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AMAZON multi-meters discounts AMAZON oscilloscope discounts This SECTION contains some of the theoretical aspects of balancing and balancing machines, to give a better understanding of the process of balancing a rotor and of the working principles of balancing machines. Definition of Terms: Definitions of many terms used in balancing literature and in this text are contained in SECTION A. Commonly used synonyms for some of these standard terms are also included. For further information on terminology, refer to ISO Standard No. 1925 (see SECTION 6C). Purpose of Balancing An unbalanced rotor will cause vibration and stress in the rotor itself and in its supporting structure. Balancing of the rotor is therefore necessary to accomplish one or more of the following: 1. Increase bearing life. 2. Minimize vibration. 3. Minimize audible and signal noises. 4. Minimize operating stresses. 5. Minimize operator annoyance and fatigue. 6. Minimize power losses. 7. Increase quality of product. 8. Satisfy operating personnel. Unbalance in just one rotating component of an assembly may cause the entire assembly to vibrate. This induced vibration in turn may cause excessive wear in bearings, bushings, shafts, spindles, gears, etc., substantially reducing their service life. Vibration sets up highly undesirable alternating stresses in structural supports and frames that may eventually lead to their complete failure. Performance is decreased because of the absorption of energy by the supporting structure. Vibrations may be transmitted through the floor to adjacent machinery and seriously impair its accuracy or proper functioning. The Balancing Machine as a Measuring Tool A balancer or balancing machine is necessary to detect, locate, and measure unbalance. The data furnished by the balancer permit changing the mass distribution of a rotor, which, when done accurately, will balance the rotor. Balance is a zero quantity, and therefore is detected by observing an absence of unbalance. The balancer measures only unbalance, never balance. Centrifugal force acts upon the entire mass of a rotating element, impelling each particle outward and away from the axis of rotation in a radial direction. If the mass of a rotating element is evenly distributed about its shaft axis, the part is "balanced" and rotates without vibration. However, if an excess of mass exists on one side of a rotor, the centrifugal force acting upon this heavy side exceeds the centrifugal force exerted by the light side and pulls the entire rotor in the direction of the heavy side. FIG. 1 shows the side view of a rotor having an excess mass m on one side. Due to centrifugal force exerted by m during rotation, the entire rotor is being pulled in the direction of the arrow F. FIG. 1. Unbalance causes centrifugal force. Causes of Unbalance: The excess of mass on one side of a rotor shown in FIG. 1 is called unbalance. It may be caused by a variety of reasons, including: 1. Tolerances in fabrication, including casting, machining, and assembly. 2. Variation within materials, such as voids, porosity, inclusions, grain, density, and finishes. 3. Non-symmetry of design, including motor windings, part shapes, location, and density of finishes. 4. Non-symmetry in use, including distortion, dimensional changes, and shifting of parts due to rotational stresses, aerodynamic forces, and temperature changes. Often, balancing problems can be minimized by symmetrical design and careful setting of tolerances and fits. Large amounts of unbalance require large corrections. If such corrections are made by removal of material, additional cost is involved and part strength may be affected. If corrections are made by addition of material, cost is again a factor and space requirements for the added material may be a problem. Manufacturing processes are the major source of unbalance. Unmachined portions of castings or forgings which cannot be made concentric and symmetrical with respect to the shaft axis introduce substantial unbalance. Manufacturing tolerances and processes which permit any eccentricity or lack of squareness with respect to the shaft axis are sources of unbalance. The tolerances, necessary for economical assembly of several elements of a rotor, permit radial displacement of assembly parts and thereby introduce unbalance. Limitations imposed by design often introduce unbalance effects which cannot be corrected adequately by refinement in design. For example, electrical design considerations impose a requirement that one coil be at a greater radius than the others in a certain type of universal motor armature. It’s impractical to design a compensating unbalance into the armature. Fabricated parts, such as fans, often distort non-symmetrically under service conditions. Design and economic considerations prevent the adaptation of methods which might eliminate this distortion and thereby reduce the resulting unbalance. Ideally, rotating parts always should be designed for inherent balance, whether a balancing operation is to be performed or not. Where low service speeds are involved and the effects of a reasonable amount of unbalance can be tolerated, this practice may eliminate the need for balancing. In parts which require unbalanced masses for functional reasons, these masses often can be counterbalanced by designing for symmetry about the shaft axis. A rotating element having an uneven mass distribution, or unbalance, will vibrate due to the excess centrifugal force exerted during rotation by the heavier side of the rotor. Unbalance causes centrifugal force, which in turn causes vibration. When at rest, the excess mass exerts no centrifugal force and, therefore, causes no vibration. Yet, the actual unbalance is still present. Unbalance, therefore, is independent of rotational speed and remains the same, whether the part is at rest or is rotating (provided the part does not deform during rotation). Centrifugal force, however, varies with speed. When rotation begins, the unbalance will exert centrifugal force tending to vibrate the rotor. The higher the speed, the greater the centrifugal force exerted by the unbalance and the more violent the vibration. Centrifugal force increases proportionately to the square of the increase in speed. If the speed is doubled, the centrifugal force quadruples; if the speed is tripled, the centrifugal force is multiplied by nine. Units of Unbalance: Unbalance is measured in ounce-inches, gram-inches, or gram millimeters, all having a similar meaning, namely a mass multiplied by its distance from the shaft axis. An unbalance of 100 g · in., For example, indicates that one side of the rotor has an excess mass equivalent to 10 grams at a 10 in. radius, or 20 grams at a 5 in. radius (see FIG. 2). In each case, the mass, when multiplied by its distance from the shaft axis, amounts to the same unbalance value, namely 100 gram-inches. A given mass will create different unbalances, depending on its distance from the shaft axis. To determine the unbalance, simply multiply the mass by the radius. Since a given excess mass at a given radius represents the same unbalance regardless of rotational speed, it would appear that it could be corrected at any speed, and that balancing at service speeds is unnecessary. FIG. 2. Side view of rotors with 100g· in. unbalance. FIG. 3. Static unbalance. This is true for rigid rotors as listed in TBL. 5. However, not all rotors can be considered rigid, since certain components may shift or distort unevenly at higher speeds. Thus they may have to be balanced at their service speed. Once the unbalance has been corrected, there will no longer be any significant disturbing centrifugal force and, therefore, no more unbalance vibration. A small residual unbalance will usually remain in the part, just as there is a tolerance in any machining operation. Generally, the higher the service speed, the smaller should be the residual unbalance. In many branches of industry, the unit of gram· inch (abbreviated g · in.) is given preference because it has proven to be the most practical. An ounce is too large for many balancing applications, necessitating fractions or a subdivision into hundredths, neither of which has become very popular. Types of Unbalance The following paragraphs explain the four different types of unbalance as defined by the internationally accepted ISO Standard No. 1925 on balancing terminology. For each of the four mutually exclusive cases an example is shown, illustrating displacement of the principal axis of inertia from the shaft axis caused by the addition of certain unbalance masses in certain distributions to a perfectly balanced rotor. Static Unbalance Static unbalance, formerly also called force unbalance, is illustrated in FIG. 3 below. It exists when the principal axis of inertia is displaced parallel to the shaft axis. This type of unbalance is found primarily in narrow, disc-shaped parts such as flywheels and turbine wheels. It can be corrected by a single mass correction placed opposite the center-of-gravity in a plane perpendicular to the shaft axis, and intersecting the CG. Static unbalance, if large enough, can be detected with conventional gravity-type balancing methods. FIG. 3A shows a concentric rotor with unbalance mass on knife edges. If the knife-edges are level, the rotor will turn until the heavy or unbalanced spot reaches the lowest position. FIG. 3B shows an equivalent condition with an eccentric rotor. The rotor with two equal unbalance masses equidistant from the CG as shown in FIG. 3C is also out of balance statically, since both unbalance masses could be combined into one mass located in the plane of the CG. Static unbalance can be measured more accurately by centrifugal means on a balancing machine than by gravitational means on knife-edges or rollers. Static balance is satisfactory only for relatively slow-revolving, disc-shaped parts or for parts that are subsequently assembled onto a larger rotor which is then balanced dynamically as an assembly. Couple Unbalance Couple unbalance, formerly also called moment unbalance, is illustrated in FIG. 4 and 6-4A. It’s that condition for which the principal axis of inertia intersects the shaft axis at the center of gravity. This arises when two equal unbalance masses are positioned at opposite ends of a rotor and spaced 180° from each other. Since this rotor won’t rotate when placed on knife-edges, a dynamic method must be employed to detect couple unbalance. When the workpiece is rotated, each end will vibrate in opposite directions and give an indication of the rotor's uneven mass distribution. Couple unbalance is sometimes expressed in gram· inch · inches or gram· in.^2 (or ounce-in. ^2), wherein the second in. dimension refers to the distance between the two planes of unbalance. FIG. 3A. Concentric disc with static unbalance. FIG. 3B. Eccentric disc, therefore static unbalance. FIG. 3C. Two discs of equal mass and identical static unbalance, aligned to give statically unbalanced assembly. FIG. 4. Couple unbalance. FIG. 4A. Discs of FIG. 3C, realigned to cancel static unbalance, now have couple unbalance. FIG. 4B. Couple unbalance in outboard rotor component. It’s important to note that couple unbalance cannot be corrected by a single mass in a single correction plane. At least two masses are required, each in a different transverse plane (perpendicular to the shaft axis) and 180° opposite to each other. In other words, a couple unbalance needs another couple to correct it. In the example in FIG. 4B, for instance, correction could be made by placing two masses at opposite angular positions on the main body of the rotor. The axial location of the correction couple does not matter as long as its value is equal in magnitude but opposite in direction to the unbalance couple. Quasi-Static Unbalance Quasi-static unbalance, FIG. 5, is that condition of unbalance for which the central principal axis of inertia intersects the shaft axis at a point other than the center of gravity. It represents the specific combination of static and couple unbalance where the angular position of one couple component coincides with the angular position of the static unbalance. This is a special case of dynamic unbalance. Dynamic Unbalance Dynamic unbalance, FIG. 6, is that condition in which the central principal axis of inertia is neither parallel to, nor intersects the shaft axis. FIG. 5. Quasi-static unbalance. FIG. 5A. Couple plus static unbalance results in quasi-static unbalance provided one couple mass has the same angular position as the static mass. FIG. 5B. Unbalance in coupling causes quasi-static unbalance in rotor assembly. FIG. 6. Dynamic unbalance. It’s the most frequently occurring type of unbalance and can only be corrected (as is the case with couple unbalance) by mass correction in at least two planes perpendicular to the shaft axis. Another example of dynamic unbalance is shown in FIG. 6A. Motions of Unbalanced Rotors In FIG. 7, a rotor is shown spinning freely in space. This corresponds to spinning above resonance in soft bearings. In FIG. 7A only static unbalance is present and the center line of the shaft sweeps out a cylindrical surface. FIG. 7B illustrates the motion when only couple unbalance is present. In this case, the centerline of the rotor shaft sweeps out two cones which have their apexes at the center-of-gravity of the rotor. The effect of combining these two types of unbalance when they occur in the same axial plane (quasi-static unbalance) is to move the apex of the cones away from the center-of-gravity. In the case of dynamic unbalance there will be no apex and the shaft will move in a more complex combi nation of the motions shown in FIG. 7. FIG. 6A. Couple unbalance plus static unbalance results in dynamic unbalance. FIG. 7. Effect of unbalance on free rotor motion. Effects of Unbalance and Rotational Speed: As has been shown, an unbalanced rotor is a rotor in which the principal inertia axis does not coincide with the shaft axis. When rotated in its bearings, an unbalanced rotor will cause periodic vibration of, and will exert a periodic force on, the rotor bearings and their supporting structure. If the structure is rigid, the force is larger than if the structure is flexible (except at resonance). In practice, supporting structures are neither entirely rigid nor entirely flexible but somewhere in between. The rotor-bearing support offers some restraint, forming a spring-mass system with damping, and having a single resonance frequency. When the rotor speed is below this frequency, the principal inertia axis of the rotor moves outward radially. This condition is illustrated in FIG. 8A. FIG. 8. Angle of lag and migration of axis of rotation. FIG. 9. Angle of lag and amplitude of vibration versus rotational speed. If a soft pencil is held against the rotor, the so-called high spot is marked at the same angular position as that of the unbalance. When the rotor speed is increased, there is a small time lag between the instant at which the unbalance passes the pencil and the instant at which the rotor moves out enough to contact it. This is due to the damping in the system. The angle between these two points is called the "angle of lag" (see FIG. 8B). As the rotor speed is increased further, resonance of the rotor and its sup porting structure will occur; at this speed the angle of lag is 90° (see FIG. 8C). As the rotor passes through resonance, there are large vibration amplitudes and the angle of lag changes rapidly. As the speed is increased further, vibration subsides again; when increased to nearly twice resonance speed, the angle of lag approaches 180° (see FIG. 8D). At speeds greater than approximately twice resonance speed, the rotor tends to rotate about its principal inertia axis at constant amplitude of vibration; the angle of lag (for all practical purposes) remains 180°. In FIG. 8 a soft pencil is held against an unbalanced rotor. In (A) a high spot is marked. Angle of lag between unbalance and high spot increases from 0° (A) to 180° in (D) as rotor speed increases. The axis of rotation has moved from the shaft axis to the principal axis of inertia. FIG. 9 shows the interaction of rotational speed, angle of lag, and vibration amplitude as a rotor is accelerated through the resonance frequency of its suspension system. FIG. 10. Disc-shaped rotor with displaced center of gravity due to unbalance. Correlating CG Displacement with Unbalance One of the most important fundamental aspects of balancing is the direct relationship between the displacement of center-of-gravity of a rotor from its journal axis, and the resulting unbalance. This relationship is a prime consideration in tooling design, tolerance selection, and determination of balancing procedures. For a disc-shaped rotor, conversion of CG displacement to unbalance, and vice versa, is relatively simple. For longer workpieces it can be almost as simple, if certain approximations are made. First, consider a disc shaped rotor. Assume a perfectly balanced disc, as shown in FIG. 10, rotating about its shaft axis and weighing 999 ounces. An unbalance mass m of one ounce is added at a ten in. radius, bringing the total rotor weight W up to 1,000 ounces and introducing an unbalance equivalent to 10 ounce in. This unbalance causes the CG of the disc to be displaced by a distance e in the direction of the unbalance mass. Since the entire mass of the disc can be thought to be concentrated in its center-of-gravity, it (the CG) now revolves at a distance e about the shaft axis, constituting an unbalance of U = We. Substituting into this formula the known values for the rotor weight, we get: Solving for e we find ... In other words, we can find the displacement e by the following formula: For example, if a fan is first balanced on a tightly fitting arbor, and subsequently installed on a shaft having a diameter 0.002 in. smaller than the arbor, the total play resulting from the loose fit may be taken up in one direction by a set screw. Thus the entire fan is displaced by one half of the play or 0.001 in. from the axis about which it was originally balanced. If we assume that the fan weighs 100 pounds, the resulting unbalance will be: The same balance error would result if arbor and shaft had the same diameter, but the arbor (or the shaft) had a total indicated runout (TIR) of 0.002 in. In other words, the displacement is always only one half of the total play or TIR. The CG displacement e discussed above equals the shaft displacement only if there is no influence from other sources, a case seldom encountered. Nevertheless, for balancing purposes, the theoretical shaft respectively CG displacement is used as a guiding parameter. On rotors having a greater length than a disc, the formula e = U/W for finding the correlation between unbalance and displacement still holds true if the unbalance happens to be static only. However, if the unbalance is anything other than static, a somewhat more complicated situation arises. Assume a balanced roll weighing 2,000 oz, as shown in FIG. 11, having an unbalance mass m of 1 oz near one end at a radius r of 10 in. Under these conditions the displacement of the center-of-gravity (e) no longer equals the displacement of the shaft axis (d) in the plane of the bearing. Since shaft displacement at the journals is usually of primary interest, the correct formula for finding it looks as follows (again assuming that there is no influence from bearings and suspension): Where: d = Displacement of principal inertia axis from shaft axis in plane of bearing W = Rotor weight FIG. 11. Roll with unbalance. m = Unbalance mass r = Radius of unbalance h = Distance from center-of-gravity to plane of unbalance j = Distance from center-of-gravity to bearing plane Ix = Moment of inertia around transverse axis Iz = Polar moment of inertia around journal axis Since neither the polar nor the transverse moments of inertia are known, this formula is impractical. Instead, a widely accepted approximation may be used. The approximation lies in the assumption that the unbalance is static (see FIG. 12). Total unbalance is thus 20 oz in. Displacement of the principal inertia axis from the bearing axis (and the eccentricity e of CG) in the rotor is therefore: If the weight distribution is not equal between the two bearings but is, say, 60 percent on the left bearing and 40 percent on the right bearing, then the unbalance in the left plane must be divided by 60 percent of the rotor weight to arrive at the approximate displacement in the left bearing plane, whereas the unbalance in the right plane must be divided by 40 percent of the rotor weight. FIG. 12. Symmetric rotor with static unbalance. FIG. 13. Unbalance resulting from bearing runout in an asymmetric rotor. An assumed unbalance of 10 oz · in. in the left plane (close to the bearing) will thus cause an approximate eccentricity in the left bearing of: … and in the right bearing of: Quite often the reverse calculation is of interest. In other words, the unbalance is to be computed that results from a known displacement. Again the assumption is made that the resulting unbalance is static. For example, assume an armature and fan assembly weighing 2,000 lbs and having a bearing load distribution of 70 percent at the armature (left) end and 30 percent at the fan end (see FIG. 13). Assume further that the assembly has been balanced on its journals and that the rolling element bearings added afterwards have a total indicated runout of 0.001 in., causing an eccentricity of the shaft axis of 1/2 of the TIR or 0.0005 in. Question: How much unbalance does the bearing runout cause in each side of the rotor? Answer: In the armature end... In the fan end... When investigating the effect of bearing runout on the balance quality of a rotor, the unbalance resulting from the bearing runout should be added to the residual unbalance to which the armature was originally balanced on the journals; only then should the sum be compared with the recommended balance tolerance. If the sum exceeds the recommended tolerance, the armature will either have to be balanced to a smaller residual unbalance on its journals, or the entire armature/bearing assembly will have to be rebalanced in its bearings. The latter method is often prefer able since it circumvents the bearing runout problem altogether, although field replacement of bearings will be more problematic. Balancing Machines The purpose of a balancing machine is to determine by some technique both the magnitude of unbalance and its angular position in each of one, two, or more selected correction planes. For single-plane balancing this can be done statically, but for two- or multi-plane balancing, it can be done only while the rotor is spinning. Finally, all machines must be able to resolve the unbalance readings, usually taken at the bearings, into equivalent values in each of the correction planes. On the basis of their method of operation, balancing machines and equipment can be grouped in three general categories: 1. Gravity balancing machines. 2. Centrifugal balancing machines. 3. Field balancing equipment. In the first category, advantage is taken of the fact that a body free to rotate always seeks that position in which its center-of-gravity is lowest. Gravity balancing machines, also called non-rotating balancing machines, include horizontal ways or knife-edges, roller stands, and vertical pendulum types ( FIG. 14). All are capable of only detecting and/or indicating static unbalance. FIG. 14. Static balancing devices. In the second category, the amplitude and phase of motions or reaction forces caused by once-per-revolution centrifugal forces resulting from unbalance are sensed, measured, and displayed. The rotor is supported by the machine and rotated around a horizontal or vertical axis, usually by the drive motor of the machine. A centrifugal balancing machine (also called a rotating balancing machine) is capable of measuring static unbalance (single plane machine) or static and couple unbalance (two-plane machine). Only a two-plane rotating balancing machine can detect couple and/or dynamic unbalance. Field balancing equipment, the third category, provides sensing and measuring instrumentation only; the necessary measurements for balancing a rotor are taken while the rotor runs in its own bearings and under its own power. A programmable calculator or handheld computer may be used to convert the vibration readings (obtained in several runs with test masses) into magnitude and phase angle of the required correction masses. Gravity Balancing Machines First, consider the simplest type of balancing-usually called "static" balancing, since the rotor is not spinning. In FIG. 14A, a disc-type rotor on a shaft is shown resting on knife edges. The mass added to the disc at its rim represents a known unbalance. In this illustration, and those which follow, the rotor is assumed to be balanced without this added unbalance mass. In order for this balancing procedure to work effectively, the knife-edges must be level, parallel, hard, and straight. In operation, the heavier side of the disc will seek the lowest level- thus indicating the angular position of the unbalance. Then, the magnitude of the unbalance usually is determined by an empirical process, adding mass to the light side of the disc until it’s in balance, i.e., until the disc does not stop at the same angular position. In FIG. 14B, a set of balanced rollers or wheels is used in place of the knife edges. Rollers have the advantage of not requiring as precise an alignment or level as knife edges; also, rollers permit run-out readings to be taken. In FIG. 14C, another type of static, or "nonrotating", balancer is shown. Here the disc to be balanced is supported by a flexible cable, fastened to a point on the disc which coincides with the center of the shaft axis slightly above the transverse plane containing the center-of-gravity. As shown in FIG. 14C, the heavy side will tend to seek a lower level than the light side, thereby indicating the angular position of the unbalance. The disc can be balanced by adding mass to the diametrically opposed side of the disc until it hangs level. In this case, the center-of gravity is moved until it’s directly under the flexible support cable. Static balancing is satisfactory for rotors having relatively low service speeds and axial lengths which are small in comparison with the rotor diameter. A preliminary static unbalance correction may be required on rotors having a combined unbalance so large that it’s impossible in a dynamic, soft-bearing balancing machine to bring the rotor up to its proper balancing speed without damaging the machine. If the rotor is first balanced statically by one of the methods just outlined, it’s usually possible to decrease the initial unbalance to a level where the rotor may be brought up to balancing speed and the residual unbalance measured. Such preliminary static correction is not required on hard-bearing balancing machines. Static balancing is also acceptable for narrow, high speed rotors which are subsequently assembled to a shaft and balanced again dynamically. This procedure is common for single stages of jet engine turbines and compressors. Centrifugal Balancing Machines Two types of centrifugal balancing machines are in general use today, soft-bearing and hard-bearing machines. Soft-Bearing Balancing Machines The soft-bearing balancing machine derives its name from the fact that it supports the rotor to be balanced on bearings which are very flexibly suspended, permitting the rotor to vibrate freely in at least one direction, usually the horizontal, perpendicular to the rotor shaft axis (see Figure 16 15). Resonance of rotor and bearing system occurs at one half or less of the lowest balancing speed so that, by the time balancing speed is reached, the angle of lag and the vibration amplitude have stabilized and can be measured with reasonable certainty (see FIG. 16A). Bearings (and the directly attached support components) vibrate in unison with the rotor, thus adding to its mass. Restriction of vertical motion does not affect the amplitude of vibration in the horizontal plane, but the added mass of the bearings does. The greater the combined rotor-and-bearing mass, the smaller will be the displacement of the bearings, and the smaller will be the output of the devices which sense the unbalance. FIG. 15. Motion of unbalanced rotor and bearings in flexible-bearing, centrifugal balancing machines. As far as the relationship between unbalance and bearing motion is concerned, the soft-bearing machine is faced with the same complexity as shown in FIG. 11. Therefore, a direct indication of unbalance can be obtained only after calibrating the indicating elements for a given rotor by use of test masses which constitute a known amount of unbalance. For this purpose the soft-bearing balancing machine instrumentation contains the necessary circuitry and controls so that, upon proper calibration for the particular rotor to be balanced, an exact indication of amount-of-unbalance and its angular position is obtained. Calibration varies between parts of different mass and configuration, since displacement of the principal axis of inertia in the balancing machine bearings is dependent upon rotor mass, bearing and suspension mass, rotor moments of inertia, and the distance between bearings. FIG. 16. Phase angle and displacement amplitude versus rotational speed in soft bearing and hard-bearing balancing machines. Hard-Bearing Balancing Machines Hard-bearing balancing machines are essentially of the same construction as soft-bearing balancing machines, except that their bearing supports are significantly stiffer in the transverse horizontal direction. This results in a horizontal resonance for the machine which occurs at a frequency several orders of magnitude higher than that for a comparable soft-bearing balancing machine. The hard-bearing balancing machine is designed to operate at speeds well below this resonance (see FIG. 16B) in an area where the phase angle lag is constant and practically zero, and where the amplitude of vibration-though small-is directly proportional to centrifugal forces produced by unbalance. Since the force that a given amount of unbalance exerts at a given speed is always the same, no matter whether the unbalance occurs in a small or large, light or heavy rotor, the output from the sensing elements attached to the balancing machine bearing supports remains proportional to the centrifugal force resulting from unbalance in the rotor. The output is not influenced by bearing mass, rotor mass, or inertia, so that a permanent relation between unbalance and sensing element output can be established. Centrifugal force from a given unbalance rises with the square of the balancing speed. Output from the pick-ups rises proportionately with the third power of the speed due to a linear increase from the rotational frequency superimposed on a squared increase from centrifugal force. Suitable integrator circuitry then reduces the pickup signal inversely proportional to the cube of the balancing speed increase, resulting in a constant unbalance readout. Unlike soft bearing balancing machines, the use of calibration masses is not required to calibrate the machine for a given rotor. Angle of lag is shown as a function of rotational speed in FIG. 16A for soft-bearing balancing machines whose balancing speed ranges start at approximately twice the resonance speed of the supports; and in FIG. 16B for hard-bearing balancing machines. Here the resonance frequency of the combined rotor-bearing support system is usually more than three times greater than the maximum balancing speed. For more information on hard-bearing and other types of balancing machines, see articles on advantages of hard-bearing machines and on balancing specific types of rotors. (Reprints are available through Schenck Trebel Corporation.) Both soft- and hard-bearing balancing machines use various types of sensing elements at the rotor-bearing supports to convert mechanical vibration into an electrical signal. These sensing elements are usually velocity-type pickups, although certain hard-bearing balancing machines use magnetostrictive or piezo-electric pickups. Measurement of Amount and Angle of Unbalance Three basic methods are used to obtain a reference signal by which the phase angle of the amount-of-unbalance indication signal may be correlated with the rotor. On end-drive machines (where the rotor is driven via a universal-joint driver or similarly flexible coupling shaft) a phase reference generator, directly coupled to the balancing machine drive spindle, is used. On belt-drive machines (where the rotor is driven by a belt over the rotor periphery) or on air-drive or self-drive machines, a stroboscopic lamp flashing once per rotor revolution, or a scanning head (photoelectric cell with light source) is employed to obtain the phase reference. Whereas the scanning head only requires a single reference mark on the rotor to obtain the angular position of unbalance, the stroboscopic light necessitates attachment of an angle reference disc to the rotor, or placing an adhesive numbered band around it. Under the once-per-revolution flash of the strobe light the rotor appears to stand still so that an angle reading can be taken opposite a stationary mark. With the scanning head, an additional angle indicating circuit and instrument must be employed. The output from the phase reference sensor (scanning head) and the pickups at the rotor-bearing supports are processed and result in an indication representing the amount-of-unbalance and its angular position. In FIG. 17 block diagrams are shown for typical balancing instrumentations. FIG. 17. Block diagram of typical balancing machine instrumentations. (A) Amount of unbalance indicated on analog meters, angle by strobe light. (B) Combined amount and angle indication on Vector meters, simultaneously in two correction planes. FIG. 17A illustrates an indicating system which uses switching between correction planes (i.e., a single-channel instrumentation). This is generally employed on balancing machines with stroboscopic angle indication and belt drive. In FIG. 17B an indicating system is shown with two-channel instrumentation. Combined indication of amount of unbalance and its angular position is provided simultaneously for both correction planes on two vector-meters having illuminated targets projected on the back of translucent overlay scales. Displacement of a target from the central zero point provides a direct visual representation of the displacement of the principal inertia axis from the shaft axis. Concentric circles on the overlay scale indicate the amount of unbalance, and radial lines indicate its angular position. FIG. 18. Influence of cross effects in rotors with static and couple unbalance. Plane Separation Consider the rotor in FIG. 15 with only an unbalance mass on the left end of the rotor. This mass causes not only the left bearing to vibrate but, to a lesser degree, the right also. This influence is called correction plane interference or, for short, "cross effect." If a second mass is attached in the right plane of the rotor, the direct effect of the mass in the right plane combines with the cross effect of the mass in the left plane, resulting in a composite vibration of the right bearing. If the two unbalance masses are at the same angular position, the cross effect of one mass has the same angular position as the direct effect in the other rotor end plane; thus, their direct and cross effects are additive ( FIG. 18A). If the two unbalance masses are 180° out of phase, their direct and cross effects are subtractive ( FIG. 18B). In a hard-bearing balancing machine the additive or subtractive effects depend entirely on the ratios of distances between the axial positions of the correction planes and bearings. In a soft-bearing machine, the relationship is more complex because the masses and inertias of the rotor and its bearings must be taken into account. If the two unbalance masses have an angular relationship other than 0 or 180°, the cross effect in the right bearing has a different phase angle than the direct effect from the right mass. Addition or subtraction of these effects is vectorial. The net bearing vibration is equal to the resultant of the two vectors, as shown in FIG. 19. Phase angle indicated by the bearing vibration does not coincide with the angular position of either unbalance mass. The unbalance illustrated in FIG. 19 is the most common type, namely dynamic unbalance of unknown amount and angular position. Interaction of direct and cross effects will cause the balancing process to be a trial-and-error procedure. To avoid this, balancing machines incorporate a feature called "plane separation" which eliminates cross effect. Before the advent of electrical networks, cross effect was eliminated by supporting the rotor in a cradle resting on a knife-edge and spring arrangement, as shown in FIG. 20. Either the bearing-support members of the cradle or the knife edge pivot point are movable so that one unbalance correction plane always can be brought into the plane of the knife edge. FIG. 19. Influence of cross effects in rotors with dynamic unbalance. (All vectors seen from right side of rotor.) Thus any unbalance in this plane won’t cause the cradle to vibrate, whereas unbalance in all other planes will. The latter is measured and corrected in the other correction plane near the right end of the rotor body. Then the rotor is turned end for end, so that the knife-edge is in the plane of the first correction. Any vibration of the cradle is now due solely to unbalance present in the plane that was first over the knife-edge. Corrections are applied to this plane until the cradle ceases to vibrate. The rotor is now in balance. If it’s again turned end for end, there will be no vibration. Mechanical plane separation cradles restrict the rotor length, diameter, and location of correction planes. They also constitute a large parasitic mass which reduces sensitivity. Therefore, electric circuitry is used today to accomplish the function of plane separation. In principle, part of the output of each pickup is reversed in phase and fed against the output of the other pickup. Proper potentiometer adjustment of the counter voltage during calibration runs (with test masses attached to a balanced rotor) eliminates the cross effect. FIG. 20. Plane separation by mechanical means. ==== TBL. 1 Classification of Balancing Machines Principle employed Gravity (nonrotating) Centrifugal (rotating) -- Unbalance indicated: Static (single-plane) Dynamic (two-plane); also suitable for static (single-plane) -- Attitude of shaft axis: Vertical Horizontal -- Type of machine: Pendulum Knife-edges Roller sets Soft-bearing Hard-bearing -- Not commercially available Soft-bearing Hard-bearing Soft-bearing Hard-bearing -- Available classes: Not classified Not classified II, III III, IV I, II, III IV ==== Next>> |