Model Development for Cutting Optimization in High-Performance Titanium Machining

[Editor's Note: This article was adapted from the Makino white paper "Model Development for Cutting Optimization in High-Performance Titanium Machining." It has been shortened for length and scope. To read the full white paper with complete details of Makino's modeling process, click on the link at the end of this article.]

Titanium alloys have been widely used in the aerospace, biomedical and petroleum industries due to their good strength-to-weight ratio and superior corrosion resistance. Critical applications requiring the ultimate in weight-optimized designs or applications that see the most extreme environmental conditions are ideal for the use of titanium. As designers look to further improve their designs and as  modeling technologies advance, industries are turning to titanium more often than ever.

The benefits of titanium come at a price, however. Where aluminum can be cut at rotational speeds exceeding 30,000 rpm with high feed rates and significant depth of cut, the inherent strength of titanium alloys causes increased cutting forces and poor machinability. Its low thermal conductivity creates elevated cutting temperatures concentrated at the tool/chip interface. Coupled with the fact that titanium has high chemical reactivity at elevated temperatures, the result is significant tool wear and cutting speeds on an order of magnitude lower than other structural metals.

Maximum cutting temperature in titanium was 200 higher than that of steel under the same cutting conditions. Credit: Makino Maximum cutting temperature in titanium was 200 higher than that of steel under the same cutting conditions. Click to enlarge. Credit: Makino

As an example of the complications that arise in machining titanium alloys, the following simulated cutting temperatures were captured during dry cutting Ti-6Al-4V and AISI 4340 with the same cutter, with a cutting speed of 60 m/min and 0.2 mm axial depth of cut. The thermal conductivity of Ti64 is 15 percent of that for AISI 4340, resulting in dramatically increased heat concentration. For Ti64, the temperature at the tool/chip interface reaches more than 600°C (1112°F); however, for 4340, the highest cutting temperature is 200°C (392°F) lower.

Compounding the thermal issue, the increased strength of the titanium alloy also results in a thinner chip and shorter tool/chip contact length. The net result is more thermal energy to be dissipated in a smaller volume of material that is inherently less able to conduct heat. This observation clearly highlights why controlling cutting temperature is the most challenging problem in high-performance titanium machining.

A material's yield strength is reduced as temperature increases. In terms of the workpiece, this is useful information in that increased temperature makes it easier to remove material. The critical factor, however, is the impact on the mechanical strength of the cutting tool material. Thus, an ideal temperature exists for maximizing productivity that softens the work material while maintaining mechanical strength of the tool. Determining this critical temperature is key to high-performance titanium machining.

Tap testing is widely used in aluminum machining to determine the cutting conditions to be used for a particular machine/holder/tool combination. The frequency response and force information from the tap test generates a plot of stable combinations of axial depth of cut and spindle speed. In general, high spindle speeds are preferable for high material-removal rates; however, they cause sharp increases in cutting temperature that must be reconciled with the tool material limits.

These plots feature "stability lobes" above which the combination of depth of cut and spindle speed results in unacceptable vibration. The key is to select the highest speed that falls under the last acceptable lobe to give the largest possible depth of cut. Reality prevails, however, and an additional consideration is the range that must be maintained at the selected speed. Choosing a combination without a large enough speed range around it can cause instability. Another challenge for machining titanium is that the relative widths of the lobes in the plots for titanium are considerably narrower than in other materials. This indicates that titanium demands much finer control to maintain the "sweet spot" at the peak of the optimal stability lobe for maximum productivity.

Makino undertook an effort to systematically study heat generation in high-performance machining of titanium alloys to develop a deep understanding of the interaction of the influences involved. Processes and theoretical models were developed for selecting optimized cutting conditions and efficient cooling strategies. Goals for this work were maximum titanium machining productivity, longest tool life, and best finished surface quality.

In order to achieve these objectives a process was developed to estimate the cutting forces, shear angle, etc., involved in cutting titanium. This was then used to model the cutting temperature distribution at the tool/chip interface, which could be used for selection of optimal cutting conditions. For verification, physical experiments were carried out for comparison to the theoretical model. This procedure was repeated and improved until the calculation error fell within a suitable threshold value to consider the model proven.

As part of this process, modeling of shear and frictional forces in the deformation zones, modeling of flow stresses, and modeling of cutting forces were performed. The forces generated in the deformation zones were calculated in order to determine the power needed to complete the cut. To do this, strain, strain rate, and cutting temperature at the shear plane and tool/chip interface were calculated and then flow stress and cutting forces were determined, all through model equations. Equilibrium conditions were checked to ensure compliance before defining the final cutting forces. The friction power at the tool/chip interface was calculated for use in determining the average cutting temperature.

After developing the model for the cutting forces and cutting heat generation, the outputs were used to evaluate the cutting conditions in the process. Based on the input data, such as cutting parameters and tool geometries, along with the in-process monitoring of spindle load and cutting power, the cutting forces and temperatures were continuously calculated using the developed model.

Using a cutting path with concave, convex, and straight portions allowed more rigorous verification of the model in one setup with varying cutting conditions. Credit: Makino Using a cutting path with concave, convex, and straight portions allowed more rigorous verification of the model in one setup with varying cutting conditions. Click to enlarge. Credit: Makino

For each calculation, if the resulting error was within the given threshold value, the calculated temperature at the tool/chip interface was checked against the tool material reaction temperature. If the error was not within the threshold, the cutting conditions were updated until the highest temperature was less than the reaction temperature for tungsten carbide-cobalt materials. Afterward, the cutting process was optimized to achieve minimum cutting power/forces.

In order to test the model results, a series of tests were performed on a titanium workpiece using a cutting path with concave, convex and straight features. This toolpath enabled comparison using three different cutting loads in one pass to truly test accuracy of the developed model. There was excellent correlation between estimated cutting forces determined from the model and the measured forces from the cutting path, in all phases of the cut.

In order to verify the cutting temperature model, an instrumented test setup was created. It had a secured workpiece for running repeated test cuts while measuring temperature in the work zone. Cutting forces were measured via an instrumented mount, and all data was fed to a PC for comparison against the estimated values developed from the model.

In practical experience, the most significant factor in the cutting temperature of titanium is the cutting speed; therefore, the first and most important comparison performed to evaluate the model against the experimental data was cutting temperature versus cutting speed. The modeled cutting temperatures closely matched the actual test data.

Once the temperature predictions were seen to be accurately tracking the physical test-cut data, physical tests were performed to optimize the cutting process. For the test setup used in the temperature measurement experiment, tap tests  were performed to identify the stable rotational speeds that were indicated as the most productive, with the greatest possible depth of cut. In these results, the highest speeds that remained in the stable cutting range and under the characteristic temperature of tungsten carbide were 1,030 and 1,174 rpm. These speeds were used to verify the results and optimization process through physical experimentation.

Test cuts were conducted at 1,174 rpm to check surface finish and tool wear under actual cutting conditions to ensure that the cutting process remained stable and the temperatures were below the critical temperature for extended tool life in the tungsten carbide cutter. During testing, the average temperature at the tool/chip interface reached 650°C (1,202°F), which was below the 800°C (1,472°F) critical temperature threshold, and the flank tool wear was less than 0.1 mm after 16 passes.


An analytical cutting-force model for milling processes in Ti64 has been developed that provides good accuracy in predicting the cutting forces when compared to experimental cutting data. Numerical simulation was performed to estimate the temperature distribution at the tool/chip interface. Cutting speeds and radial depth of cut have more dominant effects on cutting temperatures than do feed rates. Average cutting temperature at the tool/chip interface was measured in experimental testing and was found to be controlled within the characteristic temperature of tungsten carbide material to maintain reasonable tool life in a stable finishing operation optimized to achieve high productivity as well as long tool life. Physical experimentation has verified that the proposed theoretical model can achieve high-performance machining of titanium alloys.


Dr. Zhigang Wang is Senior Process Development Engineer for Makino Inc. He is a lead engineer within Makino's Global Titanium Research & Development center in Mason, Ohio. He has extensive experience as a researcher and published author. Wang's works have been published in the CIRP Annals, the International Journal of Machine Tools and Manufacture, and the International Journal of Advanced Manufacturing Technology. Wang earned his Ph.D. from the National University of Singapore and also holds a master's degree from the Nanjing University of Aeronautics and Astronautics in China and a Bachelor of Science degree from the Nanjing Forestry University in Nanjing, China.

Mark Larson is Manager of Titanium Process Development at Makino Inc. He currently leads the Global Titanium Research & Development center, where he is responsible for titanium milling process research and development on horizontal and vertical machining centers. With over 20 years of technical experienced at Makino, Mark has held positions as an applications engineering manager and turnkey engineering manager. He has vast metal-cutting experience that includes multiple years of developing specific turnkey engineered part solutions for various industries such as automotive, medical, and aerospace. Mark is a graduate of Miami University with a Bachelor of Science degree in manufacturing engineering. 

For the complete version of this Makino white paper, visit  For more on titanium machining, visit

Based in Mason, Ohio, Makino provides a wide range of high-precision metal-cutting and EDM machinery, including horizontal and vertical machining centers, 5-axis machining centers, graphite machining centers, and wire and ram EDMs. It also offers automation solutions that  provide reduced labor cossts and increaed throughput in a variety of production volumes and designs. The company's engineering services solve the most challenging applications across all industries. For more, visit


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