Study on Dynamics of a Two-Stage Gear Transmission System with and without Tooth Breakage

This paper studies the dynamics of a two-stage gear transmission system in both the normal state and the fault state with tooth breakage. The torsional vibration model of the two-stage parallel shaft gear was developed by using the lumped parameter method. The time-varying meshing stiffness of the gear transmission system is described by Fourier series which is determined by the periodical meshing characteristics of the gears with both the single-tooth and the double-tooth contacts. By introducing the pulse into the regular time-varying meshing stiffness, the tooth breakage existing in the gear transmission system is mimicked. Based on the numerical simulation of the developed dynamic model, both the time domain analysis and the frequency domain analysis of the gear transmission system under both the normal condition and the tooth breakage are compared accordingly. The influence of the tooth breakage on the dynamic characteristics of the gear transmission system is analyzed comprehensively. Furthermore, based on the developed test bench of a two-stage gear transmission system, the experimental research was carried out, and the experimental results show great agreements with the results of numerical simulation, and thus the validity of the developed mathematical model is demonstrated. By comparing the periodic motion with the chaotic motion, the fault identification for the gear transmission system is verified to be tightly related to its vibration condition, and the control of the vibration condition of the gear transmission system as periodic motion is of great significance to the fault diagnosis.

sEMG Activity in Superimposed Vibration on Suspended Supine Bridge and Hamstring Curl

Traditionally in strength and conditioning environments, vibration has been transmitted using platforms, barbells, dumbbells, or cables but not suspension devices. This study aimed to examine the effects on the lower limb of applying superimposed vibration on a suspension device. Twenty-one physically active men and women performed supine bridge and hamstring curl exercises in three suspended conditions (non-vibration, vibration at 25 Hz, and vibration at 40 Hz). In each exercise condition, the perceived exertion scale for resistance exercise (OMNI-Res) was registered, and the electromyographic signal was assessed for gastrocnemius (medialis and lateralis), biceps femoris, semitendinosus, gluteus maximus, and rectus femoris. A linear mixed model indicated a significant fixed effect for vibration at 25 Hz and 40 Hz on muscle activity in suspended supine bridge (p < 0.05), but no effect for suspended hamstring curl (p > 0.05). Likewise, the Friedman test showed a significant main effect for vibration at 25 Hz and 40 Hz in suspended supine bridge (p < 0.05) but not for suspended hamstring curl (p > 0.05) on OMNI-Res. Post hoc analysis for suspended supine bridge with vibration at 25 Hz showed a significant activation increase in gastrocnemius lateralis (p = 0.008), gastrocnemius medialis (p = 0.000), semitendinosus (p = 0.003) activity, and for semitendinosus under 40 Hz condition (p = 0.001) compared to the non-vibration condition. Furthermore, OMNI-Res was significantly higher for the suspended supine bridge at 25 Hz (p = 0.003) and 40 Hz (p = 0.000) than for the non-vibration condition. Superimposed vibration at 25 Hz elicits a higher neuromuscular response during the suspended supine bridge, and the increase in vibration frequency also raises the OMNI-Res value.

Study on the collision dynamics of integral shroud blade for high-pressure turbine in different integral shroud clearance distance

In steam turbine, turbine blades are prone to vibrate during operation, resulting in steam turbine accidents. The most common method for reducing the vibration of steam turbine blades is to design an integral shroud for blade which is termed as integral shroud blade. Most previous studies simplified straight integral blades into cantilever beam and used harmonic response analysis method to simulate the vibration response of blades. This method is suitable for simulating straight blade vibration under harmonic force conditions. For twisted blades, accurate results are hard to acquire and the specific collision process cannot be simulated. In order to observe the collision process on a microscopic scale and explore its collision damping mechanism, this study evaluated the collision process of twisted blades with different integral shroud clearance distance based on LS-DYNA software. The collision process for a two-blade system and a three-blade system with integral shroud clearance distance from 0.1 mm to 0.5 mm has been simulated. The results indicated that integral shroud clearance distance have opposite vibration damping effect when the blade under the condition of forced vibration and free vibration. For the two-blade system, the optimal integral shroud clearance distance is 0.4 mm for forced vibration condition and 0.1 mm for free vibration condition. For the three-blade system, the optimal integral shroud clearance distance is 0.1 mm for forced vibration condition and 0.5 mm for free vibration condition.