阅读说明：本技术 冷连轧机组以动态辊缝控制为目标的弯辊力综合优化方法 (Roll bending force comprehensive optimization method of cold continuous rolling unit with dynamic roll gap control as target ) 是由 邢德茂 张理扬 何乐乐 于 2021-08-30 设计创作，主要内容包括：本发明涉及冷连轧技术领域,且公开了冷连轧机组以动态辊缝控制为目标的弯辊力综合优化方法,包括以下步骤：(a)、收集冷连轧机组轧制过程中1到5机架的设备参数,主要包括：各机架工作辊直径D-(wk)、中间辊直径D-(mk)、支撑辊直径D-(bk),各机架工作辊辊型分布ΔD-(wki)、中间辊辊型分布ΔD-(mki)、支撑辊辊型分布ΔD-(bki),各机架工作辊辊身长度L-(wk)、中间辊辊身长度L-(mk)、支撑辊辊身长度L-(bk),各机架压下螺丝中间距l-(wk)、中间辊压下螺丝中间距l-(mk)、支撑辊压下螺丝中间距l-(bk)；本发明充分考虑到冷连轧机组在轧制过程中,热凸度随轧制时间而增加导致出口的板形质量不够高的原因,通过研究工作辊弯辊力和中间辊弯辊力对有载辊缝动态变化的影响,建立相应的弯辊力优化模型。(The invention relates to the technical field of cold continuous rolling, and discloses a roll bending force comprehensive optimization method of a cold continuous rolling unit by taking dynamic roll gap control as a target, which comprises the following steps: (a) collecting the equipment parameters of 1 to 5 frames in the rolling process of the cold continuous rolling unit, and mainly comprising the following steps: diameter D of working roll of each frame wk Diameter D of intermediate roll mk Diameter D of the support roller bk The roll profile of each machine frame working roll is distributed by delta D wki Middle roll profile distribution Δ D mki Roll profile distribution Delta D of support roll bki Length L of working roll body of each frame wk Length L of intermediate roll body mk Length L of the roll body of the supporting roll bk The interval l between the screw pressing of each machine frame wk Middle distance l between the middle rollers and the screw mk The interval l between the support roller and the screw bk (ii) a The invention fully considers the reason that the hot convexity is increased along with the rolling time in the rolling process of the cold continuous rolling mill set to cause the insufficient quality of the outlet plate shape, and the invention is used for the loaded roller by researching the bending force of the working roller and the bending force of the intermediate rollerAnd establishing a corresponding roll bending force optimization model under the influence of dynamic change of the gap.)

1. The roll bending force comprehensive optimization method of the cold continuous rolling unit by taking dynamic roll gap control as a target is characterized by comprising the following steps of: the method comprises the following steps:

(a) collecting the equipment parameters of 1 to 5 frames in the rolling process of the cold continuous rolling unit, and mainly comprising the following steps: diameter D of working roll of each frame_wkDiameter D of intermediate roll_mkDiameter D of the support roller_bkThe roll profile of each machine frame working roll is distributed by delta D_wkiMiddle roll profile distribution Δ D_mkiRoll profile distribution Delta D of support roll_bkiLength L of working roll body of each frame_wkLength L of intermediate roll body_mkLength L of the roll body of the supporting roll_bkThe interval l between the screw pressing of each machine frame_wkMiddle distance l between the middle rollers and the screw_mkThe interval l between the support roller and the screw_bkMinimum bending force delta of working rolls of each machine frame_kminAnd maximum roll bending force delta_kmaxMaximum bending force S of the intermediate roll_kminWith minimum roll bending force S_kmax；

(b) Collecting key rolling process parameters at different rolling time in the rolling process of the cold continuous rolling unit, and transversely distributing the thickness h of the material coming from the ith rack_iTransverse distribution value L of incoming sheet_iWidth B of strip, coefficient of friction μ_iResistance to deformation k_iStrength of the strip, 1 to 5 unit front tension σ of each stand_i0Unit back tension sigma with each frame_i11 to 5 maximum and minimum values delta of the bending force of the working rolls of the stand_imax、δ_iminAnd 1 to 5 maximum and minimum values S of the bending force of the intermediate roll of the stand_imax、S_imin(ii) a Optimum work roll bending force delta_kyAnd intermediate roll bending force S_ky(ii) a Working roll bending coefficient lambda of 1 to 5 frames_iAnd 1 to 5 frame intermediate roll bending coefficient beta_iAnd the optimized step length of the bending force of the working roll of 1 to 5 frames is delta_iAnd 1 to 5 machinesThe optimized step length of the bending force of the intermediate roll is delta S_iDefining control objective function G (X), etc.;

(c) initializing working roll bending force optimization coefficient lambda₁＝0、λ₂＝0、λ₃＝0、λ₄＝0、λ₅Entering step (d) when the value is 0;

(d) calculating the bending force of the working rollThen to step (e);

(e) initializing intermediate roll bending force optimization coefficient beta₁＝0、β₂＝0、β₃＝0、β₄＝0、β₅0, then go to step (f);

(f) calculating the bending force of the intermediate rollThen to step (g);

(g) calculating the on-load roll gap G (X) according to the following specific formula, and then going to step (h)

Transversely dividing an on-load roll gap into N sections, longitudinally dividing the whole roll of strip steel into N sections, and establishing a dynamic on-load roll gap optimization objective function G (X) of each machine frame, wherein the dynamic on-load roll gap optimization objective function G (X) is represented by the following formula:

(h) determining whether the target function G (X) is minimum, if yes, making delta_1y＝δ₁、δ_2y＝δ₂、δ_3y＝δ₃、δ_4y＝δ₄、δ_5y＝δ₅、S_1y＝S₁、S_2y＝S₂、S_3y＝S₃、S_4y＝S₄、S_5y＝S₅Then, step (i) is carried out for judgment, otherwise, step (i) is directly carried out;

(i) and determining delta₁<δ_1max、δ₂<δ_2max、δ₃<δ_3max、δ₄<δ_4max、δ₅<δ_5maxIf it is true, let λ₁＝λ₁+1、λ₂＝λ₂+1、λ₃＝λ₃+1、λ₄＝λ₄+1、λ₅＝λ₅+1 to step (d); otherwise, entering the step (j);

(j) and judging S₁<S_1max、S₂<S_2max、S₃<S_3max、S₄<S_4max、S₅<S_5maxIf true, let β₁＝β₁+1、β₂＝β₂+1、β₃＝β₃+1、β₄＝β₄+1、β₅＝β₅+1 to step (f); otherwise, entering the step (k);

(k) outputting the optimal working roll bending force delta meeting the optimization objective function_kAnd intermediate roll bending force S_k。

2. The method for comprehensively optimizing the bending force of a cold continuous rolling mill group aiming at dynamic roll gap control according to claim 1, characterized in that: in the step (b), i in the ith rack is 1-5 and delta_imax、δ_imin、S_imax、S_imin、λ_i、β_i、Δδ_i、ΔS_iWherein i is 1, 2, 3, 4, 5, δ_ky、S_kyWherein k is 1, 2, 3, 4, 5.

3. The method for comprehensively optimizing the bending force of a cold continuous rolling mill group aiming at dynamic roll gap control according to claim 1, characterized in that: delta delta in the formula calculated in the step (d)₁、Δδ₂、Δδ₃、Δδ₄、Δδ₅And Δ S in the formula calculated in step (f)₁、ΔS₂、ΔS₃、ΔS₄、ΔS₅Are all set optimal step lengths.

4. The method for comprehensively optimizing the bending force of a cold continuous rolling mill group aiming at dynamic roll gap control according to claim 1, characterized in that: xi in the calculation formula in the step (g) is a weighting coefficient of the dynamic roll gap, alpha is a weighting coefficient of the transverse loaded roll gap, and beta is a weighting coefficient of the longitudinal loaded roll gap.

Technical Field

The invention relates to the technical field of cold continuous rolling, in particular to a roll bending force comprehensive optimization method of a cold continuous rolling unit by taking dynamic roll gap control as a target.

Background

In the cold continuous rolling production process, the outlet plate shape condition of the cold continuous rolling mill is directly related to the dynamic distribution of an on-load roll gap, the on-load roll gap is influenced by rolling process parameters and the roll shape condition, the roll bending force of a cold continuous rolling mill set has two modes of adjusting the change of the dynamic on-load roll gap, namely work roll bending force adjustment and middle roll bending force adjustment, and once the roll bending force is set, the change cannot be changed in the rolling process. In addition, in the rolling process, the thermal crown is increased along with the rolling time, if the thermal crown is increased too much, the plate shape can generate middle waves, in order to eliminate the influence of the thermal crown on the loaded roll gap as much as possible, the dynamic change of the loaded roll gap can be adjusted by changing the bending roll force of the working roll and the middle roll, so that the change of the loaded roll gap is minimized in the rolling process, and the aim of improving the plate shape is fulfilled. Based on the method, the equipment and process characteristics of the cold continuous rolling mill set are comprehensively considered, the roll bending force is optimized by considering the control problem of an objective function on the basis of taking the minimum dynamic change of the loaded roll gap in the rolling process as a control target, and the optimization method for controlling the loaded roll gap of the cold continuous rolling mill set is established.

Disclosure of Invention

Technical problem to be solved

Aiming at the defects of the prior art, the invention provides a roll bending force comprehensive optimization method of a cold continuous rolling unit by taking dynamic roll gap control as a target.

(II) technical scheme

In order to achieve the purpose, the invention provides the following technical scheme: the roll bending force comprehensive optimization method of the cold continuous rolling unit with the dynamic roll gap control as the target comprises the following steps:

(a) collecting the equipment parameters of 1 to 5 frames in the rolling process of the cold continuous rolling mill groupMainly comprises the following steps: diameter D of working roll of each frame_wkDiameter D of intermediate roll_mkDiameter D of the support roller_bkThe roll profile of each machine frame working roll is distributed by delta D_wkiMiddle roll profile distribution Δ D_mkiRoll profile distribution Delta D of support roll_bkiLength L of working roll body of each frame_wkLength L of intermediate roll body_mkLength L of the roll body of the supporting roll_bkThe interval l between the screw pressing of each machine frame_wkMiddle distance l between the middle rollers and the screw_mkThe interval l between the support roller and the screw_bkMinimum bending force delta of working rolls of each machine frame_kminAnd maximum roll bending force delta_kmaxMaximum bending force S of the intermediate roll_kminWith minimum roll bending force S_kmax；

(b) Collecting key rolling process parameters at different rolling time in the rolling process of the cold continuous rolling unit, and transversely distributing the thickness h of the material coming from the ith rack_iTransverse distribution value L of incoming sheet_iWidth B of strip, coefficient of friction μ_iResistance to deformation k_iStrength of the strip, 1 to 5 unit front tension σ of each stand_i0Unit back tension sigma with each frame_i11 to 5 maximum and minimum values delta of the bending force of the working rolls of the stand_imax、δ_iminAnd 1 to 5 maximum and minimum values S of the bending force of the intermediate roll of the stand_imax、S_imin(ii) a Optimum work roll bending force delta_kyAnd intermediate roll bending force S_ky(ii) a Working roll bending coefficient lambda of 1 to 5 frames_iAnd 1 to 5 frame intermediate roll bending coefficient beta_iAnd the optimized step length of the bending force of the working roll of 1 to 5 frames is delta_iAnd 1 to 5 frame intermediate roll bending force optimization step length is delta S_iDefining control objective function G (X), etc.;

(c) initializing working roll bending force optimization coefficient lambda₁＝0、λ₂＝0、λ₃＝0、λ₄＝0、λ₅Entering step (d) when the value is 0;

(d) calculating the bending force of the working rollThen go to step(e)；

(e) Initializing intermediate roll bending force optimization coefficient beta₁＝0、β₂＝0、β₃＝0、β₄＝0、β₅0, then go to step (f);

(f) calculating the bending force of the intermediate rollThen to step (g);

(g) calculating the on-load roll gap G (X) according to the following specific formula, and then going to step (h)

Transversely dividing an on-load roll gap into N sections, longitudinally dividing the whole roll of strip steel into N sections, and establishing a dynamic on-load roll gap optimization objective function G (X) of each machine frame, wherein the dynamic on-load roll gap optimization objective function G (X) is represented by the following formula:

(h) determining whether the target function G (X) is minimum, if yes, making delta_1y＝δ₁、δ_2y＝δ₂、δ_3y＝δ₃、δ_4y＝δ₄、δ_5y＝δ₅、S_1y＝S₁、S_2y＝S₂、S_3y＝S₃、S_4y＝S₄、S_5y＝S₅Then, step (i) is carried out for judgment, otherwise, step (i) is directly carried out;

(i) and determining delta₁<δ_1max、δ₂<δ_2max、δ₃<δ_3max、δ₄<δ_4max、δ₅<δ_5maxIf it is true, let λ₁＝λ₁+1、λ₂＝λ₂+1、λ₃＝λ₃+1、λ₄＝λ₄+1、λ₅＝λ₅+1 to step (d); otherwise, entering the step (j);

(j) and judging S₁<S_1max、S₂<S_2max、S₃<S_3max、S₄<S_4max、S₅<S_5maxIf true, let β₁＝β₁+1、β₂＝β₂+1、β₃＝β₃+1、β₄＝β₄+1、β₅＝β₅+1 to step (f); otherwise, entering the step (k);

(k) outputting the optimal working roll bending force delta meeting the optimization objective function_kAnd intermediate roll bending force S_k。

Preferably, in the step (b), i in the ith rack is 1 to 5, δ_imax、δ_imin、S_imax、S_imin、λ_i、β_i、Δδ_i、ΔS_iWherein i is 1, 2, 3, 4, 5, δ_ky、S_kyWherein k is 1, 2, 3, 4, 5.

Preferably, Δ δ in the formula is calculated in the step (d)₁、Δδ₂、Δδ₃、Δδ₄、Δδ₅And Δ S in the formula calculated in step (f)₁、ΔS₂、ΔS₃、ΔS₄、ΔS₅Are all set optimal step lengths.

Preferably, ξ in the calculation formula in step (g) is a dynamic roll gap weighting coefficient, α is a lateral loaded roll gap weighting coefficient, and β is a longitudinal loaded roll gap weighting coefficient.

(III) advantageous effects

The invention provides a roll bending force comprehensive optimization method of a cold continuous rolling unit by taking dynamic roll gap control as a target, which has the following beneficial effects:

the invention fully considers the reason that the hot convexity is increased along with the rolling time in the rolling process of the cold continuous rolling mill set to cause the insufficient quality of the outlet plate shape, establishes a corresponding bending force optimization model by researching the influence of the bending force of the working rolls and the bending force of the intermediate rolls on the dynamic change of the loaded roll gap, eliminates the influence of the hot convexity on the loaded roll gap as much as possible by introducing the bending coefficients of the working rolls and the intermediate rolls of the cold continuous rolling mill set and setting corresponding optimization step length, realizes the control of the loaded roll gap of each rack in the cold continuous rolling process, improves the actual production efficiency and quality, and brings certain economic benefit to the mill set.

Drawings

FIG. 1 is a schematic flow chart of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The present invention will be described in detail with reference to fig. 1 by taking a five-stand six-roll cold continuous rolling mill as an example

Example 1: selecting DT0144D1 steel grade with the specification of 1488mm in width and 0.654mm in thickness

Firstly, collecting the equipment parameters of each frame of the cold continuous rolling mill group in the step (a): the five stands of the equipment are six-roller mills, and the working roll diameter d of 5 stands_wDiameter d of five frames of intermediate rolls of 475mm_cDiameter d of support roller of 5 stands of 530mm_b1370mm, maximum rolling force P_max2700t, working roll body length l of five stands_wLength l of middle roller body of five frames 2000mm_c2010mm supporting roll body length l of five frames_b1990mm, working roll bearing seat center distance L_w4070mm, center distance L of bearing seat of intermediate roll_c4070mm, support roller bearing seat center distance L_b4070mm, the elastic modulus E of the working roll 210Gpa, and the poisson ratio ν of the working roll 0.3;

then in the steps (b) and (c), collecting rolling process parameters of each rack of the five-rack cold continuous rolling mill set, and taking j as 1; 1, the inlet thickness of the strip at the set speed of the frame is 3.381mm, and the outlet thickness of the strip is 2.037 mm; 1-5 front tension sigma of frame when rolling speed is set for unit_i0{322,240,183,138,51}, KN; back tension sigma_i1＝{207,322240,183,138}, KN; 1-5 set rolling speed of standmpm; 1-5 coefficient of friction on the 1 st segment of the gantry_i0.055,0.0290.02,0.012,0.013 }; average deformation resistance k of the strip in the 1 st section of the 1-5 stand during rolling_i{619,766,850,967,998}, Mpa; 1-5 frame 1 section strip steel back tension sigma_i1,1-203, 319,240,183,136, KN; front tension sigma of strip steel on the 1 st section of the 1-5 stand_i0,1319,240,183,136, 50, KN; 1-5 frame 1 section equivalent tension psi_i1-241.5,297.4, 222.9,169.5,111.9, KN; 1-5 frame 1 section strip steel unit back tension sigma_i1,d1139.1, 216.4,161.3,123,92.7, }, Mpa; 1-5 frame 1 st section unit front tension sigma_i0,d1{216.4,161.3,123,92.7, 34.3}, Mpa; the minimum value of the bending force of the working roll of the 1-5 frames is delta_imin0.2,0.2,0.25,0.3,0.2 }; 1-5 frames with a maximum working roll bending force delta_imax0.8,0.7,0.6,0.6,0.5 }; the minimum value of the bending force of the intermediate roll of the 1-5 frames is S_imin0.2, 0.22, 0.24, 0.25,0.2 }; 1-5 frames with the maximum value of the bending force of the intermediate roll being S_imax0.6, { 0.65, 0.6,0.5, 0.45 }; roll bending force optimization coefficient lambda of initialized working roll_i0,0,0,0, the step size calculated is 0.01;

subsequently in step (d), the work roll bending force is calculatedThe roll bending forces of the working rolls of 1 to 5 frames are respectively calculated to be delta_i0.302,0.302,0.298,0.363,0.216, and proceeds to step (f);

subsequently in step (e), the intermediate roll bending force optimization coefficient beta is initialized₁＝0、β₂＝0、β₃＝0、β₄＝0、β₅＝0；

Subsequently in step (f), calculating the intermediate roll bending forceThe bending forces of the intermediate rolls of 1 to 5 frames are respectively S_i＝{0.271,0.271,0.271,0.290,0.225}；

Then in step (g), dividing the loaded roll gap into 5 sections in the transverse direction, dividing the whole roll of strip steel into 100 sections in the longitudinal direction, and establishing a dynamic loaded roll gap optimization objective function of each machine frame

Calculating to obtain the dynamic roll gap of 1 to 5 frames

Then in step (h), the minimum establishment of the target function G (X) is judged, and delta is made_1y＝δ₁、δ_2y＝δ₂、δ_3y＝δ₃、δ_4y＝δ₄、δ_5y＝δ₅、S_1y＝S₁、S_2y＝S₂、S_3y＝S₃、S_4y＝S₄、S_5y＝S₅And (ii) proceeding to step (i);

subsequently in step (i), δ is judged₁<δ_1max、δ₂<δ_2max、δ₃<δ_3max、δ₄<δ_4max、δ₅<δ_5maxIf the judgment result is not true, entering the step (j);

subsequently in step (j), S is judged₁<S_1max、S₂<S_2max、S₃<S_3max、S₄<S_4max、S₅<S_5maxIf the judgment result is not true, entering the step (k);

subsequently in step (k), the optimal work roll bending force δ satisfying the optimization objective function is output_k0.302,0.302,0.298,0.363,0.216 and intermediate roll bending force S_k＝{0.271,0.271,0.271,0.290,0.225}。

Example 2: selecting DP0161D1 steel with specification of 1721mm in width and 0.765mm in thickness

Firstly, collecting the equipment parameters of each frame of the cold continuous rolling mill group in the step (a): the five stands of the equipment are six-roller mills, and the working roll diameter d of 5 stands_wDiameter d of five frames of intermediate rolls of 475mm_cDiameter d of support roller of 5 stands of 530mm_b1370mm, maximum rolling force P_max2700t, working roll body length l of five stands_wLength l of middle roller body of five frames 2000mm_c2010mm supporting roll body length l of five frames_b1990mm, working roll bearing seat center distance L_w4070mm, center distance L of bearing seat of intermediate roll_c4070mm, support roller bearing seat center distance L_b4070mm, the elastic modulus E of the working roll 210Gpa, and the poisson ratio ν of the working roll 0.3;

then in the steps (b) and (c), collecting rolling process parameters of each rack of the five-rack cold continuous rolling mill set, and taking j as 1; 1, the inlet thickness of the strip at the set speed of the frame is 3.730mm, and the outlet thickness of the strip is 2.691 mm; 1-5 front tension sigma of frame when rolling speed is set for unit_i0644,446,307,227,70, KN, rear tension σ of the respective gantry_i1-290, 644,446,307,227}, KN; 1-5 set rolling speed of standmpm; 1-5 coefficient of friction on the 1 st segment of the gantry_i0.053,0.024, 0.014,0.013,0.173 }; average deformation resistance k of the strip in the 1 st section of the 1-5 stand during rolling_i{582,701,774,825,839}, Mpa; 1-5 frame 1 section strip steel back tension sigma_i1,1-287, 640,442,299,224, KN; front tension sigma of strip steel on the 1 st section of the 1-5 stand_i0,1-640, 442,299,224, 68, KN; 1-5 frame 1 section equivalent tension psi_i1-396.2,584.6, 404.3,283,179.9, KN; 1-5 frame 1 section strip steel unit back tension sigma_i1,d1168.5, 374.2,259.1, 178.4,132, Mpa; 1-5 frame 1 st section unit front tension sigma_i0,d1＝{374.2,259.1，178.4,132，40.7}，Mpa; the minimum value of the bending force of the working roll of the 1-5 frames is delta_imin0.3,0.28,0.32,0.3,0.3 }; 1-5 frames with a maximum working roll bending force delta_imax0.8,0.9,0.9,0.75,0.75 }; the minimum value of the bending force of the intermediate roll of the 1-5 frames is S_imin0.5,0.6, 0.6, 0.62, 0.55 }; 1-5 frames with the maximum value of the bending force of the intermediate roll being S_imax0.85,0.95, 0.90, 0.90, 0.86 }; roll bending force optimization coefficient lambda of initialized working roll_i0,0,0,0, the step size calculated is 0.01;

subsequently in step (d), the work roll bending force is calculatedThe roll bending forces of the working rolls of 1 to 5 frames are respectively calculated to be delta_i{0.408,0.379,0.423,0.387,0.398}, and proceed to step (f);

subsequently in step (e), the intermediate roll bending force optimization coefficient beta is initialized₁＝0、β₂＝0、β₃＝0、β₄＝0、β₅＝0；

Subsequently in step (f), calculating the intermediate roll bending forceThe bending forces of the intermediate rolls of 1 to 5 frames are respectively S_i＝{0.666,0.751，0.702，0.709，0.68}；

Then in step (g), dividing the loaded roll gap into 5 sections in the transverse direction, dividing the whole roll of strip steel into 100 sections in the longitudinal direction, and establishing a dynamic loaded roll gap optimization objective function of each machine frame

Calculating to obtain the dynamic roll gap of 1 to 5 frames

Then in step (h), the minimum establishment of the target function G (X) is judged, and delta is made_1y＝δ₁、δ_2y＝δ₂、δ_3y＝δ₃、δ_4y＝δ₄、δ_5y＝δ₅、S_1y＝S₁、S_2y＝S₂、S_3y＝S₃、S_4y＝S₄、S_5y＝S₅And (ii) proceeding to step (i);

subsequently in step (i), δ is judged₁<δ_1max、δ₂<δ_2max、δ₃<δ_3max、δ₄<δ_4max、δ₅<δ_5maxIf the judgment result is not true, entering the step (j);

subsequently in step (j), S is judged₁<S_1max、S₂<S_2max、S₃<S_3max、S₄<S_4max S₄<S_4max S₄<S_4max、S₅<S_5maxIf the judgment result is not true, entering the step (k);

subsequently in step (k), the optimal work roll bending force δ satisfying the optimization objective function is output_k0.408,0.379,0.423,0.387,0.398 and an intermediate roll bending force S_k＝{0.666,0.751，0.702，0.709，0.68}。

It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.