Overhead Crane Reducer Noise: Gear Eccentricity Analysis and Solutions

Overhead crane reducer noise may occur during lifting and material handling in workshops, affecting normal crane operation. This article analyzes abnormal noise from the perspective of gear pair eccentricity error. Based on structural noise calculation results from simulation analysis, it also gives corresponding solutions as a reference for improving εναέριος γερανός operating performance.

1 Gear Excitation Analysis Under Eccentricity Error

The overhead crane analyzed in this article is an LD10 t-28.5 m model, equipped with a 13 kW three-phase asynchronous motor. The reducer uses a four-stage parallel-shaft helical gear transmission. When eccentricity error is considered, the analysis first starts from a single gear pair and its meshing line length.

1.1 Gear Pair Model

When gear eccentricity is considered, the eccentricity of the driving and driven gears is used as the starting point. Based on the known number of gear teeth and driving gear speed, the time-frequency characteristic curve of the driven gear speed can be obtained and compared with the result under the no-eccentricity assumption. The eccentric gear pair model is shown in Figure 1.

O1 και O2 are the geometric centers of the gear pair under the no-eccentricity assumption. After eccentricities E1 και E2 occur, the gear geometric centers become O11 και O22. It can be seen that, regardless of the eccentricity value, the meshing line formed by connecting tangent points T1(xT1, yT1) και T2(xT2, yT2) always has a dynamic intersection point M(xM, yM) with the line connecting the gear geometric centers.

Considering the offset, the gear pair meshing line has time-varying characteristics. Its equation can be expressed as:

When the coordinate origin is placed at point O11, the dynamic transverse coordinate of point Μ can be expressed as:

The instantaneous transmission ratio of the gear pair is:

In actual calculation, the dynamic intersection point Μ has a certain relationship with the meshing line, the angle between the motion direction, and the instantaneous meshing line speed of the gear. After the eccentricity range and input angular velocity are determined, formulas (1) to (3) can be used to obtain the driven gear angular velocity and further calculate the dynamic excitation of the gear pair under eccentricity error.

In actual manufacturing, eccentricities E1 και E2 can be approximately taken as the same. With a helical gear pair eccentricity of 20 μm under the known accuracy grade, the calculated time-frequency characteristic curve of the driven gear is shown in Figure 2.

When no eccentricity error is assumed, the driven gear angular velocity is represented by the pink straight line in Figure 2a. When eccentricity error exists, the driven gear angular velocity shows obvious and regular fluctuation, concentrated in the range of 40.5-41.5 rad/s. The frequency-domain result after Fourier transform reflects the input shaft rotational frequency of 25 Hz and the driven gear output rotational frequency of 6.5 Hz. This indicates that the eccentricity fluctuation of the input-stage gear pair may continue to transfer through the gear system and radiate to the outside of the gearbox.

2 Numerical Calculation of Gear Excitation in Overhead Crane Reducer Noise

2.1 Vibration Differential Equation

The vibration differential equation of the gear system in an overhead crane reducer is an important basis for studying its dynamic characteristics. By reducing the order and calculating the dynamic meshing force of the gear, vibration characteristics such as vibration intensity and structural noise can be numerically simulated. The required second-order differential equation is:

The time equation of dynamic coordinate Μ is substituted into θ, and the Runge-Kutta order-reduction principle is used to solve the dynamic meshing force of the high-speed gear pair. Figure 3 shows the meshing force calculation results for the input stage and the final output stage.

2.2 Vibration Analysis Results

Figure 4 shows the reducer structure. The bearing seat positions at the input and output ends are selected for calculation, and the frequency-domain vibration characteristic curves under 20 μm eccentricity error are obtained.

As shown in Figure 5, after eccentricity error is considered, the input shaft rotational frequency of 25 Hz affects other gear pairs at different stages, especially in the displacement curve. Noise calculation based on the vibration results can then show the influence of eccentricity error on abnormal reducer noise.

3 Radiated Noise Prediction for Bogie Axle Bridge

3.1 Acoustic Model

According to the cited references, acoustics belongs to the field of fluid research. Therefore, the acoustic wave equation can be studied from the fluid continuity equation. In terms of medium state, it can be expressed as:

In the formula, ρ, v, p, και μικρό are the density, velocity, sound pressure, and entropy of air, while φά και q are external excitation sources of the air medium.

Based on the vibration response of the overhead crane reducer, the acceleration calculation result is processed by Fourier transform and one-third octave processing. The structural noise calculation result of the high-speed-stage bearing seat of the reducer is shown in Figure 6.

When eccentricity error is considered, the structural noise of the reducer increases more clearly in the low-frequency range of 0-100 Hz. According to acoustic theory, a 6 dB difference represents a one-time difference in energy level. In Figure 6, the noise difference in some frequency bands reaches about three times, showing that eccentricity error has a major influence on low-frequency vibration of the reducer. Clear peaks also appear at 500 Hz and 1,000 Hz, which are caused by the gear meshing frequency of the input stage.

3.2 Measures to Reduce Abnormal Noise

The 20 μm eccentricity used in the calculation is selected according to the gear transmission accuracy grade. In actual operation, larger eccentricity error may exist and may greatly affect reducer vibration and noise reduction. Based on the analysis and conclusions in this article, abnormal noise can be reduced from the following aspects:

1. Improve the selection of gear transmission accuracy grade. Many overhead cranes use grade 8 generated helical gears. Ordinary crane reducers do not consider subsequent precision finishing, so eccentricity error may lead to higher radiated noise. If quenching and gear grinding, tooth surface lapping, or similar treatment is considered in the final finishing stage, grade 7 or grade 6 accuracy may be achieved. This can be a better option for workshops with stricter noise control requirements.

2. Optimize the gear transmission system. From the transmission system perspective, constraints such as closed gear contact fatigue strength, transmission ratio, and face width coefficient should be considered. A genetic algorithm may be used to slightly adjust gear module, tooth width, and driving gear tooth number without significantly changing these constraints, so that the noise transmission frequency of the reducer is kept away from the range sensitive to human hearing. The specific method needs corresponding programs and tests to verify the optimal gear parameters.

3. Optimize the reducer housing structure. The main purpose of housing optimization is to improve its natural frequency. The first ten natural frequencies of a multi-stage parallel-shaft transmission system are generally low, usually in the range of 50-500 Hz, and can easily overlap with the driving gear rotational frequency and its harmonics, causing resonance. Based on the reducer structure, material can be removed from certain positions. This not only saves material cost, but also may increase the natural frequency of the reducer and effectively reduce abnormal noise caused by eccentricity error.

4 Conclusion

This article takes an overhead crane and its reducer as the research object and analyzes the influence of gear pair eccentricity error on abnormal reducer noise. The conclusions are as follows:

1. When eccentricity error is considered, the driven gear angular velocity shows regular fluctuation. The fluctuation range is concentrated within 40.5-41.5 rad/s. It reflects the input shaft rotational frequency of 25 Hz and the driven gear output rotational frequency of 6.5 Hz, and it continues to affect subsequent gear pair transmission.

2. Under eccentricity error, the structural noise of the reducer increases more clearly in the low-frequency range of 0-100 Hz. The maximum difference reaches 15 dB, and the noise level increases by 2.5 times, clearly intensifying gearbox abnormal noise.

3. Several solutions are proposed, including improving transmission accuracy grade, optimizing gear parameters, and increasing structural natural frequency.

Η Σίντι

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