Cutting force when machining hardened steels

: This article deals primarily with the problem of determining the cutting force when machining hardened steels. Secondary issues are focused on the evaluation of surface quality on machined samples and the recommendation of cutting conditions. A wide variety of components are used in engineering, the final heat treatment of which is hardening. These components are usually critical in a particular product. The quality of these components determines the correct functioning of the entire technical equipment and ultimately its service life. In our case, these are the core parts of thrust bearings, specifically the rolling elements. The subject of the experiment is machining these components in the hardened state with cubic boron nitride tools and continuous measurement of the cutting force using a dynamometer. The following evaluation assesses the surface quality by both touch and non-touch methods. A structural equation with appropriate constant and exponents was then constructed from the data obtained using the dynamometer.


Introduction
The basic balance sheet builds on the results achieved during participation in projects where machining of hardened steels was the subject of research at the Department of Machining at the Faculty of Mechanical Engineering of Brno University of Technology. In these projects, the subject of the research was the search for optimal cutting conditions, as well as the search for the relationship between tool unloading and process stability of this machining method. The results can be found in the following published articles "Machining of hardened bearing steels"[1]," Contribution to turning hardened steel" [2]," Influence of cutting tool overhangs at machining of hardened steels" [3]," High-speed cutting of bearing rings from material 100Cr6" [4]," Analysis of selected aspects of turned bearing rings regarding required work piece quality" [5], "Tension of the surface layer in machining hardened steels" [6] and Hardened steels and their machining [7].
So far, application research of this technology has been primarily focused on machining of functional surfaces of body and shaft rings. This paper is mainly concerned with machining of rolling bodies in the hardened state, real-time measurement of the cutting force during machining and determination of the structural equation from the obtained values. These data are not widely available in the literature and have limited validity for specific cutting conditions [8]. Surface roughness parameters after finishing machining are given as a secondary output.

Materials and Methods
The experiment is focused at measuring the cutting forces when machining the functional surface of the component "Rolling Body", which is the outer diameter. The implemented manufacturing process includes:

Implementation of the cutting force measurement experiment
The experiment was carried out on 12 samples of rolling elements for larger bearing types.
The approximate dimensions of the sample shown in Figure 1:  Outer diameter (mm) 32;  Length (mm) 60. Unlike previous experiments with bearing rings, the SP280 SY machine was not used because of the practically impossible placement of the Kistler measuring system on this machine, namely the placement of the measuring probes on the vertical slide of the machine. In previous experiments [2] cutting tools from SECO were used but in this experiment alternative tools from Dormer Pramet were applied.

Technological conditions of machining when measuring with a Kistler dynamometer
The machine used for the experiment was the SV 18 RD, which is a lathe that has been verified for rigidity. The machine also has a considerable range of cutting speeds that can be continuously controlled. The main advantage of this conventional lathe is the possibility of placing the measuring probes of the Kistler dynamometer also on the back of the slide.
The specific tools used by Dormer Pramet were as follows:  Tool holder PCLNL 2525 M 12 in left-hand version;  Replaceable insert CNGA 120408 S 01020B shown in Figure 2, made of TB310, polycrystalline cubic boron nitride, suitable for use without cutting fluid.  The complete tool holder including the inserts used during the experiment placed on the probe of the Kistler 9257B dynamometer is shown in Figure 3.   [2], [3], but in a wider range, so that the mathematical dependencies could be subsequently determined. The specific values of the cutting conditions are given in Table 3. These are always four combinations of feed rate f and blade cutting width ap at three different cutting speeds vc. Sample 1 after machining is shown in Figure 4. The machining was carried out without process fluid and due to the geometry of the cutting insert (without chip sealer) a continuous segmented chip is realized, as shown in Figure 3.

Measurement of cutting forces with a Kistler dynamometer
A Kistler 9257B stationary dynamometer was used to evaluate the cutting force measurements. During longitudinal turning, the force components are measured in three directions according to the coordinate system, i.e. in the x, y and z axes, corresponding to the force components Fx, Fy and Fz. The measuring apparatus consists of a dynamometer, a Kistler 5070A hub amplifier and a data acquisition and analysis system by means of which the data are transferred to a computer. A realistic connection of the control and evaluation part of the assembly is shown in Figure 5. As each sub-sample was machined, a measurement was run and after turning was completed, the values were recorded and stored in DynoWare. The measurement was set to 60 seconds to cover all the machine times when machining each sample. Unwanted extreme measurement dates were filtered out.

Surface quality measurement by the touch method
Measurements of individual surface roughness parameters were made with a Taylor Hobson Surtronic S-128 roughness tester, shown in Figure 6. The

Surface quality measurement by non-contact method
The evaluation of the surface quality of the functional area by the non-contact method was performed on the Alicona Infinite Focus G5 (hereafter referred to as Alicona) and is shown in Figure 7. The main disadvantage is the problem with the reflectivity of some surfaces, which means that more lenses and measuring conditions have to be tried [9], [10].
The measurements were carried out under the following conditions:

Results
The results include the issue of cutting forces and the evaluation of surface integrity by both touch and non-touch methods. Due to the large amount of data, the graphical representation is limited to selected samples of components, namely parts 5, 6, 8 and 12.

Evaluation of cutting force measurements with the Kistler dynamometer
The measurement data were converted to a .txt file and then graphical dependencies of the time course on the force load were created in Microsoft Excel. Due to the very small scatter of individual force values in virtually all graphs, these are sufficient as input data for the structural equation. The average values of the individual cutting forces at the specified cutting conditions are given in Table 4.

Derivation of the structural equation
The derivation of the structural equation for the cutting force Fc for turning material in the hardened state is based on the data in Table 4 and is based on the following equation 3.1: This relationship is empirical and depends on the constant CFc, the exponents xFc , yFc and zFc and the variables in this case the blade width ap, the feed f and possibly the cutting speed vc. The values of the constant CFc. and the exponents xFc, yFc and zFc depend on the specific machining conditions and are valid within a certain range. Furthermore, the type of material and its condition have an influence, which can be expressed by the machinability class. When calculating the cutting force according to this equation, we have to take into account an inaccuracy which will be proportional to the difference between our machining conditions and those used to calculate the constant CFc and the exponents xFc , yFc and zFc .
The methodology for determining the specific form of the structural equation requires the following simplification. As can be seen in Table 4, the influence of the cutting speed is minimal, which implies the assumption of a very small value of the exponent zFc. of about ±0.05. The cutting speed term in the general formula is therefore not included and its possible influence is reflected in the value of the constant CFc. From Table 4, the individual values of Fc are averaged for the combinations of feed f and cutting edge width ap used and listed in Table 5 for use in the following calculation.
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 6 December 2021 Equation 3.2 in its modified form is the basic formula for determining the methodology for determining the values of the exponents xFc, yFc and subsequently the constant CFc. After logarithmization, xFc can be defined as the directive of the line tg α.
A graphical representation is shown in Figure 12.  Table 5: After logarithmization, yFc can be defined as the directive of the line tg α.
A graphical representation is shown in Figure 13. Figure 13 Graphical representation of yFc. Equation 3.9 to calculate yFc from the data in Table 5:  The evaluation of the quality of the functional area was carried out preferentially by the touch method and for the verification of the measured data the measurement was carried out by the non-contact method.

Evaluation of the surface quality of the functional area by the touch method
The measurements of individual surface roughness parameters were performed with a Taylor Hobson Surtronic S-128 roughness tester. Each measurement was performed 3 times and Table 6 shows the averaged values of selected surface quality parameters according to ISO 4287.  Figure 14 shows the display of the roughness meter during one measurement. The best result in terms of surface quality is of samples 5 and 6 at cutting conditions that are proven to work on larger diameters of bearing rings.

Evaluation of the surface quality of the functional area by the non-contact method
The evaluation of the surface quality of the functional surface by the non-contact method was carried out on the Alicona instrument for samples 5 and 6, where the best results were obtained, and for sample 8, where the worst results were obtained. For relevance, sample 12 with the highest values of cutting conditions was also assessed. The results are shown in Table 7. Comparison of Ra and Rz values in the touch and non-contact method shows almost the same values for samples 5 and 6, while better values were measured in samples 8 and 12 by the non-contact method. In the following Figures 15 to 22, detailed representations of the progression of the individual variables for the samples are given.

Discussion
The individual partial results of the experiment confirm the following facts:  Using inserts from another manufacturer achieved similar surface quality results.  The machined surface could be accepted for the 4 selected samples if Ra = 0.3 was considered as the cut-off value.  Measurement of surface roughness values by both the touch and non-touch methods showed similar results.  The construction of an empirical structural equation allows the prediction of the cutting force in finishing hard turning under similar machining conditions.

Conclusions
The article deals with two areas of assessing the results of hard turning of hardened materials. These are the evaluation of surface quality by the touch method, which is available in common industrial plants, and the verification of the measured values by the non-touch method, which in the case of laser-based measuring technology is more a matter of a scientific workplace. The second area focuses on the cutting force experiment, the result of which was used to develop a structural equation for the cutting force.