Assumptions for Modeling of the Hot Plate Welding Process Considering the Automatic Welding Machine Design

. Drive and conveyor belts are widely used in processing and mining industries. One of their types, which are often used in light-duty applications, are the belts with round cross-section and several millimeters in diameter. They are often made of thermoplastic elastomers, in particular ofweldable polyurethane. Their production process requires to carry out the operation of joining the belt ends to obtain a closed loop. This operation is often carried out by means of butt welding utilizing the hot plate method. This process is often performed by hand using simple tools. Authors took an effort to design the automatic welding machine, which can make durable joints of this type automatically. The design works comprise control system configuration which calls for identifying the technological parameters of the process, being the reason for undertaking the research works on the hot plate welding process. The main aim of this activity was to formulate of the mathematical model of the hot plate welding of round drive belts which is necessary to identify the process parameters and the correlations between them. In the paper, the assumptions for the hot plate welding process modeling were presented. During their formulating, technical conditions were taken into consideration resulting from some of the characteristics observed in an automatic welding device prototype which had been implemented for industry production.


Introduction
Drive belts with a round cross section and a diameter of several millimeters are commonly employed in industrial machinery as drive systems and conveyors [1,2]. In numerous cases, they are made of thermoplastic elastomers, polyurethane and polyester in particular [3,4]. The manufacturing process of these drive belts is two-stage. In the first stage, the drive belt section with length of several meters is manufactured in the process of continuous extrusion. This stage ends with the belt being wound on a reel for easy storage and transportation. The final stage of manufacturing the finished drive or conveyor belt involves cutting the belt down to the appropriate length and making a permanent connection of its ends [5].
, In many cases, the connection of the belt ends is achieved through butt welding with use of the hot plate method. This method is recognized as an inexpensive and easy means of joining thermoplastic materials [6]. This process is typically carried out by hand, using simple, dedicated tools. However, such an approach typically does not ensure an acceptable repeatability of achieved geometric parameters of the belt after welding, nor does it guarantee a high quality weld. This is due to the manual application of the force necessary to plasticize and form a connection between the belt ends which does not ensure adequately repeatable conditions for carrying out this process [7][8][9]. Answering the industry demand for an automated butt welding process for the drive belts, the authors have proposed an automated welding machine for drive belts. To achieve the correct configuration of the control system, it is required to identify and verify the technological parameters of the welding process [10][11][12][13]. Consequently, research works were taken up focusing on the butt welding of drive belts made of thermoplastic elastomers. The main goal thereof is to formulate a mathematical model of this process, in particular the plasticization of the belt material on the hot plate [14,15] allowing to supplement the design works. Typically, the design of machines to carry out specific technological processes, e.g.: biomass compaction [16][17][18][19], agglomeration of crystallized carbon dioxide [20][21][22][23] or belt perforation [24,25] begins with the formulation of mathematical models as well as analyzing and studying the machine components [26][27][28][29]. The goal of the above mentioned sequence of activities is to specify the working conditions and parameters of the designed machine in order to effectively select its construction features. This approach is also employed for devices not intended for industrial applications, e.g. quality of life solutions for the disabled [30][31][32][33]. In the case of the designed automated device for butt welding of drive belts, due to the novel approach to the welding process (automatic welding for serial production of belts),the research works begin with the development of device prototype. This activity was based on preliminary technological specification developed on the basis of the authors' experience with manual hot welding process [34]. After preliminary testing of the device prototype, further research was undertaken to develop a mathematical model of the hot welding process. The obtained model allows to describe thecourse of the hot welding operation and its dependence on the technological parameters of the process. Additionally, the planned research include verification of weld quality by means of static tensile testing, in combination with the developed model, this allows to correctly identify the technological parameters for the operation of the automated hot welding device.

The classic description of the hot plate welding process
Considering the required technological operations, the butt welding process of drive belts can be divided into 5 phases (Fig. 1) characterized by different physical phenomena [35][36][37][38]. The most characteristic is the plastic deformation of the belt end under conditions of elevated temperature and compression loads. Pressing the plasticized belt ends together allows for the chemical reactions and physical interactions to initialize between the polymer chains [6,10]. Therefore, the process and result of material plasticization affects the further phases of the hot welding process, in particular the ability of belt ends to form a permanent bond [39]. During the matching phase of the belt ends (Fig. 1a), the belt ends (1) are held by shaped grips(2) they are moved towards the hot plate surface (3) with velocity vm. After contact is achieved between the belt (1) and the hot plate (3), the belt ends are pressed towards it with force Fm. In this stage, the flash is formed as a result of preliminary plasticization and melting of the belt (1) on the hot plate (3). Partial melting of the surface causes the belt end surface (1) to match the flat surface of the hot plate (3). Consequently, the conduction of heat at points between the hot plate and protruding points of the uneven belt end changes to contact conduction present on the entire surface. This improves the efficiency of the heating process and improves the bond quality as parallel position of connected belt surfaces is assured in this way. During the matching of the belt surface end (1) on the hot plate (3), one can observe physical phenomena associated with heat exchange: conduction, convection and radiation. Accounting for each individual heat flux, the following can be identified:  heat Qp3-1transmitted from the hot plate (3) onto the belt surface (1) via contact conduction,  heat Qp1conducted within the belt material (1),  heat Qc3transmitted from the hot plate (3) to the belt (1) through convection,  heat Qr3transmitted from the hot plate (3) to the belt (1) through radiation,  heat Qc1dissipated by the external cylindrical surface of the belt (1) to the environment through convection,  heat Qr1dissipated by the external cylindrical surface of the belt (1) to the environment through radiation. In this case, the dominant processes of heat exchange evidently causing the increase of belt temperature are: contact conduction between the hot plate (3) and the belt (1) and internal conduction within the material of the belt (1). Thermal radiation is not as significant as conduction as the process temperature is low and its value typically does not exceed 300°C [3,[34][35][36][37]. For the purpose of further analysis, it is also possible to omit convectionsince there is no forced circulation of gas in the area of plasticized material. Consequently, the forced convection phenomenon which is characterized by higher efficiency of thermal transmission in comparison to natural convection does not occur [40].On the other hand, the phenomenon of natural convection is negligible in comparison to conduction, considering fact that the ends of the belts are surrounded by shaped grips, which play the role of shields in sense. Pressing the flat end surface of the belt to the hot plate causes a non-linear increase of its temperature along the axis [36]. Therefore, during heating, two characteristic geometric dimensions can be identified:  length p, at which the belt temperature in its central axis exceeds the weld temperature Tw (the temperature at which the material is plasticized and ready to form a permanent connection),  length h, at which the belt temperature in its central axis exceeds the ambient temperature T0. Fmforce of matching the belt end on the hot plate, Fhpressing force of the belt towards the hot plate during heating, Fjpressing force of the belt during joining operation, Fcpressing force during the cooling of the joined area, vm-velocity of pressing motion towards the hot plate in the matchingphase,vhvelocity during heating,vjvelocity during joining,vc-velocity during cooling operationTphot plate temperature, Tw -welding temperature, T0ambient temperature, pbelt plasticization distance, hthe section heated to temperature exceeding ambient temperature; Qp3-1heat transmitted between the hot plate and the belt,Qp1-2heat transmitted between the belt and the grip, Qp1heat conducted inside the material, Qr1heat dissipated to the surroundings through radiation, Qr3heat dissipated to the surroundings from the hot plate through radiation, Qc1heat dissipated to the surroundings from the belt through convection, Qc3heat dissipated to the surroundings from the hot plate through convection.
During the proper heating phase (Fig. 1b), the belt ends (1) are pressed towards the hot plate (3) using jaw grips (2) with force Fh. In this stage, the physical phenomena related to heat exchange are analogous to the matching of the belt end surface (1). The area of convection Qc1and thermal radiation Qr1is expanded as a result of the increased plasticization distance p. Consequently, and additional mechanism of heat transmission is observed Qp1-2which entails thermal conductance from the belt (1) to the jaws (2).The main assumptions during the actual heating phase are as follows:  increasing the distance of material plasticization of the belt pto the value allowing the best conditions for making the connection in the subsequent stages of the process, increasing the length of section h of the material heated to the temperature value exceeding ambient temperature is the side effect of the heating process,  the pressing force Fhis significantly lower than the pressing force during flattening of the belt end surface on the hot plate Fm (Fhis equal to 10% -20% of Fm) due to the rapidly decreasing material viscosity together with the increase of temperature [37]. If excessive pressing force is applied during heating, too much flashing occurs. This causes an unjustified loss of material and outflow of the plasticized material from the heating area which may cause the formation of cavities and hollows after connecting the belt ends. On the other hand, a certain, low value of force Fhis required to achieve the certain conditions required for heat transmission. In the stage of retraction of the heating device from the heating area (Fig. 1c), the belt (1) is moved away from the hot plate (3) at a small distance, and is afterwards retracted. During this stage, the process of heating belt ends is finished, at the same time the effect of cooling of these surfaces is noticeable as a result of interaction with the surrounding gas. It is important that the flat surface temperature does not decrease below the welding temperature Tw. Consequently, the hot plate temperature Tpis slightly higher than the required temperature for the weldTw. In the proper joining phase (Fig. 1d) the belt ends (1) are moved together at velocity vjto form a bond, and are afterwards pressed together with forceFj. This stage is highly important for achieving the correct result of the entire welding process as this is when interactions between the belt end material begin:  chemical reactions between the polymer macromolecules,  mechanical interactions between the macromolecules involving bonding together which facilitates further chemical reactions [11]. In the pressing and cooling phase of the bond (Fig. 1e) the belt ends (1) are pressed together. In this stage, the bond area is cooled as a result of thermal exchange with the surrounding. In the ideal scenario, the bond should be kept under the compressing force Fcfor the time necessary to reduce its temperature to T0. The main assumptions for this stage are formulated as follows:  the temperature of the belt and bonded area is balanced as a result of conduction within the material structure (Qp1heat),  continuation of the chemical reactions and mechanical interactions between the macromolecules,  cooling down of the bonded area is achieved by thermal exchange with the environment through convection (Qc1) and radiation (Qr1). When cooling is complete, the connected belt can undergo further processing, e.g. to remove the flashing.The total time required to complete the hot welding process according to the above described method is from several seconds to a dozen or so minutes, this depends on the material and dimensions of the welded components [41]. Typically, the cooling stage is the longest [37]. When designing the technology and device for butt welding, an important factor to consider is energy efficiency. The supply of thermal energy occurs in the first two phases of the process ( Fig. 1a and 1b). After accounting for the fact that at the same time losses of energy also occur as a result of the hot plate (3) and the belt (1) interacting with the surroundings, it is therefore desirable to shorten the duration of these stages as much as possible, e.g. by reducing the required length of plasticization pto the lowest possible value ensuring proper weld is achieved. The second potential method to shorten the heating time of the material is to increase the temperature of the hot plateTp; however, this method is limited due to the possibility of thermal damage to the polymer. The energy efficiency of the process can be further improved by shortening the extraction time of the hot plate (3) from the area between the belt ends (1) during the third phase of the process (Fig. 1c). Contrary to the classic hot welding method, the designed automated solution withdraws the hot plate without moving the belt ends away to them. In order to limit the deformation of plasticized material, the plate surface will be covered with a material with low coefficient of friction when contacting the end surface of the plasticized belt, e.g. Teflon.
In the case of the joining phase (Fig. 1d), the process energy efficiency can be improved by shortening the time in which the belt ends are connected. During this phase, it is important to achieve a compromise between the short duration (it is desirable to achieve high velocity of moving the belt ends together vj), ensuring reduced energy loss in the process and avoiding excessive deformation of the plasticized material and pushing it outside the weld area due to dynamic pressing of both ends together (in the case of maintaining a high value of velocity vj). During the pressing and cooling of the bonded area (Fig. 1e), it is not possible to significantly improvethe energy efficiency of the process. It is possible to accelerate the cooling of the bonded area with forced movement of surrounding gas; however, this only affects process duration and requires to provide additional energy in order to force the circulation of the cooling medium.

The current approach to the modeling of the butt welding process
There are numerous other works on butt welding of plastics considering the characteristics of the hot-welded materials, focusing of the different aspects of the process. Among others, the following study results are known:  the hot welding process of rigid plastics for the purpose of joining the components of polypropylene vessels, demonstrating the dependence of weld strength and heating time together with the pressure applied on the welded items [42],  hot welding of rectangular beams made of rigid polypropylene. The work focused on analyzing the microstructure of the bond and the influence of its imperfections on bond strength, whereas bond quality depended on the technological parameters of the welding process, e.g. pressing strength of the welded items to the hot plate during plasticization as well as the strength of pressing the items together [43],  hot welding of rigid polyamide inserts, the paper proves experimentally that there is a correlation between the strength of the welded bond and the heating temperature, heating time and pressing speed in the individual stages of the process [44],  examining the dependence of likelihood of cracks forming in the bonded area in relation to the technological parameters of the butt welding process for rigid plastics, while hot welding with controlled pressing force in the individual stages of the process [45],  optimization of the hot welding process inregards to: selection of technological parameters with use of CAx tools [46], butt welding in serial production [47] as well as selecting optimized process parameters for a given material type with measurement of thickness of the plasticized layer [48],  considerations backed by experimental results regarding the welding of different types of plastics with and without fillers while welding with controlled pressing force [49][50][51][52],  modeling of butt welding based on physical phenomena occurring in each stage of the process [38]. The listed representative examples of current research together with their results share two universal characteristics:  apply to thermoplastic materials with relatively high rigidity as evidenced by the fact that they primarily apply to construction components acting as the main frame of the devices as well as other components carrying significant loads, e.g. tanks,  in every case, the heating process is characterized by the fact that the main controlled parameter is the pressing force applied on the welded item (F m, Fh, FjandFc)and temperature Tpin all stages of the process and not the displacement or velocity (vm, vh, vjand vc) of the welded item (Fig. 1). An example cyclogramof the hot welding process taking into consideration pressure force control is provided on Fig 2. Such process is most frequently characterized by the welded item pressing force during all the process stages (Fm, Fh, FjandFc) is defined and constant. Most often, the degree of pressing is defined for a specific material by hold down pressure [37]. In the authors' opinion, in the case of automated industrial-grade hot welding of drive belts, such an approach is incorrect. This is mostly resultant from the type of processed material. Thermoplastic elastomers used to manufacture drive belts are characterized by relatively low rigidity as well as its rapid decrease with the increase of temperature. These characteristics in particular depend on the material used in the studypolyurethane thermoplastic TPU C85A, which is one of the most widely used materials in industrial production of drive belts [3,14,35]. Additionally, in the analyzed case the welded items typically have a circular cross-section with relatively low geometric dimensions. Therefore, the items are susceptible to buckling during compression and the material itself indicates a tendency for plastic flow in the area of contact with the hot plate [15]. Therefore, the process forces causing the buckling of the belt end pressed to the hot plate and plasticization in contact with its heated surface are relatively low. These factors cause difficulty in controlling the pressing force during individual process phases due to high percentage of measurement error present with low value of the measured force. If such values are fed to the control system of the automated device, this may cause lack of uniformity of welding conditions for different belts, going against the idea of automating the welding process which strives to improve the quality and repeatability of hot welds.

Essential construction solutions of the device.
Based on prior experience with manual hot welding of drive belts [4,14,15,[34][35][36] andthe specifications made for the welded material, a construction solution for an automatic welding mechanism was developed together with a prototype (Fig. 3). The proposed solution of the automated drive belt hot welding device is characterized by the general process control algorithm which accounts for control and adjustment of displacement and velocity of motion of machine assemblies. This is achieved by employing an orientation-measuring servo for controlling the displacement of the mobile grip assembly and the heating assembly. Therefore, the heating process is characterized by the possibility of making adjustments to the belt end movement velocity (vm, vh, vjand vc), during every stage of the heating process (Fig. 1). The commonly employed dynamic controls based on controlling the pressing force of the welded item was replaced with kinematic controls. Fig. 3. The prototype automated drive belt hot welding machineoverview of the heating head: Pdrive belt, 1feeding roller, 2immobile grip assembly, 3mobile grip assembly, 4heating unit.

Modified hot plate welding cycle
As a result of employing the designed construction solution for automated drive belt hot welding, the hot welding process was changed, the new course thereof is provided on Fig. 4 below. The hot welding process was simplified and reduced to 4 phases by joining the stage of belt surface matching (Fig. 1a) and actual heating (Fig. 1b) into one technological operationbelt plasticization (Fig. 4a). During this operation, the hot plate (3) is pressed to the belt end (1b) fixed in an immobile gripping jaw (2b) at velocity vm = vh = vp. Simultaneously, the other belt end (1a), fixed in the mobile gripping jaw (2a), is pressed towards the hot plate (3) on the other side. The velocity of motion of the mobile belt end (1a) in relation to the immobile belt end (1a) is 2⸳vm = 2⸳vh = 2⸳vp. Consequently, a uniform pressing down of both belt ends to the hot plate is achieved during the plasticization process. However, in this case the pressing force during plasticization (FmandFhin Fig. 1a and 1b) is not controlled. Achieving the required velocity vm = vh = vpof the hot plate (3) as well as exactly two times its value 2⸳vm = 2⸳vh = 2⸳vpfor the moving belt end (1a) and the synchronization of movement for these components is due to the employment of a single drive system which simultaneously effecting the linear motion of the movable gripper assembly (3 in Fig. 3) together with the heating system (4 in Fig. 3). This system includes one positioning servomechanism with rotating motion which drives 2 connected leadscrews which transfer the rotating motion of the drive into linear motion of indicated assemblies. The rolling P 4 3 2 1 screw of the drive transmission of the movable gripper assembly (3 in Fig. 3) has two times the lead in comparison to the leadscrew driving the heating assembly (4 in Fig. 3). This solution allowed to limit the construction cost of the device drive system by approx. 30%. Fig. 4. The diagram of the heating and cooling process of the belt material in the course of the modified 4-stage hot plate butt welding process: 1amobile belt end, 1bimmobile belt end, 2amobile belt grip, 2bimmobile belt grip, 3hot plate; vm-pressing velocity towards the hot plate during flattening, vp -belt material plasticization velocity, vjpressing velocity during the joining, vc-velocity during cooling Tphot plate temperature, Twhot-welding temperature, T0ambient temperature, pbelt plasticization distance, hsection heated to temperature exceeding ambient temperature; Qp3-1heat conducted between the hot plate and the belt, Qp1-2heat conducted between the belt and the grip, Qp1heat conducted inside the material, Qr1heat dissipated to the environment from the belt through radiation, Qr3heat dissipated to the environment from the hot plate through radiation, Qc1heat dissipated to the environment from the belt through convection, Qc3

a) Belt plasticization b) Withdrawing the hot plate c) Pressing the belt ends d) Cooling the bonded area
heat dissipated to the environment from the hot plate through convection.
The modified welding process is characterized by the fact that in the stage of withdrawing the heating device (Fig. 4b), the belt ends (1a and 1b) are not moved away from the hot plate (3). It is withdrawn while in contact with the belt material which serves to improve the energy efficiency. The hot plate surface is covered with a material ensuring low coefficient of friction value in relation to the plasticized material. The pressing of the belt ends (Fig. 4c) involves moving them closer together as a result of motion of the mobile jaw (2a) at velocity vjtowards the immobile jaw (2b). In this stage, the joining process is initialized, similarly to the actual joining process in the classic description of the process (Fig. 1d).
After finishing the pressing of the belt ends (Fig. 1d), i.e. bringing them together to perform a permanent bond, the area of the bond is cooled (Fig. 1e), in this stage, the velocity of motion of the movable belt end (1a) isvc = 0. Therefore, the external force effecting the pressing of the belt during cooling (Fcin Fig. 1e) is also equal to zero. This phenomenon is intentional due to the belt's susceptibility to bucklingwhich caused the joined area to become damaged when not fully cooled. Such simplification of the butt welding process of drive belts allowed to also simplify the control system of the device as well as to reduce the complexity of the drive system, resulting in an actual reduction of the device construction cost while maintaining the assumed functionalities.

Guidelines for modeling the welding process
The introduction of the modified butt welding cycle resulting from the simplification of the device working assembly (elimination of measurement and adjustment of the belt end pressing force) necessitates to develop detailed guidelines for the mathematical modeling of the butt welding of belt ends. In particular, this applies to the plasticization stage of the belt ends (Fig. 4a) as the phase is critical for the remaining stages of the welding process. Example graphs showing the function of the plasticization force Fpon the hot plate and the plasticization distance of the material pfor three different plasticization velocity valuesvpare provided below on Fig. 5. The results were obtained through plasticization of the belt on a durometer following the methodology provided in the work [14]. What follows from the provided characteristics, with all the analyzed values of velocity vp, a linear function of the plasticization force and displacement is observed, marked with a straight graph line determined with the linear regression method (Fig. 5). In the course of further plasticization, after exceeding the proportional curve line section, a different characteristic is observed in the function of plasticization force Fpand displacement:  in the case of low velocity vp (Fig. 5a), the plasticization force Fpassumes the characteristic of exponential decay, indicating the flow of the material. If the process is carried out in this manner, this results in lower effectiveness and the risk of pushing out the melted material from the area of welding,  in the case of a certain average velocity value vp (Fig. 5b), the plasticization force Fp, assumes the characteristic of approximately constant value, regardless of displacement value s. This allows to conclude that in this case a balance is achieved between the material plasticization efficiency and the speed of motion of the belt end  in the case of high velocity vp (Fig. 5c), the plasticization force Fpassumes the characteristic of exponential growth, indicating that the compression is effected on a solid body without full plasticization. Therefore, the plasticization at such velocity is insufficient. The carried out analysis of the belt plasticization on the hot plate proves that the correct selection of the plasticization velocity value vpin the first stage of the modified process of hot plate butt welding of drive belts (Fig. 4a) allows to carry out the operation effectively without risk of loss of the joined material.

Conclusions
The developed construction of the device prototype for automated hot plate butt welding of drive belts designed with view of industrial implementation necessitates the following assumptions during mathematical modeling of the welding process: .
 the welding process is simplified to 4 distinct phases, the most important phase being the plasticization of the belt on the hot plate (Fig. 4),  during the welding, the monitored and controlled technological parameters are: the velocity of pressing the belt end on the hot plate during the plasticization process vp, the velocity of pressing the belt ends together vj, the velocity of pressing the belt ends together during cooling (initially assumed as equal to zero) vc, the plasticization distance pand hot plate temperature Tp. The duration of the plasticization results from considering the values of the velocity vpand distance p (Fig. 4),  the pressing of the weld involves pressing together the joined belt ends and holding them under the same pressure, it is performed during the joining phase (Fig. 4c),  the cooling operation is carried out under no pressing force. The departure from the classic hot plate butt welding method which is commonly employed to describe the welding process of inflexible plastics, with inclusion of dynamic process controls (with controlled item pressing force in each process stage) in favor of a kinematic control solution requires moving away from the typically used mathematical models of the welding process. The development of a new heating model allows to correctly select the most efficient technological parameters of the process and implementing them in the designed device.