Welcome to vulcanhammer.info, the site about Vulcan Iron Works, which manufactured the durable air/steam line of pile driving equipment for more than a century. Many of its products are still in service today, providing reliable performance all over the world. There’s a lot here, use the search box below if you’re having trouble finding something.
One of the most complicated transactions I have ever been involved in during my years at Vulcan was the purchase of the patent rights for a Russian concrete pile cutter (shown at left.) The patent had around a dozen inventors and two research institutes, spread out from Moscow to Vladivostok. The sheer logistics of getting everyone to agree to this, to say nothing of the financial considerations, made it a daunting task.
After six years of work on it we had actually made quite a lot of progress, but the Deputy Director General of the main research institute was trying to hold out for more money. Since the market for these things is pretty limited, we had to be careful.
At this point the Russian government sponsored a Russian technology exposition in Washington, DC, and the institute was one of the exhibitors. They sent their Director General; we thought it would be a good time to make some progress without the expense of another trip to Russia. So I went to Washington, was met by my translator, and we set out to have a meeting with the Director General.
On the way we stopped by the hotel room which the institute’s people were using as a headquarters. It was a mess; clothing and trash were piled everywhere, vodka bottles being the most prominent. Evidently these people were having quite a time during their trip to America.
We got to the exhibit hall and managed to pull the Director General aside for a meeting on the patent. In preparation for this meeting, I had prepared a “protocol” (we usually call it a “letter of intent” in the U.S.) which outlined what was for us an initial negotiating position. So I presented this and asked the Director General what he was prepared to sign to conclude this agreement.
At that, my translator looked me straight in the eye and said, “He is prepared to sign anything.” Needless to say, I wasn’t prepared for this; I was used to a lot more “horse trading” in negotiations, particularly with people outside the U.S. But sure enough, he was; he signed the protocol. Back in Moscow, his deputy was enraged at this, but there was nothing he could do; the negotiations were completed and we obtained the patent assignment.
We live in an age where people are said to be deceived by all kinds of “isms”: moral relativism, secular humanism, post-modernism, and the like. But having been in the real world for too long, I like to look at things a little differently. The problem with people today is that, after years of excessively rapid upward social mobility, blistering technological change, and relentless manipulation by those who own and operate the society, they are, like our Director General, prepared to sign anything, to go along with anything so long as their lives go on as they have, no matter what the long term cost is to themselves.
“For a time will come when people will not tolerate sound teaching. They will follow their own wishes, and, in their itching for novelty, procure themselves a crowd of teachers. They will turn a deaf ear to the Truth, and give their attention to legends instead.” (2 Tim 4:3-4) This is where we’re at, with the disintegrating families, eroding human rights, and the growing consumer debt which is turning a society of owners into a society of renters, at the whim of those who control the financial destiny of the nation. Christianity, which takes a definite stand on many issues, is looked on with hostility as a menace to the stability of this house of cards, proclaiming as it does an ultimate authority beyond the state.
But there’s always a payoff of some kind in the end. Our Russian inventors and institutes were paid off in U.S. dollars, a valuable commodity in Russia in those days. Those who sign with the rulers of this world have another payoff altogether: “The wages of Sin are Death, but the gift of God is Immortal Life, through union with Christ Jesus, our Lord.” (Romans 6:23) It’s your choice. Are you prepared to sign anything?
It’s been a long time since many computers ran DOS or even Windows 3.1. Given the changes in hardware, it would be difficult to get most any recent PC to run one or both. Yet every time we have a major software upgrade, we lose some of the capabilities we had in the past. It’s something we don’t think about in the advance of computer power, but it’s a fact.
That’s more true in two fields than any other: business and scientific/engineering software. Ever wonder why businesses and medical establishments, for example, still run Windows XP or 7 so often? With engineering software, it’s even worse: there are still DOS programs which do things that more recent software either does not do or does very expensively (the “per seat” cost of programs like AutoCad and most commercial finite element software, would shock most people outside of the field).
This article concentrates on two venerable pieces of DOS software: WEAP87, the wave equation program to analyse driven piles during installation, and SPILE, which estimates axial driven pile capacity. As long as XP “ruled the roost” and was capable of running 16-bit software, it was certainly possible to run both and other DOS and Windows 3.1 packages. With the creeping advance of Windows 7 and 8 (Vista wasn’t an advance) and 64-bit software, it’s become impossible to run these programs. So we’re stuck with two choices: either forget about using them or purchase expensive wave equation software. The latter option is OK if you use it all the time, but for occasional use (and when WEAP87 was perfectly adequate for your needs) it doesn’t make sense. But what is to be done?
The solution to the problem for this and other DOS program requirements is DOSBox, an x86 emulator that runs DOS on a variety of platforms, including 32-bit Windows, Mac OS X and Linux. The purpose of this article is to give an overview of DOSBox, some tips about its installation, how to set up WEAP87 and SPILE on DOSBox, and a quick look into Windows 3.1 on DOSBox.
DOSBox is first an emulator for DOS games. That may look like an odd platform for running a scientific/engineering application with WEAP87, but it actually works well. Games have been a driving force in pushing local computer power forward. Behind the graphics and interaction are some very complex mathematics, and running those in “real-time” has been a challenge of gaming computers from the very start.
DOS gaming for its part is the classic example of taking lemons and making lemonade. Most DOS applications were text-based running on poor graphic standards such as CGA and EGA; it wasn’t until 800 x 600 VGA (or the venerable B&W Hercules standard) when graphics really began to look realistic. The operating system itself came with few integral interfaces other than the screen and keyboard; no common graphical interface like the Mac, no mouse or joystick drivers in the early versions, and the math coprocessor was optional until the “486” processors. It forced DOS gamers to write the visual output directly to the screen. They took up the challenge with zeal and DOS games squeezed every bit of output from the computer it was capable of.
With the advent of Windows 3.0/3.1/3.11 and certainly of 95, many of the routines that had to be written for the software specifically became part of the operating system. Unfortunately that, combined with the system overhead of the OS, slowed down games, which meant that Windows games lagged for a while until the hardware caught up with them. (The system overhead of Windows is still significant, something that anyone who has ventured outside of the Windows world will attest). Thus DOS gaming was something of a “golden age” and DOSBox was designed to recapture that golden age on computers that were no longer capable of running them.
Running Non-Gaming Applications on DOSBox
That having been said, DOSBox’s developers have traditionally discouraged non-gaming applications from DOSBox. For one thing, DOSBox lacks many of the facilities that non-gaming applications often need, such as printing (not an issue with either one of these programs, as they put out text files) and many of the DOS features (which are missing because of patent and copyright issues in many cases). There’s also the issue of emulation; no two computers do digital calculations the same, and that especially applies to an “operating system” which was primarily designed for gaming.
MCF, a TSR to aid in file management and program running. Especially useful with WEAP87 as you run one program to input/preprocess the data and another to actually run the analysis. Unlike many TSR programs designed for this purpose, MCF is very light on system resources.
DOSBox, for whatever operating system you’re using.
One thing you definitely need to do is to set up a “C” drive. DOSBox starts out with a “Z” drive with its basic programs to run. The process is described here. One big advantage of this over, say, a virtual machine is that you’re using the same file system for the emulator as you are for the host computer. This means that you can open the data results in either a text editor or do a screen grab of the graphics.
Once you’ve done that, the easiest way to get the programs going is to do the following:
Unpack MCF and put it in the root directory of the C drive (c:\).
Create a directory c:\WEAP87 and put the WEAP 87 files in it.
Create a director c:\SPILE and put the SPILE files in it. It’s better to use two separate directories to avoid file name conflicts.
And that’s it.
Running SPILE and WEAP87
If you’ve run these programs on, say, Windows XP, running them on DOSBox–either directly from the command line or from MCF–is a familiar experence. If you used either or both in the DOS era, it’s a trip down memory lane–down to the pace the computer runs the programs. That’s because DOSBox deliberately slows down the pace of execution to simulate a DOS-era computer, and thus (for games where it’s critical) the timing of the game isn’t thrown off by faster execution speeds. For either of these programs, it isn’t a big deal, and in any case DOSBox will “pick up the pace” for really processor intensive programs. But after watching the output of WEAP87 in particular whiz by, seeing it going more slowly brings back memories.
SPILE is pretty straightforward, since there’s only one executable file. The one thing you need to watch for is not to print out the output; just save it to a file. If using the output for WEAP87, many engineers prefer to estimate the pile capacity using a spreadsheet and other methods.
WEAP87 is a little more complicated because the preprocessing file and the file that actually executes the wave equation analysis are different. But other than that there is little difference between using it in DOSBox and elsewhere. The governing data files can be edited either with MCF or with another text editor, and the text output can be done likewise. One thing that comes back in DOSBox is shown above: the graphical bearing graph, in all of its CGA glory. I’m not sure you want to put it into a report, but it’s good to have in any case.
Other DOS Programs
I’ve also tried other DOS engineering programs in DOSBox with success, including finite element analysis. The ability to preserve the graphics using a screen grab program is a big plus (see below.) These programs, however, like WEAP87 put their output in a text file, which can then be edited by either a text editor or a word processor. Again a big advantage of DOSBox is that the file system for the program is accessible by the host operating system, which means that you can keep files generated by DOS programs and other data (such as soil boring data, for example, with SPILE and WEAP87) together.
Another interesting program in DosBOX is CFRAME, the Corps of Engineers’ structural finite element analysis program. It was used in preparing the book Sheet Pile Design by Pile Buck. Here are some screen shots showing its graphical output:
Since Windows 3.1 was basically run on top of DOS, and 16-bit software (including software written for 3.1) is becoming out of bounds for newer Windows machines, the obvious question is, “Can DOSBox run Windows 3.1”? Having a legal copy of Windows 3.11 for Workgroups, I gave it a shot, with tremendous help from this post in DOSBox’s forum vogons.org.
Although I haven’t spent much time with it, the short answer is “to some extent”. DOSBox allocates enough extended and expanded memory to run it. There are some obstacles, however, not the least of which is that DOSBox doesn’t contain a full copy of DOS, but simulates DOS 5.0. It thus lacks the key file for full Windows functionality: SHARE.EXE. If you can get this file and get it running, that will probably change. But I’ve gotten further with this approach than, say, setting up a virtual machine. (Any virtual machine I’ve seen for DOS or Windows 3.1 is challenged in accessing files outside of the virtual machine).
DOSBox is a tremendous help in using DOS (and to a lesser extent Windows 3.1) programs on current machines and operating systems. I would strongly urge anyone who wants to try this to “test drive” some of these programs to make sure the results are good.
In 1967 Vulcan opened a fabricating facility in West Palm Beach, Florida. Across the street from our new plant was “U and Me Transfer and Storage,” (see photo above) which we hired to move a lot of our machinery. We sent one of our supervisors to Florida to help set the shop up. The shop foreman in Florida told the Tennessee man that “U and Me would move this in,” and “U and Me will deliver this tomorrow,” and so on. Finally the Tennessee man threw his hands up in exasperation and asked, “When’s You and Me going to have to time to do all this?”
The plant was formally called the “Special Products Division;” one of those special products was a light trailer, also shown above. This is useful if you want to do construction work at night; just set it up, turn on the generator, turn on the lights and work. In the U.S., with the problems of doing road construction during the day, these handy devices get a workout while crews attempt to repair or rebuild our roads at night.
Back in Chattanooga, the company’s main product line went on, which was building pile drivers, many for the offshore oil industry. These machines are most easily put together vertically; you put the base on the ground, stack the ram and the columns on top, then the cylinder, tie the hammer together, lay it down on a flat bed truck and ship it (the stacking is shown at the right.) Because the hammers got so big, we did a lot of this outside, using truck cranes.
One evening we were stacking yet another hammer for shipment. It got dark; the truck was waiting for us, there was no question of waiting until the morning. The supervisor got the light trailer out, fired it up and turned it on so the men could see what they were doing and finish up. Unfortunately the plant was in a residential area. When we turned the lights on, the residents didn’t like it, so they started shooting at the plant. Needless to say, our employees and the poor truck driver found it hard to work with bullets whizzing past them.
Most residential areas like some additional light, but there are always exceptions, and obviously this was one of them. Unfortunately many people and areas don’t like the light being shined on them–any kind of light.
“…though the Light has come into the world, men preferred the darkness to the Light, because their actions were wicked. For he who lives an evil life hates the light, and will not come to it, for fear that his actions should be exposed…” (John 3:19-20)
In a world where privacy is evaporating, people still don’t like their deeds to be known. In some cases this is due to the shifting sands of our legal systems; what is okay one day is punishable by life imprisonment the next. But much of our aversion to the light is because we know that what we are doing is wrong, legal or not. We make excuses like “I’m not a bad person,” not really understanding what that means or how it might be fixed if we are in fact a bad person. We know we are hurting others–we know we are hurting ourselves–but our main motivation is not to get caught, not to have the light shined on our deeds.
“But he who acts up to the truth comes to the light, that his actions may be shown to have been done in dependence upon God.” (John 3:21)
Our God doesn’t need to turn on his light trailer to find out what’s going on in our lives and in our selves; he has “night vision” so to speak, and he knows what we are doing even if no one else does. But he doesn’t want us to just go on in the darkness until we stumble and break our neck. “Jesus again addressed the people. ‘I am the Light of the World,’ he said. ‘He who follows me shall not walk in darkness, but shall have the Light of Life.’” (John 8:12) It is his desire that we walk in his light and live in his love. Just as we used a light trailer to do our work outside the plant, so if we have Jesus Christ in our lives we can live as God’s child even under less than ideal circumstances.
For many years, Vulcan included Engineering News Formula charts and data in its literature. Vulcan dropped the EN formula out of its literature in the 1970’s, for two reasons: the wave equation was in the ascendancy, and endorsement of the EN formula was an implied endorsement of the “bearing power” of the piles they drove, an endorsement which Vulcan was justifiably reluctant to make.
Nevertheless, the use of dynamic formulae persists for smaller projects and is embedded in many specifications. For this purpose, the FHWA favours the Modified Gates Formula, and this is discussed in the latest edition of their Design and Construction of Driven Pile Foundations. The section on the Modified Gates Formula is reproduced below:
In 1988, during Vulcan’s first trip to the then Soviet Union, my brother Pem and I were given the chance to visit the Monastery of Trinity-St. Sergius, which was the administrative centre of the Russian Orthodox Church. This is located in the town of Sergeiev Posad, which was called Zagorsk during Soviet times. The trip was arranged by our Russian business hosts (V/O Machinoexport) and our Russian agent at the time, A.A. Titov. The article below was written 20:15:01 4/20/1988 (the day of the visit) with a few corrections in the text and updates at the end.
Christianity was first introduced to Russia from Byzantium (Greek Orthodox) between 860 and 867. At this time Kiev — south of the Chernobyl site — was the capital of Russia. In 957 the regent Olga was baptised in Constantinople; her grandson Vladimir made Christianity the state religion in 988. This is being celebrated this year as the 1000th anniversary of the “Baptism of Russia” and extensive celebrations are being made plans for as a result.
The Russian Orthodox Church is an Orthodox Church, and until 1448 was subordinate to the Greek Orthodox Church in Constantinople. At this time, as the Byzantine Empire was coming to an end with its conquest by the Ottoman Turks, the Russian church took the step of electing its own leader; in 1589 this leader, now residing in Moscow, took the title of Patriarch, making him in theory the equal of the Patriarch in Constantinople and also of the Pope in Rome.
In 1721 the Russian Tsar Peter the Great abolished the Patriarchate and replaced same with the Holy Synod to run the Orthodox Church. This was a council, with its head — a lay official — appointed by the Tsar. This effectively made the Orthodox Church a department of the government, a position it found itself in until the Tsar was overthrown in 1917.
With that overthrow the Church re-established the Patriarchate, but now the greater threat came of course from the Communists, who, following Marx, believe that religion of all kinds is the “opiate of the people” to dull their revolutionary drive, and which will wither away under the advance of “scientific” socialism such as their claims to be. The church’s property was nationalized and many of its clergy was jailed and killed, and parts of the church made themselves into a pro-Soviet type of church, a process that has been repeated with the Catholic Church in Nicaragua. Matters became especially desperate under Stalin, who attempted to destroy all opposition through liquidation in his purges in the 1930’s.
Matters were at their nadir when the Second World War broke out, and when the Germans invaded the Soviet Union the demoralization of the nation was so complete that Hitler nearly succeeded in conquering the country. In its desperation Stalin’s war effort turned to the Orthodox Church and other Christian groups to help with the war effort, to revitalize the people for the war effort. This they did, and in return the Soviet government has granted the Orthodox Church and some other Christian groups limited freedom of existence and activity. The Orthodox Church today runs a precarious balance today; on the one hand it attempts to carry on its liturgical and spiritual activities to nurture the flock in the Orthodox faith, on the other it must to secure its existence meet Soviet regulation and to assist the Soviet government in various activities, such as the promotion of the peace movement in the West, which is a major project of the Soviet regime today.
Outline of the Trip
Arrived about 1130 with Pem, Alex Titov, and Alexander Tikhanov and assistant Natasha from V/O Machinoexport. Were greeted at Monastery office.
We were first given tour by Father Alexander of several of the churches in the compound. Zagorsk is the administrative centre of the Russian Orthodox Church, founded by St. Sergius in 1337. The Orthodox complex is within the town itself, being a walled fortress, a format dictated by military considerations in past times, similar in concept to missions in our own Southwest such as the Alamo. The last time it was used for military purposes was against a siege by the Poles in the 15th century. These churches, such as the Trinity Cathedral (which contains St. Sergius’ relics), the Dormition Cathedral, the Church of the Holy Spirit, were very impressive. When not in liturgical use, these churches are the site for all kinds of devotions, such as prayers, adorations, and Bible reading, and, in the case of Trinity Cathedral, singing which has an ethereal quality beyond words to describe. Then we returned to office where we signed the guest register, and I wrote congratulations to them for the 1000th anniversary of what they call the “Baptism of Russia”.
After this, we were given tour of the seminary museum by a seminarian. This contains historical articles of the Orthodox church of all kinds and a special section on the life and work of the Patriarch Alexis, who helped bring the Orthodox Church back to life after its near extinction by Stalin. There was a scale model of a large cathedral in Moscow built to commemorate the victory over Napoleon in 1812. Titov asked what happened to it and the seminarian replied “What happened to thousands of other churches in Russia? There is a swimming pool where that one was.”
We then went to the seminary office, where we were greeted warmly by Father Vladamir Kucherjavy, Assistant Rector of the seminary, who then fed us snack. He gave us description of the work of the seminary, and in the process told that full course in seminary was a four year course followed by two year course, similar to our own BA/MA system; however, some went directly to the field after the first four years. This reminded me of our church’s internship program, so I asked Father Kucherjavy if the two were alike. He said yes, and then asked what church I belonged to. I told him that I belonged to the Church of God, that it was started in 1886, that it was the oldest Pentecostal church in North America, but that Russian Orthodox people had had the Pentecostal experience earlier. His first question was whether we were a member of the National Council of Churches or not, and I replied that we were not. I then explained that I knew about the Orthodox people because the founder of the FGBMFI, Demos Shakarian, an Armenian, had had grandparents and parents brought to it by these believers coming to Turkey from Russia. He then reminded us that this year was the 1000th anniversary; I replied that I was appreciative of this event. He said that they were more than that; they were working hard to make the actual celebration a reality this summer, including having to rebuild the seminary’s church after a disastrous fire two years ago. Having seen the restoration, I said that I was impressed with the speed of the work. He said, in effect, that I didn’t know the half of it! He went on to describe his travels in the U.S., which he makes mostly for Soviet sponsored peace groups. We then finished our session and he wished us good bye. I told him that I would tell those officials and such in our church of my visit, as I live in the denominational headquarters city and attend church with these people.
Note: the “large cathedral” was of course the Cathedral of Christ the Saviour, dynamited in 1931 under Stalin. It was in fact rebuilt during the 1990’s, which I discuss in my Easter piece Rising From the Pool. I did present this account to Church of God officials; the church eventually established a legal presence in Russia which it has to the present day.
The fixed end method used for the design of anchored sheet pile walls has been used with success since before World War II; however, computational limitations have forced designers to use simplifications such Hermann Blum developed. The original method called for the use of an “elastic line” solution, where the penetration of the sheet piling below the excavation line was estimated using statically indeterminate beam theory. This paper develops the governing equations for the “elastic line” method for a simple case and presents the solution in two ways: parametrically using charts, and for specific cases using an online computer algorithm. Comparison with other solution techniques is presented, and suggestions for broader applications are made. The adjustment of the penetration for the residual toe load is also discussed, and the limitations of current practice in this adjustment are detailed.
Most of our fluid mechanics offerings are on our companion site, Chet Aero Marine. This topic, and the way we plan to treat it, is so intertwined with the history of Vulcan’s product line that we’re posting it here. Hopefully it will be useful in understanding both. It’s a offshoot of Vulcan’s valve loss study in the late 1970’s and early 1980’s, and it led to an important decision in that effort. I am indebted to Bob Daniel at Georgia Tech for this presentation.
Basics of Compressible Flow Through Nozzles and Other Orifices
Consider a simple orifice configuration such as is shown below.
The mass flow through this system for an ideal gas is given by the equation
mass flow rate,
throat area of orifice,
adjusted throat area of orifice (see below,)
upstream pressure, psfa
downstream pressure, psfa
ideal gas constant or ratio of specific heats for air
upstream absolute temperature
At this point we need to state two modifications for this equation.
First, we need to eliminate the density, which we can do using the ideal gas equation
Second, we should like to convert the mass flow rate into the equivalent volumetric flow rate for free air. Most air compressors (and our goal is to determine the size of an air compressor needed to run a test through this valve) are rated in volumetric flow of free air in cubic feet per minute (SCFM.) This is also the basis for the air consumption ratings for Vulcan hammers as well, both adiabatic and isothermal. This is accomplished by using the equation
Making these substitutions (with a little algebra) yields
In this article the coefficient of discharge is discussed. It is also the ratio of the effective throat area to the total throat area, or
We are basically considering the energy losses due to friction as an additional geometric constriction in the system.
One final–and very important–restriction on these equations is the critical pressure, given by the equation
The critical pressure is the downstream pressure for a given upstream pressure below which the flow is “choked,” i.e., the mass or volumetric flow rate will not increase no matter how much you either increase the upstream pressure or decrease the downstream pressure. This limitation, which was observed by Saint-Venant, is due to achieving the velocity of sound with the flow through the nozzle or valve. A more common way of expressing this is to consider the critical pressure ratio, or
As you can see, this is strictly a function of the ideal gas constant. It’s certainly possible to get around this using a converging-diverging nozzle, but most nozzles, valves or orifices are not like this, and certainly not a Vulcan 06 valve. We now turn to the analysis of this valve as an example of these calculations.
Application: the Vulcan 06 Valve
The first thing we should note is that pile driving equipment (except that which is used underwater) is designed to operate at sea level. Using this calculator and the standard day, free air has the following properties:
Temperature: 518.67 °R
Pressure: (or psfa)
Now let’s consider the valve for the 06 hammer (which is identical to the #1 hammer.) A valve setting diagram (with basic flow lines to show the flow) is shown below.
Note the references to steam. Until before World War II most of these hammers (along with most construction equipment) was run on steam. With its highly variable gas constant and ability to condense back to liquid, steam presented significant analysis challenges for the designers of heavy equipment during the last part of the nineteenth century and the early part of the twentieth. For our purposes we’ll stick with air.
There are two cases of interest:
The left panel shows the air entering the hammer and passing through the valve to the cylinder. Pressurising the cylinder induces upward pressure on the piston and raises the ram. The valve position (which shows the inlet port barely cracked) is shown for setting purposes; in operation the valve was rotated more anti-clockwise, opening the inlet port.
The centre panel shows exhaust, where air is allowed to escape from the cylinder. The piston is no longer pressurised and the ram falls to impact.
According to the vulcanhammer.info Guide to Pile Driving Equipment, the rated operating pressure for the Vulcan 06 at the hammer is 100 psig = 14,400 psfg = 16,516.22 psfa = 114.7 psia. For simplicity’s sake, we can consider the two cases as mirror images of each other. In other words, the upstream pressure in both cases is the rated operating pressure. This should certainly be the case during air admission into the hammer. For the exhaust, it should be true at the beginning of exhaust. Conversely, at the beginning of intake the downstream pressure should be atmospheric (or nearly so) and always so for exhaust.
From this and the physical characteristics of the system, we can state the following properties:
Upstream pressure = 114.7 psia
Downstream pressure = 14.7 psia
Upstream area (from hammer geometry, approximate)
Coefficient of Discharge, assuming sharp-edge orifice conditions
Adjusted throat area
At this point calculating the flow in the valve should be a straightforward application of the flow equations, but there is one complicating factor: choked flow, which is predicted using the critical pressure ratio. For the case where , the critical pressure ratio . Obviously the ratio of the upstream pressure and the downstream pressure is greater than that. There are two ways of considering this problem.
The first is to fix the downstream pressure and then compute the upstream pressure with the maximum flow. In this case 27.84 psia = 13.14 psig. This isn’t very high; it means that it doesn’t take much pressure feeding into the atmosphere to induce critical flow. It is why, for example, during the “crack of the exhaust,” the flow starts out as constant and then shortly begins to dissipate. The smaller the orifice, the longer the time to “blow down” the interior of the hammer or to fill the cylinder with pressurised air.
The reverse is to fix the upstream pressure and then to vary the downstream pressure. The critical downstream pressure is now 60.59 psia = 45.89 psig. This means that, when the cylinder is pressurising at the beginning of the upstroke, the cylinder pressure needs to rise to the critical pressure before the flow rate begins to decrease.
We will concentrate on the latter case. If we substitute everything except the downstream pressure (expressed in psia,) we have
If falls below the critical pressure, the flow is unaffected by the further drop and is constant. In this case the critical flow is 795 CFM. For downstream pressures above the critical pressure, the flow varies as shown below.
As noted earlier, when air is first admitted into the cylinder the flow is constant. Once the critical pressure ratio is passed, the flow drops until the two pressures are equal.
It is interesting to note that the rated air consumption of the hammer is 625 cfm. This is lower than the instantaneous critical flow. Although on the surface it seems inevitable that the hammer will “outrun” the compressor, as a further complication the hammer does not receive air on a continuous basis but on an intermittent one. For much of the stroke the compressor is “dead headed” and no air is admitted into the cylinder from the compressor. To properly operate such a device, a large receiver tank is needed to provide the flow when it is needed. The lack of such large tanks on modern compressors is a major challenge to the proper operation of air pile hammers.
Calculations of Main Details (Strength
Strength calculations assume that the inertial forces during impact are 150 times those of the weight.
We checked the rotor shaft strength in the optimal mode, i.e., when the impacting force direction formed a 90° angle with the direction of the blow. To simplify calculations consider that the forces act at one point. In the vertical place the shaft is loaded with impact inertia forces from the shaft weight and parts which are located on it.
where Q1 = inertial force from eccentric weight(s) and part of the shaft ahead of the eccentric.
Q2 = inertial force from the part of the shaft under the bearing.
Q3 = inertial force from the rotor weight and the middle part of the shaft.
A diagram of the shaft assembly is shown below.
A diagram of the beam forces in the vertical plane is shown below.
A diagram of the beam forces in the horizontal plane is shown below.
The forces which act on the shaft in the horizontal plane arise from the vibrating forces of the eccentrics.
The reactions in the vertical plane are
The reactions in the horizontal plane are
The bending moment in the vertical plane in section A-A is
In section C-C it is
In section B-B it is
The bending moment in the horizontal plane in Sections A-A and C-C is
and for Section B-B
The sum of bending moments in Section A-A is
In Section B-B they are
and in Section C-C they are
The bending tension is calculated in the same way at all points.
For Section A-A
For Section B-B,
and Section C-C,
The tension in this section will be much less because the calculations do not take into account the force from the rotor shaft. Calculation of the shaft deflection will be done in Part C.
The calculations consider that the shaft is of uniform diameter, equal to 62 mm. In the vertical plane the deflection is equal to
= axial inertial moment of cross-section of the shaft
E = spring modulus of shaft material = 2,000,000 kg/cm²
The deflection in the horizontal plane is equal to
The total deflection from horizontal and vertical moments is
In reality deflections will be smaller because we did not take into account the rotor forces.
Determination of Tensions in Vibrator Casing
The casing is subjected to loading tensions when the vibrator impacts on the pile cap. As the ram is located in the centre of the casing the critical sections are two perpendicular sections which are located at the planes of symmetry of the vibrator.
Let us determine the moment of resistance of the section which is shown in the drawing of bending tensions in this section, shown below.
This section is weakened by a hole for the ram but this weakness is compensated for by the local boss. So we do not take into account the hole and its boss.
The moment of inertia for the section relative to axis X-X is determined as
where = sum of inertial moments of the separate elements.
= sum of multiplication of squared distances from the mass centre of element ot the axis X-X by the area of the element.
The moment of resistance for this section is
The distance between the axes of the electric motors is mm. So the bending moment is equal to
The bending tension is equal to
Let us determine the bending tensions in the section perpendicular to the axis of the rotors. The section is shown in the drawing below.
To simplify the calculations consider the section of the casing is symmetrical and consists of two circles and two rectangles.
The inertial moment is equal to
The moment of resistance equals to
Let us now determine the bending moment considering that the load from the weight along the axis parallel to the rotor axis is distributed uniformly.
The bending tension is equal to
Spring Deflection Calculation
The maximum force for which spring deflection is required is P = 1000 kgf. The number of spring N = 2. The maximum deformation of the springs is f = 200 mm. The load for each spring is
As the springs are operating in relatively easy (not hard) conditions we can consider the permissible tension equal to 5500 kgf/cm². So the permissible tension per 1 kgf of load is equal to
The necessary spring stiffness is equal to
So we choose the spring with the following specifications:
Hardness of One (1) Turn
Number of Working Turns
Npad = 14.5
Total Number of Turns
N = 21.5
Tension per 1 kgf of Load
A = 11.18
Hardness of the whole spring
So the spring we have chosen meets all of the requirements.
Determination of the Geometrical Configuration of the Eccentrics
Consider that the balanced part of the eccentrics (I and II; see diagram below) cancel each other.
So the coordinate of the center of mass of the rest of the eccentric (in the shape of a sector of a circle) is determined by the equation
The weight of the unbalanced part of the eccentric for a 1 cm thickness is equal to 1.7 kg. The eccentric moment of this eccentric is
The dynamic force of the eccentric is
The angular speed is rad/sec. The necessary eccentric moment of the eccentric is
The necessary total thickness of the eccentrics is
As during the determination of the eccentric moment it was increased a little, consider the thickness of the eccentrics equal to 80 mm.
This configuration of the eccentrics which we have come up with gives us an increase of its weight in comparison with the weight which is necessary to provide the required eccentric moment. So decreasing the moment of the rotary parts makes it easy to operate the motors.
Sizing the Bearings
The rotor shafts are mounted to spherical, double-row roller bearings No 3614 which have a coefficient of workability C = 330,000. The rotor weight Gb = 25 kgf. The eccentric weight is Gg = 28 kgf.
For the calculation of dynamic loads consider that the accelerations during impact are equal to 150 times the free weight.
As the shaft is symmetrical, each bearing is subjected to half the dynamic load
The shaft rotates at n = 950 RPM. Consider a factor of safety Kd = 1.5 and a dynamic load coefficient Kk = 1. The durability of the bearing “h” is determined as