Experimental Research on Mechanism of Hull Plates Curved Forming by a Clean Energy Source

,-,,,,-,-,

(Ship Intelligent Manufacturing and Ship Intelligence Integrated Laboratory,Jiangsu University of Science and Technology,Zhenjiang 212003,China)

Abstract: Line heating is the main practical method for manufacturing curved surfaces in the outer hull plates of a ship. Normally, oxyacetylene flames are used as the heat source. However, performing the line heating method with oxyacetylene flames has challenges in most of shipyards, including large energy consumption, heavy pollution and low automation degree. In order to solve the aforementioned problem,it was intended to utilize the oxyhydrogen flame as the non-emission heat source.Many studies on the deformation mechanism and law of plates were performed through establishing mechanism models and finite element numerical simulation.Then experiments were carried out to evaluate the accuracy and availability of models and energy-saving effect.Different aspects,including the determination of processing parameters,verification of the temperature field and deformation field, and economical comparisons between oxyhydrogen and acetylene flames, were investigated in this regards. It was found that the results obtained from the finite element analysis had a good agreement with that of the experiment.Moreover,it was observed that the processing effect and efficiency of the oxyhydrogen flame met the requirements of curved surface deformation process of the plates.The present study shows that the overall expense of the oxyhydrogen flame is fairly less than that of the oxyacetylene flame.

Key words:line heating;curved surface deformation;oxyhydrogen flame;clean and non-emission energy

0 Introduction

The outer hull surface of a ship is commonly composed of a complex and non-expandable three-dimensional shape with special curves[1]. The marine steel plates are processed into the designed curved shape by means of the dieless forming. At present, shipbuilding companies all over the world generally adopt the line heating method in this regards (Terms‘the process’and‘the method’refer hereafter to‘the ship’s outer surface forming process’and‘the line heating method’in the ship manufacturing process respectively)[2]. It is widely used in shipyards around the world due to its fast processing, flexible operation, no need for other equipment and suitability for the complex forming processing. It should be indicated that‘the method’belongs to the range of the thermal stress forming,whose heating process schematic diagram is shown in Fig.1

Fig.1 Schematic diagram of plate forming by the line heating process

However, in view of the long-term application and modern ship manufacturing requirements,the oxyacetylene flame has considerable drawbacks, including low heating efficiency, heavy environmental pollution,serious harm to workers’health and high operational costs.

Many researchers have tried to replace oxyacetylene with other sources of heat.Siqueira[3]studied the laser forming of high-strength aluminum alloy plates, and investigated the influence of different powers, scanning speeds and spot diameters on the bending angle of a 1.6 mm thick highstrength aluminum alloy plate through experiments. Shi[4]studied the effect of multi-channel laser forming on the forming accuracy of sheet metal. However, the laser is of a high operational cost so that only low-power lasers are used to form thin plates. In other words, the laser cannot meet the power demand of thick plates for the hot stress forming. Therefore, the laser is not popular in shipbuilding[5].

Jin[5]studied the effect of high frequency induction heating on diagonal deformation,and established the efficiency of high frequency induction heating system, and compared and analyzed the temperature of measurement and finite element analysis. Li Rui[6]processed 5083 aluminum alloy plates with a high frequency electromagnetic induction heat source, used ANSYS software to carry out finite element modeling and simulation, and studied the influence of the processing time of induction heat source and the pulse current amplitude of electromagnetic induction heat source on the forming effect of ship’s plate.But high frequency induction heating is still in the research stage of forming mechanism,it needs to be studied for a long time.

With the development of technology,hydrogen as a clean energy,has attracted more and more attention of all walks of life. Oxyhydrogen flame was used as the heat source to heat ship’s plates and its forming mechanism was studied.It is of great significance to the development of ship’s plate processing industry.

1 Mathematical model of the heating process for hull plates

1.1 Heat source model of the gas flame

The Gaussian distribution is used to model the heat flux and study the combustion of the oxyhydrogen gas[7]. The combustion equation of the oxyhydrogen gas is:

Fig.2 shows the heat flux in accordance with the Gaussian distribution. The applied heat flux density of the oxyhydrogen flame to the surface of the plates varies along the radius.

Considering the Gaussian distribution,q″ can be expressed as

Fig.2 Heat flux model of the Gauss distribution

1.2 Mathematical model of the temperature field

The oxyhydrogen gas initially (i.e.t= 0) moves from the edge along the pre-designed heating line with a uniform speed ofvf.The temperature fieldT(x,y,z,t)of the plate can be expressed as

wherea=λ/( )ρ·cp.In the present study,it is assumed that the plate is infinitely large and the heating time is long enough.Then the relative coordinate system on the center of the heat source is used as the center of the moving axis so that the temperature field can be treated as a steady state problem.Consideringx′=x,y′=y-vf t,z′=z,Eq.(4)can be simplified to the following form:

Eq.(5)should satisfy the following three boundary conditions:

(1)Initial condition:t= 0;

(2)T(x,y,z,0 )=T0，whereT0= 23 ℃is the room temperature;(

3)Input condition of the oxyhydrogen gas.

It is assumed that the linear equation of the heating line isx= 0,z= 0. Then, the heat flux density of thet-moment heating surfaceq″can be expressed as

Forced conditions of the heat convection for the air-cooling and the water-cooling are shown as belows:

When the air-cooling is utilized, the problem of the heat convection involves the heat transfer between the plate and air.Surface coefficients of the plate should be selected accordingly:

On the other hand,the membrane boiling heat transfer theory should be applied to the process of water-cooling when the plate temperature exceeds 200 ℃.

1.3 Mathematical model of the deformation field

In this section,the deformation kinematics of the plate is used to determine the residual deformations[8-9]. The plate is initially flat, while the target surface is the desired shape in accordance with the hull design.The following assumptions are made in the surface forming process of the plate:

(1)The thickness of the plate in the deformation process is constant;(2)Surface shrinkage and bending deformation occur during the plate deformation process;(3)The shear deformation is negligible so that it is ignored in the present study.

1.4 Finite element theory

1.4.1 Finite element theory for the temperature field

The finite element solution steps for the temperature field are as follows[10]:

(a)Discretization:The temperature fieldT(x,y,z,t)is discretized within the plate as

Eq.(9) can be combined with the differential equation and the corresponding boundary condition.Applying the finite element approach to the heat source term of the gas flame results in the following expression for the conducted heat

When the temperature field is solved, the boundary heat transfer should also be considered.The expressionQsis the boundary heat loss in the form shown below:

In practical and engineering applications, the correlation between the heat transfer coefficient and the temperature is expressed in a piecewise linear model. Moreover, studies show that material characteristics vary as the temperature changes. If{ }Teshows the temperature of a node at timet{ }Te,thermophysical properties of the node can be calculated as the following:

1.4.2 Finite element theory of the deformation field

The finite element solution for the deformation field of the plate in "the method" is shown as belows[11-12]:

Similar to the finite element approach of the temperature field, the displacement field increment Δu(x,y,z,t)is discretized on the plate as below

‘The method’can be summarized in a three-dimensional,transient,and thermo-elastic-plastic problem. It should be indicated that an appropriate time step should be selected to simulate the deformation process.

2 Experiment of oxyhydrogen flame

The research on the oxyhydrogen flame is composed of determination of processing parameters,verification of the temperature field,and deformation field.

2.1 Experimental device

The experimental devices consist of such basic measuring tools as the oxyhydrogen machine,infrared thermal imager,water-cooling device,welding torch,tape measure and the vernier caliper.

The required oxyhydrogen gas for the experiment is produced by the oxyhydrogen machine.Fig.3 shows the appearance of the oxyhydrogen machine and Fig.4 shows the appearance of the infrared thermal imager. This machine effectively electrolyzes the water and produces a remarkable amount of oxyhydrogen gas, and the gas flux rate can be read from the HMI. In the experiment, an infrared thermal camera (Ruice AI50) with a measuring accuracy of ±2 ℃is utilized to collect the temperature data of the plate during the heating process.

Fig.3 Oxyhydrogen machine

Fig.4 Infrared thermal imager

2.2 Calculating parameters of the oxyhydrogen flame processing technology

A key problem in performing the finite element analysis for the temperature and deformation fields of the plate is calculating the corresponding processing parameters. In the present study, the Gaussian distribution is used to model the heat source. There are two parameters in this model, the radiusr0of the heat source and heating efficiencyη,which are normally identified by other parameters such as the flux of hydrogen gasQ,the height of the nozzleHand the moving speed of the heat source[13]. Therefore,ηandr0must be initially determined to utilize the model in the actual test case.

2.2.1 Calculating the processing parameters

In Eq.(2), many parameters, such as the nozzle diameter, nozzle height, flame movement speed,plate thickness and the material properties[14-18],can affectηandr0.In‘the process’,the effect of other factors except the gas flux is negligible and can be ignored for the optimal value ofH.Therefore,the values ofηandr0mainly depend on the amount of gas flux.

In order to verify the temperature field of the oxyhydrogen flame,the optimal values ofHandr0should be initially measured.Then the value ofηis modified to adjust the finite element model until the numerical results are consistent with the experimental ones.Finally,the obtained optimal value ofηshows the heating efficiency of the corresponding flux.

2.2.2 Experimental scheme

(1)Determining the optimal value ofH

In order to initially obtain the correlation between the hydrogen fluxQH2,ηandr0, the optimal value ofHshould be determined. The same testing plate is processed for different gas flux rates in this regard.The surface temperatureT1of the plate is measured by the infrared measuring device in the same heating time. The optimal height for different flux rates can be obtained through comparison of the results.

(2)Calculatingηandr0

After determining the optimal value ofH, the value ofr0for different hydrogen gas fluxesQH2can be measured. Moreover, the value ofηis obtained by finite element analysis. Six groups of different gas fluxes are taken within the gas production ranges of the oxyhydrogen machine, which are combined with the actual process to give six sets of processing parameters.

2.2.3 Experimental results

Tab.1 shows the experimental data of optimal value ofHfor the oxyhydrogen flame.

Tab.1 Optimum height

The experiment is carried out by the above mentioned scheme for the optimal value ofH, and the value ofr0is measured.

The value ofηis modified to adjust the finite element model until the numerical results are consistent with the experimental ones. Then the heating efficiencyηfor different hydrogen flux rates is obtained.Tab.2 shows the specific data.

Tab.2 Experimental determination of η and r0

Tab.2 shows the values ofQH2,ηandr0for different fluxes.The values ofηandr0are constant at 1 533(L/h)of the hydrogen flux.With the change of the speed,the finite element numeration temperatures of each group are compared with the measuring temperature. The value ofηis verified through comparison.Tab.3 illustrates the experimental results.

Tab.3 Experimental verification

Tab.3 shows that there exist errors in the measurement and numerical analysis, and the error range between the experimental data and the computed data is acceptable. Therefore, it is concluded that the obtained heating efficiency by this experimental scheme is effective and reliable.

2.3 Result verification of the oxyhydrogen flame deformation field

2.3.1 Experimental scheme

The verification steps of the deformation field results are as the following:

(1)Mark four sets of measuring points on the upper and lower surfaces around the heating line as illustrated in Fig.5;

(2)Measure the three-dimensional coordinate data of the measuring points before and after deformation of the plates;

(3) Employ Eqs.(21)-(23) to calculate ΔLandθin accordance with the deformation principle.If the numerical simulation data approach to the experimental data, it is proved that the numerical simulation is valid.

Fig.5 Marked ship points on the measuring plateFig.6 Schematic principle of the deformation

Fig.6 shows schematic principle of the deformation and the principle of the numeration method is as follows:

2.3.2 Measurement and analysis of the deformation field data of the oxyhydrogen flame

The data of the deformation field are mainly obtained by calculating the displacement of measuring points[19].The data before and after point deformation of four groups are measured accordingly. According toL0，LTandLB, values of the line and angular deformations corresponding to each set are calculated.Then they are averaged to obtainLandθ.

Tab.4 shows the comparison of the obtained numerical results through ANSYS with the ones of the experiment.

Tab.4 Comparison of plate deformation results

The results indicate that the corresponding errors of ΔLandθbetween the ANSYS simulation and the experimental results are 4% and 14% respectively[20-23]. The measurement process and the indirect process of the measured values produce different degrees of errors. It is concluded that results of the deformation experiment are reliable within the allowable range[4,6].

2.4 Discussion on temperature field results

According to the established finite element model for the temperature field of the plate,the numerical model of the ANSYS software results in the temperature field distribution.

Contours of abovementioned temperatures show the range and trend of the temperature variation in the plate and the movement of the heat source in the heating process[24]. Fig.7(a) shows that during the heating phase of‘the method’, the high temperature region is concentrated near both ends of the heating line.Moreover,Fig.7(b)indicates that at the end of the heating process,the heat input spreads from the region near the heating line (high temperature region) to the surrounding region (cryogenic region). Furthermore, Fig.7(c) shows that when the plate is cooled, the heat continues to spread while the temperature of the plate continues to reduce.Eventually,the plate temperature approaches to the steady state value.

Fig.7 Temperature distribution at 2 500(L/h)flux for different moments

In order to analyze the temperature field distribution during‘the process’,the temperature change of the feature points on the heating line is studied and three feature points on the heating line, including the start, middle and end points, are selected. Fig.8 shows the three feature points. It is observed that the maximum temperatures in the three points are different due to the asymmetry of the material between the two ends and the middle point. It is found that the maximum temperatures of the plate surface at the start, end and middle points are about 670 ℃,800 ℃and 840 ℃respectively.

Fig.8 Temperature variation trend of three feature points

2.5 Discussion on the results of deformation field

According to the finite element model for the deformation field of the plate, the displacement distribution for different moments is generated in‘the process’by ANSYS simulation.Figs.9(a)-(d)illustrate the displacement contours for the start, middle, end and cooling phases of‘the process’.Moreover,Fig.10 shows the overall deformation effect.

Fig.9 Displacement distribution at 2 500(L/h)flux for different moments

Fig.10 Overall deformation result

Fig.11 Displacement variation trend of three feature points

Fig.11 shows that thez-displacement change history of feature points at the plate is different.The obtained results in different positions of the displacement and the bending angle are not the same, which verifies the existence of the‘uneven deformation’phenomenon[12-13]. Uneven deformation brings challenges to the precise control of‘the process’.Moreover,Figs.9-10 indicate that the deformation effect of the plate with single heating line is small.

3 Comparison and analysis of two flames

In order to further compare the differences between the two flames,the temperature and deformation field of the two flames were established by finite element simulation, and the surface maximum temperature was made similar by adjusting heating speed at the same flow rate. Then the differences of heating width, heating depth, angular deformation and line deformation were compared and analyzed. Furthermore, in order to verify the energy-saving effect, the same plates were processed with similar deformation requirements by using the oxyhydrogen and oxyacetylene flames.Then the energy consumption was computed and the results were compared with each other to verify the energy-saving effect.

3.1 Comparison of the two flames

3.1.1 Temperature field contrast

In previous studies, the surface temperature of a hull plate should be controlled between 450 ℃and 850 ℃[25]. If the temperature is higher than 850 ℃, the properties of the metallographic structure for the hull plate will change irreversibly, affecting the performance of the hull plate. If the temperature is lower than 450 ℃,the steel plate will not be deformed significantly.Therefore,in the actual processing, the maximum temperature of the heating surface for a hull plate is often required to be close to 850 ℃, and the maximum temperature of the back of the hull plate can also reach 450 ℃.

Fig.12 shows the surface temperature field of oxyhydrogen and oxyacetylene gas flame. Fig.13 shows the heating depth of the two flames. Tab.5 shows the effective surface heating area of oxyhydrogen flame heat source is smaller than the oxyacetylene flame heat source,but the flame penetration of oxyhydrogen flame is stronger and the heating depth is deeper.

Fig.12 Comparison of surface temperature fields

Fig.13 Comparison of heating depths

Tab.5 Comparison of two flame effects

3.1.2 Deformation field contrast

As can be seen from the data in Tab.6, under the same maximum temperature and flow rate,the deformation generated by the heating of oxyhydrogen flame is slightly smaller than that of oxyacetylene flame. The average linear deformation of oxyhydrogen flame is 87% of oxyacetylene flame,and the average angular deformation is 91%.In combination with the comparison of temperature field above[26], the calorific value and the radius of oxyhydrogen flame heat source are both smaller than those of oxyacetylene flame,so it is necessary to heat plates at a smaller heating speed.Therefore the‘penetrability’of oxyhydrogen flame is stronger.This enables ship’s plates to achieve better heating depth and makes up for the lack of heating width.

Tab.6 Comparison of two flame deformation effects

3.2 Energy-saving verification of the oxyhydrogen flame

3.2.1 Experimental scheme

According to the finite element simulation case, the oxyacetylene and oxyhydrogen flames are used to process two plates with the same specification and material and the same deformation requirements. The energy consumption of two plates is compared mainly considering the heat source and use cost.

3.2.2 Energy consumption comparison

The plates are curved after‘the process’through the actual experiment. Fig.14 illustrates the final processing effect of the oxyacetylene flame while the final processing effect of the oxyhydrogen flame is shown in Fig.15. The comparison of the two flame processing effects is shown in Fig.16.The comparative results indicate that the final deformation effect has a good consistency with each other.Then the energy consumption is computed from the viewpoint of raw material and operational costs.

Fig.14 Plate deformation by oxyacetylene flame

Fig.15 Plate deformation by oxyhydrogen flame

Raw material cost numeration:

According to the relevant statistics, each cubic meters of the acetylene consumes 21.8 kW of electricity.The production of the same amount of hydrogen requires 4.8 kW of electricity. In other words, the direct use of the hydrogen gas rather than using the acetylene, reduces the electricity costs by up to 22%.

Use-cost numeration:

According to the usage statement, two bottles of acetylene and one bottle of oxygen are consumed in the oxyacetylene processing experiment. The time consumption of the mixed oxyhydrogen gas processing experiment is 6 h. Tab.7 shows the numeration of costs.

Fig.16 Comparison of plate deformations of two schemes

Tab.7 Comparison of consumption costs

According to the relevant literature, the oxyhydrogen flame is not only zero emission but also has obvious energy-saving effects. With the same processing effect, the cost of the oxyhydrogen flame is 66.6%lower than that of the oxy-acetylene flame on average.

Energy consumption comparison shows that the oxyhydrogen machine can fully meet the process requirements and can also save energy costs.It is unnecessary to change the bottle when using the oxyhydrogen flame, which can save the bottle changing time and improve the work efficiency.Moreover, water is used as the raw material by electrolysis of water. After combustion of the oxyhydrogen flame,the oxyhydrogen gas reverts to the water,so no waste gas is generated and there is no pollution to the environment.So it is environment-friendly and safe.

4 Concluding remarks

This paper presents the use of the oxyhydrogen flame as the heat source for the first time in‘the process’.The experiments and ANSYS simulation show that it is feasible to use the oxyhydrogen flame as the heat source for‘the process’.Moreover,compared with the conventional oxyacetylene flame,the oxyhydrogen flame is more efficient and produces no carbon dioxide emissions.Furthermore,experimental data show that the operational cost of the oxyhydrogen flame is 66.6% lower than that of the acetylene flame. It is believed that the efficiency of the oxyhydrogen flame is only higher than the oxyacetylene flame if it is applied on a large scale in industrial applications.The research provides support for the subsequent automated processing of‘the process’.