Mohamed Taoufik Khabou

Influence of the non-linear Hertzian stiffness on the dynamics of a spur gear system under transient regime and tooth defects

The non-linear dynamic behaviour of a single stage spur gear reducer is investigated in transient regime. The gear pair excitation is the result of motor torque variation and the fluctuation of meshing stiffness. The non-linearity is induced by the Hertzian contact force between teeth. Tooth crack and breakage are also modelled. The equations of motion of the transmission are solved iteratively using implicit type numerical integration technique Newmark-β with Newton-Raphson method. The numerical simulation results are analysed in time and frequencies fields. These results confirm the influence of the Hertzian stiffness on the dynamic behaviour of the system especially in the transient regime. Tooth defects contribute to the aggravation of the vibration levels.

Nonlinear modeling and simulation of spur gear with defected bearings

Purpose – The aim of this paper is to present a theoretical model to simulate the dynamic behavior of a spur gear, taking into account its ball bearings defects.Design/methodology/approach – The proposed model is based on the implicit Newmark‐β with Newton‐Raphson numerical integration technique in order to analyze the impact of the worn bearings on the non linear dynamic behavior of one stage spur gear transmission system.Findings – The dynamic behavior of spur gear is studied taking into account ball bearings defects thanks to the proposed model.Originality/value – A new numerical model is proposed to simulate the dynamic behavior of rotating spur gear system taking into account both waviness and backlash defects.

Dynamic analysis of gearbox behaviour in milling process: Non-stationary operations

Dynamic behaviour of gearbox transmitting power to milling tool in a milling process application is considered in this paper. The gearbox is subjected to variable cutting torque induced by the milling operation. This variability will lead to fluctuating speed. The dynamic behaviour of the system should be investigated according to this non-stationary operating condition. To achieve this objective, a simple model of motor-gearbox-milling tool system is developed. The influence of variable cutting torque on driving motor speed is taken into account. The gearmesh function which describes the meshing phenomena is modified according to this specific operating condition. Simulations of the dynamic behaviour of the gearbox show a simultaneous frequency and amplitude modulation. These modulations are highlighted using time frequency representation which is necessary to implement so that it is possible to achieve a correct diagnosis of the transmission. Simulations in presence of tooth crack defect confirmed the necessity to implement time frequency techniques to characterize time varying systems.

Influence of disk brake friction on the dynamic behaviour of a directly coupled spur gear transmission

Purpose – The purpose of this paper is to study the influence of friction phenomenon generated by a disc brake on the dynamic behaviour of a one-stage spur gear. Design/methodology/approach – A theoretical model is proposed and is based on both theories of Coulomb and Dahl in order to analyse the influence of disc brake friction phenomenon on the dynamic behaviour of one-stage spur gear transmission. Findings – The influence of brake friction on the dynamic behaviour of the transmission is investigated using the proposed model and leads to observe higher vibration levels when the braking is occurring as well as the emergence of significant efforts at the gear teeth. Originality/value – A new numerical model based on the implicit numerical integration technique of Newmark coupled with Newton-Raphson method is proposed to study the influence of friction phenomenon of a disc brake on the dynamic behaviour of one-stage spur gear.

Modal Analysis of Spur Gearbox with an Elastic Coupling

Coupled shafts are considered as the main source of vibration in rotating systems. In this work, a mechanical system composed of an electric motor, an elastic coupling and one stage spur gear is investigated to analyze dynamic behavior of elastic coupling, its influence on the natural frequencies, the vibrations, and the response of the system. A lumped parameter model of the corresponding system is developed to identify the natural frequencies and vibration modes. In addition, distributions of modal kinetic and strain energies are studied.

Dynamic Behavior of Spur Gearbox with an Elastic Coupling Under Acyclism Regime

For many researchers and industrials the dynamic behavior of gearbox remains a paramount concern. In fact the diagnosis as well as the improvement of efficiency of gearbox is an ultimate goal for users such as machine builders, aeronautic and automotive manufacturers or energy producers. We should remind that the dynamic behavior of a gearbox depends on its design parameters and is also influenced by the engine operating conditions as well as the type of driving unit. A single stage spur gearbox is considered in this paper to investigate its dynamic behavior under acyclism regime. In fact the studied spur gear is powered by a four strokes four cylinders diesel engine using an elastic coupling modeled by Nelson and Crandell approach [7]. A numerical model is proposed taking into account the excitations induced by the motor torque fluctuation as well as the load variation and the fluctuation of meshing stiffness cased by acyclism regime. The implicit Newmark algorithm is used to investigate dynamic response of the studied system and the obtained results show the significant influence of both acyclism effect and elastic coupling on it.

Dynamic Behavior of Spur Gearbox with Elastic Coupling in the Presence of Eccentricity Defect Under Acyclism Regime

In this paper, the effect of eccentricity defect on the dynamic behaviour of one stage spur gearbox running under acyclism regime is studied. In fact, acyclism regime is generated by a combustion engine motor which produced fluctuations of load and speed. The motor torque is periodic and it modeled in the force’s vector. The rotational speed of the Diesel engine is a harmonic function and it generates a periodic fluctuation of the gear meshing stiffness function. This driven motor is joined to the gearbox through an elastic coupling in which the model of Nelson and Crandall is adopted. The eccentricity defect is introduced in the pinion. This defect produces an additional potential energies and kinetic energy and it is modelled through additional forces. The equation of motion is obtained using Lagrange formalism and the algorithm of Newmark is used to compute the dynamic response of the studied system and the Wigner–Ville distribution shows the dynamic behaviour of the gearbox under this cyclo-stationary regime. Results show the variability of the meshing frequency and its harmonics which excites the system. Also, natural frequencies are observed in the spectrum and Wigner–Ville distribution of the dynamic signal. Nevertheless, these methods fail to detect the frequencies of eccentricity and acyclism.

Analytical Method for the Calculation of Tool Machine Energy Consumption

There is no doubt that the industrial revolution has a monumental effect on the prosperity and the improvement of human conditions but on the other hand the bill was too expensive due to environmental degradation especially. Indeed the weather changing and global warming are directly linked with energy consumption. Industrial manufacturing is one of the biggest consumers of energy which needs a deep care especially in machining sequences to reduce energy consumption and to achieve the balance of humanity. To reduce the waste of energy during machining sequences, a new numerical approach to predict machine tool energy consumption is proposed in this study. It is about the spindle rotation and axis feed modeling as well as considering a nonlinear behavior between the tool and the workpiece during the manufacturing process. The proposed model provides an accurate tool for process planning in metal cutting which helps manufacturers to determine the optimal energy process plan.

Vibration Suppression of a Cantilever Plate During Milling Using Passive Dynamic Absorber

During milling process, the vibration is an unavoidable phenomenon which causes damage in the tool and spindle bearings and leads to poor dimensional accuracy and surface finish of the workpiece. With the ultimate goal of vibration suppression of a thin-walled workpiece during milling process, this paper provides a comparative study of the dynamic behavior simulation of a cantilever rectangular thin plate submitted to a milling operation with and without passive dynamic mass-spring absorbers attached to it. The simulation is carried out taking into account the Kirchhoff model for the plate and the Moradi et al. (2015) model for the cutting force of milling. To solve the equation of motion of the plate with the finite element method the MATLAB software is used. The plate natural frequencies and mode shapes are first identified and then two cases of the plate deflection are determined by the cutting force and taking or neglecting additive absorbers. The obtained results show that the attachment of vibration absorbers to the plate workpiece enlarges its range of natural frequencies. Thus, it can minimize undesired vibration and improves the milling conditions and the surface quality. The proposed vibration absorber design includes other advantages such as design simplicity, intuitive clarity, and hardware and development effective cost. However, the plate deflection remains relatively high because this type of vibration absorber is efficient just in case of one resonance frequency.

Influence of the Acyclism on the Dynamics of a Spur Gear System

The aim of paper is to study the dynamic behavior of a single stage spur gear reducer in transient regime. The gear excitation is the result of the motor torque variation in addition to the fluctuation of meshing stiffness due to the variation of input rotational speed. Then, the dynamic response is solved using implicit type numerical integration technique Newmark-β. A parameter study is made on spur gear powered by four strokes four cylinders diesel engine. Dynamic responses come to confirm a significant influence of the transient regime on the dynamic behavior of a gear set.