From concept to optimized gearbox in just a few steps
©️Chakrit Yenti/ShutterstockGearbox design concepts are similar across all industries. However, gearbox design remains a common challenge. Different tools are often used for different steps of the design process. This means that the same data must be entered several times, which is time consuming and error prone. The FVA-Workbench gearbox design software solves this problem by providing integrated methods for preliminary design, standard calculations, and detailed gear analysis. This makes it possible to reproduce the entire design process.
The typical design process
A typical design process can be divided into the following steps:
Step 1: Determination of the gearbox type, number of stages, and the ratio distribution
Step 2: Preliminary gear design
Step 3: Optimization of the gear geometry and calculation of the load capacity
Step 4: Bearing selection and verification of the bearing lifetime
Step 5: Load capacity calculations for shafts and shaft-hub connections
Step 6: Design and optimization of gear modifications
The FVA-Workbench simplifies each of these steps, enabling a seamless process from conception to an optimized gearbox. This can be demonstrated using the following example of a fan gearbox with a horizontal drive shaft and vertical output shaft, with consideration of the following specifications:
| Nominal fan power | PN,fan | 120 kW |
|---|---|---|
| Input speed | n1 | 1485 1/min |
| Nominal motor torque | TN,mot | 800 Nm |
| Max. starting torque | Tmax,mot | 2.5 x TN,mot |
| Total gear ratio | iges | 15 +/- 0.1 | Application factor | KA | 1.25 | Min. flank safety | SHmin | 1.2 | Min. root safety | SFmin | 1.8 | Bearing life | Lnmh | 100,000 h |
Table 1: Example of a fan gearbox
Step 1: Gearbox type, number of stages, and ratio distribution
Due to the 90° angle of the fan shaft to the motor, a helical-bevel gearbox is selected for the basic gear design. For gearbox types consisting of a combination of cylindrical, planetary, and bevel gear stages, the FVA-Workbench offers a pre-design tool in which only the load data and the desired total gear ratio must be specified (see Figure 1). The number of stages and the distribution of the ratios to the individual stages are determined based on FVA Research Project 421 [1] and the Römhild dissertation [2] to minimize the overall weight of the gears. Consideration of the weight development is also useful for stationary gears, as the weight not only determines the material costs but also serves as an indicator for the subsequent maintenance costs.
Figure 1: The FVA-Workbench pre-design tool
Figure 2 compares the estimated weights of the gears for preliminary designs of the fan gearbox with one, two, and three gear stages.
Figure 2: Weight development of a fan gearbox with an overall ratio of i=15
It can be seen that the single-stage variant is significantly heavier than the other two designs. This is due to the very large diameter of the output gear needed to achieve the overall transmission ratio, which determines the overall weight. In the two-stage variant, on the other hand, the output gear can be considerably smaller, as the ratio can be distributed to two stages. This weight reduction has a greater effect than the weight of the two additional gears. With the three-stage variant, the total weight increases slightly, as the reduced diameter of the drive gear no longer sufficiently compensates for the weight of the additional gears.
Step 2: Preliminary gear design
Figure 3: Model created by the pre-design tool with additional details
Following the determination of the number of stages and the ratio distribution, the macrogeometry of the individual stages (module, number of teeth, addendum modification, etc.) are also determined in the pre-design tool. The geometries are determined such that the specified minimum safeties are achieved. ISO 6336 (2019) is used as the calculation method for the cylindrical gear stages and ISO 10300 (2014) is used for the bevel gear stages. The proposed values can also be modified in the tool. This data is then used to create an FVA-Workbench model of the gear unit which is fully configured for a deformation calculation of the entire system, including the subsequent load capacity calculation of the gear stages. This makes it possible to create a complete gearbox calculation model that can reliably transmit the required power within a few minutes.
Step 3: Optimization of the gear geometry and calculation of the load capacity
Automated variational calculations can be performed for further optimization of the geometry of the cylindrical stage in the FVA-Workbench model. To do so, the normal pressure angle, helix angle, addendum modification, and tooth depths for the cylindrical stage of the pre-dimensioned gearbox are varied while the center distance is assumed to be constant. The results can be displayed and compared according to various criteria (here: contact ratio εγ, maximum transferrable power Pmax, gear efficiency ηZP, and weight m). In this example, approximately 2700 geometric variations were simulated and compared in approximately two minutes:
Figure 4: Parallel plot of the gear variants, sorted by maximum transferrable power
These calculations produce several geometric variants within the specified parameter range that achieve an increase to the maximum transferrable power according to ISO 6336 by up to 1.4x compared to the initial variant from the preliminary design. In Figure 4, the variants are sorted according to the maximum transferrable power, with the color gradient from red to blue corresponding to a decrease in power. Here, it can be observed that the contact ratio has a positive influence on the transferrable power while the efficiency decreases, which corresponds to the theoretical considerations. The FVA-Workbench variation tool makes it easy to identify the optimum variant or variants that represent a compromise between multiple target criteria and transfer them to the FVA-Workbench model.
Step 4: Bearing selection and verification of the bearing lifetime
The next step in the gearbox design process is typically the selection and verification of the gearbox bearings. In the FVA-Workbench, bearings can be imported directly from the SKF, Schaeffler, and Timken EDP catalogs. In this example, the lifetime is verified using the modified lifetime according to ISO 281. Tapered roller bearings were selected for all positions. The size of the bearings was increased until the required minimum lifetime of 100,000 h was achieved. The shaft contours were adapted accordingly. Figure 5 shows the overview of the bearing lifetimes in the FVA-Workbench report.
Figure 5: Overview of bearing lifetimes
Step 5: Load capacity calculations for shafts and shaft-hub connections
Verification of the load capacity of the shafts and shaft-hub connections is also required in addition to the bearing lifetimes. In the FVA-Workbench, this can be performed according to DIN 743 and the FKM Guidelines. Figure 6 shows the overview diagram for the shaft safeties of the intermediate shaft according to DIN 743 based on the specified notch geometries.
Figure 6: Intermediate shaft safety according to DIN 743
The notch effect can also be determined using automated mesh generation and FE calculations, especially for overlaid notches and notches on inner diameters. The critical location of the pinion cutter outlet of the intermediate shaft was meshed in this model (see Figure 7).
In addition to shaft safeties, the FVA-Workbench can also calculate the load capacity of shaft-hub connections, as shown in Figure 8 using the example of a feather key connection.
Figure 7: Automated mesh generation at the pinion cutter outlet of the intermediate shaft
Figure 8: Load capacity of the feather key connection between the output gear and the output shaft
Step 6: Design and optimization of gear modifications
Figure 9: Chipping due to local overloads in the meshing area of the tip edge of the mating gear
Practice-oriented design of the relevant microgeometries is required to make targeted use of the load capacity reserves of cylindrical and bevel gears required in standard calculations. To do so, the deformations of the gear system must be known. This is determined by default in the FVA-Workbench, and modifications are proposed which lead to uniform loading of the flanks. At the same time, modifications can be used to minimize the noise excitation. The required methods and results for this are also available in the FVA-Workbench. As the high inertia of the fan wheel typically leads to very high starting torques in fan gearboxes, this operating condition must also be considered in the design of the microgeometry.
Figure 9 shows chipping on a pinion tooth of a fan gearbox that has developed as a result of a local overload in the meshing area of the tip edge of the mating gear. In this case, the local overload can be attributed to excess torques during start-up. Figure 10 shows an example of the pressure distributions of the cylindrical stage of the gearbox with consideration of an optimized flank modification for the nominal fan torque and the specified start-up torque.
It can be seen that very high load peaks which greatly exceed the static strength of the material occur in the meshing area during start-up, which can explain damage such as the chipping shown in Figure 9. With the FVA-Workbench, a microgeometry can be designed for these cases which ensures that the flank stress is adequately limited for both operating states (see Figure 11).
Figure 10: Pressure distribution of the cylindrical stage with optimized microgeometry for nominal fan torque
Figure 11: Pressure distribution of the cylindrical stage with microgeometry optimized for both operating states
As with cylindrical stages, the FVA-Workbench can also calculate the local loads of bevel gear stages. The pre-designed gear geometry according to ISO 23509 can be further detailed with extensions from FVA 223 XIII, with consideration of a selected production process and the option to specify gear modifications. The settings data for the bevel gear cutting machine can also be output as an additional result of this process. This data can then be directly imported and processed in all standard calculation tools from machine manufacturers, such as KIMOS from Klingelnberg [4]. The comparison of the local pressure distributions of the bevel gear stage of the fan gearbox in Figure 12 shows that a microgeometry can also be defined that yields a suitable flank load for both the nominal and start-up conditions
Figure 12: Pressure distribution of the bevel gear stage with optimized microgeometry
Conclusion
The FVA-Workbench is a powerful tool for preliminary gear design, which makes it possible to create and optimize gearbox models within a few minutes. The predefined safety factors and mass optimizations ensure the development of reliable, cost-effective gearboxes.
The variation is a simple and useful tool for detailed optimization of the gear geometry in which precise target values can be defined. The high-performance calculations ensure that the results are available immediately.
The innovative and reliable calculation methods in the FVA-Workbench make it possible to simulate critical stresses before damage occurs. This leads to increased customer product satisfaction and reduces the need for a high number of test bench runs.
References
[1] Bansemir, G. FVA-Getriebeauslegungsprogramm GAP Benutzeranleitung. s.l.: FVA-Heft 890, 2009.
[2] Römhild, I. Design of Multistage Cylindrical Gearboxes – Ratio Distribution for Minimal Mass and Selection of Addendum Modifications Based on New Calculation Principles. Dresden: Dissertation, 2007.
[3] Sigg, AGMA Paper 109.16, October 1965
[4] KIMOS
Author
Dr.-Ing. Ferdinand Wikidal
GearConsult
The expert worked for six years at the Gear Research Center (FZG) at the Technical University of Munich, where he further developed the FVA's RIKOR calculation program and completed his doctorate on flank pressure at cylindrical gears . He has been involved in the further development of the FVA-Workbench since 2008. Prior to this, he was Technical Manager for extruder gearboxes at A. Friedr. Flender AG and gained experience as a damage assessor at the Allianz Center for Technology (AZT), specializing in gearboxes, rolling bearings and drive trains for wind turbines. He has been working as a freelance expert for gearbox and rolling bearing damage since 2008.