 𝜔) + 𝐾𝑖 ∫(𝜔𝑟𝑒𝑓 − 𝜔)𝑑𝑡 + 𝐾𝑑
𝑑(𝜔𝑟𝑒𝑓−𝜔)

𝑑𝑡
 (2.2) 

Where 𝐾𝑝, 𝐾𝑖,𝐾𝑑 − regulator coefficients. 

The influence of ore parameter variability. To account for ore parameter variability, stochastic 

disturbances are introduced in the form of random processes affecting 𝑚𝑟 , 𝑑𝑟 − and other parameters. 

The Monte Carlo method is used to model these disturbances. The stochastic change model:  

𝑚𝑟(𝑡) = 𝑚𝑟𝑜+ξ1(t) 

𝑑𝑟(𝑡) = 𝑑𝑟𝑜+ξ2(t) 



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where ξ1(t) and ξ2(t) are random processes with given statistical characteristics. The proposed 

mathematical model allows for the impact of ore characteristic variability on the operation of a ball 

mill electric drive. Implementation of the model in a digital environment will enable the development 

of adaptive control algorithms that compensate for the impact of input parameter instability. 

 

Table 1. 

Parameter Average value Range  
Density ρ\rho 2800 kg/m³ 2600–3000 kg/m³ 

Humidity W 8% 6–12% 

Particle diameter d 20 mm 10–30 mm 

 

Equation of motion of a mill 

The motion of a ball mill can be written as follows based on Newton's second law: 

𝐽
𝑑𝜔(𝑡)

𝑑𝑡
= 𝑇дв(𝑡) − 𝑇наг     (1) 

Here: 

J — moment of inertia, ω(t) — angular velocity, 𝑇дв— motor torque, 𝑇наг — load torque (torque of 

ore, ball and resistances). 

Based on the above, a mathematical model of the grinding mill MMS 70x23 ball mill operating with 

synchronous motors was developed. Variability in incoming ore parameters was taken into account. 

The modeling results showed that changes in ore parameters can directly impact energy consumption. 

It is recommended to configure the control systems using an adaptive (neuro-adaptive) approach. 

 

Conclusion 

The paper examines various types of excitation of synchronous motors and the resulting performance 

characteristics with variable frequency drive control for new or upgraded installations, and develops 

mathematical models for automatic control of excitation current and variable frequency drive, taking 

into account the variability of incoming ore parameters, for synchronous motors of ball mills. 

 

References 

1. Ishnazarov O.X. Mavlonov J.A. Basic Directions of Improvement and Improvement of Efficiency 

Ore Grinding // International Journal of Advanced Research in Science, Engineering and 

Technology Vol. 6, Issue 4, April 2019. India 

2. Mavlonov J.A., Sayidov M.K. Assessment of the Reliability of Power Supply for Mining 

Enterprises Taking into Account Changes in the Technical Condition of Transformers // 

https://doi.org/10.5281/zenodo.15743063 Problems of Energy and Resource Saving. Tashkent – 

2025. No. 2 – pp. 40–45 

3. Mavlonov J.A., Sayidov M.K. Influence of Changes in the Technical Condition of Transformers 

on the Reliability of Power Supply in Mining Enterprises // Scientific and Technical Journal 

"Mashinasizlik". www.andmiedu.uz Andijan – 2025. No. 1 – pp. 172–180 

https://doi.org/10.5281/zenodo.15743063
http://www.andmiedu.uz/


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4. Ishnazarov O.Kh., Mavlonov J.A. Optimization of Energy Consumption of Ball Mills in Mining 

Metallurgy by the Two-Criteria Approach // Scientific and Technical Journal "Vestnik TF NRNU 

MEPhI". Tashkent – 2025. No. 1 – pp. 115–124 

5. Ishnazarov O.Kh., Mavlonov J.A. Study of the Energy Efficiency of Ball Mills in the Mining and 

Metallurgical Industry // Scientific and Technical Journal "Vestnik TF NRNU MEPhI". Tashkent 

– 2025. No. 1 – pp. 124–132