Research On Dynamic Properties Of Fabric And Drum System At High-Speed

This subject originates from the National Natural Science Foundation of China financing project,named "Some Research about the Machinery-Fiber, Fabric Coupled System Dynamics"(No.50575039),with the object of studying basic dynamic characteristics of fiber and fabric coupled system under high-speed.In the textile and dyeing and finishing processing,the fabric and processing equipment(especially the drum) form a complex system.Under high-speed,the dynamic characteristics of system will affect the fabric processing quality and the performance of equipments,lead to the decline in the quality of printing,dyeing and finishing and degrade the quality of fabrics and value-add performance,aggravate the vibration of the key parts, accelerate the damage of equipment.Therefore,it is very important to study the dynamic properties of the fabric and drum systems at high-speed.On account of the fact that the fabric and drum are two kinds of quite different materials and a coupling exists between them.Up till now,few literature,at home and abroad,is found to study the system consisting of the fabric and drum.For the purpose of revealing the most basic principle and providing feasible suggestions for the independent development of our advanced textile machinery,some explorations of the dynamics characteristic of the fabric -drum system under high-speed have been made with the help of the dynamics method for moving system in the paper.The establishment of the model is the research foundation;in the paper, the system dynamics model is established by elasticity theory method and Hamilton principle.The vibration of a longitudinal moving fabric is the vibration of three dimensions and the fabric can vibrate in x,y,z directions.In the dyeing and finishing processes,the transverse vibration of the fabric is far larger than the longitudinal vibration;therefore,the vibration is simplified as the two-dimensional vibration.Concerning the forces exerting on moving fabric in the dyeing and finishing processes,there are two different cases.In one case,two opposite edges of the fabric are pulled by the forces;however,four edges are pulled in the other one.The first situation has been analyzed in the paper,the formula for calculating natural frequency of the longitudinal moving fabric and related resonating condition are obtained.The natural frequency of the longitudinal moving fabric decreases gradually with the increase of the running speed and the drum spacing,but rises gradually with increase of the pulling forces exerting on the two opposite edges.Resonating will occur when the natural frequency of a longitudinal motion fabric is integral times drum speed and the fabric vibrates intensely.The dynamics characteristics of the longitudinal moving fabric pulled by forces in four edges are very complicated with its unique property.When the dimensionless speed is smaller than the first critical speed,the fabric natural frequency increases continually with the reduction of the dimensionless speed. When the dimensionless speed is between the first and second critical speed, the fabric natural frequency is plural and the fabric is in instable state.When the dimensionless speed is larger than the second critical speed,the fabric natural frequency increases unceasingly with the rise of dimensionless speed. Therefore the vibration state of the longitudinal moving fabric varies from stability to instability and returns to the stability.It is very significant to know its characteristics and advise the machine designers reasonable parameters to enable the system to work in a stable area.The longitudinal moving fabric and the drum form a kinematical system with complicated dynamics properties and both of them interact on each other. In this paper,transfer matrix method is used to analyze the torsion vibration of the fabric and drum system and the interaction between them is also discussed.The frequency of torsion vibration of the fabric and drum system rises with the increase of the fabric elastic modulus and drops with the increase of the fabric length.The natural frequency of fabric increases gradually with the increase of drum torque and decreases gradually with the increase of the distance between the drums.It is found the larger the distance the smaller the natural frequency.In the paper,the homotopy perturbation method is used to solve the longitudinal moving fabric's nonlinear vibration,which is quite different from the linear vibration.It is indicated that the natural frequency of fabric nonlinear vibration is related to fabric velocity,the breadth of fabric,the drum distance,the tension,the rigidity of fabric,and the oscillation amplitude of fabric.The natural frequency increases with the increase of vibration amplitude.Besides the general resonating,inner resonates may also occur in the fabric.The natural frequencies of two modality are coupling,moreover, when they are equal,inner resonate will occur.The natural frequency of fabric and drum system under the state of moving is not the same as that under static state and the resonating condition is not the same either.The measuring of the natural frequency of the fabric and the drum system under static condition can be made by mature technology, however,few measurements for the state of moving are present to us.So the indirect test method is used.When the drum speed reaches the resonating speed,the amplitude of drum and the fabric system will be at its maximum. The different methods are used respectively to measure the oscillation amplitude of fabric and drum.The experimental results are close to the theoretical value basically.