Trajectory Optimization in Face Milling Operations: Impact on Costs, Energy, and CO₂ Emissions

Types of trajectories in Face Milling

Thanks to the development of CAM systems, we now have a wide range of options for machining trajectories for roughing and finishing surfaces. Among all these options, there is a main difference: some operations keep the tool always in contact with the workpiece, while others include idle (non-cutting) movements.

We can classify them into four basic categories:

• Unidirectional: The most basic and easiest operation to program. The tool works with linear trajectories in the same direction and returns without cutting. Acceptable surface finishes are obtained, but if direct entry is used, it can affect tool life and increase the total cycle time.
• Zig-zag (bidirectional): Linear movements with the tool moving in both directions, reducing idle times, but with negative effects on the resulting surface quality. Managing the changes in direction can affect tool life.
• Spiral: Either towards or from the inside of the workpiece, it allows for continuous cutting with controlled engagement, offering good surface finishes and good control of tool life while reducing machining times.
• Adaptive and trochoidal: Trajectories that optimize tool-material contact by maintaining controlled radial engagement, improving surface quality. They usually include small idle movements in hard-to-reach areas but aim to keep the tool in contact as much as possible. They are highly recommended for difficult-to-machine materials.
  
  Each of these trajectories has different implications in terms of machining time, workload, energy consumption, and heat generation.

CO₂ Emissions

In this article, we will mainly address the energy effect of trajectories by comparing those that maintain constant contact between the tool and the workpiece with those that, due to their configuration and different orientation, involve idle (non-cutting) movements. To illustrate this comparison, we will use, an alternative unidirectional trajectory and a spiral trajectory from the outside, both under the same cutting conditions, and compare the energy consumption of both options. Subsequently, we will compare both trajectories with improved cutting conditions.

We can calculate the power consumed on different materials, selected from a wide data base, and using specific combination of tools and inserts geometries, during a milling operation using “ToolGuide,” available at this link. ToolGuide

For a face milling operation with the CM345 ref 345-050Q22-13H Z=6, with inserts 345R-1305M-PM 1230, on a 32CrMoV12-28 P3.0.Z.AN steel workpiece with 230 Hb, we will start from these two cutting conditions, which will give us two different cutting power consumptions.

During rapid movement at speeds of 5,000 to 10,000 mm/min (without cutting load) on a conventional 5-axis CNC machine with a maximum power of 40 kW, typical energy consumption ranges between 4 and 7 kW. For our example, we will use 5.5 kW as the calculation value.

The components that make up this basic machine consumption are:

• Software and electronic equipment of the machine.
• Machine movement, plus the rotation of the cutting spindle itself. The higher the feed rate, the greater the energy demand.
• Machine movement, plus the rotation of the cutting spindle itself. The higher the feed rate, the greater the energy demand.

This range is useful for estimating energy consumption during rapid positioning phases or movements between operations, especially in intensive machining cycles.

Case Studies

Case 1: Unidirectional vs. Spiral trajectories.

In a face milling operation on a 250x250 mm steel plate, two trajectories were compared: unidirectional and spiral. The spiral trajectory has a total cutting length of 1,250 mm, which is equivalent to 38.26 seconds of cutting time. In the unidirectional trajectory, there are 5 paths of 300 mm each, and we must add 4 return paths with a table feed of 7,500 mm/min. This allows the total machining to be completed in 45.918 + 9.6 = 55.51 seconds, an increase due to the non-cutting return time.

The cutting power is 16.7 kW, and the power consumed during idle movements is 5.5 kW. Therefore, the total energy consumption during the cutting time is 0.2276 kWh for the unidirectional trajectory and 0.1774 kWh for the spiral trajectory. The graph provides a clearer view of the kWh savings.

Comparison between unidirectional and Spiral trajectories

Case 2: Comparison between original and higher Fz=0,4 cutting conditions.

We have already seen how idle movements of the machine affect energy use. Now, if we take our second set of cutting conditions, with a feed per tooth of 0.4 mm, we can observe the effect of increased cutting parameters on both energy consumptions. The working power will increase to 18.1 kW, but the cutting time for the spiral trajectory will decrease to 33.48 seconds. In the unidirectional operation, the cutting time will be 40.17 + 9.6 = 50.07 seconds. Therefore, the new total energy consumption during cutting time is 0.2166 kWh for the unidirectional trajectory and 0.1683 kWh for the spiral trajectory. This is a counterintuitive result, cause with higher cutting power, we obtain lower energetic total consumption thanks to cycle time reduction.

Energy and CNC Machine Cost Analysis by Region

The following table presents a comparative analysis of energy costs, CNC machine hourly rates, and average CO₂ emissions per kilowatt-hour (kWh) across different regions. This data is useful for evaluating the environmental and economic impact of CNC operations globally.

And here are the data for all the cases studied. kwh y CO2 emissions and cost based on average data for all regions.

Conclusion

The choice of trajectory in face milling operations not only affects quality and productivity but also has a direct impact on process sustainability—energy costs, direct machine costs, and CO₂ emissions into the atmosphere. Adopting optimized trajectories through advanced CAM software allows you to:

• Improve energy efficiency.
• Reduce tool wear.
• Decrease CO₂ emissions.
• Lower direct machining cost and increase productive capacity.

For CO₂ consumption, the reduction is 26% when comparing the unidirectional trajectory with Fz=0.35 to the spiral trajectory with Fz=0.4. This also results in a 40% economic reduction.

In an industrial environment increasingly focused on sustainability, these technical decisions can make a significant difference. Selecting tools that allow us to work at the highest cutting conditions will achieve both direct economic savings and reductions in CO₂ emissions.