Within this article, the power skiving process of gear tooth machining was evaluated and developed with respect to cutting tool orientation. The impact of minor variations to the orientation of three factors related to the cutting tool were explored to determine the effect of cutting tool orientation on the output metrics of finished gear geometrical characteristics within the design space.
The aim of the study was to use the knowledge gained to develop a statistical based model with the ability to predict how adjustments to the chosen three factors would affect the quality of the gear features produced. This would theoretically allow for tooling errors (or indeed other repeatable errors) to be counteracted through positional changes within the power skiving process based on the design space of the trials.
The initial phase of the work used a Design of Experiments (DoE) methodology. This was used to assess the gear-quality implications of alterations made to the three chosen factors related to the tool position when power skiving with tooling made to drawing specifications. The statistical-based model fit was formed of quadratic, interaction, and independent coefficients analyzed to map responses in the gear. Following the experimental trial, the statistical model was reviewed and refined. Ahead of a validation trial, predictions were made to estimate the results of a final block within the DoE, which proved the statistical model fit to possess a high level of predictive power.
In most cases, responses were within 10 percent of the predicted tolerance, and all results were within 50 percent. This was extremely encouraging, and the work confirmed that a statistical based approach could be adopted to support future predictability of the process.
The University of Sheffield Advanced Manufacturing Research Centre (AMRC) has conducted this project and prepared this article through collaboration with tooling supplier and partner, OSG Corporation.
Collaboratively through this project, the power skiving process of gear tooth machining was evaluated and developed with respect to cutting tool orientation. The impact of varying the orientation of three factors related to the cutting tool (cross-axis angle (CAA), X-axis and Y-axis positions) were explored to determine the characteristic effect of cutting tool orientation on the output parameters of finished gear geometry.
The overarching aim of the project was to use the knowledge gained to generate a preliminary statistical model with the ability to predict how adjustments to the chosen three factors would affect the quality of the gear features produced. Theoretically this would allow for tooling errors to be counteracted through positional changes within the power skiving process, thereby increasing the quality attainable with a given tool, even if that tool’s geometry were suboptimal.
The objectives were achieved through a Design of Experiments (DoE) methodology to baseline the performance of a pulsator gear power skiving tool and establish the effect of deliberate minor changes from nominal of cross-axis angle, X-axis, and Y-axis positions of a power skiving tool on an Okuma U3000 machine tool.
Following the experimental trial, the statistical model generated in the DoE software, MODDE 12.1, was reviewed and refined before being converted to the first version of a Microsoft Excel based predictive calculator.
The statistical model developed was then tested through an application trial where three different erroneous tools were used to produce a set of baseline gears. The baseline results were inserted into the calculator and a following set of gears were produced with factor adjustments to cross axis angle, X-axis, and Y-axis positions. The predicted results generated by the calculator were compared to the actual results to assess the predictive power and further refine the calculator developed.
This article briefly outlines the background of the power skiving cutting process and the previous development work in Section 1. It then progresses to detail the equipment used throughout the project in Section 2 and methodology applied in Section 3. Results and observations are discussed in Section 4 followed by the conclusions in Section 5 and closing with further work required in Section 6.
1 Background
Power skiving is a generative gear cutting process applicable to both internal and external gear forms and splines. This process holds significant advantages in productivity over more traditional gear-manufacturing processes, including shaping and hobbing, although it has similarities to the two in its makeup. As a concept, the power-skiving process has existed since it was patented in 1910 [1] although, due to the required accuracy in the high rotational speed synchronization of the cutter and work piece, it is not until recent years that the process could be satisfactorily applied, with the development of CNC machines with high accuracy encoders and increased rigidity having made this possible. Many machines that can apply this process are single-purpose skiving machines, although multi-function machine manufacturers are adopting the process, and this is something that has been considered in this work.
Prior to this project, the AMRC has carried out a number of investigations into the power-skiving process. Work has progressed from initial power-skiving development on a Mori Seiki NT5400 multifunction platform where a set of parameters was manually optimized using a trial-and-error procedure through to the application of force-normalized and non-normalized parameter calculators based on dynamic stability [2, 3]. Application trials were extended across different gear forms, both internal and external, with extensive testing on a ring gear of approximately 20-inch diameter [4].
In wider published works, research has begun to focus on how errors within the power-skiving process — including tooling, workpiece, and machine deviations — affect the quality of the gear produced. E. Guo et al. found profile deviations of the workpiece are insensitive to the position and orientation errors of the cutter in skiving; however, the tool eccentricity error did affect the skiving accuracy, creating periodic waves on the teeth flanks [5]. Z. Guo et al also found profile slope deviation was sensitive to cutter tilt error, the cumulative pitch deviation was sensitive to eccentric error, and the diversity of tooth deviation was mainly influenced by the phase angle of the workpiece and cutter eccentricity [6]. While investigating flank twist during power skiving, E. Guo et al developed a corrective method by adapting the cutter profile to account for the observed error [7]. Similarly, L. Trong-Thuan and W. Yu-Ren investigated how tool pressure angles, protuberances, and polynomial coefficients on the rack could achieve more even grinding allowance on a power-skived gear [8].
The focus of this study was to understand whether machine deviations could be used to account for errors on the tool. This could allow tolerances to be relaxed in tool manufacturing, creating more affordable tooling solutions while maintaining the ability to produce high-quality gears.
2 Equipment
2.1 Work piece
The gear geometry selected for this work was a gear geometry known as the pulsator from Newcastle University’s Design Unit. It is a 29-tooth gear of 4.760-inch major diameter with a diametrical pitch of 6.513. This geometry has become a baseline geometry for investigations around alternative gear form generation strategies. On review of the proposed geometry, the tooling partner adapted the design to create a similarly sized component with a reduced module to create results on a geometry with a module they had previously manufactured during initial development trials. The final component is illustrated in Figure 2-1.
The basic attributes are included in Table 2-1.
The spur gear was manufactured from EN8 GRADE 080M40+AR BS970/3-91 billets with an approximately 4.9” outer diameter and 1.575” in thickness. This material has a hardness of 201-255 BHN and was selected as a suitable alternative to the material used in upfront trials undertaken to determine appropriate cutting parameters in unhardened S45C(JIS).
2.2 Power-skiving tooling
The power-skiving tooling selected for this project was designed and supplied by OSG Corporation. These cutters are made from CPM high speed steel with a WXL coating applied. The patented coating is designed for rigidity and performance specifically tailored for nonferrous materials, mild steels, and steels up to 50 HRC. An image of the tool can be seen in Figure 2-2.
The basic details of the tool design can be seen in Table 2-2.
Four examples of power-skiving tools, manufactured accurately to nominal drawing specification, were supplied for the first work package. Three of these were used in the DoE, and the fourth acted as a spare. For the later work package, six deliberately erroneous tools were supplied, with three separate profile errors related to profile angle (fHα) and profile form (ffα). These erroneous tools are further described in Table 2-3 through a metric inspection report.
The power skiving tooling was mounted with a torque of 95 Nm onto an ERICKSON HSK63ASMC125225 tool arbor with an HSK63A spindle interface.
2.3 Machine tool
The trials were completed on an Okuma MULTUS U3000 pictured in Figure 2-3. The OSP-P300 (Okuma branded machine controller software) controlled machine had a maximum turning spindle speed of 5000 rpm, maximum milling spindle speed of 12,000 rpm, and could turn diameters up to 25.591”. The machine was stocked with Hangsterfers S-787 coolant with a strength of 8-10%, maintained through daily checks. The machine was originally trialed on a similar gear geometry used in this project, known as the pulsator, before leaving the supplier factory where an acceptance test was completed to assess the machine’s power-skiving capabilities. This test was repeated after the machine’s installation to validate capability.
The power-skiving activity was performed with the tool loaded in the H1 Turret B-Axis (milling spindle) of the machine and a prepared blank in the main spindle. A Hainbuch chuck (SPANTOP nova Kombi Axzug Gr.80 #2702/0011), mandrel (MANDO T212 Gr.3 #2524/0027 & SB230R65,0) and backstop (A230R62,60 DIA62.6), pictured in Figure 2-4, were used as an internal clamping system for workholding when generating the gear form and were mounted to the Spindle C-Axis. The manufacturer had stated the setup to consistently achieve a positional accuracy of at least 0.0004”.
The machine specifications can be seen in Table 2-4.
2.4 Metrology equipment
The manufactured gears were inspected on a coordinate measurement machine (CMM) in a dedicated metrology lab maintained at 20°C, ±1°C. The CMM used is a Leitz PMM-C; the specification of this machine is covered in Table 2-5. This CMM has proven capability for measuring gears and was ratified in a British Gear Association (BGA) round robin assessment.
The tooling was inspected for wear or damage on a Nikken E46LTWA pre-setter. This allowed for images of individual teeth at 60x magnification from the top of the tool and at 90° to this view giving a visual of the tool tip.
Tooth 1 was selected and indicated with a paint marker prior to starting the trial. Tooth 1 was chosen based on its seating position on the tool arbor. Images were captured in approximately 90° intervals: Tooth 1, 7, 14, and 21.
3 Methodology
The foundation of the project was broken down into multiple stages; ahead of activity at the AMRC, a trial was undertaken at OSG Corporation Japan to determine the appropriate cutting parameters and to baseline the capability and performance of the power-skiving tooling on the same machine platform as used in the later trials. Figure 3-1 summarizes the flow of activity.
3.1 Design of experiments
Four repeat tools were available for this phase of the project, all manufactured to the drawing as described in Section 2.2.
The aim of the DoE was to assess how positional changes to these tools applied during the power-skiving process affected the quality of the gears produced. The DoE mapped the three factors (cross-axis angle (CAA), X-axis shift and Y-axis shift) described in Figure 3-2.
A Determinant-Optimal (D-Optimal) model in MODDE 12.1 was used to map how alterations to the above outlined factors affected the 13 responses listed in Table 3-1. This is a computer-generated optimization design with three levels per factor in which the quadratic design allowed for interactions and quadratic relationships to be analyzed and included in the statistical model produced by assuming that all three factors have a non-linear quadratic response. The model included all three linear terms, all second order interactions (e.g., CAA*Y-a), and three quadratic terms (e.g., CAA*CAA).
The DoE consisted of two optimization blocks (WP1) exploring a design range of minus-0.5° to 0.5° for the cross-axis angle and minus-0.012” to 0.012” for the X-axis and Y-axis. Following this, a final validation block (WP3) where new offsets that were within the design space of the first two blocks but had not directly been tested were trialed. Prior to this final validation block, the data collected from the first two blocks was collected and analyzed (WP2) to be used to predict the results of the final validation block ahead of the trial. These predictions were later compared to the actual results to begin to understand the predictive power of the DoE model.
Table 3-2 details the experiment layout, the offsets applied, and tool iteration used through each stage of the DoE.
Each batch of trials was separated by a tool change to allow for an understanding of whether the differences within iterations of the same tool were affecting the results independent of the analysis of the three factors. Within each batch, three center point repeats were made. In WP1 Batch 1, the repeats were done upfront to baseline the performance and compare against the results that were observed in the preliminary trial at OSG Corporation Japan to ensure the machine tools and tooling were performing comparatively in the two different machining environments.
The center point repeats in WP1 Batch 2 were staggered through the rest of the experiments to give a perspective of whether any external variables such as temperature, daily machine utilization, or tool wear were affecting the results. Finally, as WP3 Batch 3 was acting as a validation trial for the previous two experimental batches, the center points were again all run at the beginning of the experiments to allow for comparison against the previous two tools performance prior to continuation with the factor validation.
The final block (WP3) was built up of single variable changes in both a positive and negative direction for each variable to allow for an understanding of the independent results without the requirement to access and understand the chosen DoE software, MODDE 12.1, to assist with data analysis.
3.2 Application
The application of the predictive statistical model developed involved a set of three baseline gears without any adjustment to the monitored factors to observe how the tooling error had directly affected the quality of the gear produced. The responses were used in the Excel calculator to predict the responses after adjustments were applied during the power-skiving process. A minimum of four adjustments were trialed for each of the three erroneous tools supplied, all with three repeats to aid in the identification of outliers and improve confidence in the accuracy of the results. At least one adjustment to each factor (cross-axis angle, X-axis, and Y-axis shifts) were made through each tooling batch to allow for the calculator predictability to be assessed for all the monitored factors. Table 3-3 summarizes the adjustments made throughout the experimental trial.
The results of these trials were then used to further refine the calculator, improving the predictability of the mathematical model.
3.3 Power-skiving methodology
The stock material condition acquired was loaded into the sub-spindle of the Okuma MULTUS U3000, where material preparation began before an automated spindle transfer and the final operations of material preparation, and the datum features were machined ready for power skiving.
To ensure concentricity and repeatability in all trials, the gear-tip diameter was turned along with any datum faces or diameters in the same setup in which the gear teeth were produced via power skiving. Power skiving tool runout was captured at the tool setup stage using a dial-test indicator (DTI) on three locations of the supplied tool. The tool was then adjusted to the correct offset by running iterative fresh-air passes adjusted in the Y-axis until a witness mark was seen on the part; at that that stage it was deemed that the tool was correctly set. This allowed the full assembly, including the machine spindle alignment, to be understood. In production, once tool repeatability had been achieved with regular maintenance including spindle run out checks, this would not be required for each tool change.
As introduced at the start of Section 3, the cutting parameters were determined through a preliminary trial using the same make and model of machine tool (Okuma MULTUS U3000), gear, and tooling geometry. Cutting velocities trialed ranged from 2.362 inch/min-3.937 inch/min and Table 3-4 details the finalized parameters recommended for this study. The provided parameters included spindle velocity, feed rate and iterative depths of cut.
Data capture during the power-skiving process included vibration and load monitoring via the built in Okuma Trace Data Logging function as well as video capture using a Go Pro. All produced gears were then inspected on the CMM detailed previously.
4 Results and observations
The following sections detail the results of two experimental phases of machining: one in the format of a DoE and a second application of the calculator developed from the statistical model. This is followed by an analysis of tool performance including tool wear. The remainder of this section details the workings of the predictive calculator.
4.1 Design of experiments
The results of the DoE have been discussed in two sections. The first detailing the initial optimization trials in WP1 where two blocks of trials were completed to gather data and subsequently refine that data in WP2. This is followed by discussion on WP3, the validation stage where a further trial block was completed after predictions were made using the statistical model within MODDE 12.1.
4.1.1 Optimization and model refinement – WP1 & 2
The DoE used a multiple linear regression model, which assumes that all the data is normally distributed for analysis. In some cases, the data was transformed to allow the data to be analyzed. Table 4-1 details the transformed responses.
In WP2, after transformation, where required, the model was refined within MODDE 12.1 to eliminate coefficients, which were not statistically significant from the model (assuming a 95 percent confidence interval). Table 4-2 indicates the remaining coefficients for each response with an “X.”
Most responses are showing both quadratic and interaction coefficients that are statistically significant and therefore included in the model fit. This supports the use of a DoE to analyze and produce the data with the design space investigated. Without the use of such a statistical approach it would have only been possible to evaluate linear coefficients.
Six main criteria, listed in Table 4-3 alongside their values for each response, were used to assess the refined statistical model generated for each of the mapped responses:
The coefficient of multiple determination (R2): A statistical measure of how close the data are to the fitted regression line.
Predictability of the data (Q2): An estimation of how well the model will predict in the future.
Residual Standard Deviation (RSD): Which informs us that the data is predictable to within a tolerance of the RSD value.
Model validity (MV): A measure of how well distributed the data is and therefore how well the data fits the model as well as the presence of outliers. When the Model Validity is larger than 0.25, there is no Lack of Fit of the model.
Reproducibility (Rp): The variation of the replicates compared to the variability of all the results.
Degrees of freedom (DF): Where a value over 8 is desirable and indicates sufficient experimental trials.
All responses are showing at least 10 DF, confirming that sufficient experimental trials were completed.
The majority of R2, Q2, and Rp values are over 0.5, indicating the model has good fit, with approximately a quarter of the responses for R2 and Rp showing a high significance of over 0.9. The difference between the R2 and Q2 values is less than 0.3 for all profile, pitch, runout, dimension over balls, and load data. This further increases the confidence in the statistical model based on the baselines set within MODDE and adopted in literature; “A model with R2 of 0.5 is a model with rather low significance ~ Q2 should be greater than 0.1 for a significant model and greater than 0.5 for a good model. The difference between R2 and Q2 should also be smaller than 0.3 for a good model.”
Similarly, more than 50 percent of the responses are showing an RSD of less than 0.4 thou, indicating the model is anticipated to predict over half of the responses to a tolerance of 0.4 thou with the statistical model at this stage. In support of this, Figure 4-1 shows the metric observed vs. predicted plot for fHα where all points are shown to be along the dashed line indicating the predictions were very close to the observed results.
The model validity for FHβ is missing in the table. This is due to the spread of the center point repeats being so small as shown by the metric replicate plots in Figure 4-2, that the replicates are deemed identical by MODDE, and, therefore, the model validity is labeled “Missing,” as it cannot be calculated.
The model validity for all other responses is approximately 0.5 or higher, which provides confidence in the statistical model and is encouraging when understanding the missing values described as MODDE state “when the model validity column is larger than 0.25, there is no Lack of Fit of the model (the model error is in the same range as the pure error).”
Results for the profile of the gear were affected by changes in cross-axis angle, or offsets in either the X or Y-axis, as can be seen by the large variability in results in the metric replicate plot shown in Figure 4-3. It was anticipated the model developed could accurately predict how the factors would affect the response. In contrast, the results for the gear lead or pitch did not appear to be at all affected by the changes, as the metric replicate plots in Figure 4-2 show a smaller variability in results. Results for the gear runout also did not appear to be largely affected by changes; however, some variation indicated there could be an external factor affecting performance.
As anticipated, the dimension over balls was directly affected by Y-axis offsets. This required consideration in the later stage of the project when implementing any adjustments to compensate for tool error. In parallel to, and likely as a result, the M-spindle load increased by offsets in the Y-axis. The increased level of load remained within acceptable limits so was not of concern.
In most of the responses, the cross-axis angle appeared to be the main effect, an example of this can be seen by the coefficients plot in Figure 4-4.
As can also be observed in Figure 4-4 by the Tool 1 and Tool 2 coefficients, the change of tool between the first and second machining block in the DoE highlighted that the differences in the tool, while having a minimal effect on the responses, indicated high repeatability between the tools including their set up. In most cases, the Tool coefficients were eliminated but for fHα right, fHβ left, Fβ right and left, ffβ right and left, fp right and fri. The Tool coefficients remained to become part of the constant in the statistical model. In all cases, the coefficients were approximately equal and opposing, which later reduced their impact as a constant in the equations. The assessment of the effect of a tool change was important to understand and eliminate for the validation stage of the DoE and the future development of the calculator.
After refinement of the statistical model in MODDE, which included the elimination of coefficients and the transform of data where relevant, equations were generated for each of the mapped responses to produce the predictions discussed in the next section, 4.1.2.
4.1.2 Predictions and validation – WP3
As described in Section 3.1, prior to producing the DoE validation gears on machine, MODDE 12.1 was used to predict the results using the statistical model generated from the results of the optimization trial in WP1. The software generated two ranges of predicted results for each of the mapped responses for the nine validation gears. A range was generated from each block (B1 or B2) of the optimization trial. Table 4-4 details the color coding used through the analysis of the predictive power of the DoE to ease understanding.
The results of WP3, the validation trial have been broken down into three tables: Table 4-5 shows the results for the gear profile; Table 4-6 shows the results for the gear lead. and Table 4-7 shows the results for gear pitch, runout, cutting load, and dimension over balls for the nine validation gears.
Based on the results shown, the statistical model derived from the initial DoE proved to show a high level of predictive power. In most cases, responses were within 10 percent of the predicted tolerance, and all results were within 50 percent.
4.2 Application
The results of the application trial were assessed using two methods: The gear feature quality to provide an insight of whether the calculator could assist in counteracting tooling errors through positional offsets applied to the tool. The main assessment factor used to judge the success of the trials was an assessment of the accuracy of predictions generated by the calculator compared to the actual inspected results to understand the potential predictive power.
4.2.1 Inspection results
The results taken from the gear-inspection reports for each of the trialed erroneous tools with applied offsets was reviewed and has been listed for Tool 2_1 in Table 4-8. Color coding has been applied to better indicate the size of the deviations from nominal. The darker shading indicates the largest deviation for the listed gear feature, with no shading indicating the smallest deviation, and, therefore, best performing gear for that feature.
The table shows improvements were made to each gear feature through at least one of the applied offsets. The offsets, however, affect each of the gear features in different ways. The color coding in the tables highlights how some offsets only improve certain gear features, while the same offsets will have a negative impact on other gear features. This is representative of the results for each of the three tools trialed. This highlights that, in many cases an aspect of compromise was required to decide which features to improve. For example, an offset of minus-0.22° to the cross-axis angle combined with an offset of minus-0.008” to the Y-axis with Tool 2_1 improves some profile and most lead features but reduces the pitch, runout, and dimension over balls. Adjustments made to the Y-axis have shown the greatest impact on the dimension over balls figures and, therefore, are likely to be the offsets, which will require compromise over the improvements made by the offset.
Based on the results for each tool, Table 4-9 shows an extract of the metric inspection report of the most improved profile alongside the baseline profile, which was generated without any positional offsets applied to visualize the improvement observed.
Each of the gears compared shows a visible improvement on the profile graph, confirming the applied offsets have successfully counteracted the effects of the tooling errors on the profile of the gears produced to some degree. All three tools have less figures highlighted in red as out of tolerance on the gear produced with offsets applied. Tool 3_1 shows the greatest numerical and visual improvement on the profile graphs; this was expected due to this tool having the greatest error and, therefore, the most potential improvement to be made.
4.2.2 Predictive power
Table 4-10 details the color coding used through the analysis of the predictive power of the calculator to aid analysis.
To understand the predictive power of the model, the difference between the predicted and actual results taken from the gear inspection reports for each of the trialed erroneous tools with applied offsets were reviewed and have been listed for Tool 2_1 in Table 4-11. The smaller the difference in the two results indicates a more accurate prediction generated by the calculator.
Analysis of the predictive accuracy across the three erroneous tools tested shows that 49 percent of the results were predicted to within 0.004 thou of the actual result on inspection of the produced gear; 88 percent were predicted to within 0.012 thou, and 90 percent were predicted to less than smallest applied tooling error of 0.018 thou. The results for lead and runout show these calculations to have the greatest predictive power, followed by the profile and pitch. All lead and pitch results for Tools 1_2 and 3_1 was predicted to within 0.012 thou; for Tool 1_2, this also includes the pitch, and for Tool 3_1 the runout. Finally, the predictions for the dimension over balls showed the least predictability using the calculator.
When judging the predictability of the calculator, it was essential to consider the collective accuracy of the setup used to both manufacture and inspect the gears produced and compared to the calculator’s predictions:
The PMM-C used to inspect the gears has a first term accuracy of 0.002 thou. This is the uncertainty of the machine before any external factors (measurement length, temperature, and operator skill) are considered.
The manufacturer of the Hainbuch collet system used for workholding has stated the setup to consistently achieve a positional accuracy of better than 0.039 thou.
Finally, the positional accuracy of the machine tool, including the repeatability of a tool change, must be considered. Typically, HSK spindles repeat within 0.020 thou for a tool change.
Further to this, the workshop where the machine was situated was not a temperature-controlled environment, and temperature fluctuations were observed daily, which would further affect the machine tool’s positional accuracy, as well as material characteristics.
Finally, a consideration of the design space and where the applied offsets sit within that space will influence the accuracy of the predictions. Moreover, any discrepancies in the build-up of the trial from that used in the DoE to generate the initial statistical model will increase speculation within the predictions and reduce confidence. For example, the tooling used in the application trial was intentionally created with differences to the drawing specification.
4.3 Tool performance
Within each tooling trial, at least one gear was produced at “baseline.” This was a gear produced without any positional offsets made to the tool. This allowed a comparison and understanding of how the intentional tooling errors were specifically affecting the performance of the tool and subsequently the quality of the gear produced. Table 4-12 compares the inspection results for gears produced by a tool without error, B1, and the three erroneous tools used in the application trial: 1_2, 2_1, and 3_1. Color coding has been applied to indicate which tool had the least and greatest deviation from nominal for each gear feature. The darker shading indicates the largest deviation for the listed gear feature, with no shading indicating the smallest deviation.
The results shown in Table 4-12 demonstrate how the tooling errors affect different features of the produced gear, with the four different tools having a range of the best and worst results.
Further to this, as the erroneous tools were anticipated to have the largest impact on the profile of the gear produced, Figure 4-5 shows extracts of the metric inspection reports to compare how the different tooling errors affected the profile generated.
Each tool produced a different profile, and, as expected, due to having the largest applied error, Tool 3_1 showed the greatest error with both a lean and crowning visible of the profile graph. Based on previous experience, the differences in the dimension over balls figures for each gear was anticipated to be having minor impacts on the profile observed; however, the predominant cause of the differing profiles was accredited to the intentional differences in the tooling that were being investigated.
As detailed in Section 3.2, during the Application trial, each gear was produced in a batch of three repeats. All three gears were inspected to highlight any anomalies. Across all gears produced, the spread was monitored separately for each inspected gear feature. The maximum spread of data for any of the batches observed was 0.051 thou (Tool 2-1, CAA -0.22°, X 0”, Y 0”, Mdk max) with the minimum spread observed being 0” (Tool 3-1, CAA 0°, X 0”, Y 0”, ffβ right). Throughout the trials 44.5 percent of the batches had a spread of results less than 0.004 thou, with only 2.5 percent having a spread greater than 0.039 thou. The profile and lead results were the most repeatable within their batches predominantly repeating to less than 0.004 thou. In contrast, the dimension over balls appears to be the least repeatable with most batches having a spread of at least 0.020 thou.
4.4 Predictive calculator
The predictive calculator uses equations to calculate how the relationship between each of the potential positional offsets that can be applied will affect each of the gear features independently. The equations are used alongside results from the initial DoE where no offsets were applied to calculate an adjustment quantity, which is then applied to the baseline data from each individual erroneous tool to produce a prediction that is applicable to each specific tool.
The constants within each equation were initially generated through the DoE phase. They were later refined based on the results of the application trial to improve the predictive power of each of the equations to achieve the results discussed in Section 4.2.2. The calculator uses a table of the constants to formulate the equations. This increased the ease of comparison and adjustment.
At this stage, the equations have undergone limited testing with only a single gear geometry, limited tooling errors, and a restricted design space. Further testing would be required to extend the design space and understand the predictive power of the calculator when applied to different gear geometries and tooling errors. It should be further noted the trials were conducted in a semi-production environment in a facility that did not have temperature control. Therefore, production variations between components will be a function of temperature as well as other unmeasured effects.
4.4.1 Application of the predictive calculator
This section provides an overview of how to apply the calculator to a power-skiving tool. All figures in this example of the calculator are in metric.
1: For each new power skiving tool, a gear must first be produced using baseline parameters (without any positional offsets applied). The results of this gear are to be copied into the “Baseline inspection” column as can be seen in Figure 4-6.
2: From here, manual adjustments can be made in the “Offsets” column shown in Figure 4-7 to see the predicted impact the combination of offsets will have on the gear produced. The “Adjustment” column in Figure 4-6 shows how much the baseline result is predicted to alter by, whereas the “Correction prediction” column also shown in Figure 4-6 predicts the actual figures each feature the combination of offsets with the selected tool is anticipated to produce.
3: At this stage, the design space/tested range of the calculator is limited. If an offset outside of this range is applied within the calculator, the warning shown in Figure 4-7 will bring attention to this and the prediction accuracy may be reduced from expected performance.
4: The “Correction prediction” column is formatted to show whether the predictions are expected to be within an assigned tolerance band. The tolerances are currently set to match ISO 1328 Edition 1997 Class 6; however, through adjustment of the figures in the table shown in Figure 4-8, the conditional formatting will automatically be adjusted to match the tolerances assigned. Values predicted to be in tolerance show in green, and out of tolerance in red (with reference to the “Correction prediction” column also shown in Figure 4-6).
5 Conclusions
Overall, this project successfully initiated development of a calculator designed to predict how positional offsets applied to the tool in the power skiving process affect the geometry of the produced gear within a limited design space. Application of the predictive calculator to aid in counteracting the performance of erroneous power-skiving tools to improve the quality of a gear produced was also successful. In all cases trialed, the gear quality was improved through the application of positional offsets to either the cross-axis angle, X-axis, or Y-axis position.
The initial phase of the project used a Design of Experiments (DoE) methodology, which was used to assess the gear-quality implications of alterations made to the three chosen factors related to the tool position when power skiving with tooling made to drawing specifications.
All responses showed at least 10 degrees of freedom confirming that sufficient experimental trials were completed to produce a significant model. The majority of R2, Q2, and reproducibility values were over 0.5, indicating a significant model, with approximately a quarter of the responses for R2 and reproducibility showing a high significance of more than 0.9. In further support, the difference between the R2 and Q2 values was less than 0.3 for all profile, pitch, runout, dimension over balls, and load data. This further increased the confidence in the statistical model. Similarly, more than 50 percent of the responses are showing an RSD of less than 0.039 thou, indicating the model is anticipated to predict over half of the responses to a tolerance of 0.039 thou with the mathematical model at this stage.
Following the experimental trial, the mathematical model was reviewed and refined. The DoE indicated the responses for profile were most affected by the chosen variables, and lead did not appear to be largely affected by the offset adjustments. Of the three variables, the cross-axis angle was shown to give the main effect.
Ahead of a validation trial, predictions were made within MODDE to estimate the results of a final block within the DoE, which proved the mathematical model to possess a high level of predictive power. In most cases, responses were within 10 percent of the predicted tolerance, and all results were within 50 percent. This was extremely encouraging for the upcoming calculator development work where predictability was key.
These results fed directly into the development of the first version of the statistical model in Microsoft Excel. The statistical model was tested through an application trial where three different erroneous tools were used to produce a set of baseline gears, and at least a following four sets of gears were produced with factor adjustments to cross axis angle, X-axis, and Y-axis positions. The predicted results generated by the calculator were compared to the actual results to assess the predictive power and further refine the calculator developed.
This project closed after these application trials showed the calculator’s accuracy at this initial stage of development across the three erroneous tools tested to predict 49 percent of the results to within 0.004 thou of the actual result on inspection of the produced gear; 88 percent were predicted to within 0.012 thou, and 90 percent were predicted to less than smallest applied tooling error of 0.018 thou.
6 Future vision
The results of the predictive statistical model have been highly encouraging, possessing great predictive power. However, more work would be required to finalize and increase the confidence and applicability of the calculator further. A summary of some suggestions of further work include:
The model has currently been tested to a limited design space, meaning the predictive accuracy is likely reduced outside of this range. Further testing to expand the design space would increase understanding of the relationship between the position of the power-skiving tool and the gear produced, allowing for larger axis adjustments to be confidently predicted.
Rework of the calculator to focus on an empirical method as opposed to a statistical model through use of the geometry or CAD / element of the gear and cutter. This would potentially yield a more expandable solution space that can be validated and compensated for through experimental trial and error compensation in the predictive model.
The calculator has currently only been tested on a single spur gear geometry and a single tool geometry. The expansion of testing to a range of gear and tool geometries would add extended value to the predictive calculator.
A manual iterative process is currently required to operate the calculator and find a combination of offsets that best improves the quality of the gear. Conversion of the mathematical models into an application-based software would allow for a looped analysis to automate and formalize the process.
Testing of the predictive calculator across a range of machine platforms would increase the applicability and confidence of the calculator.
The AMRC and our partners are actively pursuing routes to furthering the research on power skiving in these areas and would welcome engagement from AGMA members and others in opportunities to collaborate.
7 Acknowledgements
The authors would like to thank the University of Sheffield Advanced Manufacturing Research Centre’s (AMRC’s) partnership for their keen interest in the area and for funding the research detailed in this article to allow the AMRC to develop and understand the capability of the power-skiving process and continue working towards making the process more accessible.
Thanks to OSG Corporation for their continued development, interest, and support in the area. The machine supplier NCMT who have assisted with data collection, analysis, and development through much of the AMRC’s power skiving development work on the OKUMA platforms for several years that reach beyond the remit of this article.
References
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Printed with permission of the copyright holder, the American Gear Manufacturers Association, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314. Statements presented in this paper are those of the authors and may not represent the position or opinion of the American Gear Manufacturers Association. (AGMA) This paper was presented October 2023 at the AGMA Fall Technical Meeting. 23FTM15
