DFM Engineering, Inc.
1035 Delaware Ave. Unit D
Longmont, CO 80501
Phone: 303-678-8143
Fax: 303-772-9411

by
Dr. Frank Melsheimer, DFM Engineering, Inc. Longmont, Colorado, USA

( EXPANDED 03 / 09 / 05 )

ABSTRACT

Astronomical telescopes, satellite trackers, siderostats, heliostats, and gimbals (generically referred to here as telescopes) all require that they are driven in rotation about their axes. Traditionally, astronomical telescopes have been driven by worm gears.

During the past 40 years or so, other drive systems have been used on telescopes. This article investigates the various drive technologies and discusses the advantages, disadvantages, and performance of these ways to drive a telescope.

An example of a metal band drive is presented to show its lack of stiffness compared to gear and friction drives.

INTRODUCTION

The following discussion assumes that the telescope is driven by an electrically powered servo motor rather than falling weights, or clock springs, or squirrels running around in a cage, although most of the discussion is independent of the prime mover used. The discussion primarily investigates the final drive of the telescope and is not as concerned with the secondary drive stages.

Worm gears have traditionally been used to drive telescopes because they provide a large gear reduction in a single stage. Often a 360 to 1 (360:1) gear ratio is used. The old rule of thumb was that the Right Ascension (R.A.) worm wheel (the large diameter gear attached to the polar axle) diameter should be the same size or larger than the telescope primary mirror.

The Declination drive gear could be smaller because the inertia of the Optical Tube Assembly (OTA) is smaller than for the entire telescope. This advice is still valid for any of the 'gear' drives used today even with Cassegrain telescopes with fast primary mirrors.

Modern Cassegrain telescopes tend to use a primary mirror considerably faster (a numerically smaller focal ratio) than did the older telescopes resulting in an OTA considerably shorter and lower in inertia than before. One would think that this would allow smaller gears to be used.

However, today we expect the telescope to be considerably stiffer than the old telescopes which begs for a larger gear.

The various forms of gearing used on telescopes include:

Each system will be discussed as they apply to driving a telescope.

The secondary drive gearing is not as critical as the primary drive stage because the errors introduced by the secondary drive are divided by the primary drive ratio. However, stiffness, smoothness, efficiency, and backlash are still valid concerns.

POSITIONING and TRACKING

The telescope axes need to be driven quickly to provide positioning and driven at a low velocity to track the object being observed. The positioning accuracy can be provided by accurate encoders. Affordable encoders are available with sufficient resolution and accuracy that they may be attached directly to the respective axle so they are independent of the drive or other gearing.

However, to provide smooth tracking and stiffness requires positioning resolution between 5 times and 10 times better than the positioning resolution. New encoders are becoming available to allow this level of resolution, but their size and/or cost limits them to larger telescopes.

STIFFNESS

When external and inertial loads are applied to the telescope, the telescope structure and drives must resist these loads with very small deflections. Typically, telescopes structures are stiffer than the drive stiffness, so the deflections are seen as rigid body rotations about the relevant axes.

The telescope should be very stiff to allow fast motion commands and to resist wind loads. In order to develop stiffness, the drive system needs to either have inherent mechanical stiffness or to develop stiffness through the servo motor controller.

Servo motor stiffness is developed by detecting very small motions (position errors) and commanding the motor to reduce these errors. The detectable motions need to measured to a small fraction of an arc second. This requires high resolution position detection.

As mentioned above, the high resolution can be detected on axis with very high resolution encoders, or with a lower resolution encoder driven by adequate gearing. Backlash (lost motion) can reduce the stiffness to zero for small motions. In most gear systems, there must be clearance between the gear teeth mesh for lubrication. This clearance can be reduced to nearly zero in one direction by torque preloading the gearing. In any gear system requiring lubrication, the lubrication film between the gear teeth will significantly lower the stiffness.

SMOOTHNESS

The drive system needs to be able to make very small incremental motions so the rotation of the axes appears to be a continuous movement at the fraction of an arc second level and do this at very slow speeds.

A measurement of the smoothness is called "jitter" and is expressed in amplitude and frequency. Even a fairly large amplitude periodic error can be guided out using optical feedback (from the object or from a nearby guide star) if the frequency is low (conversely, the period is long).

If the frequency is high, the motion can be guided out but the cost of the fast steering optical system becomes high, and the intensity of the guide star needs to be correspondingly higher because the integration time has to be less.

Having a drive system with inherent smoothness is very desirable. It is now possible to build a drive system which is seeing limited for many minutes of open loop (without optical feedback from the object) tracking.

GEAR RATIO

With all other considerations, a high numerical gear ratio is advantageous because it reduces the mechanical complexity, the cost, and reduces the effect of the errors in the secondary gearing.

GEAR EFFICIENCY

The gear efficiency is the ratio of the input power to the output power. A highly efficient drive system is desirable for two reasons. A high efficiency system requires less power so less heat is dissipated in the dome reducing the dome seeing caused image degradation.

High efficiency drives will allow the drive system to remove energy from the moving telescope. Removing energy allows faster deceleration and significantly improves the telescope response to position changes.

Worm gears with high gear ratios have very low efficiency and usually do not allow this back driving, so worm drive telescopes must be decelerated very slowly increasing the time required to respond to a position change command.

WORM GEAR DRIVES

Worm gear drives are the traditional means to provide the final gear stage for telescopes. The primary benefit is the large gear ratio possible in a single stage.

Lubrication is required, so there must be some gear mesh clearance and the lubrication film significantly reduces the stiffness. Accurate machining is critical and the worm shaft axis of rotation must be very concentric with the tooth form (or thread, as it is called).

The worm can be spring loaded into mesh with the worm wheel to minimize backlash. A well made worm gear stage can be very accurate and smooth because there is significant averaging of the tooth to tooth machining errors. The worm and gear can be lapped together to reduce the machining and concentricity errors.

The efficiency of typical telescope worm gears is very low and does not allow back driving. This significantly increases the time required to respond to a position change command.

Worm Drive: a typical worm gear set including the worm, the worm wheel (the large gear), and secondary gearing. The telescope is a 1.2 Meter Cassegrain telescope in Greece.

SPUR GEAR DRIVES

A spur gear drive consists of a small pinion gear driving a large gear. Typical gear ratios are in the 6:1 to perhaps 10:1 range. As the gear ratio increases, there is less gear error averaging because there are fewer teeth in mesh.

The stiffness is also lowered. Lubrication is also required reducing the stiffness.

The smoothness is a function of the accuracy of the machining of the gear teeth. It is possible to use spur gear drives on astronomical telescopes with high resolution position feedback derived from the telescope axis rotation.

The servo system uses the spur gear as a drive system only and drives the servo motor to correct the gear errors based upon the actual rotation of the telescope axis.

A helical gear drive is an improvement over straight cut spur gears because the number of teeth meshing together is increased providing more averaging of the gear errors. Additional sliding in the gear mesh requires additional lubrication and is less efficient.

The efficiency of the straight cut spur gear system is high and allows back driving.

BELT, CHAIN, and CABLE DRIVES

Various kinds of belt, chain, and cable drives have been used for telescopes.

The toothed belt system (timing belts and chains) have problems with tooth to tooth machining errors and the usable gear ratio is small - typically 6:1 to 10:1. The belts and chains tend to have very low stiffness due to the length of belt between the drive sprocket (or pulley) and the driven sprocket. The efficiency is high.

Belt Drive: a timing belt drive stage used on a DFM Engineering general purpose gimbal.

BAND DRIVES

Another form of the belt drive uses a thin metal band (pictured below). The band must be thin enough to allow flexing the band to the radius of the small drive pulley with a reasonable fatigue life. The required tensile strength of the belt material is very high. A manufacturer of commercial belt drives (used for instruments) produces a stainless steel (type 301 or 302) belt with tensile properties of 175,000 psi (pounds per square inch) yield strength, for example.

The band can be driven by teeth on the pulley and corresponding slots on the band, or can be driven using friction between the band surface and the pulley. The toothed form makes a positive drive but introduces tooth to tooth errors. The friction drive band system can be very smooth, but again the stiffness is very low due to the length of the band running between the contact points on the pulleys. The calculations below demonstrate the low stiffness of the band drive compared to a gear or friction drive.

The obtainable gear ratio of the friction drive band system can be significantly increased by spiral wrapping the band around a fairly small drive pulley to obtain nearly 360 degrees of wrap angle. Often the band drive small pulley is driven by a small worm gear. This system has been used for telescopes built in the 1870's, so is not new.

Using a cable or several cables instead of a band has also been done. The cable may be wrapped around a smaller diameter pulley because it is made up from a number of very small wires. Unfortunately, the cable is not as stiff as an equivalent cross section of a band due to the spiral wrapping of the cable.

Band Drive: A band drive results in a highly reduced stiffness drive when compared to other types of drives. Note the length of band between the small pulley and the large pulley. The band must be thin to allow flexing over the small pulley and the small pulley is relatively large to reduce the stress in the band to a level that allows a reasonable fatigue life. The long length of band between the two pulleys results in a highly reduced stiffness drive.

FRICTION DRIVE

The friction drive, pictured below, (sometimes called a roller drive) consists of a small diameter roller pressed against a large diameter disk. A 'gear' ratio of 20:1 is often used. No lubrication is needed, the efficiency is very high, the drive is very smooth, and this drive is the stiffest form of gearing.

Although the system appears to be very simple, the material selection, processing, machining, and heat treating must be done very carefully. The accuracy and smoothness depends upon the machining, but the machining is very straight forward as only cylindrical surfaces are needed.

The concentricity and roundness of the roller are very important. The contact stresses are fairly high at the contact surface between the roller and the drive disk, but because the contact load produces compressive and partly hydrostatic stresses, the material strength (yield and ultimate stress properties) are no higher than for a metal belt drive.

The friction drive has zero backlash and because there are no teeth acting in bending, the stiffness is very high-many times stiffer than any other gearing system.

Friction Drive: a typical friction drive used on DFM Engineering telescopes. The small diameter roller and the large diameter disc allows a relatively large gear ratio. The stiffness is very high because no lubricating film between the two metal parts is required and there are no gear teeth acting in bending.

DIRECT DRIVE

A direct drive system directly connects the armature of the servo motor to the driven axle. Often the servo motor components are built around the axle. This system has the simplest mechanical configuration. The stiffness of the system is entirely due to the servo control. The stiffness and the smoothness must be derived from high resolution position feedback. Typically, the resolution needs to be 0.1 arc seconds or finer.

The disadvantages of this system are the cost of the encoding and the very low energy coupling between the servo motor and the telescope axis because of the large mismatch between the inertia of the motor and the inertia of the telescope.

The direct drive system has been used on many fast tracking telescopes.

OTHER FORMS OF GEAR DRIVE

Several other types of gear reduction systems are available including harmonic drives and forms of hyper-cycloidal systems. In a few telescopes, these have been used for secondary drives. These forms of gearing tend to have rather large periodic errors.

TELESCOPE GEARING COMPARISONS

The following chart can be used to compare the various drive criteria in each application.

BAND DRIVE EXAMPLE

The following example shows the theoretical expected performance and limitations of a metal band drive used to drive a telescope.

Geometry:

A 7:1 "gear" reduction final drive for a telescope using a final drive pulley of 20-inches in diameter and a drive pulley of 2.857 inches in diameter (D) is assumed. The two pulleys are placed conveniently close to each other, but not as close as they could be. See the illustration. Placing the pulleys with minimum clearance only changes the unsupported length of the belt by about 6% and the stiffness by the same amount.

Materials:

The belt will be 2-inches wide and made from stainless steel with properties as published by Belt Technologies, Agawam, Massachusetts (413-786-9922) in an article in Machine Design Magazine, December 8, 1988. The yield stress is 175,000 pounds/square inch (psi), Poisson's ratio (u) is 0.285, Young's modulus (E) is 28,000,000 psi and the recommended maximum stress is 1/3 of the yield stress for a life of >1,000,000 cycles. (Note, 1,000,000 cycles is about 50 years of use at a good site).

The engineering questions are:

1. What is the recommended thickness (t) of the metal belt?

2. What is the stiffness of the drive (lb-inches of torque per arc second rotational

deflection) for the belt of the recommended thickness?

3. What are the failure modes?

4. What are the safety concerns?

These engineering considerations are discussed in detail below.

CONCLUSIONS

The band form of drive may be used for moving light loads where stiffness is not important. The band drive needs to be fully enclosed to protect the operator and to protect itself from contaminants. Possible uses for the band drive are for moving optics within an instrument. For example, a band drive is used to position the read head in a modern computer hard drive.

There are better ways to drive a telescope than using the band drive. The lack of stiffness and the problems of producing reliable and very high tensile strength steel for the band are the probable reasons that the band drive was abandoned in the early 1900's. Production of reliable high tensile strength steel has improved considerably since the 1900's, but the stiffness of the band drive has not.

For additional information, please see the following links:

• Engineering Articles for the Optimal Telescope

• How to Buy a Telescope

• US Naval Observatory 1.3M Telescope

• Retrofitting Telescopes

For additional information about DFM instruments using various forms of drives and gearing techniques, please see the following links:

• Satellite Trackers

• Siderostats

• Heliostats

• Gimbals