Oscillations of a Typical Fork Mounted Telescope.
As well it should be, the issue of vibration or oscillation of a fork mounted telescope is of high interest to users of LX200 type telescopes. I have investigated this problem in considerable detail and present my data and analysis herewith.. I have taken extensive data on two telescopes, a 10 inch and a 12 inch Meade LX200. The 12 inch is mounted on a superwedge on a 4.8 ton concrete pier imbedded in bedrock. The 10 inch is mounted on a superwedge on a giant field tripod sitting on a very large concrete slab.
Both wedges are set for 43 degrees which is my latitude and all data and conclusions drawn are for this setup. Some conclusions can be easily extrapolated to other setups but be warned that these instruments are full of surprises. Most of the conclusions can also be extrapolated with a bit of thought to German mounts since they also exhibit serious oscillations. Because I did an extensive amount of work on gathering data and working out the results and conclusions, I will take time and care to explain my techniques and results at some length. Thus be warned that this is a very long memo.
All telescopes and their mounts, consisting of forks, rods, bearings, tubes, shafts, masses and the like can be thought of as mechanical systems that are basically masses and rods which have compliance connected in some fairly complex configuration. Notice I use the term compliance. This is the inverse of springiness. A soft spring has high compliance and a stiff spring has lower compliance. The masses move because of the necessary forces applied by the drive motors which guide the telescope optical tube. But they move in unwanted ways as well do to forces from wind, shaking of the support, or by irregular drive forces from the very motors that move the telescope or irregularities caused by the mount and bearings. The unwanted vibrations, oscillations, jiggles and wobbles must be minimizes to accomplish good viewing and particularly good imaging.
All forces on the telescope and the subsequent motions from whatever source are mostly measurable and predictable within the accuracy of the model used for the telescope mechanical system. A rather simple, first order model used in this analysis gives relatively accurate results. The trick needed to make sense of the problem stated is to make a model that is trackable but still one that gives some useful results for the most important deviant motions of the observing/imaging tube. I have found that the simplest model, fortunately, accounts for the main oscillation of the tube that effects viewing and imaging. While there are numerous secondary jiggles and wobbles they are mainly of second order. If the main oscillations can be reduced or damped, greatly improved imaging will result.
The simplest model consists of three parts. The first is a base consisting of the pier/tripod and the wedge. With the pier/tripod and super wedge used, this base can in first order analysis be considered stationary. To be sure, there are inadequate piers and tripods sitting on unsatisfactory concrete pads and unstable ground, but for the setup used for this data, the wedge surface upon which the telescope base is mounted can be considered rigid and unmoving. It is certain that less than 10 % of all unwanted motion can be traced to the wedge and its mounting.
The second part of the mechanical structure is the fork, in the case of the LX200, and its bearing structure. Within this part, the fork is quite rigid (stiff) but the bearing structure is quite compliant. Essentially all of the flexure in the RA/Asmuth drive is in the bearings. Thus close attention must be paid to the bearing structure as the "weak" point and the largest source of unwanted motion and oscillation.
The final element is the main telescope tube, the toys attached to it and how it is held by the Declination/Altitude bearings. The tube and items fastened to it may in the first order be considered a single rigid mass. This mass moves on the declination bearings. These bearings are so strong and stiff that they do not contribute much to the dynamic oscillations of the structure. That is not to say that they a free of problems, but they contribute very different problems from the vibration and wobbles which are of primary interest here. For the first part of the analysis we consider the tube and fork to be a single rigid mass.
The mechanical structure becomes a first order system with a spring of some compliance holding a mass out at an angel of 45 degrees. The large mass consists of the main tube, its attachments and an appropriate part of the fork mass. Fortunately this is the simplest mechanical vibratory system possible. It will have two important properties. Frequency of oscillation and damping. The frequency is simple to understand and is measured in Hz. (used to be called cycles per second, cps) The structure is similar for the Alt/Azm mounted telescope but the forces are arranged very differently. This case will be discussed later in the analysis.
The second factor is a bit harder to understand. I will use the term damping (or its inverse, Q, or quality factor) in this discussion. It is only necessary to understand that a weakly damped system will oscillate for a long time and a highly damped system will not oscillate very long at all. The inverse, Q, means that a high Q system oscillates for a long time and a low Q system does not oscillate very long. Long and not very long are relative terms. In the case of a telescope long might be 10 seconds while not very long only a second or less. Clearly for the telescope we want high damping and low Q. Such a system will stop oscillating quickly when it is excited by unwanted forces.
Unwanted forces are wind, bumping, pier/tripod movement of any sort and any irregularity in the forces from the drive motors. Additionally, any irregularities in the moving bearings or surfaces in sliding contact an be interpreted as irregular forces. Some of these forces are random and seldom. Others, like that from the drive motors are regular and constant.
My study of the two telescopes in question consists of two parts. The first was to take some data and the second to try to figure out what in the world the data meant and just what was going on within the structure. I believe I have deciphered some of the mechanical problems and pinned them down to specific parts of the mechanical design of the telescope. On the final part of this discussion I make some suggestions to minimize the oscillatory problems.
To take vibration data at low frequencies I used a geophone transducer (low frequency magnetic type). The output went to an HP spectrum analyzer which could record and print out amplitude and frequency data. The telescope was excited by careful, measured tapping on it in a variety of directions and at many locations. I did not use the more sophisticated impulse hammer since the structure is not too complex and I did not need transfer function information for the approximate analysis done.
The transducer measures in only one direction at a time so it was moved to several locations (clamped on) on the fork and mirror tube. Almost all of the motion of the mirror tube turned out to be in a direction up and down with respect to the fixed base of the telescope. Lateral jiggling of the fork and tube was relatively much smaller. Thus I concentrated attention on the major mode of oscillation. Measurements were made on the vibrational spectra to determine amplitude and frequency components. Time domain measurements on the damped oscillations yielded the damping factor. The results are described below.
Measurements made of velocity of motion at various frequencies. These were converted to amplitude of motion of the mirror tube and finally into angular motion of the mirror tube. It is this angular motion in arc seconds that is important in seeing and imaging. The compliance of the fork mount was calculated by measuring the deflection of the fork with a known weight placed on the fork at the declination axis. Many positions of the transducer and location of excitation (tapping) were tried. The following are my general conclusions and they apply almost equally to the 10 and 12 inch telescopes.
In all cases the resonant frequencies of the telescopes were in the range of 8 to 18 Hz. Several frequencies occur at the same time and vary in amplitude as the oscillation damps out. This is because there are several modes of oscillation in the tube and fork and they interact by exchanging energy since they are not orthogonal. (i.e. the structure, while fairly rigid is of complex shape.) Damping of the main frequencies was in the order of 8 to 10 seconds. This is bad news since it means that for short exposures up to a minute or so one must wait after touching or disturbing the telescope for at least 10 seconds for the scope to settle down. This is longer than generally mentioned in the literature.
The immediate force caused by camera mirror flip must be allowed to damp out before the shutter is released. The forces external to the camera caused by a shutter releasing are probably not enough to cause problems. (depends on the camera of course) Lateral motion of the fork/mirror tube, in response to tapping, was very small and damped in less than 1 second. Thus it is reasonable to conclude that unsharp images are caused mainly by up and down motion of the fork structure no matter what the pointing direction of the optical tube. This motion will manifest itself at the image in differing directions depending on the orientation of the tube and camera with respect to horizontal.
Because the fork is very stiff, low compliance, it can be concluded that essentially all of the compliance is in the bearing mount. To put that simply, the bearings are slightly weaker than they should be. The actual numbers for these two telescopes are given here. Because they are so similar it seems to me that they are indicative of what other telescopes of the same type would show. But remember that these figures are specific to these two instruments.
The main mode of oscillation along with cross coupled modes was at frequencies of 8 to 18 Hz. Strong modes were at 8, 10, 12, 14 and 18 Hz. Some smaller but measurable oscillations were at 25 to 40 Hz. With a rather large collection of small modes within that range. Tapping the mirror end of the tube caused the larger oscillations as did tapping the dew hood. All North, South, East and West jogging of the scope using the keypad controls caused oscillations which persisted for as long as 10 seconds. The North, South jogging caused the worst jiggling. Additionally, there was a distinct but small jiggling due to the steady running of RA motor and the declination motors as described below.
The compliance of the fork was about 1 1/2 X 10E-5 meters/newton. It was about the same for both telescopes. (not surprising since the bearings are the same for the two telescopes) This value taken with the known mass of the fork/tube structure gives a calculated oscillation frequency of 9 Hz which is in agreement with the measured value. It was slightly higher for the 10 inch telescope at about 11 Hz.. The compliance of the fork mount can be attributed mainly to the bearing and/or its mounting in the base structure. The precise springiness will depend upon the exact construction details of the bearing and their mounting. I doubt that attempts to reconstruct the bearing and mounting would be practical. It is actually quite good for a mount of this type and cost.
Interestingly, the running of the RA. drive motor causes a small bit of vibration of the fork/tube structure. This vibration is at a very low level (less than 0.3 arc sec RMS) for the RA drive in the polar mounted position. This should cause no trouble since it is so much smaller than atmospheric image jiggle. Recent data showed the declination motor vibrational noise to be about 3 to 5 time as great as the RA motor vibrational noise. This is to be expected since the measurements were made on the optical tube and it is very close to the declination motor as compared to the RA motor. This factor is about the same for polar or Alt/Azm mounting of the telescope. However, in the Alt/Azm mode, both motors run all of the time. While in the polar mode the RA motor runs all the time but the Dec motor just runs occasionally. (depending on the accuracy of polar alignment)
The amplitude of the oscillation of the main fork mode is by no means negligible. A static force caused by a weight of 10 grams causes a deflection of about 1 arc second. This is a very small force. Larger forces cause proportionally larger angular fluctuations. With good seeing, which can be 1 to 2-arc seconds (even in Wisconsin), forces caused by slight winds are definitely deleterious to good images.
The previous section gives a general description of how the vibration problems can be found and a very qualitative description of their magnitude. At this point, we need to ask if these qualitative measures, like a tap on the side or fork, can be quantified a bit better. First let me say that getting quantitative measures is very difficult. A force due to just touching the telescope causes shaking which is very large compared both to the accuracy necessary for good imaging. Touching is a large disturbance compared to the measure of shake and force applied in my more precise measures of mechanical vibration in a structure as sensitive as a telescope.
The precision required in imaging while actually moving the imaging tube in a precise way is near the very limit of what can be done mechanically. (with a non feedback, passive system) I am assuming that the goal of this investigation is to determine the problems and possibilities of solving them for imaging that lies at the limit of viewing. For convenience I will set this limit at 1 arc second. We know that on nights of very good seeing we can easily resolve the double double in Lira so that 1 arc second seeing is not uncommon. Also we know that any reasonably good optics will give us arc second resolution from the instrument itself. In any case, I have chosen to use 1 arc second as the unit of measure for most of the following specification of units of jiggle and wobble of the telescope. I have also found that it is very easy to see one arc second of motion of the telescope viewing tube when it is moving at typical frequencies of 8 to 12 Hz.
We need to quantify the unit of "tapping" used so loosely in the previous sections. A major question is whether to define the "tap" in terms of energy or momentum transferred to the telescope structure via the "tap." By experimenting with a variety of small weights dropped from various heights on the telescope structure I have found that a weight of 10 grams dropped from a distance of 10 cm gives just perceptible visual oscillations in the image. Thus, this unit of energy and momentum is used as the basic unit for the "tap." This is quite arbitrary but it provides a unit which is of convenient size and can be applied in reasonable fractional terms or in terms of a few or a few tens of "taps." Thus for this work I hereby establish the standard "tap" as 1400 gram-cm/sec (momentum) or 196E3 ergs (energy). This unit of energy or momentum can be obtained by dropping a 10 gram weight (like a bolt or nut) on the telescope from a height of 10 cm (about 2.5 inches.) It is easy to adjust the size of the tap by using a more massive bolt/nut or by dropping from a greater height. This is a very convenient unit of measure. I will call it 1 (one) standard "tap" in the following discussion.
Note that both the momentum and the energy increase in proportion to the mass but the momentum goes in proportion to the height of the drop and the energy goes in proportion to the square of the height. Since the energy of the impact may or may not be conserved but the momentum is always conserved, I will generally do my measurements and report the results in units of momentum. Thus the standard MOMENTUM tap will simply be called one "Gtap." (a unit of momentum obtained by dropping a 10 gram weight 10 cm in a Gravity field of 1 g) So what does a unit Gtap do to a typical telescope. In the previous section a qualitative discussion of the various motions of the fork mounted telescope was discussed. Here are some of the results for Gtap tapping the 10 and 12 inch Meade telescopes.
The telescope is mounted as stated previously on a fixed super wedge set at 43 degrees, with the tube set to point to the southern horizon, one (1) Gtap applied to the fork mount at the declination bearings will cause 5 arc second of motion of the tube. If the Gtaps are applied to the eyepiece, one gets about twice that much motion. That is, about 10 arc seconds. This makes very good sense since the momentum transfer at the eyepiece is further from the point of flexure. The flexure is mainly at the lower fork bearing but with some at the declination axis as well.
At this point you can do some measurements of your own by viewing an object, dropping a weight on the telescope structure and estimating through the eyepiece how much motion in arc seconds results. This is really easy and fun to do. The results are however not fun to contemplate at all. The motion is large for very tiny forces and resulting oscillation takes 5 to 10 seconds to damp out.
An interesting question is that of camera operation shaking the telescope. I use Canon F1 mechanical cameras of the second style for film imaging. (Canon experts will know what that means) I have tried to measure the vibrations caused by operating the camera without mirror lock. It is so small, I cannot measure it with any accuracy. Thus I believe that mirror flop causes very little problem in the case of the Canon camera. The momentum kick that the camera gives to the telescope is surely less than 0.2 Gtaps. The shutter function alone causes no mechanical motion problem at all. Other cameras may be much different, I do not know.
I have found that touching the telescope even with the most gentle and careful touch causes motions of the telescope that are very large compared to those caused by even a few Gtaps. DO NOT TOUCH THE TELESCOPE WHEN IMAGING. Bumping it when manually guiding is even a worse disaster since this level of "tap" can even cause permanent mis-adjustment of the mount. I have found for example that when using the 201XT auto-guider or the 216XT as an auto-guider in stand alone mode that touching the button on the rear of the guider can cause loss of star lock. This is one reason that it is better to use a computer controlled guider like the 208 or 216 since the guider does not have to be touched.
We now have both qualitative and quantitative measure of the mechanical problems with a class of fork mounted telescopes. All telescopes, whether fork or German mounted have the similar problems with rigidity and sensitivity to taping. Do not underestimate this problem. The discussion below is on what works and what does not work to solve the very real problem of telescope oscillation, vibration, shake and wobble. I have thought about these problems very hard and long but have not really solved the problem. At this point I think there are three paths to take. The right and proper one is to consider what can be done to the fork mounted SCTs to improve them to the point where they are as good as possible without drastic rebuilding or possibly with only a minor modification or addition of a modest attachment of some sort.
Almost all telescope mounts with a few notable exceptions are of the three basic types: fork mount in polar or Alt/Azm configurations, variations of the German mount, always polar, and Dobson type mounts, mainly Alt/Azm. For an overview of very interesting variations see "Unusual Telescopes" by Peter L. Manly, Cambridge Press 1991. Fascinating book!!
It is convenient to have the fork mount and German mount (GEM) in mind at the same time when discussion mounts that will generally be set in a polar orientation. (The Alt/Azm mounting of the fork is really limited to visual work, unless some day a suitable de-rotator is developed.) So I will limit this discussion to polar mount and imaging quality. Both the fork mount and the GEM are really similar. They have a main rotating bearing pointed toward the pole and a structure to hold the viewing tube and allow it to be set at an appropriate declination. The fork mount holds the tube between its two tines while the GEM holds the tube on one end of a rod and a big weight on the other to balance out the tube. The fork mount has the problem that the declination axis has to be extended out along the polar axis so that the tube clears the polar axis bearing structure. The GEM can have the cross bar mounted very close to the polar axis bearing for great rigidity. The fork mount has a very rigid and strong declination axis since it has very short coupling shafts to the declination drive motor. The GEM has a very long declination shaft which must hold the viewing tube which is long and has a great moment of inertia on one end and an equal weight on the opposite side. We should have no illusions that either a good or bad mount of either type can be made. Each mount has its strong and weak points. Clearly a good design must resolve the weak points of each approach. The difficulty of designing the mechanical structure can be appreciated if we recognize that to hold the tube to 1 arc second (which is 5 millionths of a radian) requires the ends of a 12 inch tube to be held firm to 0.05 thousandths of an inch. This is very hard to do. The compliance in the mount must be exceedingly small so that slight irregularities in the force on the tube will not cause unwanted motion. In other words, the mount must be very rigid (strong, low compliance). Additionally it must move freely in both declination and right ascension. The design problems are to a great extent in the bearings. I will say right here I think it is amazing how good modestly priced mounts are in reality. It is going to be very difficult to improve them without major modifications and probably major expense. But let us discuss some ideas for improvement.
There will be disturbances from wind, mount motion and irregularities in the driving forces from the motor drives. These can be minimized by very high precision gearing and motors that are strong enough to easily move the loads placed upon them. Generally it is not possible to do much to change the drive motors provided by the manufacturer. Unfortunately almost all of the motors provided are too small to do the job with any reasonable margin for error. In the fork mount instruments, we already know that the fork is mechanically very strong, that the declination bearings and mount are intrinsically strong and that the weak point in the design is in the RAE bearing.
We know from the specifications that the 10 and 12 inchers have 4" and 2 1/2" ball bearings. The 16" has 6" and 4" roller bearings. This seems like proportionate design except that the 10" is a bit sturdier than the 12" in proportion. The bearing design is probably adequate for the 10 incher. The bearings are very asymmetrically loaded for the polar mount (in the US it varies from 25 to 50 degrees) and adjustment of the bearings might be a factor in getting the maximum stiffness out of them.
Now in the Alt/Azm mode, the bearings are symmetrically loaded and will probably work more smoothly and be better loaded for highest stiffness. So we would expect the telescope to be more stable in the Alt/Azm setup. So for viewing, where field rotation is no problem or for very short exposures such as one can sometimes get with CCD imagers the Alt/Azm mounting should be considered.
The above arguments show why amateurs are salivating over availability of a modestly priced de-rotator for the smaller SCTs. (note that there are serious difficulties with de-rotators as well as described in another article on this web site) For straight visual viewing I believe the Alt/Azm setup is quite attractive with a scope that has full computer guiding of the pointing action. Again, if any imaging, photography or piggy back photography is to be used, the scope must be in the polar mode. So we still have to consider what to do to improve the oscillations of the telescope in this mode.
I believe it is difficult to improve the bearings very much, and I suspect that that is the case we have to come up with other ideas. Three things can be done to reduce the oscillations. They can be made smaller for a given disturbance by making the fork mechanism more rigid, oscillations can be damped more quickly to reduce their net effect on an image or they can be reduced by applying a counter force to cancel the original disturbance. The first of these requires adding strengthening members to the fork mount in some way. Two obvious ways to add to the mount would be either an English type mount like that used on the 100 inch Hooker at Mt. Wilson or a Palomar type mount like that used on the 200 inch at Mt. Palomar. Unfortunately either of these modifications requires a large structure added to the top end of the fork and associated bearings. Certainly such modifications would be only for a fixed mount and would require so much effort that an entirely new mount would be a better choice.
If one is willing to make major modifications of the base of the LX200
it might be possible to go up from the wedge area into the bottom of the
fork shaft and add a third stabilizing bearing below the other two and
residing in the area between the wedge sides. This modification seems
to be impossible because of the design of base bearings. There are
still several ways to reduce the oscillations that are less intrusive mechanically.
One is a mechanical damper system. This would consist of a rod of
rubbery material to provide energy loss and a mass. The principle
this damper is that the rod and mass resonate with the telescope motion
thus exercising the rubbery material and removing energy from the oscillation.
This increases the damping and quickens the rate at which the disturbances
die down. This technique is used with many structures from larger motors
to buildings.
It is called a tuned damper. Another way to reduce amplitude
and increase damping is to mount a motion detector and a force transducer
on the telescope and with appropriate electronics force the telescope to
remain still by canceling vibrations. This technique is one used
by Digisonix in Madison, WI to reduce vibration and one I am working on
for my own LX200. I hope to have good results, but it might be a
year or more before I have a completely successful system.
I have decided to build a new fork mount with adequate strength as an alternate path to having a precision mount suitable for accurate imaging. The design concept and details are explained in another article on this web site.