2.1. Noise Source Localization

To identify the origin of the thumping noise, a fault tree analysis (FTA) was conducted on the entire vehicle. By sequentially removing the transmission and torque converter, it was observed that the noise intensity diminished but did not cease entirely. Further analysis revealed that after transmission removal, the overall modal characteristics of the engine and transmission changed, disrupting the resonance frequency. After removing only the torque converter, the noise persisted at a lower level, confirming the transmission was not the source. Subsequently, an engine swap test was performed on the complete vehicle: the knocking sound disappeared after the replacement engine was installed, and reinstalling the original engine caused the sound to reappear. This confirmed that the knocking noise originated from the engine assembly (ABA validation).

2.2. Key Frequency Band Analysis

During motoring testing (engine running without ignition) on the engine test bench, a characteristic noise (6 times per second) was consistently detected, ruling out combustion noise as the primary factor. Further testing at idle speed with an additional 50 N·m torque applied verified the load’s impact on mechanical meshing characteristics. The noise knocking intensity significantly increased, indicating that increased load exacerbates impact vibration in moving components [14].

Analysis of near-field noise measurements revealed that noise energy was concentrated in the 200–300 Hz frequency band, with a stable knocking frequency of 6 times per second. This frequency closely matches the engine’s half-order operating frequency of 6.25 Hz. Preliminary suspicion points to a modulation effect caused by periodic excitation in the 200–300 Hz band interacting with the 6.25 Hz frequency, leading to periodic amplification of noise intensity [15].

2.3. Part Inspection and Positioning

The simplified diagram of this engine’s transmission mechanism is shown in Figure 2. Based on the preceding analysis, we first investigated components operating at the 6.25 Hz half-order frequency. Analysis of the collected noise revealed intermittent vibrations at 270 Hz in the vacuum pump body, occurring six times per second. This frequency is close to the half-order of 6.25 Hz. Furthermore, the vacuum pump has a speed ratio of 0.5 and an order of 0.5, matching the order of the abnormal noise. Verification on the entire vehicle showed that the noise persisted even after removing the vacuum pump, indicating its minor contribution to the noise.

Figure 2. Schematic Diagram of the Internal Transmission Mechanism of the Engine.

Subsequently, based on the engine transmission mechanism schematic, components operating at half-order frequencies were systematically investigated according to internal order sequence (e.g., single-cylinder piston, high-pressure fuel pump, valves, intake camshaft, exhaust camshaft, as listed in Table 1). None of these components produced noticeable noise improvement. The investigation focus was ultimately shifted to components operating in the 200–300 Hz range.

The oil pump sprocket operates at a 24th-order mode. At engine idle, its operating frequency is 300 Hz, overlapping with the characteristic noise frequency band (200–300 Hz). To verify the sprocket’s impact on noise, a cross-replacement test was designed: installing the same oil pump from a vehicle without abnormal noise significantly reduced the thumping sound. Upon reinstalling the original oil pump, the noise intensity returned to its initial state. Preliminary analysis identified the oil pump sprocket as the primary noise source. Subsequently, the oil pump from another vehicle exhibiting a pronounced knocking noise was transplanted into the test vehicle. The knocking noise intensity became more pronounced than in the original vehicle, definitively confirming the oil pump sprocket as the core source of this noise [16]. As shown in Figure 3, the spectrogram of abnormal parts shows significant energy at 300 Hz compared to normal parts.

Figure 3. Spectrogram of Normal Parts vs. Abnormal Parts (Abnormal parts show significant energy at 300 Hz).

2.4. Differential Analysis of Abnormal-Sounding Components

Comparing the dimensions and performance of abnormal-sounding components with normal oil pump components revealed significant differences in the tooth flank chamfer dimensions of the sprockets (as shown in Figure 4). The specific findings are as follows (as shown in Table 2):

(1) Tooth Flank Chamfer Dimension: The measured chamfer dimension on abnormal parts was 0.58 mm, while all normal parts measured above 0.66 mm (including 1 normal part without abnormal noise and 5 production-inspected parts). The drawing specification requires 0.7 ± 0.2 mm, indicating that the abnormal parts’ actual measurement falls below the lower limit.

(2) Synchronous comparison with counterpart design specifications reveals that the counterpart crankshaft sprocket tooth flank chamfer design requirement is 0.8 ± 0.2 mm. The abnormal-sounding parts exceed this design requirement.

Analysis of measured data and technical design requirements indicates that the tooth flank chamfer dimension of the oil pump sprocket is a critical factor in the knocking noise. Theoretical calculations and finite element simulation analysis were first conducted to systematically investigate the influence mechanism of this chamfer dimension on the knocking noise [17].

Figure 4. Finite Element Simulation.

3.1. Impact Force Model Based on Hertzian Contact Theory

The meshing process between sprockets and chains can be simplified as an elastic contact problem. According to Hertz’s contact theory, the relationship between the contact stress amplitude and the contact curvature radius is:

In the equation, σ_max denotes the contact stress amplitude, F represents the impact force, a is the contact area, R is the contact curvature radius, and E* is the equivalent elastic modulus.

Reducing the chamfer dimension, such as from 0.66 to 0.58, leads to a decrease in the contact curvature radius R and a reduction in the contact area a, resulting in an increase in the maximum contact stress. Finite element simulations conducted with relevant sprocket and chain parameters revealed that the peak contact stress reached 160 MPa when the chamfer was 0.58, decreased to 139 MPa at 0.66, and achieved the lowest value of 122 MPa at 0.8 (as shown in Figure 4) [18].

3.2. Impact Energy and Vibration Excitation

The Fourier transform of the time-domain signal F(t) for the meshing impact force is:

(1) The impact force pulse of the 0.58 chamfered specimen exhibits a narrow pulse width and high amplitude, with its spectrum showing concentrated energy at 300 Hz (Figure 5a);

(2) The impact energy of the 0.66 chamfered specimen spreads toward lower frequencies, with the 300 Hz component attenuating (Figure 5b).

Figure 5. (a) Time-Domain Impact Force Waveform and (b) Normalized Sound Pressure Spectrum

Resonance Frequency Response Analysis

When the meshing impact frequency f = 24 × 750/6 = 300 Hz couples with the crankshaft’s half-order rotational excitation (6.25 Hz), the system resonates. The impact energy of the 0.58 chamfered sample is amplified in the 300 Hz frequency band, with NVH testing showing a sound pressure level reaching 65 dB. For the 0.66 chamfered sample, energy attenuation reduces the 300 Hz sound pressure level to 47 dB. Key dimensional parameters of the input sprocket and chain were analyzed via MATLAB simulation. Results indicate that a tooth flank chamfer of 0.80 achieves the lowest 300 Hz sound pressure level at 43 dB, as shown in Figure 6 [19].

Figure 6. Comparison of Sound Pressure Levels for Different Chamfer Sizes.

5.1. Verification of Sprocket Tooth Flank Chamfer Dimensions

To further validate the accuracy of the aforementioned theoretical analysis, six sets of samples were prepared by grouping according to chamfer dimensions (lower limit 0.5 mm, median 0.7 mm, upper limit 0.9 mm) for in-vehicle testing (as shown in Table 3). Results indicate: Specimens with the lower limit (0.5 mm) exhibited higher noise intensity accompanied by pronounced knocking sounds; specimens with the mid-range value (0.7 mm) showed significantly reduced noise intensity and were evaluated as acceptable by the NVH specialist team; specimens with the upper limit (0.9 mm) demonstrated markedly lower noise intensity than the mid-range specimens, with abnormal noise characteristics eliminated and performance exceeding design requirements.

5.2. Small-Batch Trial Assembly Verification

Based on the optimized solution, sprockets with adjusted tooth flank chamfer dimensions to 0.8 ± 0.1 mm (balancing machinability and noise reduction requirements) underwent small-batch trial assembly (50 units total). Testing and evaluation by the NVH team confirmed that the trial samples exhibited no noticeable knocking sounds, with significantly reduced noise compared to the original vehicle state, validating the engineering effectiveness of the dimensional optimization [20].

Tooth Profile Chamfer Tolerance Optimization

The original design of 0.7 ± 0.2 mm posed a risk of reaching the lower limit. Engineering optimization adjusted it to 0.8 ± 0.1 mm. Monte Carlo simulation validation confirmed that the optimized tolerance reduces NVH failure rate from 15% to 0.1%.