Recent tests were conducted to calculate the sensitivity of a model gear set to both macro and micro error in noise vibration harshness.

The use of planetary gear types is increasing because they can be smaller, lighter, and offer a high-reduction ratio. In generally, a reduction of up to 40 percent in size and a 50 percent weight reduction can be achieved. As the demand for quieter gear sets increases, the number of hard-finished gears grows as well.

In planetary gear sets, the ring gear is the last frontier for hard finishing to satisfy NVH (noise vibration harshness) requirements. Many applications now include pinions and sun gears that have been hard finished to a high quality. However, most internal ring gears are not hard finished, which presents an opportunity for improvement.

A simulation was recently conducted by Nidec Machine Tool Corporation of Ritto, Japan, in collaboration with FEV of Aachen, Germany, to estimate the sensitivity of a model gear set to both macro and micro error in NVH behavior. In parallel, another test was undertaken using bench testing of hard-skived gears, which revealed a sensitivity to process variables such as infeed in NVH excitation. This portion of the testing is beyond the scope of this article. Interested readers are invited to contact the authors for more information.

The NVH CAE (computer aided engineering) simulation of planetary EDU (electric drive unit) transmission compared the nominal vs. conventional (no hard finishing) vs. generatively ground internal gears. This concept planetary transmission for EDU of passenger EVs was used to evaluate the effect of a hard-finished ring gear. This can carry 240Nm, 125kW as input on the sun gear and output from a carrier by reduction ratio 3.7. This is simple but enough to evaluate the impact of ring-gear excitation to transmission NVH behavior. The subject model is shown in Figure 1.

Figure 1

The basic kinematics of the internal generating method are shown in Figure 2.

Figure 2

The process is capable of producing an internal gear of ISO 3-5 quality with surface finish of <Ra 0.3 and <Rz 2.0. As will be shown, this process can positively reduce pitch error, which will be shown to be a dominant influence in NVH. Figure 3 depicts an achievable reduction in Fp after generative grinding of the internal gear.

Figure 3

The simulation project was designed to model the influence of micro geometry and macro geometry to minimize excitation force. The modifications possible using internal generative grinding were used. Conventionally manufactured (without hard finishing) internal gears cannot be optimized for microgeometry. However, the internal generative grinding process can be optimized for the desired tooth contact, which can lead to a reduction in excitation force and potentially longer life. Figure 4 shows the contact pattern model and the microgeometry modifications used in the simulation.

Figure 4

The simulation was carried out in two parts: process analysis and sensitivity analysis. Process analysis was designed to investigate the influence of different manufacturing processes, in this case, with grinding and conventional process without hard finishing.

The sensitivity analysis was undertaken to understand which parameter has the biggest leverage on improving NVH behavior. See Figure 5.

Figure 5

Figure 6

Two steps were carried out for each simulation: Step 1 is a torque sweep to evaluate P2P system transmission error as system excitation. Step 2 is a speed sweep to evaluate surface acceleration as system response. This is shown in Figure 6.

Simulation 1 – Process Analysis

Setup 1 is an ideal gear with zero manufacturing errors. Setup 2 is internal generating grinding tolerance ISO3 to 5, and Setup 3 is a conventional process without hard finishing. Figure 7 shows the ring-gear parameter set up by the different processes.

Figure 7

Simulation Results – Torque Sweep

The results of the torque sweep are shown in Figure 8. The horizontal axis is input torque from 10 percent to 100 percent, and vertical axis is the P2P (peak to peak) system transmission error.

Figure 8

The black line is the ideal gear without manufacturing deviation; the red surface shows the ground gear, and the gray surface shows conventional gears without hard finishing.

The simulation shows that P2P system transmission error, which is an index of excitation, can theoretically be reduced by approximately 70 percent.

Simulation Results – Speed Sweep

The observation point is Location 1 at the upper surface of ring gear housing, which is sensitive to ring-planet excitation.

Acceleration was measured by m/s2 and converted to acceleration level dB by the equation shown and plotted on the graph.

The black line depicts the ideal gear; red is the ground gear, and gray is the conventional gear without hard finishing.

The results of the simulation show a theoretical reduction of noise by grinding compared to the conventional gear. At almost all speeds, there is a reduction in noise: minus-10dB as average, minus-22dB as maximum. Figure 9 shows the results of the speed sweep simulation.

Figure 9

Simulation 2 – Sensitivity Analysis

A series of torque sweeps were simulated to model the sensitivity to micro and macro variations: pitch (Fp), runout (Fr), and the various profile and helix parameters.

The graph in Figure 10 shows the influence of each parameter on transmission error. It can be seen that pitch and runout are the biggest influence to system excitation.

Figure 10
Figure 11

The system response was evaluated, and the influence of pitch and runout were analyzed. It can be seen that pitch and runout increase the housing acceleration level individually.

As a result of this sensitivity analysis, it can be concluded that the reduction of pitch and runout have a positive effect to improve system response vibration and, therefore, reduce NVH in internal gears. Figure 11 shows the results of the sensitivity analysis.


Planetary gear sets are the key components to achieve high reduction ratio with light weight.

The internal ring gear manufacturing process is the last challenge to satisfy high quality at reasonable cost for an improved level of NVH performance.

The simulation of EDU transmission shows internal generating grinding can reduce transmission error 70 percent and housing acceleration 24dB (1/10). Major factors of this improvement are reduction of pitch and runout error.

ISO3 to 5 class quality including pitch and run out can be achieved positively without influence of heat-treatment distortion, leading to reduced noise and vibration of transmissions.

Various tooth modifications can increase design optimization to minimize excitation force. 

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Noritaki Fujimura, P.E. is the engineering manager in charge of Europe for Nidec Machine Tool Corporation. He leads Nidec’s research and development of skiving, high speed hobbing, and internal gear grinding.
Dwight Smith is vice president of Nidec Machine Tool America and has more than 30 years in the gear manufacturing industry, including metrology, analysis, and project management. Smith also serves as a committee chairman for AGMA and is an instructor for the AGMA Basic Gear School.