COMPARATIVE ANALYSIS OF THE ENERGY CONSUMED BY NEEDLE BAR MECHANISM AND THE MECHANISM DRIVING THE FEED DOG OF A TOP DRIVE SEWING MACHINE

The paper focuses on the energy consumed by two mechanisms of sewing machine for straight lockstitch (stitch line 301): needle driving mechanism and the transporting mechanism. The first mechanism needle driving, is a simple structure, but it is the most dynamic one. The second – to moving the fabrics, is the most complicated mechanism of the sewing machine. A comparative analysis of the energy consumed by the two mechanisms for the implementation of their propulsion is made. The correct work of the machine, the seam quality and the quality of the entire sewing product depend to a large extent, on the workings of these two mechanisms. The needle is driven by a slider-crank mechanism, while for the movement of the connected details, at the distance one step is done by a working part – a feed dog. It is attached to a carrier and its trajectory is a closed planar curve, close to the ellipse. The feed dog receives the horizontal and vertical component of its motion from two conditionally separate kinematic chains that have a common drive. The aim is analytical research and comparative analysis of the energies of needle bar mechanism and a mechanism driving the feed dog of the sewing machine. The energy consumed by each of the links of chains, of the chains themselves and total energy consumed by each of the two mechanisms for a full turn of the main shaft of the machine was studied. A comparative analysis of the energies and their distribution was carried out during the working process and the free movement of each of them. The results of the comparative analysis are presented in graphs and diagrams. It can be seen that the energy consumed by the needle mechanism is significantly greater than that of the transport mechanism. This fact is due to the much higher speeds of the links of the first one. KEYWORDS


Introduction.
As a basic method of connecting the details in the garment industry, the method by a sewing thread has been mainly used. The most common application in practice are the universal sewing machines (SMs) for stitch class-301 (lockstitch formed with two threads). In order to form a stitch, several basic mechanisms in the sewing machine (SM) interact: the needle, the thread take-up lever, the loop taker (shuttle) and the feed dog (FD). The trend is to improve the machine to  13 increase productivity, improve service conditions and stitch quality. For this purpose, many improvements have been made to the SM's design mechanisms [1].

ENGINEERING SCIENCES
New possibilities for improving the process of forming stitch are provided by studying, analyzing and optimizing the kinematic and dynamic parameters of the Needle Bar Mechanism (NBM) and the Feed Dog Mechanism (FDM) when they interact with the other mechanisms in the SMs. A number of studies have been conducted in [2][3][4][5][6][7][8][9][10][11] as well as in many others.
The first mechanism (NBM) is with a simple structure, but it is the most dynamic one. Stitch quality, seam strength, and sewing machine's productivity depend largely on his work. The second mechanism (FDM) is the most complicated of the SM's mechanisms and also influences significantly the productivity, the quality of the stitch line and the sewing product.
By the mechanisms of each machine that perform the necessary movements, the mechanical energy is transferred from the source to the executive links. Studying their dynamics is a complex and labor-intensive task. It can be simplified by examining the change of energy and its distribution between the units of the mechanism over a certain period of time.
By applying the kinetic energy theorem, the law of conservation of mechanical energy and the basis of virtual work, it is easier to find the relations between kinematic (velocity, acceleration) and dynamic (forces, moments, mass characteristics) parameters of the rigid bodies' movement and of the rigid body systems. There is no need to be studied the differential law of motion. Therefore, an important issue for the SM's work is the distribution of energy between the units of the mechanisms and its change over the period of working of a machine.
The aim of the presented research is analytical study and comparative analysis of the energy used to drive the units, as well as the total energy of NBM and MTM of SM with upper driven: -for one full turn of the main shaft of the machine; -during the working and free movement of each of the mechanisms.
According to the classification made in [6], depending on the way of driving the chains for horizontal and vertical movement of the feed dog, the machines are with below and upper drive. In the study as an example of a machine with upper driven it was used Textima 8332.
2. Exposition. The carried out technological processes on the SM required proper operation of all machine mechanisms. In order to realize the most commonly used stitch line 301, the needle performs reciprocation motion in a vertical direction. The movement of the connected details, at the required distance (stitch line step), into lockstitch machines, is done most often by a working part -a FD.
The task of the NBM is to convert rotary motion of the main shaft into a vertical linear motion of the needle bar (NB) in which the needle is fixed. For this purpose, a slider-crank mechanism is most commonly used in SMs. In the recent years, the analytical methods: "instantaneous center of velocity method" [12], [13] and "modeling method" [14][15][16][17][18] have been proposed for the study of the mechanisms of textile and SMs.
In the Textima 8332 main shaft is located at the top of the SM. The motion is convert by a slider-crank mechanism with a crank 1, a connecting link 2 and a slider 3 - Fig.1. This slider-crank mechanism is in-line (axial). The line of motion of the needle passes through the center of rotation point O1 of the crank O1A. These mechanisms are simple in design, provide greater motion uniformity and smaller inertial forces than the offset (non-axial) crank-slider mechanisms. That is the reason they to be mainly used in modern high-speed SMs. The connection between the connecting link and the NB is direct -with an axle between them. A slider is used to stabilize the vertical motion of the NB.
In order to drive the FD and to perform the technological operations, FDM is required to provide the possibility of changing the stitch step and the direction of material movement (to tighten the seam at the beginning and at the end). The implementation of this condition requires the usage of branched poly-contour mechanisms. In Fig.2 is shown the mechanism with upper drive of SM Textima 8332. FDM consists of four, conditionally separate kinematic chains: for horizontal motion of the FD; for its vertical motion of the FD itself and for adjusting the stitch step (not shown in the figure). Both chains for horizontal and vertical movement of the FD have a common drive from the main shaft O1 of the machine located at the top of the machine.  The size of the stitch step needs to be adjusted before the start of the sewing process. This is done by the step adjustment chain by changing the position of point K. During operation of the machine, point K takes an invariably position relative to point O2 on the axis 4 of the frame 3 and the distance between these two points is Δ = const. The basis for this assumption is the results of a study performed in [7]. After replacement of the actual FDM of Textima 8332 containing a III class Assur group, it is assumed that the chain for horizontal movement of the FD -O1ABO2KMO3 is constructed of two consecutively linked hinged four-bar mechanism (O1ABO2 and O2KMO3). The results in [7] show that the error in this substitution is below 1%, which is within the acceptable range. For vertical movement of the FD is used the O1ADEO4 chain containing a hinged four-bar mechanism.
The FD is installed on the rocker (coupler link) CN of the five-bar mechanism O3CNFO4 and performs a general plane motion. The FD is driven simultaneously by the chains for horizontal and vertical movement, which consist of units, some having a general plane motion, and others rotating about one axis.
The Law of Conservation of Energy is valid for the mechanical energy in the NBM and FDM at Textima 8332. The current study ignores the potential energy generated by the rising of the center of gravity and the deformation of the links as it is negligible. Only the kinetic energy is considered in the energy balance. Friction is not considered in the study. The resistance exerted by the material being treated is also not taken into account since the force is different for different types of material and it would not be correct to work with generalized values.
Each mechanism is a mechanical system of connected rigid bodies. According to König's theorem, the kinetic energy of such a system, at every time is a sum of the energies of its links (n number): where: Ekjthe kinetic energy of the mechanism in this moment, kg.m 2 /s 2 ; mithe mass of the i-th link, kg; -the velocity of the center of gravity of the i-th link in the j-th moment, m/s; Jithe moment of inertia of the i-th link, with respect to an axis passing through the mass' center of the link, for the general case of planar motion, kg.m 2 ; ωij -the angular velocity of the i-th link, s -1 .
In [3] was conducted a study on NBM using the mathematical apparatus proposed in [13]. Тhe mass data, mass moments of inertia and kinematic characteristics of the links were taken into account according to them. Based on the above characteristics in [19] the kinetic energy of each unit and the total energy of the mechanism for the main shaft`s one turn of the SM are determined. The energy consumed by the FDM is determined in [20] using the information for mass, mass moments of inertia, and kinematic characteristics of the links according to the conducted studies in [10] and [11].
When studying the kinematics of the mechanisms, in the aforementioned studies, the "Method of the instantaneous center of velocity" [13], which is universal and easily applicable. This method the question of the particular values of trigonometric functions is solved (0, /2, , 3/2), the ambiguity of arc-functions, dividing by zero, numerical methods used, accuracy of work, etc.
By this method, the first two transfer function of the mechanism, respectively velocities, and accelerations, are determined by the instantaneous centers of velocity. It is present in summary form in the table 1.
The studies were done with sufficient accuracy, discretely for 72 points in the range of motion of each unit. Generalized coordinate step:  [12]. The mass of the links, the mass moments of inertia and the position of their mass centers are constant values. Therefore, the change of kinetic energy depends on the angular velocity only. For simplicity, in the current study is accepted ω0 = 1. Furthermore, the resistance of the jointed parts is not considered as it is different for each particular case and depends on the type of textile materials processed on the SM.  . .
The working process (according to Fig.1) of the sewing needle begins at about 180 (the moment of penetration of the material) and finishes about 360 (when the needle leaves the material)the rotation angle of the main shaft of the machine [3]. The period is 180° and consists of two phasesmoving down to the extreme lower position (lower dead point) and upward movement until the needle leaves the material.
The results of the analysis of the energy consumption by the units of the NBM, carried out according to (1), are presented in Fig.3 and Fig.4. The study reveals that the energy peaks are at angles of rotation of the main shaft of the machine approximately 15-20 after the start of the needle working and about 15-20 before its end. The maximum energy values of the links of the mechanism are [19]: 1) of the connecting link Ek,AB = 1,3864 kg.m 2 /s 2at 195 and at 345 - Fig.3 2) of the executive link (needle bar) Ek,nb = 4,3696 kg.m 2 /s 2at 200 and at 340 - Fig.4.
Extremes of E = E (φ) on the NBMs' rocker have abscissa that do not coincide with the abscissa of the extremes of ω = ω (φ). This is due to the fact that the kinetic energy is proportional to both ω 2 and the reduced moment of inertia Jr = Jr (φ), which is a function of φ.

. Kinetic energy of the NBM`s needle bar
Much more complex is FDM (Fig.2). As mentioned above, it is built up of several conditionally separate kinematic chains. The movement of the FD over the needle plate is realized by rotating of the kg.m 2 /s 2   main shaft of the SM from 60° to 170°. This is the working process of the mechanism. It starts after the needle has completed its working process, i.e. it has left the material. The period is 110° and consists of two phases -raising and lowering. Its highest point of the FD is between 110° -120° [11]. The results of the energy research of the links and the chains of the FDM are conducted according to (1) and are presented in Fig.5-7. The indices correspond to the numbers of the units according to Fig.2.
The energy of the chain for horizontal movement of the FD (Fig.5) is most significantly influenced by the energy of the coupler link AB by the six-bar mechanism O1ABO2KMO3. At 160° and 340° rotation angles of the main shaft of the machine, the graph has extreme values, respectively Ek = 62,96.10 -2 kg.m 2 /s 2 and Ek = 62,05.10 -2 kg.m 2 /s 2 [20].

Fig.5. The kinetic energy of the chain of horizontal movement of the feed dog O1ABO2KMO3 and its links
On the kinetic energy of the chain for vertical movement of the FD, the main effect cause the kinetic energy of the chain of DE of the four-bar mechanism О1DEO4 (Fig.6). The maximum values, Ek = 18,46.10 -3 kg.m 2 /s 2 and Ek = 18,55.10 -3 kg.m 2 /s 2 are achieved at the angles of rotation of the main shaft -60° and 240° [20].
From the chain on the FD (the five-bar mechanism О2CNFO4), the energy of the bearer CN on which the FD is attached is greatest (Fig.7). CN performs plane motion. At the angles rotation 0° and 160° the chain has maximum values on the kinetic energy -Ek = 24,01.10 -2 kg.m 2 /s 2 and Ek = 24,61.10 -2 kg.m 2 /s 2 [20].
And here extremes of E = E (φ) on the NBM's rockers have abscissa that do not coincide with the abscissa of the extremes of ω = ω (φ). The kinetic energy is proportional not only ω 2 , but also the reduced moment of inertia Jr = Jr (φ), which is a function of φ.
The analysis of the NBM energy balance reveals that the main influence on the total energy consumed and the law for its distribution has the kinetic energy of the NB (position 3 in Fig.1). The energy of the NBM (Fig.8) has two peaks -Ek = 5,7416 kg.m 2 /s 2 , which are during the needle workat 200 and at 340 [19]. Textima 8332 receives at the angles of rotation of its main shaft 160° and 350° (Fig.9) its maximum values (Ek = 95,66. 10 -2 kg.m 2 /s 2 and Ek = 93,72. 10 -2 kg.m 2 /s 2 ) of the total energy of the FDM [20]. The results reveal that the NBM energy peak is nearly 6 times higher than that of FDM. This is due to the much higher speeds of the needle bar mechanism than the speed of the FD and its drive mechanism links.
The energy changing of the mechanism for a given period of time is equal to the work generated by the forces and moments acting on the links of the NBM and the FDM, for the same period.
The energy form of the motion equation is integrated: taking into account that the work done by the external forces acting on the systems is: where: A -the work performed by the external forces acting on the system in the 0 to 2π angle of rotation φ of the main shaft of the machine, kg.m 2 /s 2 ; J -the mass inertia moment, kg.m 2 ; ω -the angular velocity of the main shaft, s -1 ; M -the moment of active forces acting on the mechanism. For each of the both considered mechanisms of Textima 8332, the total energy is determined for a full turn of the main shaft of the machine.
The distribution of the full energy consumed by the NBM is shown in Fig.10. Approximately 1/3 (28.57%) is applied by the mechanism's rocker and slightly over 2/3 by the NB -71.43%. During the needle's working process, a slight increase in the energy consumed by the NB (from 71.43% to 74.15%) and a small reduction in energy consumed by the rocker (from 28.57% to 25.85%) was recorded.