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b - Centrum Textil

b - Centrum Textil

calculation of flexural

calculation of flexural rigidity, input value are angle and longitude overhanging of sample and fineness of fibre or yarn. When we bend yarn or fibre with eaves is it compared to bend of fabric much more complicated. Free ends of eaves yarn or fibre, they yaw about his axes, free ends yarn untwist, problem amounts also crimpiness of fibre or yarn. That is why method of measuring was perfected. Free ends were fixed. Fixation of free ends of yarns or fibres was applied as well like weighting. Therefore were eliminated undesirable effects, like were untwisting of yarns or crimpiness of fibre or yarn. Influence weight at the end overhanging sample is behind - compose to the computational relation. 3. EXPERIMENT For calculation flexural stiffness it is necessary obtain flexural curve from outhang of yarn or fibre. Yarns or fibres were affixing near side by side on paper frame, thereby was both ends of sample of yarn or of fibre fixate. Subsequently was overhanging end of sample shorn on size one mm. Lateral parties of frame were cutaway, otherwise would lateral parties of frame hold under bend of yarn or of fibre. Sample from vertical position will turn about 90 degree and will fix on margin experimental table. Flexural curve from minimally ten fibres or yarn was photographed. It was input data to the programme for calculation flexural stiffness. 4. COMPUTATIONAL RELATIONSHIP Calculation coming - out from known relation M i i = k ϕ + b ϕ (1) i i ( M i − kiϕ i )/ bi i i ϕ = (2) ψ = ϕ , 1 1 1 x = l cosψ , y = l sinϕ 1 1 1 We calculate geometrical parameter of the next segment always from parameter of previous segment: ψ = , ϕ (4) 2 ψ 1 + ϕ 2 x 2 = x1 + l cosψ 2 , y2 = y1 + l sin 2 (3) M i M i EJc ki EJ ϕ ι ϕ ι M i ϕ b i M i i ϕ ι Flexural moments in individual joint, they are: M M M 1 2 3 = f = f = f ( x1 + x2 + x3 ), [( x2 − x1 ) + ( x3 − x1 )], ( x − x ) 3 2 (5)

2k ψ 1 =ϕ 1 l k y i ψ 2 ψ y 2 2b b ϕ 2 x 1 f l k 2 y 3 x 2 b f l ϕ 3 x 3 ψ 3 m.g f Conformable with equation (2) rated angle: ϕ = 1 ϕ = 2 ϕ = 3 ( M 1 − 2k ⋅ϕ1 )/ 2b = ( 0.5M 1 − k ⋅ϕ1 ) ( M 2 − k ⋅ϕ 2 )/ b, ( M − k ⋅ϕ )/ b 3 3 / b, (6) Acknowledgements The Textile Research Centrum LN 00B090 supported this work 5. REFERENCES [1] S. Kawabata, Y.Yamashita, K.Nakano, Y.Kawashima: Bending Stiffness Measurement Form Single Fibre, PROCEEDINGS OF THE 29 TEXTILE RESEARCH SYMPOSIUM AT MT. FUJI, JAPAN 2000 [2] Fridrichová, L.- Mevald, J.:Modelling Of Large Deformations Of Fabrics With Respect To Their Viscoelastic Properties, Dresden 2002

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