Due to its high productivity and accuracy, generation manufacturing of gearing is widely used in gear production [1, 2]. When deviations occur, however, it is not easy to pinpoint the causes due to the tool design and complex kinematics. This is particularly true of multiple-start tools, which are being used with increasing frequency due to their higher productivity. In such cases, the effect of tool deviations and clamping errors on workpiece quality can only be predicted in a simplified manner and with a great deal of expert knowledge. This article demonstrates how the causes of error and cause variables can be determined through the use of a newly developed simulation tool.
Searching for reasons for variance
As the tolerance requirements for gears become ever more stringent, manufacturing well within the tolerance limits becomes increasingly challenging. If tolerance violations occur during testing, it is imperative to quickly determine the causes and correct them. This is equally true when impermissible noise levels are measured on the end-of-line test rig. The problematic component in the transmission is first identified through component replacement testing.
If a gear is the reason for tolerance violations or noise problems, good and bad components are measured and compared. The comparison is made based on numerical parameters, which are calculated from the deviation curves and describe the curves. Examples of this include the profile and tooth trace angle deviations of a tooth and the pitch and runout deviations of the gear. These parameters can be further compressed to average values, variation ranges, or distributions of a gear or a random sample.
If this results in no significant difference between good and bad components, further investigation is needed , as shown in Figure 1. A comparison of the patterns and form of the measured deviation curves is frequently performed in practice by superposing two measurement printouts and holding them up to the light (see top right in Figure 1). Every user is familiar with this method and knows it is tedious and inconvenient. Due to the ability to save measurement curves, there are evaluation programs today that enable a simple digital comparison of curves. The simulation program presented here enables such an easy comparison of deviation curves based on measurements and simulations.
With noise problems in particular, this graphical comparison is often insufficient for detecting differences between quiet and noisy gears. The noise may be caused by periodic structures on the tooth flank, which exhibit amplitudes of just a few tenths of a micrometer and are overlapped by the deviations in form [4, 5]. Calculation of the common ripple spectrum of the profile and tooth trace curves enables a more detailed analysis of noisy and quiet gears and a targeted search for the noise-provoking influences .
The process of comparing parameters, deviation curves, and ripple spectra still does not provide an explanation of the reasons for the deviations. The comparison is merely an important component of comprehensive investigations undertaken to identify the cause (see Figure 1). In this process — which often takes place according to the trial-and-error principle — tools or process parameters are modified, and workpieces are then manufactured. The comparison after the measurement shows whether significant changes have occurred. This process is extremely costly in terms of time and outlay, since tools must be modified and actual production is required. The test results are also always affected by the sum of all influences from the tool and machine tool, which are never ideally error-free. Thus, the influence of a small change in a single parameter frequently cannot be evaluated in practice.
An alternative to this complex process is a simulation of the production process (and the resulting deviations) with computer programs [7, 8]. Compared with production and measurement, the calculations in this case are significantly faster, and error-free tools and error-free machine movements can be assumed. The influence of a small parameter change is clearly detectable if an effect occurs.
Simulation of hobbing and generation grinding
To study the manifold effects and complex interplay between the tool cutting edge and workpiece surface, in particular with multiple-start tools, a software application has been developed that enables simulation of errors during hobbing and generation grinding. The software has been fully introduced , and a description of the basics is presented here. In this software, the tool is represented by the contour of the cutting edge and the position of the blades over the circumference. Tool errors can easily be generated by modifying the position of individual blades. The workpiece is defined by points with an allowance, which the user can freely select as a profile or helix curve or as pitch points.
As illustrated in Figure 3, the kinematics of all movements of the tool and workpiece are represented — up to continuous diagonal shifting. The calculation of deviations is carried out by determining the distance of every measuring point of the workpiece from the blades of the tool in every conceivable position of the movement. The curve resulting from these cutting calculations is treated as a measuring point curve in the further course of calculation. In this way, all possibilities of the comparison of curves or ripple analysis are also available for simulated curves.
In addition to error-free machining, the cutting can be simulated using a defective tool. The lower part in Figure 3 shows the possible tool errors that can be easily generated as well as overlapped by a few mouse clicks. Corresponding to the clamping error in the hobbing or grinding machine, the tool can run wobbling or eccentric. This is described on the reference collar by radial and axial runout deviations. The tool can have a sine-shaped thread lead deviation if the hob or the grinding worm does not run to the reference collars during its manufacturing process; the tool can also have a linear thread lead deviation if a temperature expansion occurs. With multi-start tools, threads can be axially displaced with respect to the first thread. Finally, all results of the measurement of a hob can be downloaded for the simulation. This allows the influences of this specific tool to be estimated in terms of the quality of a workpiece produced with it.
Simulation of influences of the tool and process parameters
Various examples are presented here to demonstrate the influence of process parameters and tool definition. It should be noted that all shown effects are valid for a particular configuration of the workpiece and tool and are certainly not general effects. The extensive data set of this configuration is not included in the paper but can be delivered by the author on request. Figure 4 shows the simulated profile and tooth trace curves with error-free machining. Due to the relatively low number of flutes, a fairly rough profile curve (shown far left in Figure 4) is produced by a three-start tool. The curve next to it shows the simulation result of a ground profile curve with the same parameters. The generating cut deviations disappear due to the continuous form of the grinding worm. The curve further inward shows the results of a two-start cylindrical worm with the same lead. The inner curves show the influence of a decreased axial feed, which also expresses itself in the profile in a shorter shaft length. The example shows overall how easy it is to study influences on the creation of generating cut deviations and feed markings.
The influence of clamping errors of the hob in conjunction with various tool parameters is examined in the next example . The left side in Figure 5 shows the profile of the right and left tooth flank of a gear that was machined with an eccentrically set hob.
If the runout motion is increased at the main bearing and thrust bearing, the periodic deviations also increase. A wobbling hob with runout only at the main bearing generates a smaller deviation with a modified phase relation (see middle part in Figure 5). If the wobble is generated by runout at the thrust bearing, the error pattern changes substantially. A very large deviation curve appears on the left side and disappears almost entirely on the right. The error pattern of the left tooth flank can be explained by the proximity of the machining position to the thrust bearing, but the disappearance of the deviations on the right tooth flank is surprising to many users.
Finally, the right side in Figure 5 shows the deviations that result when a three-start wobbling tool with the same lead and a larger diameter is used for the simulation. Here, the curves exhibit completely different patterns. In summary, this example shows that the effect of the tool clamping error on the workpiece can vary greatly. In practice, problematic workpieces often exhibit similar deviation patterns, which can be attributed in the simulation to a bearing error.
The following example shows the influence of protuberance and the tip rounding radius on the generated workpiece profile. The simulated workpiece profile of the left tooth flank is shown on the left side in Figure 6, alongside the definition of the tool profile. As expected, an addendum modification shifts the profile up (next curve to the right). A decrease in the tip rounding radius generates only a small change in the form of the fillet curve in this configuration. A smaller protuberance value on the tool appears accordingly on the workpiece. On the right side in Figure 6, the curves are superimposed to facilitate comparison of the form of the fillet curve. The example shows how the effect of the tool profile parameters on the workpiece profile can be examined.
The last example describes the ways to carry out a simulation with measured tool deviations. In order to test the assignment of measuring points in the software, a special two-thread hob was made where all flutes except one were reground. The teeth on this one raised flute generate a large negative deviation on the workpiece, which is not reworked by other teeth. The deviations of the hob measurement are shown at the top part in Figure 7 [11, 12]. The results of the measurement of a workpiece produced with the hob, as well as the simulation results, are shown in a side-by-side comparison in the lower part of Figure 7. The curves of all teeth are superimposed and exhibit in alternation the deviations generated by start one and two.
In the center of Figure 7, only the form deviations of the cutting edge profile for the hob measurement were used for the simulation. The deviations caused by the lead disappear, and the transfer of the form deviations at the tip of the hob onto the root area of the workpiece becomes apparent. In summary, this example shows an excellent match between the measurement of manufactured components and the results of simulation using the data from the hob measurement.
Ripple analysis of simulated deviation curves
The simulation results can also be used for further ripple analysis. The top part in Figure 8 shows the ripple analysis spectrum on the right flank obtained for a honed gear from a measurement. During the noise test, this gear exhibited a 37th-order violation of the upper tolerance threshold. The ripple analysis spectrum shows this 37th order alongside many orders. For troubleshooting, an error-free simulation of the workpiece pre-machining was carried out in an initial step by means of hobbing. This error-free simulation spectrum appears in the center of Figure 8. It shows characteristic orders, which can also be found in the spectrum of the honed gear. By changing the parameters accordingly, some of these orders can be assigned to the axial feed and number of flutes.
In a second step, an eccentric hob setting was simulated with runout deviations of 5 μm each at the main bearing and thrust bearing. The resulting spectrum now also shows the 37th order alongside many new orders. The many orders occur as side bands to the mesh orders  obtained from the ratio of the number of workpiece teeth to the number of tool starts, which is equal to 28:3. A simulation with numerous profile curves produces the topography shown on the right side in Figure 8. The deviation pattern is complex and consists accordingly of many periodic deviations that occur at various lead angles along the flank. The sloping line on the topography corresponds to the base helix angle. Tooth contact during generating with the mating gear takes place on lines that are parallel to this one.
The comparison of measurement frequencies and simulation suggests that almost all frequencies of the honed gear occur during the cutting stage. Since the workpiece has been completely reworked during honing, the honing wheel appears to follow the existing ripples. It should be noted that simulation with these small deviations cannot describe the actual resulting workpiece surface. The effects of chip generation and the machine-tool-workpiece vibration system also come into play here. The simulation in this case merely provides evidence of excitations resulting from tool errors, which can thus aid in troubleshooting.
The search for the causes of deviation in quality or noise problems is extremely time-consuming and costly, in particular with the complex processes involved in generating gear production. The use of simulation programs can be helpful in these instances. This article has presented applications for a newly created simulation software program. Alongside error-free machining, the effects of typical tool and clamping errors can be simulated with a high degree of accuracy and easily compared. Examples demonstrate how changes in tool and process parameters affect the gear surface.
The comparison of the simulation results from a measured hob with the deviations of a gear produced with that hob is impressive. Further use of the simulation results for ripple analysis makes it possible to identify excitations in the machining process — and hence the causes of noise problems — by comparing measured and calculated spectra. The examples show that this simulation software is a powerful tool for planning and design as well as troubleshooting and optimization of processes in generation production.
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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 2015 at the AGMA Fall Technical Meeting in Detroit, Michigan. 15FTM12.