Abstract:
The present invention provides a minus bottom cylinder end having a crown portion, a shoulder portion and a peripheral annular skirt, the crown portion being substantially spherical and located at the centre of the minus bottom cylinder end and the shoulder portion being located between a terminus of the crown and said skirt portion, and wherein said shoulder portion substantially conforms, in cross section, to one of the following: a three point spline, or a part elliptical segment.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]     This application is a continuation-in-part of PCT international application PCT/AU02/01379 having an international filing date of Oct. 10, 2002. The disclosure of such prior international application is incorporated herein by this reference. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention relates to minus bottom cylinder ends. Minus bottom cylinder ends are used in water heater storage tanks and provide a concave, inwardly domed end for the tank bottom. Such ends can also be called dished ends subjected to external pressure. They are used for water heaters operating at mains pressure and have a heat supply generally being generated by electricity.  
       BACKGROUND OF THE INVENTION  
       [0003]     There are three types of dished ends described in Pressure Vessel Code AS1210-1997 namely torispherical, elliptical and spherical. Prior water heaters manufactured by the applicant contain a minus end which is spherical. The Pressure Vessel Code AS1210-1997 describes these minus ends as dished ends subjected to external pressure meaning that the pressure is on the convex side of the dome.  
         [0004]     A tank such as that currently manufactured by the applicant is illustrated in  FIG. 1 . The minus tank end being at the bottom of the tank is generally manufactured from 3.5 mm thick steel, and as is illustrated in  FIG. 3 , has a height of approximately 140 mm and a spherical radius of 375 mm. The hydrostatic testing regime contained in Pressure Vessel Code AS1210-1997, required that the test be run at the working pressure of the vessel, in this case 1,000 Kpa, with the tank needing to be able to withstand a spike of pressure equal to twice the working pressure for a very short time, with the pressure then falling again back to the working pressure.  
         [0005]     The tank and minus end of FIGS.  1  to  3  had no difficulty with this testing regime. However, a new hydrostatic testing regime and a new code being AS/NZS3350 has been implemented. This hydrostatic testing regime requires that the tank be operated at its working pressure and then for a period of 30 minutes it must be operated at a pressure being twice the working pressure. It must do this without any leaks or structural failure.  
         [0006]     The spherical minus end of FIGS.  1  to  3  however repeatedly fails under the new hydrostatic testing regime, because the steel continues to stretch even though the pressure was held constant. This is due to a cold creep effect and happens when the steel reaches its elastic limit and starts to become plastic. As the shape of the cylinder is stretched under pressure, the shape of the cylinder bottom end slowly changes until such time as the minus bottom cylinder end buckles, that is, portions of the minus end change their radius of curvature and protrude into the space below the minus end.  
         [0007]     Any reference herein to known prior art does not, unless the contrary indication appears, constitute an admission that such prior art is commonly known by those skilled in the art to which the invention relates, at the priority date of this application.  
       SUMMARY OF THE INVENTION  
       [0008]     The present invention provides a minus bottom cylinder end having a crown portion, a shoulder portion and a peripheral annular skirt, the crown portion being substantially spherical and located at the centre of the minus bottom cylinder end and the shoulder portion being located between a terminus of the crown and said skirt portion, and wherein said shoulder portion substantially conforms, in cross section, to one of the following: a three point spline, or a part elliptical segment.  
         [0009]     Preferably the cross section of the shoulder portion conforms to either, the three point spline, or a part elliptical segment, to within 5%. It is also preferable that the crown portion conforms to the shape of a sphere to within 5%. More preferably the shoulder portion conforms to either, the three point spline, or a part elliptical segment, to within 3%. It is also referable that the crown portion conforms to the shape of a sphere to within 3%.  
         [0010]     In a first preferred embodiment the crown portion is spherical. In a particularly preferred embodiment the cross section of the shoulder portion is a three point spline, or a part elliptical segment.  
         [0011]     The three point spline or part elliptical segment should preferably have a tangent at the point of intersection with the crown which is equal to the tangent at the terminus of the crown.  
         [0012]     The three point spline or part elliptical segment at the skirt preferably has a tangent at the point of intersection which makes an angle of between 20° to 35° to the vertical. More preferably the angle of intersection is 30°.  
         [0013]     Preferably the skirt makes an angle of approximately 3 degrees to the vertical, that is the skirt has a divergent tapering shape from the top of the skirt to the lower periphery.  
         [0014]     A knuckle portion is preferably located between the shoulder and the skirt. A knuckle portion is provided due to manufacture in a press and the need to stress relieve the intersection of the skirt and the shoulder portion. The knuckle portion has a radius applied to it in order to smooth out the transition between the skirt and the terminus of the three point spline or part elliptical section. Preferably the radius is in the range of 15 millimetres to 40 millimetres.  
         [0015]     Preferably the end is manufactured from 3.5 mm thick steel. The steel is preferably the equivalent to a US steel specification UNS G 10 100 or G 10 160.  
         [0016]     The following preferences refer to a cross section of either a die on which the minus bottom cylinder end is formed, or to measurements on the inside concave surface of the minus bottom cylinder end. Preferably the minus bottom cylinder end is 536 millimetres in diameter, with a theoretical skirt height of 20 mm. The crown preferably has a spherical radius of 490 mm and preferably terminates 126.8 millimetres from the centre at a height of 113.3 millimetres above the base of the skirt. The three point spline or part elliptical segment intersects the skirt at 268 millimetres away from the centre and some 20 millimetres above the base of the skirt. An intermediate point of the part elliptical segment or a third point for the three point spline is preferably located at a radius of 205.7 millimetres from the centre and 81.6 millimetres above the base of the skirt.  
         [0017]     Preferably the thickness of the end is 3.5 millimetres.  
         [0018]     A method of producing a pressure vessel minus end, said method including the provision of a spherical crown, a peripheral cylindrical or conical skirt and a shoulder connecting the top of said skirt to the terminus of said crown, said shoulder being characterised by being, in cross section, either an elliptical segment or a three point spline.  
         [0019]     An advantage of the present invention is that for the same diameter and thickness a stronger minus end is produced, one which will be particularly be able to cope with the more stringent hydrostatic testing of AS/NZS3350.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0020]     An embodiment or embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:  
         [0021]      FIG. 1  illustrates a front elevation of a prior art water tank having a plus top end and a minus bottom end;  
         [0022]      FIG. 2  is a cross section through the point of intersection of the minus end with the tank cylinder wall;  
         [0023]      FIG. 3  illustrates the minus end of  FIG. 1  in cross section;  
         [0024]      FIG. 4  illustrates a die on which the improved minus end can be formed; and  
         [0025]      FIG. 5  illustrates a comparison of the old and the improved theoretical (ie without a radiused knuckle being present) top surfaces of the die. 
     
    
     DETAILED DESCRIPTION  
       [0026]     As illustrated in FIGS.  1  to  3  the prior art tank  1  has a spherical minus end  2  being some 541 millimetres in diameter with the spherical minus end  2  being formed from a 375 millimetres spherical radius.  
         [0027]     A peripheral skirt  3  is provided which is tapered at  30  to the vertical with a knuckle  16  (being the intersection of the end spherical portion with the skirt  3 ) having a radius of 12 millimetres formed thereon. As can be seen from  FIG. 2  the external wall  4  of the cylinder is welded to the skirt of the minus end by a GMA weld.  
         [0028]     As illustrated in  FIGS. 4 and 5  the minus end  10  according to the preferred embodiment of the present invention has a dramatically different profile compared to the spherical end of the FIGS.  1  to  3 . It is important to note that in  FIGS. 4 and 5  the illustration depicts the top surface of a die to make the cylinder end, not a representation of the cylinder end. Typically the minus end of the preferred embodiment is made from 3.5 mm thick steel and thus, a 3.5 mm layer (or other thickness) needs to be take into account when determining the shape of the upper side of the minus end produced by the die of  FIGS. 4 and 5 . Thus the following dimensions are to be considered to be either on the outside convex surface of a die which will form the cylinder end or on the inside concave surface of the cylinder end.  
         [0029]     As illustrated in  FIG. 4  the die  10  (or the concave surface of the cylinder end) has a profile that varies across its radius. Thus the minus end of the preferred embodiment has the following profile segments, sequentially in a radially outward direction from its centre: a centre crown portion  12 , a shoulder portion  14 , a knuckle portion  16  and a peripheral skirt  18 . The base of the skirt  18  is used as the reference point for most of the dimensions used in  FIG. 4 . As will readily be understood, by those skilled in the art,  FIGS. 4 and 5  show cross sections through a die or the concave surface of a cylinder minus end. It will be understood that the cylinder end or die from which it is produced is three dimensional and figure of revolution.  
         [0030]     The shape of the minus end  10  can be defined by the revolution generator about the centre point of the minus end. The generator can be either in the form of a “radial” generator or a “diametrical” generator. The generator can be formed from a piecewise function or by fitting a polynomial, or other mathematical approximation, to such a piecewise function, or even by empirically fitting a shape to a minus end designed to conform to such a piecewise function.  
         [0031]     Returning to  FIG. 4 , the centre crown portion  12  of the minus end  10  is approximately 130 mm above the base of the skirt  18  and is spherical in shape, being formed at a 490 millimetre radius. The crown  12  extends out to a radius of 126.8 millimetres measured from the centre, terminating 113.3 millimetres up from the base of the skirt  18 .  
         [0032]     The theoretical skirt  18  measures 20 mm in height and is circular with an external diameter of 536 mm. While the die will have the skirt  18  in the vertical, a pressed cylinder minus end coming off the die the skirt will flare or taper outwardly by approximately 3° once the pressing force is removed.  
         [0033]     A three point spline will interconnect the terminus of the crown  12  to the top of the vertical skirt  18 , which is located at a radius of 268 millimetres from the centre, and 20 millimetres up from the base of the skirt  18 .  
         [0034]     At the intersection of the crown  12  and the shoulder  14 , the tangent in cross section, of the terminus of the crown and the tangent of the three point spline, are the same or have the same equation. Further, the second derivatives of the respective curves at this intersection also are the same or have the same equation.  
         [0035]     At the intersection of the shoulder  14  with the theoretical skirt  18  (that is without a knuckle  16  being present) the tangent (in cross section) to the terminus of the shoulder  14  is at approximately 30 degrees to the vertical. This angle of 30 degrees to the vertical may vary between 20° to 35°.  
         [0036]     A three point spline is a curve which results from a cubic polynomial which must pass through the three points in the cross section of: (1) the terminus of the crown; (2) the upper end of the skirt and (3) an intermediate third point.  
         [0037]     In the present instance the third point in the three point spline is located approximately 205.7 millimetres out from the centre of the end and approximately 81.6 millimetres above the base of the skirt. A person skilled in the art should be able to determine other suitable points for use with such a three point spline to implement an embodiment of the present invention.  
         [0038]     Thus the generator of the preferred embodiment can be described, in a piecewise manner to be, from the centre out, as a circular portion followed by a 3 point spline.  
         [0039]     As will be appreciated by those skilled in the art the generator, or diametrical cross section can be approximated by a polynomial, or other mathematical function. The profile of the minus end of the preferred embodiment, excluding the skirt portion and knuckle portion, can be approximated by the following 6th order polymomial: 
 
 z=− 0.215589 r   6 +0.1313798 r   4 −0.030653728 r   2 +0.46746 
 
         [0040]     Where z is the vertical separation of a point on the minus end, and r is the radial distance from the centre of the minus end. Clearly, as this is a 6th order polynomial this function represents a diametrical cross-section, rather than a radial cross section. An odd order polynomial could be calculated that would approximate the radial profile of the minus end of the preferred embodiment. It is expected that so long as a tolerance of 5%, in terms of variation from a piecewise defined cross section is maintained, an approximation to the calculated shape of the minus end should work to within acceptable limits. Clearly closer conformance to the chosen piecewise defined cross section is preferable.  
         [0041]     The formula of paragraph [040] whilst being a good approximation does produce a curve with some undulations in parts thereof. A better approximation is given by the following 6 th  order polynomial: 
 
 Z=V   6   |r|   6   +V   5   |r|   5   +V   4   |r|   4   +V   3   |r|   3   +V   2   |r|   2   +V   1   |r|   1   +V   0  
        where:     V 0 =0     V 1 =0.993387135     V 2 =−0.000476874     V 3 =−5.44472×10 −5       V 4 =4.43609×10 −7       V 5 =−1.45647×10 −9       V 6 =1.74435×10 −2          
 
         [0050]     The three point spline provides a steeper tangent to the vertical by comparison to the spherical minus end  2  at the point of intersection with the top of the theoretical skirt when measured at the same height above the base of the skirt. Similarly the angle between the tangent of the shoulder portion and the vertical is lower than in prior art spherical minus ends ie. approximately 30° as opposed to approximately 45° for typical prior art minus ends. As described below this acts to reduce vertical component of the hydrostatic force near the periphery of the minus end. Thus a theoretical hydrostatic force P being at 90° to the tangent to the sphere at a height X above the base of the skirt of the minus end  2 , has a smaller horizontal component of force, and a larger vertical component of force, transmitted to the minus end  2  by comparison to the force P 1  acting against the end  10 , also acting at 90 degrees to the tangent at the same height X above the skirt base.  
         [0051]     This larger horizontal component, and lesser vertical component tends to reduce the amount of secondary loads acting at the join of the cylinder wall and the skirt of the end  10 . By reducing these secondary loads the hoop stress produced at the intersection of the minus end  10  and the cylinder seems to be reduced and as such helps to prevent the minus end  10  from buckling under the hydrostatic test regime of AS/NZS3350.  
         [0052]     The above described dimensions of minus end  10  are suitable for a 540 mm diameter end, at a thickness of 3.5 mm, that is to be used under a working pressure of 1000 KPa and to withstand a 2000 KPa pressure for approximately 30 minutes. A person skilled in the art will readily determine that the end thickness, the material properties of the material chosen, the diameter and the working pressure will all have a determining influence on whether an end will buckle or fail. Notwithstanding, the present invention allows a person skilled in the art to produce a stronger minus end for a predetermined working pressure, diameter, thickness of the minus end and material grade by comparison to a spherical, or elliptical or torispherical shaped end for the same predetermined working pressure, diameter, thickness of the minus end and material grade.  
         [0053]     A further advantage of the inventive shape of the minus end  10  is that the volume of the tank which receives this minus end is marginally increased with respect to the spherical minus end that it replaces. The same would be true by comparison to an elliptical minus end.  
         [0054]     While the above description discusses a three point spline, the three point spline between the terminus of the crown and the top of the skirt can be replaced by an elliptical segment. Whilst this may not lead to a structure as good as one having a three point spline, it is believed that it will work better than a spherical minus end  2 .  
         [0055]     It will be understood that the invention disclosed and defined herein extends to all alternative combinations of two or more of the individual features mentioned or evident from the text. All of these different combinations constitute various alternative aspects of the invention.  
         [0056]     While particular embodiments of this invention have been described, it will be evident to those skilled in the art that the present invention may be embodied in other specific forms without departing from the essential characteristics thereof. The present embodiments and examples are therefore to be considered in all respects as illustrative and not restrictive, and all modifications which would be obvious to those skilled in the art are therefore intended to be embraced therein.