The following is based on two avenues of research, one from the model steam boiler community, the other from the copper industry - the latter is perhaps more pertinent finally.
The massively skilled Don R. Giandomenico, aka rcdon, built a model steam boiler based on instructions from "Model Boilers & Boilermaking” by K.N. Harris (1967).
To make the boiler shell (outer cylinder of the pressure vessel) I am using a piece of solid drawn (seamless) type “L” copper tubing (seen below). This tubing is 6.125” in OD and has a wall thickness of .140”. According to the Harris book (page 31) it is satisfactory to have a seamless boiler shell at 5.845” ID x 0.094” wall operating at a working pressure of 100 PSI. This is calculated by multiplying the the working pressure (P) by the internal diameter of the shell in inches (D). You then divide this value by two times the derated tensile strength of the material being used (t). T is equal to the thickness of the boiler shell in inches:
(P X D) ÷ (2t)= T
The normal tensile strength of copper is around 25,000 pounds per square inch which in this case is derated by the factor of 8 times for a safety margin (3,125 X 8 = 25,000 PSI). This means that the boiler can handle 8 times the stress that would be applied to it under normal operating conditions. Knowing these values I can then plug them into the equation:
(100 x 5.845) ÷ (2 X 3125) = T ................... 584.5 ÷ 6250 = 0.094” thick
The boiler shell I am going to use would effectively handle a working pressure of 150 PSI. In fact, the manufacturers listed burst pressure of this type of tubing is at around 2,690 PSI !!!! I will have no trouble trusting this tubing at 80 PSI. Of course copper starts to lose it’s strength at elevated temperatures so it is important to keep it within it’s operating temperature.
The Aurora is rated to 1.5 atmospheres (or 1.5 bar) with an operating pressure of between 0.8 and 1 atmosphere.
From Harris p.28:
In all boilers it is usual to allow a comparatively high factor of safety, that is to say that if a boiler is required to work at 100 lb. per sq. in., its plates, stays, etc., are calculated on a basis of its bursting at anything from six to ten times this pressure. A good all round factor for model work is eight and that will be the one adopted in what follows.
p.31
This brings us to the strength of boiler shells. In calculations relating to the strength of a boiler shell; so far as the plate is concerned it makes no difference whether it is a rolled plate with a longitudinal joint or a solid drawn tube, that is to say so far as the stressing of the shell is concerned. What does have to be taken into account, however, is the strength of the longitudinal joint, a solid drawn tube having no joint is the strongest form.
The next best arrangement (model practice) is probably one with an inside butt strap riveted and hard soldered, the rivets being only to hold the whole issue together during the brazing or silver soldering operation. If all the contacting surfaces of butt -strap and boiler shell are clean and well fluxed and a proper job is made of the soldering, which entails on the one Land plenty of heat and on the other the avoidance of over-heating, the value of the joint should be about 95 per cent. of that of a solid drawn tube. A joint made with a double butt -strap, see sketches of of joints and double or treble riveted, which means either two or three rows of rivets each side of the joint, should have a strength equal to about 80 per cent. of that of a solid tube.
A double riveted lap joint will have around 75 per cent. and a single riveted lap joint 55 per cent of the strength of a solid drawn tube, so that it is very obvious that it pays handsomely to use the butt-strap plus brazing technique in making longitudinal joints. Best of all, of course, is
to use a solid drawn tube.
As I am not interested in riveting, the approximately 7" diameter boiler must be butt-strap and (hard) brazed construction as 7" nominal tube is not to be had. t, the derated tensile strength for copper is 25,000psi / 8 = 3125psi. The construction technique further derates the thickness by a factor of 100/95%.
T = (P x D)/2t x 100/95
T - thickness of the shell
P - working pressure in psi
D - internal diameter of the shell in inches
t - derated tensile strength of the material
The working pressure is 1 bar or 14.7 psi so:
T = (14.7psi x 7")/(2 x 3125psi) x 100/95
T = 0.017in which is around 26 gauge or not very thick at all...
Too thin in fact to make it easy to braze the fittings in place.
_______
The Copper tube handbook contains all the tables, formulas and recommendations discussed here.
Further reading on the copper.org site suggests that brazing or welding will anneal the copper considerably lowering its tensile strength. The brazing temperature threshold is 840F (450C) with most brazing alloys considerably higher than that (~1200F (650C)). Copper begins to anneal at 700F (370C). The hotter temperature and the longer the heat is applied, the quicker the annealing takes place.
Since brazing temperatures must exceed the melting point of the brazing alloys, between 1,150°F/621°C and 1,550°F/843°C, the process of making a brazed joint causes the base metals to anneal or soften, resulting in a reduction in the overall strength of the assembly.
Consequently, copper.org offers tables of the maximum safe working temperatures and pressures for various diameters of annealed tube.
Working pressure for the machine is 1 bar gauge (which is 2 bar absolute pressure i.e. 1 atmosphere above atmospheric pressure). At 2 bar, water boils at 120C (250F). So from tables 14.3 A, B and C:
Raising the temperature to 300F results in a lowering the safe working pressures by around 6psi.
An explanation of the formula used to calculate these values is here.
Furthermore:
In designing a system, joint ratings must also be considered, because the lower of the two ratings (tube or joint) will govern the installation. Most tubing systems are joined by soldering or brazing. Rated internal working pressures for such joints are shown in Table 14.4a. These ratings are for all types of tube with standard solder joint pressure fittings and DWV fittings. In soldered tubing systems, the rated strength of the joint often governs design.
From table 14.4a - the working pressure rating for brazed joints on all diameters of tube for use with saturated steam is 120psi gauge. Soldered joints, with all alloys and for all diameters and for use with saturated steam are limited to 15psi gauge.
The very conservative working pressure ratings give added assurance that pressurized systems will operate successfully for long periods of time. The much higher burst pressures measured in tests indicate that tubes are well able to withstand unpredictable pressure surges that may occur during the long service life of the system. Similar conservative principles were applied in arriving at the working pressures for brazed and soldered joints. The allowable stresses for the soldered joints assure joint integrity under full rated load for extended periods of time. Short-term strength and burst pressures for soldered joints are many times higher. In addition, safety margins were factored into calculating the joint strengths.
So what are the conclusions to be drawn from this? The numbers from copper.org are far more conservative than those from Harris. However, the desired working pressure of 1 bar (14.7 psi) is exactly on the money for soldered systems! My guess, given that espresso machines are low-pressure steam systems, is that the boiler is soft soldered!
Once again copper.org gets the last word:
Temperature and pressure are directly proportional for steam. As the pressure in the system is increased, the temperature increases accordingly. Saturated steam, a condition where steam contains as much water as it can and still be a vapor, at 15 psig has an absolute pressure at sea level of 29.7 psia (pounds per square inch absolute). At this pressure it would have a corresponding temperature of approximately 250°F which is the maximum recommended temperature for soldered joints as shown in Table 4 of the Copper Tube Handbook. Therefore, rather than the allowable pressure of the soldered joints controlling the rating, the allowable temperature is the controlling factor, leading to the rating of 15 psig regardless of the solder alloy used.
...
As with any piping system, the pressure rating of the system is controlled by the lowest allowable pressure of the tube, fitting, joint or joining material. For steam systems constructed using copper tube of Types K or L, the maximum allowable pressure at which the system could be designed would be 120 psig. As shown in Tables 3a and 3b of the Copper Tube Handbook, the lowest maximum operating pressure for Type L copper tube is 127 psig (corresponds to 12-inch nominal Type L tube in annealed form). Since this is more than the allowable pressure for the brazed joint, the 120 psig allowable for the joint is the controlling factor, regardless of the fact that smaller diameter tubes have higher allowable pressures. However, to use copper tube and fittings in a steam system at this pressure the joints must be brazed.
As long as these temperature and pressure limits are met, copper tube and fittings can be used in both high- and low-pressure steam systems. The system must still be designed and installed to meet the requirements of all applicable local, state and federal construction and safety codes for steam applications.
The massively skilled Don R. Giandomenico, aka rcdon, built a model steam boiler based on instructions from "Model Boilers & Boilermaking” by K.N. Harris (1967).
To make the boiler shell (outer cylinder of the pressure vessel) I am using a piece of solid drawn (seamless) type “L” copper tubing (seen below). This tubing is 6.125” in OD and has a wall thickness of .140”. According to the Harris book (page 31) it is satisfactory to have a seamless boiler shell at 5.845” ID x 0.094” wall operating at a working pressure of 100 PSI. This is calculated by multiplying the the working pressure (P) by the internal diameter of the shell in inches (D). You then divide this value by two times the derated tensile strength of the material being used (t). T is equal to the thickness of the boiler shell in inches:
(P X D) ÷ (2t)= T
The normal tensile strength of copper is around 25,000 pounds per square inch which in this case is derated by the factor of 8 times for a safety margin (3,125 X 8 = 25,000 PSI). This means that the boiler can handle 8 times the stress that would be applied to it under normal operating conditions. Knowing these values I can then plug them into the equation:
(100 x 5.845) ÷ (2 X 3125) = T ................... 584.5 ÷ 6250 = 0.094” thick
The boiler shell I am going to use would effectively handle a working pressure of 150 PSI. In fact, the manufacturers listed burst pressure of this type of tubing is at around 2,690 PSI !!!! I will have no trouble trusting this tubing at 80 PSI. Of course copper starts to lose it’s strength at elevated temperatures so it is important to keep it within it’s operating temperature.
The Aurora is rated to 1.5 atmospheres (or 1.5 bar) with an operating pressure of between 0.8 and 1 atmosphere.
From Harris p.28:
In all boilers it is usual to allow a comparatively high factor of safety, that is to say that if a boiler is required to work at 100 lb. per sq. in., its plates, stays, etc., are calculated on a basis of its bursting at anything from six to ten times this pressure. A good all round factor for model work is eight and that will be the one adopted in what follows.
p.31
This brings us to the strength of boiler shells. In calculations relating to the strength of a boiler shell; so far as the plate is concerned it makes no difference whether it is a rolled plate with a longitudinal joint or a solid drawn tube, that is to say so far as the stressing of the shell is concerned. What does have to be taken into account, however, is the strength of the longitudinal joint, a solid drawn tube having no joint is the strongest form.
The next best arrangement (model practice) is probably one with an inside butt strap riveted and hard soldered, the rivets being only to hold the whole issue together during the brazing or silver soldering operation. If all the contacting surfaces of butt -strap and boiler shell are clean and well fluxed and a proper job is made of the soldering, which entails on the one Land plenty of heat and on the other the avoidance of over-heating, the value of the joint should be about 95 per cent. of that of a solid drawn tube. A joint made with a double butt -strap, see sketches of of joints and double or treble riveted, which means either two or three rows of rivets each side of the joint, should have a strength equal to about 80 per cent. of that of a solid tube.
A double riveted lap joint will have around 75 per cent. and a single riveted lap joint 55 per cent of the strength of a solid drawn tube, so that it is very obvious that it pays handsomely to use the butt-strap plus brazing technique in making longitudinal joints. Best of all, of course, is
to use a solid drawn tube.
As I am not interested in riveting, the approximately 7" diameter boiler must be butt-strap and (hard) brazed construction as 7" nominal tube is not to be had. t, the derated tensile strength for copper is 25,000psi / 8 = 3125psi. The construction technique further derates the thickness by a factor of 100/95%.
T = (P x D)/2t x 100/95
T - thickness of the shell
P - working pressure in psi
D - internal diameter of the shell in inches
t - derated tensile strength of the material
The working pressure is 1 bar or 14.7 psi so:
T = (14.7psi x 7")/(2 x 3125psi) x 100/95
T = 0.017in which is around 26 gauge or not very thick at all...
Too thin in fact to make it easy to braze the fittings in place.
_______
The Copper tube handbook contains all the tables, formulas and recommendations discussed here.
Further reading on the copper.org site suggests that brazing or welding will anneal the copper considerably lowering its tensile strength. The brazing temperature threshold is 840F (450C) with most brazing alloys considerably higher than that (~1200F (650C)). Copper begins to anneal at 700F (370C). The hotter temperature and the longer the heat is applied, the quicker the annealing takes place.
Since brazing temperatures must exceed the melting point of the brazing alloys, between 1,150°F/621°C and 1,550°F/843°C, the process of making a brazed joint causes the base metals to anneal or soften, resulting in a reduction in the overall strength of the assembly.
Consequently, copper.org offers tables of the maximum safe working temperatures and pressures for various diameters of annealed tube.
Working pressure for the machine is 1 bar gauge (which is 2 bar absolute pressure i.e. 1 atmosphere above atmospheric pressure). At 2 bar, water boils at 120C (250F). So from tables 14.3 A, B and C:
Calculated Rated Internal Working Pressures for Annealed Copper Tube
Nominal Tube type and diameter inches
|
S = 4800psi 250F
|
Wall thickness inches
|
Inside diameter inches
|
6 K
|
277
|
0.192
|
5.741
|
8 K
|
295
|
0.271
|
7.583
|
6 L
|
201
|
0.14
|
5.845
|
8 L
|
216
|
0.2
|
7.725
|
6 M
|
175
|
0.122
|
5.881
|
8 M
|
183
|
0.17
|
7.785
|
Based on
maximum allowable stress in tension (psi) for the indicated temperatures (°F).
Raising the temperature to 300F results in a lowering the safe working pressures by around 6psi.
An explanation of the formula used to calculate these values is here.
Furthermore:
In designing a system, joint ratings must also be considered, because the lower of the two ratings (tube or joint) will govern the installation. Most tubing systems are joined by soldering or brazing. Rated internal working pressures for such joints are shown in Table 14.4a. These ratings are for all types of tube with standard solder joint pressure fittings and DWV fittings. In soldered tubing systems, the rated strength of the joint often governs design.
From table 14.4a - the working pressure rating for brazed joints on all diameters of tube for use with saturated steam is 120psi gauge. Soldered joints, with all alloys and for all diameters and for use with saturated steam are limited to 15psi gauge.
The very conservative working pressure ratings give added assurance that pressurized systems will operate successfully for long periods of time. The much higher burst pressures measured in tests indicate that tubes are well able to withstand unpredictable pressure surges that may occur during the long service life of the system. Similar conservative principles were applied in arriving at the working pressures for brazed and soldered joints. The allowable stresses for the soldered joints assure joint integrity under full rated load for extended periods of time. Short-term strength and burst pressures for soldered joints are many times higher. In addition, safety margins were factored into calculating the joint strengths.
So what are the conclusions to be drawn from this? The numbers from copper.org are far more conservative than those from Harris. However, the desired working pressure of 1 bar (14.7 psi) is exactly on the money for soldered systems! My guess, given that espresso machines are low-pressure steam systems, is that the boiler is soft soldered!
Once again copper.org gets the last word:
Temperature and pressure are directly proportional for steam. As the pressure in the system is increased, the temperature increases accordingly. Saturated steam, a condition where steam contains as much water as it can and still be a vapor, at 15 psig has an absolute pressure at sea level of 29.7 psia (pounds per square inch absolute). At this pressure it would have a corresponding temperature of approximately 250°F which is the maximum recommended temperature for soldered joints as shown in Table 4 of the Copper Tube Handbook. Therefore, rather than the allowable pressure of the soldered joints controlling the rating, the allowable temperature is the controlling factor, leading to the rating of 15 psig regardless of the solder alloy used.
...
As with any piping system, the pressure rating of the system is controlled by the lowest allowable pressure of the tube, fitting, joint or joining material. For steam systems constructed using copper tube of Types K or L, the maximum allowable pressure at which the system could be designed would be 120 psig. As shown in Tables 3a and 3b of the Copper Tube Handbook, the lowest maximum operating pressure for Type L copper tube is 127 psig (corresponds to 12-inch nominal Type L tube in annealed form). Since this is more than the allowable pressure for the brazed joint, the 120 psig allowable for the joint is the controlling factor, regardless of the fact that smaller diameter tubes have higher allowable pressures. However, to use copper tube and fittings in a steam system at this pressure the joints must be brazed.
As long as these temperature and pressure limits are met, copper tube and fittings can be used in both high- and low-pressure steam systems. The system must still be designed and installed to meet the requirements of all applicable local, state and federal construction and safety codes for steam applications.
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