By Subhash Jadhave (Application Engineer) and Pradeep Deshmane (Principal Engineer), Portescap
Although gearboxes are a well-understood technology, they don’t always operate as designed. For example, many different manufacturing and assembly factors, vibrations from the gears, and various running conditions can produce noise and transmission errors. These errors typically occur because the gears cannot operate at a standard centered distance within their predetermined tolerances. To provide a framework for creating a more optimal gearbox design, we recently simulated how center distance variation influences noise.
Simulation Methodology
Our simulation uses a compound gearbox with three spur gear pairs mounted on respective shafts that are supported by ball bearings connected to the housing. The simulation illustrates the center distance variation by displacing the housing bore connected to bearings. This, in turn, results in shaft misalignments, which were captured as TE and noise amplitude. The gearbox setup is shown in Figure 1.
Gearbox layout and gearbox cut section.
Because the housing bore position can vary during manufacturing, we defined three conditions:
- A tolerance of 30, 60, and 80 microns as the displacement.
- The bearings, which are manifested in shaft misalignment.
- TE and noise.
In addition, we defined and analyzed:
- No load condition.
- Load condition — 0.5-Nm torque.
We considered an input shaft speed range of 0 to 5,200 rpm and analyzed the first, second, and third harmonics of the gear mesh covering the maximum frequency of 4,000 Hz. The study revealed that the third gear mesh exhibits a higher TE than the other two gear meshes. The remainder of this article will focus on the third gear mesh pair in the layout and explain the significance of TE harmonics and its impact on acoustic behavior.
Misalignment Considerations and Center Distance Variation
There are two ways to consider the misalignment of the shaft: out of parallel, where the output gear is displaced in the skew direction from the mating gear; and skew condition, where the output gear is displaced in the skew direction from the mating gear. In this simulation, the skew position is selected because the noise levels are more sensitive than those of the out-of-parallel condition. For reference, Figure 2 shows the out-of-parallel shaft arrangement.
Figure 2. Shaft misalignment is skew condition and out-of-parallel condition.
When the 30-, 60-, and 80-micron radial displacement was applied for the outer race of the rear bearing and for the front bearing, the shaft was displaced away from the original shaft position in the gearbox in an outward direction in the skew plane. In the skew condition, the bearings are displaced in the -X and +Y directions along the resultant vector with the output gear displaced in the skew direction from the mating gear. In the out-of-parallel condition, the bearings are displaced in the +X and +Y directions along the resultant vector, with the output gear displaced away from the mating gear. The preload condition and the procedure for the rear bearing are shown in Figure 3.
Shaft misalignment is a critical factor in demonstrating the importance of how the change in center distance impacts the TE and noise. Accordingly, displacements of bearings supporting shafts are used in the simulation.
Misalignment Variation Simulation Results
The front and rear bearings were displaced in the X and Y directions, and the shaft misalignment in skew position was used. The no-load condition has lower TE when the front bearing is displaced in the X and Y directions versus the rear bearing. We allowed displacement tolerances of 30, 60, and 80 microns. When we analyzed the skew positions, the peak-to-peak TE for X-80 and Y+80 microns was higher than the skew positions of X-30, Y+30 microns, and X-60, Y+60 microns. The simulation results are provided in Table 1.
| Torque | Misalignment Condition-CW-Output gear pair | Misalignment value | TE 1st Harmonics (Micron) | TE 2nd Harmonics (Micron) | TE 3rd Harmonics (Micron) | Peak to peak (Micron) |
| No load | Skew -brg 5 | No Misalignment | 0.09 | 0.02 | 0.03 | 0.14 |
| X-30 Micron, Y+30 micron | 0.32 | 0.06 | 0.10 | 0.54 | ||
| X-60 Micron, Y+60 micron | 0.44 | 0.08 | 0.13 | 0.73 | ||
| X-80 Micron, Y+80 micron | 0.49 | 0.09 | 0.15 | 0.82 | ||
| No load | Skew -brg 6 | No Misalignment | 0.09 | 0.02 | 0.03 | 0.14 |
| X-30 Micron, Y+30 micron | 0.33 | 0.06 | 0.10 | 0.55 | ||
| X-60 Micron, Y+60 micron | 0.44 | 0.08 | 0.13 | 0.73 | ||
| X-80 Micron, Y+80 micron | 0.50 | 0.09 | 0.15 | 0.82 |
Table 1. TE results for no-load condition.
The TE results are provided in Table 2 for a load condition with 0.5-Nm torque. The TE results for the displacement of the front bearing are higher than those of the rear bearing.
| Torque | Misalignment Condition-CW-Output gear pair | Misalignment value | TE 1st Harmonics (Micron) | TE 2nd Harmonics (Micron) | TE 3rd Harmonics (Micron) | Peak to peak (Micron) |
| 0.4 Nm | Skew -brg 5 | No Misalignment | 0.32 | 0.06 | 0.10 | 0.54 |
| X-30 Micron, Y+30 micron | 0.63 | 0.11 | 0.19 | 1.04 | ||
| X-60 Micron, Y+60 micron | 0.85 | 0.16 | 0.25 | 1.42 | ||
| X-80 Micron, Y+80 micron | 0.96 | 0.18 | 0.29 | 1.59 | ||
| 0.4 Nm | Skew -brg 6 | No Misalignment | 0.32 | 0.06 | 0.10 | 0.54 |
| X-30 Micron, Y+30 micron | 0.64 | 0.12 | 0.19 | 1.06 | ||
| X-60 Micron, Y+60 micron | 0.86 | 0.16 | 0.26 | 1.43 | ||
| X-80 Micron, Y+80 micron | 0.97 | 0.18 | 0.29 | 1.61 |
Table 2. TE results for load condition.
Acoustic Analysis
As part of the acoustic analysis, we used a shrink-wrap mesh to link the structural vibration domain and the acoustic domain. The mesh is watertight, and it completely and closely encloses the structural mesh of the component being analyzed. Because the shrink-wrap mesh affects the quality of the radiated noise predictions, it had to be in excellent condition.
We placed a response node on the surface of the gearbox housing. The noise at the surface location and the vibrations at this node are captured by a microphone located 1 meter from the gearbox surface. The higher TE of the third gear pair with misalignment is factored into the simulation.
The acoustic results cover the first to third harmonic of the third gear pair, which corresponds to excitations of the first order as 2.3, the second order as 4.6, and the third order as 6.9 at various motor shaft speeds (rpm) frequencies (Hz) and sound pressure levels. The violet lines represent the response frequency (Hz) respective to the orders.
Figure 4. No misalignment, with a maximum noise value of 38 dBa.
Figure 5. Rear bearing with skew x-30, y+30 microns, and maximum noise value of 50 dBa.
Figure 6. Rear bearing with skew x-60, y+60 microns, and maximum noise value of +50 dBa.
Figure 7 – Brg 6 with (skew x-80, y+80): +52 dBA.
Here is what we observed for the rear bearing under different conditions:
- No misalignment, with a maximum noise value of 38 dBA. Normal conditions.
- With a skew of X-30, Y+30 microns, and a maximum noise value of 50 dBA: As compared to nominal conditions, the displaced condition resulted in higher deflection in the shaft and the housing due to higher TE and noise levels. The maximum noise amplitude was observed at 3,200 rpm.
- With a skew of X-60, Y+60 microns, and a noise value of +50 dBA: Similar results were found at 60 microns as were found at 30 microns, which includes no load and no misalignment where there are nominal conditions.
- With a skew of X-80, Y+80 microns and a noise value of +52 dBA: Similar results were found at 80 microns and at 30 and 60 microns.
- The displacement applied for bearings and the impact of shaft deflections on noise are provided in Figures 6 and 7.
System Level Deflection
The acoustic analysis demonstrates that shaft misalignment can influence noise predictions; some frequencies and a particular speed range may have yielded higher noise levels. Similarly, system-level static deflection —based on the boundary condition — is also a reliable indicator of the overall system deflection, especially when defined torque is applied to the system. System-level static deflection also gives specific findings about the localized deflection of the system based on how the gearbox is mounted in the device. This helps to check the maximum level of deflections the system has at maximum load and whether any improvements are needed to control deflections, such as by altering the mountings on the gearbox, material combinations, or the application’s load conditions. For example, Figure 8 shows the deflection in the gearbox at the system level when 0.5-Nm torque is applied with a displacement of x-30 and y+30 microns for the rear bearing. The maximum deflection is approximately 68 micons, which is somewhat high. Increasing the stiffness in this area may help reduce the deflection.
Figure 8. Rear bearing when 0.5 Nm torque is applied with a displacement of x-30 and y+30 microns.
Portescap
www.portescap.com
Filed Under: Gears • gearheads • speed reducers