Abstract:

Objective The separating roller gear transmission mechanism in most combing machine consists of differential wheel system and spur gear system, with spur gear system as its main input. With the increase of combing machine speed, under the influence of time-varying parameters (backlash and pressure angle) of spur gear system, its vibration and noise would also increase, resulting in the reduction of stability and precision of the transmission mechanism, which in turn leads to the increase of vibration of the combing machine. Therefore, in order to reduce the vibration of the combing machine, it is necessary to study the effect of the initial backlash of the driving spur gear of the separating roller differential wheel system on the vibration and noise of the system.

Method First, by analysing existing separated roller gear transmission mechanisms, a dynamic model of the spur gear system was established using the concentrated mass method. Based on Newton's second law, its dynamic differential equations were derived, yielding a backlash vibration model that relates initial backlash, vehicle speed, and vibration. Subsequently, the backlash vibration model was solved using the Runge-Kutta method. The accuracy of the relationship model was verified experimentally using a laser vibrometer, with varying carriage speeds and initial backlash as variables. Finally, analysis of the relationship model and experimental results determined the optimal initial backlash corresponding to the minimum vibration displacement at each speed for carding machines operating between 450 and 550 strokes per minute. This resolves the requirement for matching straight gear initial installation backlash to different carding machine speeds to achieve minimal vibration.

Results Firstly, to address the issue of exacerbated precision machinery vibration caused by mismatched initial backlash adjustment and vehicle speed in hybrid drive mechanisms. Considering the impact of initial backlash on vibration and noise within spur gear systems, a dynamic model was derived for the spur gear system using Newton's second law. The resulting differential equations for spur gear dynamics enable optimisation of the relationship between initial backlash, vehicle speed, and vibration.Secondly, with the fixed spur gear initial backlash set at b₀ = 50 μm, the cutting speed was varied in increments of 10 cuts per minute from 300 to 550 cuts per minute. The vibration displacement was measured and recorded at different cutting speeds. With the combing machine speed fixed at 550 strokes per minute, the initial backlash b₀ was varied in increments of 5 μm within the range of 5-50 μm. Vibration displacement data was calculated and collected for different initial backlash values. By comparing theoretical and experimental vibration displacement values across varying speeds and initial backlashes, the derived dynamic differential equation demonstrated excellent accuracy in characterising the relationship between initial backlash, speed, and vibration.Finally, employing the Runge-Kutta method to solve the dynamic differential equations at increments of 10 strokes per minute, and integrating experimental results of vibration displacement at varying speeds and initial backlashes, the optimal initial backlash corresponding to the minimum vibration displacement was determined for carding machine speeds ranging from 450 to 550 strokes per minute.

Conclusion In this paper, the dynamic model of spur gear system is established by using the concentrated mass method, and its power differential equation is deduced according to Newton's second law, which shows the relationship between initial backlash, vehicle speed and vibration, and the experiments are carried out by using laser vibration meter with different vehicle speeds and initial backlashes as the variables, which verifies that the power differential equations can accurately show the relationship between the three, and the analytical analysis obtains the initial tooth gap corresponding to the minimum vibration displacement under the vehicle speed of combing machine of 450-550. The initial tooth gap corresponding to the minimum vibration displacement of the combing machine is analyzed and obtained.

Key words: comber, separating roller, spur gear, initial backlash, time-varying backlash, gear transmission mechanism