In modern manufacturing, energy efficiency has become a critical concern due to rising energy costs and environmental regulations. High-speed dry gear hobbing, as an advanced gear manufacturing process, eliminates the use of cutting fluids, reducing environmental impact but introducing significant energy consumption challenges. The gear hobbing machine, with its complex electrical components and dynamic processing parameters, exhibits varying energy distribution patterns. Understanding these patterns is essential for optimizing energy usage in gear hobbing operations. This study focuses on analyzing the energy consumption distribution characteristics of high-speed dry gear hobbing machines under variable process parameters and developing a predictive model to estimate energy consumption based on these parameters. By examining the power demands of different machine subsystems, such as the drive system and general electrical systems, we aim to provide insights into energy-saving strategies for gear hobbing processes.
The energy consumption of a gear hobbing machine is influenced by numerous factors, including spindle speed and feed rate, which directly affect the machining time and power requirements. In high-speed dry gear hobbing, the absence of cutting fluids shifts the energy burden to other components, such as cooling systems and drive motors. This paper establishes a comprehensive power model for the gear hobbing machine, divides the energy consumption into key subsystems, and validates the model through experimental gear hobbing tests. The results reveal how changes in process parameters alter the energy distribution across the machine, leading to the development of an energy consumption prediction model. This model facilitates the optimization of process parameters in gear hobbing to minimize energy use while maintaining productivity.
Energy Consumption Distribution Characteristics in Gear Hobbing Machines
The high-speed dry gear hobbing machine consists of multiple energy-consuming components, each contributing to the total power draw. Based on the machine’s circuit distribution, the total power can be divided into the drive system power and the general electrical system power. The drive system includes servo-driven axes (e.g., X, Y, Z, A, B, C axes) and associated losses, while the general electrical system encompasses auxiliary systems like cooling, chip removal, and lubrication. The power balance equation for the gear hobbing machine is given by:
$$ P = P_{dr} + P_{co} $$
where \( P \) is the total machine power, \( P_{dr} \) is the drive system power, and \( P_{co} \) is the general electrical system power. The drive system power further decomposes into the power of individual axes and motor losses:
$$ P_{dr} = P_X + P_Y + P_Z + P_A + P_C + P_B + \sum_{i=1}^{6} \left( \frac{dE_{m,i}}{dt} + \frac{dE_{k,i}}{dt} + P_{Lel,i} \right) $$
Here, \( E_{m,i} \) and \( E_{k,i} \) represent the magnetic field energy and kinetic energy of the i-th motor, respectively, and \( P_{Lel,i} \) denotes the motor losses, including copper losses, iron losses, mechanical losses, and additional circuit losses. The general electrical system power is split into AC-powered and DC-powered subsystems:
$$ P_{co} = P_{al} + P_{di} $$
The AC-powered system includes components like water cooling, air/water heat exchange, chip conveyor, oil mist separation, lubrication, and hydraulic systems. For instance, the water cooling system power \( P_{cw} \) depends on the operational state (standby or cooling), and the chip conveyor power \( P_{ct} \) involves motor power and transmission losses. The DC-powered system covers the CNC system, lighting, solenoids, contactors, and other auxiliary elements. The total energy consumption over time \( T \) is the integral of power:
$$ E = \int_0^T P \, dt = \int_0^T (P_{dr} + P_{cw} + P_{aw} + P_{ct} + P_{om} + P_{lr} + P_{lm} + P_{di}) \, dt $$
This model highlights the distributed nature of energy consumption in gear hobbing machines, where each subsystem’s contribution varies with operational conditions.
Experimental Analysis of Energy Distribution Under Variable Process Parameters
To investigate the energy distribution characteristics, experiments were conducted on a high-speed dry gear hobbing machine. The workpiece material was 20CrMnTiH, and the gear had a module of 1.52 mm, 59 teeth, a pressure angle of 15°, a helix angle of 34.6°, and a width of 18.5 mm. The process parameters varied were spindle speed and feed rate, with fixed depth of cut. The experiments included two sets: one with variable spindle speed at a fixed feed rate of 1.8 mm/r, and another with variable feed rate at a fixed spindle speed of 1200 r/min. Power data were collected at multiple points using a power analyzer, focusing on total power, drive system power, general electrical system power, AC-powered system power, and DC-powered system power.
The results for variable spindle speed at fixed feed rate are summarized in Table 1, showing the peak power values and additional losses. As spindle speed increased from 700 to 1300 r/min, the total power and drive system power rose, while the general electrical system power remained relatively stable. The additional power loss, calculated as the absolute difference between the sum of subsystem powers and total power, varied between 7.00% and 10.60%. The energy consumption data in Table 2 demonstrate that higher spindle speeds reduced machining time, leading to lower total energy consumption despite increased power. This inverse relationship highlights the trade-off between power and time in gear hobbing energy dynamics.
| Spindle Speed (r/min) | Total Power (kW) | Drive System Power (kW) | General Electrical System Power (kW) | AC-Powered System Power (kW) | DC-Powered System Power (kW) | Additional Power Loss (kW) | Additional Power Loss Rate (%) |
|---|---|---|---|---|---|---|---|
| 700 | 6.703 | 3.415 | 3.966 | 3.543 | 0.4202 | 0.678 | 10.11 |
| 900 | 7.788 | 4.387 | 3.956 | 3.798 | 0.4237 | 0.555 | 7.13 |
| 1100 | 8.172 | 4.766 | 3.978 | 3.828 | 0.4231 | 0.572 | 7.00 |
| 1300 | 8.492 | 5.417 | 3.975 | 3.783 | 0.4225 | 0.900 | 10.60 |
| Spindle Speed (r/min) | Time (s) | Total Energy (J) | Drive System Energy (J) | General Electrical System Energy (J) | AC-Powered System Energy (J) | DC-Powered System Energy (J) | Additional Energy Loss (J) | Additional Energy Loss Rate (%) |
|---|---|---|---|---|---|---|---|---|
| 700 | 55 | 293854 | 96042.3 | 164669 | 144353 | 23012.1 | 33142.7 | 11.28 |
| 900 | 46 | 260239 | 99728.4 | 145314 | 123931 | 22620 | 15196.6 | 5.84 |
| 1100 | 40 | 238670 | 92277.9 | 118054 | 108431 | 16898.9 | 28338.1 | 11.87 |
| 1300 | 36 | 209123 | 82885.7 | 109621 | 100287 | 15203.5 | 16616.3 | 7.95 |
For variable feed rate at fixed spindle speed, the power and energy data are shown in Tables 3 and 4. Increasing the feed rate from 1.4 to 2.0 mm/r resulted in higher total and drive system power, but the general electrical system power remained constant. The additional power loss rate ranged from 9.05% to 16.36%, indicating higher energy dissipation at intermediate feed rates. Energy consumption decreased with higher feed rates due to reduced machining time, emphasizing the importance of feed rate selection in energy-efficient gear hobbing. The drive system energy consumption showed a non-linear trend, decreasing at the highest feed rate as time reduction outweighed power increase.
| Feed Rate (mm/r) | Total Power (kW) | Drive System Power (kW) | General Electrical System Power (kW) | AC-Powered System Power (kW) | DC-Powered System Power (kW) | Additional Power Loss (kW) | Additional Power Loss Rate (%) |
|---|---|---|---|---|---|---|---|
| 1.4 | 7.551 | 4.326 | 3.908 | 3.822 | 0.4242 | 0.683 | 9.05 |
| 1.6 | 7.549 | 4.857 | 3.908 | 3.894 | 0.4227 | 1.216 | 16.11 |
| 1.8 | 7.853 | 5.178 | 3.960 | 3.818 | 0.4243 | 1.285 | 16.36 |
| 2.0 | 8.306 | 5.611 | 3.939 | 3.839 | 0.4226 | 1.244 | 14.98 |
| Feed Rate (mm/r) | Time (s) | Total Energy (J) | Drive System Energy (J) | General Electrical System Energy (J) | AC-Powered System Energy (J) | DC-Powered System Energy (J) | Additional Energy Loss (J) | Additional Energy Loss Rate (%) |
|---|---|---|---|---|---|---|---|---|
| 1.4 | 45 | 247704 | 92504.7 | 134529 | 123121 | 18996.1 | 20670.3 | 8.34 |
| 1.6 | 41 | 217229 | 95347.6 | 123410 | 113398 | 17312.9 | 1528.6 | 0.70 |
| 1.8 | 38 | 216434 | 96012.7 | 113003 | 101552 | 16104.5 | 7418.3 | 3.43 |
| 2.0 | 36 | 206412 | 86683.2 | 109032 | 98273 | 15147.5 | 10696.8 | 5.18 |
The analysis reveals that spindle speed has a more pronounced effect on power than feed rate in gear hobbing machines. However, both parameters influence energy consumption through machining time, which is calculated as:
$$ t_c = \frac{B z}{z_0 n f} $$
where \( t_c \) is the machining time, \( B \) is the gear width, \( z \) is the number of teeth, \( z_0 \) is the number of hob threads, \( n \) is the spindle speed, and \( f \) is the feed rate. This equation shows that higher spindle speeds and feed rates reduce machining time, potentially lowering total energy consumption despite increased power. The drive system is particularly sensitive to spindle speed changes, while the general electrical systems remain stable, underscoring the need for parameter optimization in gear hobbing processes.
Development of an Energy Consumption Prediction Model for Gear Hobbing
Based on the experimental data, an energy consumption prediction model for high-speed dry gear hobbing machines was developed using spindle speed and feed rate as independent variables. The model structure is a nonlinear equation:
$$ E = b_0 n^{b_1} f^{b_2} $$
where \( E \) is the total energy consumption, \( n \) is the spindle speed, \( f \) is the feed rate, and \( b_0 \), \( b_1 \), \( b_2 \) are coefficients determined through regression analysis. Applying logarithmic transformation linearizes the equation:
$$ \ln E = \ln b_0 + b_1 \ln n + b_2 \ln f $$
This can be expressed as a linear regression model \( y = a_0 + b_1 x_1 + b_2 x_2 \), where \( y = \ln E \), \( x_1 = \ln n \), \( x_2 = \ln f \), and \( a_0 = \ln b_0 \). Using the experimental data from Tables 2 and 4, the parameters were fitted, resulting in the coefficients shown in Table 5. The regression statistics indicate a high goodness-of-fit, with \( R^2 = 0.949558 \), confirming the model’s accuracy.
| Coefficient | Value |
|---|---|
| \( a_0 \) | 16.642 |
| \( b_1 \) | -0.57818 |
| \( b_2 \) | -0.42771 |
| \( R^2 \) | 0.949558 |
| F-statistic | 47.06184 |
| P-value | 0.000571 |
| Error Variance | 0.001077 |
The final energy consumption prediction model is:
$$ E = 1.6886 \times 10^7 \, n^{-0.5782} \, f^{-0.4277} $$
This model demonstrates that energy consumption decreases with increasing spindle speed and feed rate, as indicated by the negative exponents. The prediction accuracy was validated by comparing predicted and experimental energy values, as shown in Table 6. The relative errors are generally below 5.5%, with most cases under 2%, confirming the model’s reliability for energy estimation in gear hobbing applications.
| Spindle Speed (r/min) | Feed Rate (mm/r) | Predicted Energy (J) | Experimental Energy (J) | Relative Error (%) |
|---|---|---|---|---|
| 700 | 1.8 | 297379.51 | 293854 | 1.20 |
| 900 | 1.8 | 257160.18 | 260239 | 1.18 |
| 1100 | 1.8 | 228988.40 | 238670 | 4.06 |
| 1300 | 1.8 | 207904.88 | 209123 | 0.58 |
| 1200 | 1.4 | 242462.86 | 247704 | 2.12 |
| 1200 | 1.6 | 229003.47 | 217229 | 5.42 |
| 1200 | 1.8 | 217753.00 | 216434 | 0.61 |
| 1200 | 2.0 | 208158.26 | 206412 | 0.85 |
The model provides a practical tool for optimizing process parameters in gear hobbing to achieve energy savings. For example, selecting higher spindle speeds and feed rates can reduce total energy consumption, but care must be taken to balance this with tool life and surface quality requirements. This approach enhances the sustainability of gear manufacturing processes by integrating energy efficiency into production planning.
Conclusion
This study comprehensively analyzes the energy consumption distribution characteristics of high-speed dry gear hobbing machines under variable process parameters. The power model, dividing the machine into drive and general electrical systems, effectively captures the energy dynamics during gear hobbing. Experimental results show that spindle speed significantly influences drive system power and total power, while feed rate has a lesser effect. However, both parameters impact total energy consumption through machining time, with higher values reducing energy use. The developed prediction model, based on spindle speed and feed rate, accurately estimates energy consumption with errors generally below 5%. This model aids in optimizing gear hobbing parameters for energy efficiency, contributing to greener manufacturing practices. Future work could extend this approach to different materials and machine configurations, further advancing energy-saving strategies in gear production.