Utafiti huu unachunguza frame vibration na stress concentration katika high-speed air-jet looms na ku-optimize main geometric parameters za frame. Researchers walifanya modal hammer test na operating-vibration measurements kwenye actual loom frame, wakahamisha measured dynamic loads kwenye finite-element analysis, na kisha waka-model relationship kati ya six frame-thickness parameters na equivalent stress kwa surrogate model inayotegemea BA-HHO-SVR. Experiments zilionyesha kwamba vibration increase ilikuwa more pronounced karibu na operating speed ya 900 r/min, na katika condition hii maximum equivalent stress ya initial model ilikuwa 36,992 MPa. Baada ya BA-HHO-SVR optimization, maximum stress ilishuka hadi 32,933 MPa katika finite-element validation; study iliripoti hili kama reduction ya %10,9. Hata hivyo, final validation ya optimized geometry inategemea finite-element simulation; study haikutest directly durability ya optimized frame katika long-term real production conditions wala improvement katika fabric quality.

Frame ndiyo main structural system inayobeba dynamic loads zinazotokana na moving mechanisms tofauti za air-jet loom. Katika study, warp let-off linkage mechanism, shedding mechanism, connecting-rod system na beat-up mechanism zilichukuliwa kama main vibration sources. Rotation speed ilipoongezeka, vibration acceleration katika evaluation points zote nne iliongezeka; especially Y-direction vibration katika rear section ilikuwa more pronounced kuliko front section.

Katika model validation, experimental na finite-element modal results zililinganishwa directly. First natural frequency ilikuwa 20,628 Hz katika simulation na 18,515 Hz katika experiment; second natural frequency ilikuwa 32,861 na 29,323 Hz mtawalia; third natural frequency ilikuwa 59,674 na 57,571 Hz. Shapes za first six modes na Modal Assurance Criterion (MAC) evaluation ziliunga mkono conclusion kwamba dynamic model iliyotumiwa na researchers iliwakilisha experimental system behavior kwa sufficient agreement.

Kwa mtazamo wa Uturuki, study si direct validation ya local loom au production line. Hata hivyo, approach iliyotumika inatoa practical engineering method ya jinsi modal testing, vibration measurement, finite-element analysis na data-driven parameter optimization vinaweza kuendeshwa together katika weaving-machine frames. Kwa sababu different loom geometries, materials used, connection stiffnesses, operating speeds, foundation na damping conditions nchini Uturuki zinaweza kutofautiana, reported optimum thicknesses hazipaswi kuhamishwa directly kwenye machine nyingine bila kufanya measurement na validation upya kwenye machine husika.

Main problem ya study ni nini?

Katika air-jet loom, production speed inapoongezeka, machine frame hufanya kazi chini ya continuous na complex dynamic loads. Main-shaft rotation, changes katika airflow, reciprocating motion ya beat-up mechanism, shedding system na movements za different connecting elements hupeleka repeated forces kwenye frame. Frame stiffness ikiwa insufficient, si vibration level pekee inayoongezeka; stress concentration katika connection regions na structural deformation pia zinaweza kuongezeka.

Gap inayolengwa na study ni kuchunguza dynamic behavior ya frame inayobeba whole loom chini ya operating conditions kwa kutumia experiment, finite-element model na optimization algorithm together, badala ya kuangalia only dynamics za moving sub-mechanisms za loom.

Frame ilimodeliwaje?

Wall panels na beams zilimodeliwa kwa SolidWorks 2022, na three-dimensional structure ikahamishwa kwenye ANSYS Workbench 2022R2. Q345B, HT300 na QT500-7 materials zilitumika kwa wall panels, beams na other components mtawalia. Baadhi ya small holes ambazo hazikuwa important kwa stress zilitolewa kwenye model ili kupunguza computational load.

Mesh size ilirefined hadi 10 mm katika critical beam connections na load-application points, huku 15 mm ikitumika katika regions nyingine. Model iliyoundwa na tetrahedral elements ina approximately 120.000 elements na 250.000 nodes.

Finite-element model ilikaguliwaje kwa experiment?

Bolt holes zinazounganisha frame na floor zilifungwa fully, na Block Lanczos method ilitumika kupata natural frequencies. Sambamba na hilo, actual frame iliboltiwa kwenye steel test platform na vibration dampers zikawekwa chini yake kuwakilisha actual operating condition.

Katika modal experiment, PCB 086D20 impact hammer na PCB TLD356A16 triaxial accelerometers zilitumika. Total sensors 16 zilitumika kwa zamu katika different measurement points. Data zilikusanywa kwa LMS SCADAS Mobile SCM05 system; sampling frequency ilikuwa 1024 Hz, na recording duration ya kila test ikawekwa 15–20 seconds. Five valid hammer impacts zilitumika katika kila measurement point na linear averaging ikatumika kwenye frequency-response functions. First six modes zilitambuliwa kwa PolyMax algorithm.

Katika first mode, side walls zilioscillate katika Y direction, upper beams zikasogea in phase na walls, huku smaller deformation ikionekana kwenye lower beams. Katika second mode, lower beam ilionyesha forward-backward bending behavior katika X direction. Katika third mode, vertical bending katika Z direction ikawa dominant katika upper na lower beams.

Researchers walieleza kwamba simulation natural frequencies kuwa kidogo higher kuliko experimental frequencies katika first modes kunatokana na linear model kutowakilisha fully nonlinear damping na energy losses za real structure. Error values za six modes ziko kati ya −%12,9 na %10,7. Pia, diagonal elements za MAC matrix kuwa close na 1 na off-diagonal elements kuwa close na 0 kulitafsiriwa kama high agreement kati ya experimental na calculated mode shapes.

Vibration ilibadilikaje operating speed ilipoongezeka?

Operating vibration ilichunguzwa katika range ya 600–1000 r/min. Four evaluation points zilichaguliwa katika front-left, front-right, rear-left na rear-right regions za frame; RMS vibration accelerations katika X, Y na Z axes zilitathminiwa.

Katika all evaluation points, vibration iliongezeka rotation speed ilipoongezeka. Change iliyosisitizwa especially na researchers ilitokea karibu na 900 r/min: RMS increase curves zikawa steeper kuanzia point hii. Y-direction vibration ilikuwa more dominant upande wa rear. Kwa mfano, katika 1000 r/min, Y-direction RMS vibration acceleration kwenye rear-left measurement point ilikaribia approximately 8,0 m/s². Value hii ni approximate magnitude iliyosomwa kutoka graph; haipaswi kutathminiwa kama exact table value.

Katika front region, X na Y-direction vibrations zilikuwa closer kwa kila nyingine, lakini after 900 r/min X-direction component ikawa slightly dominant. Study ilihusisha hali hii na inertia effect inayotokana na reciprocating motion ya beat-up mechanism.

Actual vibration measurements zilibadilishwaje kuwa simulation loads?

One important methodological feature ya research ni kwamba experimental acceleration data haikuingizwa directly kwenye finite-element analysis kama simple acceleration boundary condition; kwanza ilibadilishwa kuwa dynamic external forces kupitia multibody inverse-dynamics solution.

Kinematic relationship kati ya absolute acceleration kwenye measurement point na generalized coordinates ilitolewa kama:

\[ a_{\mathrm{meas}}(t)=J(q)\ddot{q}+\dot{J}(q,\dot{q})\dot{q} \]

Hapa \(a_{\mathrm{meas}}(t)\) ni acceleration iliyopimwa kwenye experiment, \(J(q)\) ni Jacobian matrix ya measurement point relative kwa generalized coordinates, na \(q\), \(\dot q\), \(\ddot q\) zinawakilisha generalized position, velocity na acceleration mtawalia.

Kwa kutumia known motion trajectories, generalized acceleration ilihesabiwa kwa inverse relationship hii:

\[ \ddot q(t)=J^{+}(q)\left[a_{\mathrm{meas}}(t)-\dot J(q,\dot q)\dot q\right] \]

\(J^{+}\) inawakilisha pseudo-inverse ya Jacobian matrix inayotumika katika least-squares solution.

Kisha multibody dynamic equations za system:

\[ M(q)\ddot q+\Phi_q^{T}\lambda = Q(q,\dot q,t)+F_{\mathrm{ext}}(t) \]

na constraint equation:

\[ \Phi(q,t)=0 \]

ziliandikwa. Hapa \(M(q)\) ni mass matrix, \(\Phi_q\) constraint Jacobian, \(\lambda\) constraint reactions, \(Q\) Coriolis, centrifugal, damping na other internal forces, na \(F_{\mathrm{ext}}\) ni dynamic external excitation force inayotafutwa.

Kwa hiyo external excitation ilitatuliwa inversely kama:

\[ F_{\mathrm{ext}}(t) = M(q)\ddot q(t)+\Phi_q^{T}\lambda-Q(q,\dot q,t) \]

na kutumika kwenye relevant bearing seats na critical connection points. Calculations hizi zilifanywa katika MATLAB R2024a.

Stress na deformation ziliconcentrate wapi?

Katika dynamic finite-element solution kwa 900 r/min, maximum equivalent stress ya frame ilipatikana kuwa 36,992 MPa. Most critical region ilikuwa connection ya rear lower beam na left wall panel. Study inaeleza kwamba combining vibrations kutoka connecting rod na cam box katika region hii huongeza mechanical loading.

High-stress regions kwenye wall panel zilitokea especially karibu na beat-up shaft positioning holes na cam box. Katika overall deformation behavior, frame ili-sway sideways na deformation ikawa more pronounced kadiri wall-panel height ilivyoongezeka. Maximum deformation kwenye wall panel ilionekana katika upper region.

Operating speed ilipoongezwa kutoka 600 hadi 1000 r/min, maximum stress na deformation zote ziliongezeka. Researchers walichagua 900 r/min condition kama main operating condition ya subsequent structural optimization kwa sababu increase slope ikawa more pronounced na vibration behavior ilihusishwa na natural frequency.

Kwa nini BA-HHO-SVR ilitumika?

Kufanya detailed dynamic finite-element analysis kwa every possible geometric-parameter combination ya frame ni computationally expensive. Researchers kwa hiyo waliunda surrogate model inayoweza kujifunza nonlinear relationship kati ya six geometric input parameters na equivalent stress.

Kwanza, Back Propagation Neural Network (BPNN), Random Forest (RF) na Support Vector Regression (SVR) zililinganishwa. Miongoni mwa base models, SVR ilitoa highest value kwenye test set kwa \(R^2=0,8265\). Kisha SVR hyperparameters zilioptimized kwa GA, PSO, HHO na improved BA-HHO methods.

Main regression relationship ya SVR ilitolewa katika study kama:

\[ y(x)=\omega \cdot \phi(x)+b \]

. Hapa \(x\) ni input variables, \(\phi(x)\) ni transformation kwenda high-dimensional feature space, \(\omega\) ni weight vector na \(b\) ni bias term.

Katika SVR optimization, balance kati ya error tolerance na model complexity ilidhibitiwa kupitia penalty coefficient \(C\), epsilon tolerance \(\varepsilon\) na kernel parameter \(\gamma\).

BA-HHO ilileta changes zipi?

Katika improved Harris Hawks Optimization approach, initial search range ilipunguzwa hadi %50 ya total range ili kuzuia initial population kusambaa excessively kwenye whole range:

\[ hawks=lb+rand(0,1)\times(ub-lb)\times0.5 \]

Badala ya single best individual kuongoza entire population, top %30 ya best-performing individuals ilihifadhiwa kama elite hawk group. Iteration iliposonga, local step size:

\[ step=0.05\left(1-\frac{iter}{max\_iter}\right) \]

na exploration intensity:

\[ explore\_intensity = 0.3-iter\left(\frac{0.25}{max\_iter}\right) \]

zilishushwa.

Elite individuals zilifanya fine search karibu na positions zao, huku normal individuals zikielekezwa kuelekea randomly selected elite solutions; worst %20 group ilibadilishwa na mutated variants za elite individuals. Lengo lilikuwa both kupunguza premature trapping katika local optimum na kuhamia precise parameter search katika final stages.

Ni frame parameters zipi zilioptimized?

Six geometric variables zilichaguliwa kama inputs:

• T1: upper rear beam thickness,
• T2: upper front beam thickness,
• T3: lower rear beam thickness,
• T4: lower front beam thickness,
• T5: middle support thickness,
• T6: beat-up/striking shaft support-plate thickness.

Parameter combinations zilizoundwa kwa Central Composite Design na Variance Inflation Factor optimal design zilianalizwa dynamically katika ANSYS na corresponding equivalent stresses zikabadilishwa kuwa dataset. Katika gray relational analysis, all six variables zilipatikana highly related na equivalent stress na zikahifadhiwa kama model inputs.

Prediction performance ya model iko katika kiwango gani?

BA-HHO-SVR ilitoa highest R² na lowest RMSE na MAE among compared models. Katika prediction-example graph ya study, predicted na reference values zilionekana kufuatana closely, na reported error ratios zilibaki ndani ya ±%2 boundary.

Kuna important source note hapa: results section inasema kwamba performance metrics zote tatu ni “highest values”. Kulingana na Table 6, correct quantitative situation ni kwamba R² ndiyo highest, huku error measures RMSE na MAE zikiwa lowest. Katika article hii numerical table imechukuliwa kama msingi na wording ya source haijabadilishwa kimya kimya kuwa finding tofauti.

Ni geometry gani ilipatikana baada ya optimization?

Katika dynamic finite-element validation iliyofanywa kwa parameters zilizopendekezwa na BA-HHO-SVR, maximum equivalent stress ilihesabiwa kuwa 32,933 MPa. Kwa kuwa model prediction ilikuwa 33,0248 MPa, study inaripoti prediction-simulation difference ya %0,28.

Hata hivyo, kuna clear parameter-range issue katika source. Katika five-level design table, maximum values zilizotolewa kwa T1–T6 ni 16, 12, 12,5, 13,5, 100 na 25 mm mtawalia, huku all reported BA-HHO-SVR optimum values zikiwa slightly above levels hizi. Study haielezi separately kama exceedance hii inatokana na continuous optimization range, rounding au different boundary definition. Kwa hiyo optimum parameters zinapaswa kuhifadhiwa exactly kama zilivyoripotiwa katika study, na haipaswi kuassume kwamba production design limits definitely zinajumuisha values hizi.

Matokeo yanayoungwa mkono na utafiti

• Modal finite-element model ya air-jet loom frame iliyochunguzwa ilionyesha reasonable agreement na physical modal experiment.
• Katika 600–1000 r/min operating range, vibration level katika evaluation points nne iliongezeka speed ilipoongezeka.
• Katika system iliyochunguzwa, region ya approximately 900 r/min ilihusishwa na noticeable dynamic-response increase.
• Katika 900 r/min condition, maximum equivalent stress ya initial frame ilihesabiwa kuwa 36,992 MPa na critical region ikaainishwa kama rear lower beam–left wall panel connection.
• Miongoni mwa compared prediction models, BA-HHO-SVR ilitoa highest R² na lowest RMSE na MAE.
• Katika finite-element validation ya BA-HHO-SVR geometry, maximum stress ilishuka hadi 32,933 MPa na %0,28 difference ikaripotiwa kati ya prediction na simulation.

Matokeo ambayo utafiti hauungi mkono au haujatesti

• Haijaonyeshwa kwamba optimum geometry ni universal optimum kwa all air-jet looms.
• Hakuna long-term physical production experiment iliyoreported kwa optimized new frame geometry.
• Haijatestwa kwamba %10,9 reduction katika stress inatoa direct increase ya fabric quality kwa specific percentage.
• Haijabainishwa optimized design inaongeza fatigue life kwa kiwango gani.
• Haiwezi kuhitimishwa kutoka problem hii moja kwamba BA-HHO-SVR ni superior kuliko other algorithms katika all engineering-optimization problems.
• Reported geometric optimum values haziwezi kuhamishwa directly kwenye different loom sizes, materials au operating conditions.

Mbinu na Matokeo ya Utafiti

Experimental na numerical workflow

1. Geometric design ya air-jet loom frame iliundwa.
2. Finite-element model yenye approximately 120.000 elements na 250.000 nodes iliundwa katika ANSYS Workbench.
3. Modal analysis ilifanywa kwa Block Lanczos method.
4. Modal experiment ilifanywa kwenye actual frame kwa impact hammer na triaxial accelerometers.
5. First six natural frequencies na mode shapes zililinganishwa; modal agreement ikatathminiwa kwa MAC matrix.
6. Vibrations katika four critical points za frame zilipimwa katika 600–1000 r/min operating range.
7. Experimental accelerations zilibadilishwa kuwa external excitation forces kwa multibody inverse-dynamics calculation.
8. Forces hizi zilitumika kwenye finite-element model na stress pamoja na deformation regions zikatambuliwa.
9. Parametric dataset ilitengenezwa kwa six geometric thickness parameters.
10. BPNN, RF na SVR base models zililinganishwa.
11. SVR ilioptimized kwa GA, PSO, HHO na improved BA-HHO.
12. Parameter combination inayolenga minimum stress ilitambuliwa kwa BA-HHO-SVR.
13. Proposed geometry ikavalidated tena kwa finite-element dynamic simulation.

Modal-test parameters

Operating vibration na critical condition

Vibration tests zilijumuisha operating levels za 600, 700, 800, 900 na 1000 r/min. RMS acceleration iliongezeka katika X, Y na Z directions speed ilipoongezeka. Katika rear evaluation points, especially Y direction ikawa dominant, na researchers wakatathmini operating region ya approximately 900 r/min kama critical vibration condition inayohusishwa na natural frequency.

Katika dynamic analysis ya 900 r/min:

• initial maximum equivalent stress: 36,992 MPa,
• critical stress region: rear lower beam–left wall panel connection,
• critical wall-panel regions: beat-up shaft positioning hole na area karibu na cam box,
• deformation behavior: mainly lateral sway ya frame na increasing deformation katika upper part ya wall panel.

Machine-learning data structure

Model inputs ziliundwa na six geometric parameters, huku output ikiwa equivalent stress. Dataset iligawanywa randomly kuwa %70 training na %30 test.

Initial SVR parameters:

• \(C = 2\)
• \(\varepsilon = 0,1\)
• \(\gamma = 0,1\)

Katika HHO-SVR na BA-HHO-SVR optimization, population ya 20 na maximum iteration count ya 200 zilitumika. Ranges za optimized SVR parameters:

• \(C: [1,500]\)
• \(\varepsilon: [0,01;0,3]\)
• \(\gamma: [0,001;5]\)

Model-evaluation metrics

Coefficient of determination:

\[ R^2 = 1- \frac{\sum_i (y_i-\hat y_i)^2} {\sum_i (y_i-\bar y)^2} \]

Mean absolute error:

\[ MAE = \frac{1}{M} \sum_{i=1}^{M} |y_i-\hat y_i| \]

Root mean square error:

\[ RMSE = \sqrt{ \frac{1}{M} \sum_{i=1}^{M} (\hat y_i-y_i)^2 } \]

Katika metrics hizi, higher \(R^2\) inaonyesha higher fit ya predictions kwa explained variance, huku lower MAE na RMSE zikionyesha reduced numerical prediction error. Kwa BA-HHO-SVR, source inaripoti \(R^2=0,9906\), RMSE = 0,1798 na MAE = 0,1419.

Finite-element validation ya optimum design

Katika comparison hii, BA-HHO-SVR ilitoa both lowest validated maximum equivalent stress na lowest reported error rate kati ya prediction na simulation. Ikilinganishwa na 36,992 MPa katika initial model, simulation result ya 32,933 MPa ilihesabiwa na study kama %10,9 reduction katika maximum stress.

Hata hivyo, validation si long-term loading experiment iliyofanywa upya kwenye physical prototype ya optimized geometry. Final-stage validation ni dynamic finite-element calculation. Distinction hii inapaswa kuhifadhiwa wakati wa kutafsiri long-term reliability ya result katika real production conditions.

Maelezo ya Chanzo na Mbinu

Jina kamili asilia la utafiti: Study of Dynamic Analysis and Structural Parameters Optimization of the Air-Jet Loom Frame System

Waandishi: Jiacheng Zhou, Zhuo Chen, Shengli Lv, Libin Zhang, Feng Hu, Min Shen, Fei Fan, Lianqing Yu, Mingzhang Chen, Chengcheng Wang, Xiaoshuang Xiong.

Corresponding author: Chengcheng Wang.

Taasisi: Hubei Key Laboratory of Digital Textile Equipment, School of Mechanical Engineering and Automation, Wuhan Textile University, Wuhan, China; Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, China.

Jarida: Machines.

Mchapishaji: MDPI.

Bibliographic record: Machines 2026, 14, 640.

DOI: 10.3390/machines14060640.

Publication date: 1 June 2026.

Source type na peer-review status: Ni peer-reviewed original research article.

Official publication link:https://doi.org/10.3390/machines14060640

Leseni: Creative Commons Attribution (CC BY).

Funding: Natural Science Foundation of Hubei Province, 2025AFB365 na 2024AFB756; Key R&D Program of Shandong Province, 2024CXGC010215; Science and Technology Research Project of Hubei Provincial Department of Education, D20241603.

Data availability: Waandishi wameripoti kwamba data zinaweza kutolewa upon request.

Conflict of interest: Waandishi wametangaza kwamba hakuna conflict of interest.

Author contributions: Jiacheng Zhou na Zhuo Chen katika design/execution ya simulations na experiments pamoja na writing ya first draft; Shengli Lv, Libin Zhang na Feng Hu katika data curation na experimental analyses; Min Shen, Mingzhang Chen na Fei Fan katika literature review na data extraction. Lianqing Yu, Chengcheng Wang na Xiaoshuang Xiong walichangia funding ya research na provision ya experimental equipment. Source inaeleza kwamba authors wote wamesoma na kuapprove published version.

Scientific findings, numerical values, method explanations na algorithm performances katika Verianla article hii zinategemea source study iliyochunguzwa. Hakuna new experimental au scientific finding kutoka external sources iliyoongezwa isipokuwa bibliographic identity.

Source-internal parameter-boundary note: Katika five-level parameter table ya source, maximum values za T1–T6 ni 16, 12, 12,5, 13,5, 100 na 25 mm. Kwa upande mwingine, BA-HHO-SVR optimum imetolewa kama 16,1545; 12,0493; 12,5620; 13,6456; 100,8555 na 25,1106 mm. Source haielezi separately sababu ya small boundary exceedances hizi. Values zimehifadhiwa kama zilivyoripotiwa katika source.

Source-internal performance-expression note: Katika results section, R², RMSE na MAE values zote za BA-HHO-SVR zinaelezwa kama “highest”. Katika Table 6, R² ndiyo highest, wakati RMSE na MAE ndiyo lowest values miongoni mwa compared models. Difference hii kati ya numerical table na verbal statement haipaswi kupuuzwa kimya kimya.

Main methodological boundary: Modal na operating-vibration measurements za existing frame zinategemea physical experiments. Kwa upande mwingine, stress validation ya final new geometry iliyopatikana kwa optimization ilifanywa kwa finite-element dynamic simulation. Study hairipoti long-term physical fatigue experiment ya optimized frame, serial-production field test au direct fabric-quality performance validation.