Theoretical calculation of the natural flock restoration time of a cotton comber

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1 Indian Journal o Fibre & Textile esearch Vol. 40, September 05, pp Theoretical calculation o the natural lock restoration time o a cotton comber Li Xin-rong a, Jiang Xiu-ming, Yang Jian-cheng & Wang Xiao-wei School o Mechanical Engineering, Tianjin Polytechnic University, Tianjin , China eceived 5 February 04; revised received and accepted 7 June 04 Based on the overhanging beam theory, the stress on the lock o a cotton comber has been analyzed, and the natural requency o the natural lock restoration is calculated in combination with energy method. Finally, a theoretical model o the natural lock restoration time has been developed. The model illustrates that the natural lock restoration time o a cotton comber is determined by cotton properties, combing process and mechanical structure. The established theoretical model corrects the previous calculation method or the natural lock restoration time o a cotton comber. The inding provides inormation or the development o a new type o cotton comber with high velocity. Keywords: Bending rigidity, Cotton comber, Cotton ibre, Elastic modulus, Natural restoration o lock Introduction The imum velocity o a cotton comber is an important measure o its modernization level. The theoretical imum velocity is closely related to the natural lock restoration time. ecent studies on lock restoration mainly concentrate on the properties o cotton and examine natural lock restoration using the mechanical theory o the cantilever. However, this method has several deects. First, only the stress on the lock is analyzed without considering the structure o the cotton comber. Thus, the lock is generally equivalent to an overhanging beam with respect to its stress pattern, which is inconsistent with the stress on the lock o a cotton comber. Second, the inluence o the combing process on the natural lock restoration time is not considered. Thereore, the imum velocity o a cotton comber is oten incorrect, which seriously hinders the cotton comber development -0. In view o the above, present study has been undertaken to analyze the stress on the lock in a cotton comber and proposes a mathematical model or overhanging beam displacement through mechanical displacement superposition. A calculation model has also been developed or the natural requency o natural lock restoration using the energy method. The parameters or the cotton properties, mechanical structure and combing process can be represented in the mathematical model. The development o a a Corresponding author. lixinrong7507@hotmail.com theoretical model or the natural lock restoration time o a cotton comber has several beneits. The model corrects the previous calculation method or natural lock restoration time o a cotton comber and provides inormation or studying the basic combing process. The study also provides a theoretical calculation model or investigating the imum velocity o a cotton comber. This study may also help in the development o a new type o cotton comber with high velocity. Methodology Flock restoration reers to the process in which the lock bounces back and straightens out ater comber cylinder combing. Flock restoration consists o active lock restoration and natural lock restoration. The ormer indicates that the lock bounces back and straightens out under an external orce such as the relative motion o air low or bottom nipper plate, whereas the latter indicates that the lock bounces back and straightens out through its own elasticity ater comber cylinder combing. The combing process can only be smoothly completed when the straightened out lock links to the lock returned by the detaching roller. Thus, the calculation o the imum velocity o a cotton comber should be based on the analysis o lock restoration. The study o active restoration lock must also be based on a thorough understanding o natural lock restoration. Thereore, calculating natural lock restoration time has practical value and scientiic signiicance.

2 XIN-ONG et al.: THEOETICAL CALCULATION OF NATUAL FLOCK ESTOATION TIME OF A COTTON COMBE 89 To analyze the stress on the lock, the lock model should be irst simpliied into a cotton ibre pole with elastic modulus (E, density (, cross-sectional area (S and moment o inertia o cross-sectional area (I (Fig.. The cotton ibre pole was used or mechanics analysis. Then, the combing location parameter o the lock in a cotton comber was determined with the lock length (L inside the nipper jaw (Fig.. The combing process parameters were determined with the lock length (L outside the nipper jaw (Fig.. Based on Fig., the lock was ound equivalent to an overhanging beam with respect to its stress pattern. Based on the mechanical theory o an overhanging beam, the above-mentioned parameters were used to establish the mathematical model o or analyzing natural lock restoration time o a cotton comber. The established mathematical model consists Fig. Flock in a cotton comber o parameters or lock properties, lock location in a cotton comber and combing processing.. Parameters or Flock Properties and Flock Location It is assumed that the top nipper plate remains open upon the completion o comber cylinder combing (Fig.. Then, the lock begins to bounce back and straighten out through its elasticity. By analyzing the stress acting on the lock in a cotton comber, it is ound that natural lock restoration has a close relationship with the ollowing parameters... Flock Properties Cotton ibre elastic modulus (E is an important mechanical constant in the stress-strain relationship o the material and indicates the deormation resistance o the material to external orce. The elastic modulus o the cotton ibre is usually determined by the slope o the irst part o the stress-strain curve in the tensile test and is reerred to as the initial elastic modulus. The elastic modulus o the lock determines the velocity at which the lock bounces back, i.e. the length o lock restoration time. Thereore, the elastic modulus o the lock should be irst analyzed when studying the natural lock restoration time o a cotton comber. In textile engineering practice, direct measuring o elastic modulus (E and moment o inertia o a crosssectional area (I in the cotton ibre is rarely possible. Thereore, we usually deine other technical parameters such as speciic bending rigidity (, as shown below: ( N t where is the bending rigidity; and N t, the cotton ibre ineness. Based on the deinition o bending rigidity, =, and hence N ( t Fig. Natural lock restoration in a cotton comber [-eeding roller, -bottom nipper plate, 3-cylinder, 4-location beore lock restoration, and 5- location ater lock restoration, L -lock length o lock inside the nipper jaw, and L -lock length outside the nipper jaw].. Flock Location The lock state in a cotton comber was analyzed as shown in Fig.. Based on the stress pattern, the lock can be equivalent to an overhanging beam. L is the distance between the lock holding point o the eeding roller and ront end o the bottom nipper. L is also the mid-span length o the overhanging beam and closely related to the restoration o the ree end o the overhanging beam. In addition, L aects the natural lock restoration time o a

3 90 INDIAN J. FIBE TEXT. ES., SEPTEMBE 05 cotton comber and is the location parameter o the lock in a cotton comber...3 Process Parameters Figure shows that the lock length (L outside the nipper jaw is the length o the ree end o the overhanging beam. The lock length (L outside the nipper jaw has a close relationship with the restoration o the ree end o the lock, inluencing the natural lock restoration time o a cotton comber. L is determined by the detaching distance B (the distance between the lock holding point o the detaching roller and the ront end o the bottom nipper, eeding length S (eeding lock length per nipper and eeding method o the eeding roller.. Mathematical Calculation Model To analyze the lock stress and displacement, the constraint and load on the lock were irst simpliied. As shown in Fig., the lock holding point o the eeding roller was simpliied into a ixed support hinge, and the ront end o the bottom nipper was simpliied into a roller support hinge. The ront end o the lock was stretched out o the bottom nipper plate. That is, the lock in a cotton comber was simpliied into an overhanging beam as illustrated in Fig.3. In this igure, Y=lock displacement, L =distance between the lock holding point A and the ront end B o the bottom nipper plate, and L (length o lock stretching out o nipper= distance between the ront end B o the bottom nipper plate and the ront end C o lock. The dashed line represents the location beore lock restoration, and the solid line represents the location ater lock restoration. The stress acting on the lock at section AC was analyzed. To calculate the displacement, section AC was divided into section AB, where the stress acted on the lock inside the nipper plate, and section AC, where the stress acted on the lock outside the nipper plate. First, the stress acting on section AB was analyzed (Fig.4. Two simple loads acted on the lock in section AB, its own weight and torque at point B. The lock displacement (Y was obtained using the ollowing method. In the premise o small deormation and line elastic deormation, it proves a linear relationship between the displacement and the load o the beams. When beam was acted by multiple load, the displacement o beam could be calculated by superimposing the displacement acted by single load, called mechanical superposition method 3. As shown in Fig 4, the lock AB was orced by gravity and torque load on point B, and the orce was decomposed (Fig. 5. Here Y was the displacement o beam acted by gravity and Y was the displacement o beam acted by torque load on point B. Y and Y could be obtained by adopting dierential method 4, as shown below: qx 3 3 Y ( L X X L (0 X L 4... (3 Fig.4 Force diagram o section AB [L -distance between the point A and B; and Y - lock displacement] Fig.3 Diagram o the simpliied lock stress pattern [Y-lock displacement, L -distance between the point A and B, L -distance between the point B and C, X -distance between the point A and the point which displacement is imum at section AB, X -distance between the point B and the point where the stress acted on the lock] Fig 5-Force decomposition diagram o section AB

4 XIN-ONG et al.: THEOETICAL CALCULATION OF NATUAL FLOCK ESTOATION TIME OF A COTTON COMBE 9 ql X Y ( L X 6L (0 X L... (4 Y was obtained by adopting the mechanical superposition method, as shown in the ollowing equation : Y = Y +Y qx 3 3 ql X ( L X X L ( L X 4 6L...(5 q 3 4 ( L X X (0 X L 4 where q=ρsg. To calculate the displacement o point C, the overhanging beam AC is divided into cantilever BC and simply supported beam AB (Fig. 6. Flock displacement Y was obtained by the superposition method using the ollowing equation. qx Y Y '( L X (4L X 6 L X (0 X L 4 (6 3 q 3 3 ql Y '( L ( L 4 X 4 8 (7 By substituting Eq.(7 into Eq.(4, ollowing equation is obtained: 3 ql qx Y X (4L X 6 L X (0 X L 8 4 q (4L X 6L X X 3 L X 8 4 Fig.6 Force diagram o section BC [Y - lock displacement on hal o the beam; and Y - lock displacement o point C] Because the movement o lock restoration is under the condition o simple harmonic vibration, the system observes the law o conservation o energy. It means that energy transorms between the kinetic energy and potential energy. All harmonic vibration system, including vibration system with multiple reedom degree, are ollowing the above rules. The angular requency o simple harmonic vibration system could be obtained directly by using energy equation. In this study, only the elastic potential energy was considered in analyzing the stress acting on the lock. The natural requency (ω was calculated via energy method using the ollowing equation 3,4. : L Y L Y ( dx 0 ( dx 0 X X L L S Y 0 d( X S Y 0 d( X 96( L L S 5 L L (35 L 34L L 04 L Hence 96( L L S 5 L L (35L 34L L 04 L (9 The lock restoration time (t is ound to be /4 o the vibration period T. Thus, ollowing equation o t was obtained: T t 4 96( L L S 5 L L (35 L 34L L 04 L 96( L L Nt 5 L L (35 L 34 L L 04 L (0 3 esults and Discussion We used a ieter Combers E60 or this experiment to veriy the correctness o the calculation model. The lock analyzed in the paper was manuactured rom pure cotton with a speciic bending rigidity ( o Nmm /tex (re. 5. The cotton ibre ineness (N t ranged rom tex to tex (re. 6. For this study, we set N t = tex. To ensure the spinnability and reliability o the cotton comber, the study used the minimum orward eeding (L min and imum backward eeding

5 9 INDIAN J. FIBE TEXT. ES., SEPTEMBE 05 (L or the analysis. For the orward eeding, L = B, and or the backward eeding, L = B + S. The minimum detaching distance or the ieter Combers E60 was B min = / = The distance o the eeding roller ranges rom 4.3 mm to 6.7 mm. Then, L min = B = 8.74 mm, and L = B + S = = 5.44 mm. Thereore, we set L = 5.44 mm. By measuring the nipper plate structure o the cotton comber, the distance rom the lock holding point o the eeding roller to the ront end o the bottom nipper plate was L = 7.3 mm. Substituting the above parameters into Eq.(0, yielded t = The cotton comber considered one rotation o the cylinder shat as the motion cycle, being divided into 40 indexes. The indexing number o the lock restoration o the ieter Combers E60 is γ, and L = 5.44 mm corresponds to γ = 9.5. By substituting the value o t and γ into ollowing equation [Eq.(], the ollowing equation [Eq.(] was obtained: 60 3 t ( n 40 n n t ( Thus, the theoretical imum velocity o the cotton comber was 600 nips/min. It proves that the calculation model or natural lock restoration is correct. 4 Conclusion The imum velocity o cotton comber is an important measure o modernization level, and theoretical imum velocity is closely related to the time o lock natural restoration. This study analyzes the actual orce on the lock in the cotton comber by leading the process parameters and proposes the mathematical model o displacement o overhanging beam. In addition, we build a calculation model o the natural requency o lock natural restoration by energy method, i.e. the model o time o lock natural restoration. The ollowing conclusions are obtained rom the preceding analysis and calculation: 4. The time o lock natural restoration is not a ixed value but depends on the lock properties, the length o the lock outside nipper plate and the length o the lock inside nipper plate. 4. The perormance indicators o cotton ibre such as bending rigidity and ineness decide the time o lock natural restoration. 4.3 The length o the lock outside nipper plate depends on detaching distance, eeding length and eeding method, i.e. combing process. 4.4 The length o the lock inside nipper plate depends on the location o eeding roller above the bottom nipper plate, i.e. nipper mechanism o comber. 4.5 The time o lock natural restoration on a cotton comber is a variable value, which depends on lock properties, combing process and combing mechanism. This study combines lock properties, combing process and comber structure or the irst time. A calculation model o lock natural restoration time based on cotton comber is deduced. esearchers can design cotton comber with higher velocity and better adaptability according to the calculation model proposed in this study, by taking into account o lock properties, mechanical structure and combing process, to increase the output o cotton comber and to reduce cost. Acknowledgement Authors acknowledge with thanks the unding support by the National Basic esearch Program o China (973 Program in 00 (Grant number 00CB3347 and or the Textile Vision Science & Education Fund o China in 0. eerences Zhang S T, J Text Inst, 86(4 ( Liu L L, Study on the combing process o cotton comber driven by multiple spindles, M.E thesis, Donghua University, Shanghai, 008, Asian Textile Business Group, Asian Textile Business, 005, Norbert S, Melliand Textilber, ( 005 E. 5 The Textile Magazine Group, Textile Magazine, ( Bogdan J F, Woo H K C & Pan C H, Text es J, 9 ( Wichtermann Fredy Mondini, Text es J, (3 ( Stephan Fichtner, China Text Leader J, ( Klein W, J Overseas Text es, 08 ( Vadhani H, J Overseas Text es, 04 ( Yan H J & Yang X G, J Eastern China Inst Text Sci Technol, 8( (98-0. Narasimhan P L & Fang J, J Overseas Text es, 6 ( Xing J Z & Liu CT, Oceanic Engineering J, 6( ( Chen G & uan Z Z, Phys Eng J, 6(4 ( Morton W E & Hearle J W S, Physical Properties o Textile Fibres, 4th edn (The Textile Institute and Heinemann, Manchester, London, 975, Yan H J, Introduction to Fibrous Materials (Textile Industry Press, Beijing, China, 999, 58.

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