STARTING-UP OF KNITTING MACHINES WITH PRESTRESSED DRIVE CONNECTIONS

Introduction. One of the most significant factors affecting the knitting machines’ operation efficiency is represented by dynamic forces arising when transitional modes (starting, braking, mechanisms’ switching, etc.) [1...3]. The dynamic analysis of machines in order to find the dynamic overloads coefficients is of high importance to solve the current problem of improving the knitting machines efficiency (increasing machine productivity and the produced tissue quality). Analysis of recent research and publications. Modern dynamic analysis of machines [1...4] is effected in order to calculate the mechanical systems’ dynamic parameters associated with significant expenses reducing the effectiveness of existing dynamic analysis methods. The research object relates to elaborating the dynamic analysis method for mechanical system which analytical model can be represented as three-mass in-line system with first driving host of weight at drive’s prestressed elastic connections. This problem solving we used modern methods of theoretical research based on the mechanical systems’ dynamics theory and the theory of elasticity. This research goal. Given the urgency of improving the knitting machines’ efficiency by reducing the dynamic loads, the purpose of the present research refers to amelioration of dynamic analysis method applicable to knitting machines with pre-strained drive linking. Problem statement. According to studies [1...3] and others, at dynamic processes’ analysis most knitting manually-operated and automatic machines can be presented as equivalent to three-systems where the first leading mass has prestressed connections with the initial conditions of motion

Introduction.One of the most significant factors affecting the knitting machines' operation efficiency is represented by dynamic forces arising when transitional modes (starting, braking, mechanisms' switching, etc.) [1...3].The dynamic analysis of machines in order to find the dynamic overloads coefficients is of high importance to solve the current problem of improving the knitting machines efficiency (increasing machine productivity and the produced tissue quality).
Analysis of recent research and publications.Modern dynamic analysis of machines [1...4] is effected in order to calculate the mechanical systems' dynamic parameters associated with significant expenses reducing the effectiveness of existing dynamic analysis methods.
The research object relates to elaborating the dynamic analysis method for mechanical system which analytical model can be represented as three-mass in-line system with first driving host of weight at drive's prestressed elastic connections.This problem solving we used modern methods of theoretical research based on the mechanical systems' dynamics theory and the theory of elasticity.
This research goal.Given the urgency of improving the knitting machines' efficiency by reducing the dynamic loads, the purpose of the present research refers to amelioration of dynamic analysis method applicable to knitting machines with pre-strained drive linking.
Problem statement.According to studies [1...3] and others, at dynamic processes' analysis most knitting manually-operated and automatic machines can be presented as equivalent to three-systems where the first leading mass has prestressed connections with the initial conditions of motion (12)0 2 3 where (1)0 T , 1 T -initial and starting сcouples applied to the first mass;  C , 23 C system's linkages elasticity couples and their respective first derivatives..The effected studies have shown that the specified conditions of dynamic processes present, it is possible to simplify significantly the existing methods of calculating the coefficient of sytem's masses elastic connections' dynamic loads that requires to define the four cosine amplitudes in solving differential equations of mechanical system motion.
Considering the correlation betwwen three-mass system frequency fluctuations and the proper vibration frequencies corresponding to two-mass systems.The equation of three-mass system motion can be written in the form [1] (dissipative forces are not included)  β -two-mass systems' proper frequencies: p -differentiation symbol; 1 J , 2 J , 3 J -respective system masses' inertial couples.Through solving the differential equations system (2) in the form sin( ) In accordance with the theorem of positivity and сharacteristic equiation roots' separation , the equation roots ( 5) are positive and separated with minor roots, that corresponds to the first element [1].The minor root corresponding to the first element of the determinant (4) is: In accordance with the Viyeta formulas the polynomial roots' sum, taken with the opposite sign, is equal to the coefficient when 2  ω at (5), and the roots product is equal to the free member, ie , .

C C J
Let we show further that the frequency property expressed through an inequality (6) can be extended up to inequality Reformulating equation ( 7), we substitute β > β , we get the inequality (8), which shows that most of the three-mass system elasticity couples' frequencies is greater than most of the two-mass systems' proper vibrations frequency, and the lower three-mass system's frequency is less than the lower of two-mass system frequencies.
The obtained dependences (7), (8) can be used to verify the accuracy of i ω determining as well as for analysis of expression obtained when solving the equations of considered masses' motion.Solution of differential equations (2) with initial conditions (1) has the following form [ According to the initial conditions (1) at 0 t = (12)0 (12)1 (12) 2 12 The maximum possible value of the dynamic coefficient according to (11) Value amplitudes are expressed in cosine dependences [1] Let we reformulate equations ( 14),(15) taking into account (18). ( We can solve the algebraic equations system (21) ( ) where Results obtained.The equations (25) allows to obtain the dynamic system coefficients without finding amplitude of mass vibration, thus significantly reducing the calculations.
Conclusions.Analyzing the research results, we conclude that the proposed method can more efficiently solve the problem of dynamic analysis of any mechanical system which dynamics model can be represented as three-mass in-line system with first leading mass when prestressed elastic connections.
The obtained equations allow to find the dynamic overload coefficients for elastic connections of mechanical systems drive (including knitting operated and automatic machines) without preliminary calculating the amplitude of the system mass vibration, that significantly reduces the calculations.
V.V. Chaban, B.F. Pipa.Starting-up of knitting machines with prestressed drive connections.The article is sanctified to improve method of dynamic calculation of dynamic coefficients of the mechanical systems, the dynamical model of which can be presented by the three-mass row system with the first leading mass at preliminary tension of resilient connections of drive.The study used modern methods of theoretical studies, which are based on the theory of the dynamics of mechanical systems and the theory of elasticity.More perfect method of the dynamical coefficients finding is suggested.Obtained equations allow finding the coefficients of dynamic overloads of resilient connections of the mechanical systems drive without finding amplitudes of vibrations of the system masses that significantly reduces calculations.
Keywords: knitting machine, starting of knitting machine, dynamical loads, dynamical coefficient.