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AMAZON multi-meters discounts AMAZON oscilloscope discounts Prev. Classification of Centrifugal Balancing Machines Centrifugal balancing machines may be categorized by the type of unbalance a machine is capable of indicating (static or dynamic), the attitude of the journal axis of the workpiece (vertical or horizontal), or the type of rotor-bearing-support system employed (soft- or hard-bearing). In each category, one or more classes of machines are commercially built. The four classes are described in TBL. 1. Class I: Trial-and-Error Balancing Machines. Machines in this class are of the soft-bearing type. They don’t indicate unbalance directly in weight units (such as ounces or grams in the actual correction planes) but indicate only displacement and/or velocity of vibration at the bearings. The instrumentation does not indicate the amount of weight which must be added or removed in each of the correction planes. Balancing with this type of machine involves a lengthy trial-and-error procedure for each rotor, even if it’s one of an identical series. The unbalance indication cannot be calibrated for specified correction planes because these machines don’t have the feature of plane separation. Field balancing equipment usually falls into this class. A programmable calculator or small computer with field balancing pro grams, either contained on magnetic strips or on a special plug-in ROM, will greatly reduce the trial-and-error procedure; however, calibration masses and three runs are still required to obtain magnitude and phase angle of unbalance on the first rotor. For subsequent rotors of the same kind, readings may be obtained in a single run but must be manually entered into the calculator and then suitably manipulated. Class II: Calibratable Balancing Machines Requiring a Balanced Prototype. Machines in this class are of the soft-bearing type using instrumentation which permits plane separation and calibration for a given rotor type, if a balanced master or prototype rotor with calibration masses is available. However, the same trial-and-error procedure as for Class I machines is required for the first of a series of identical rotors. Class III: Calibratable Balancing Machines Not Requiring a Balanced Prototype. Machines in this class are of the soft-bearing type using instrumentation which includes an integral electronic unbalance compensator. Any (unbalanced) rotor may be used in place of a balanced master rotor without the need for trial and error correction. Plane separation and calibration can be achieved in one or more runs with the help of calibration masses. This class also includes soft-bearing machines with electrically driven shakers fitted to the vibratory part of their rotor supports. Class IV: Permanently Calibrated Balancing Machines. Machines in this class are of the hard-bearing type. They are permanently calibrated by the manufacturer for all rotors falling within the weight and speed range of a given machine size. Unlike the machines in other classes, these machines indicate unbalance in the first run without individual rotor calibration. This is accomplished by the incorporation of an analog or digital computer into the instrumentation associated with the machine. The following five rotor dimensions (see FIG. 21) are fed into the computer: distance from left correction plane to left support (a); distance between correction planes (b); distance from right correction plane to right support (c); and r1 and r2, which are the radii of the correction masses in the left and right planes. The instrumentation then indicates the magnitude and angular position of the required correction mass for each of the two selected planes. The compensation or "null-force" balancing machine falls into this class also. Although no longer manufactured, it’s still widely used. It balances at the natural frequency or resonance of its suspension system including the rotor. FIG. 21. A permanently calibrated hard-bearing balancing machine, showing five rotor dimensions used in computing unbalance. Maintenance and Production Balancing Machines Balancing machines may also be categorized by their application in the following three groups: 1. Universal balancing machines. 2. Semi-automatic balancing machines. 3. Full automatic balancing machines with automatic transfer of work. Each of these is available in both the nonrotating and rotating types, the latter for correction in either one or two planes. Universal Balancing Machines Universal balancing machines are adaptable for balancing a consider able variety of sizes and types of rotors. These machines commonly have a capacity for balancing rotors whose weight varies as much as 100 to 1 from maximum to minimum. The elements of these machines are adapted easily to new sizes and types of rotors. Amount and location of unbalance are observed on suitable instrumentation by the machine operator as the machine performs its measuring functions. This category of machine is suitable for maintenance or job-shop balancing as well as for many small and medium lot-size production applications. Semi-Automatic Balancing Machines Semi-automatic balancing machines are of many types. They vary from an almost universal machine to an almost fully automatic machine. Machines in this category may perform automatically any one or all of the following functions in sequence or simultaneously: 1. Retain the amount of unbalance indication for further reference. 2. Retain the angular location of unbalance indication for further reference. 3. Measure amount and position of unbalance. 4. Couple the balancing-machine drive to the rotor. 5. Initiate and stop rotation. 6. Set the depth of a correction tool depending on indication of amount of unbalance. 7. Index the rotor to a desired position depending on indication of unbalance location. 8. Apply correction of the proper magnitude at the indicated location. 9. Inspect the residual unbalance after correction. 10. Uncouple the balancing-machine drive. Thus, the most complete semi-automatic balancing machine performs the entire balancing process and leaves only loading, unloading, and cycle initiation to the operator. Other semi-automatic balancing machines provide only means for retention of measurements to reduce operator fatigue and error. The features which are economically justifiable on a semi-automatic balancing machine may be determined only from a study of the rotor to be balanced and the production requirements. Fully-Automatic Balancing Machines Fully automatic balancing machines with automatic transfer of the rotor are also available. These machines may be either single- or multiple station machines. In either case, the parts to be balanced are brought to the balancing machine by conveyor, and balanced parts are taken away from the balancing machine by conveyor. All the steps of the balancing process and the required handling of the rotor are performed without an operator. These machines also may include means for inspecting the residual unbalance as well as monitoring means to ensure that the balance inspection operation is performed satisfactorily. In single-station automatic balancing machines, all functions of the balancing process (unbalance measurement, location, and correction) as well as inspection of the complete process are performed sequentially in a single station. In a multiple-station machine, the individual steps of the balancing process may be performed concurrently at two or more stations. Automatic transfer is provided between stations at which the amount and location of unbalance are determined; then the correction for unbalance is applied; finally, the rotor is inspected for residual unbalance. Such machines generally have shorter cycle times than single-station machines. Establishing a Purchase Specification A performance type purchase specification for a balancing machine should cover the following areas: 1. Description of the rotors to be balanced, including production rates, and balance tolerances. 2. Special rotor requirements, tooling, methods of unbalance correction, other desired features. 3. Acceptance test procedures. 4. Commercial matters such as installation, training, warranty, etc. Rotor Description To determine the correct machine size and features for a given application, it’s first necessary to establish a precise description of the rotors to be balanced. To accumulate the necessary data, ISO 2953 suggests a suitable format. Refer to SECTION 6C. Supporting the Rotor in the Balancing Machine Means of Journal Support A prime consideration in a balancing machine is the means for sup porting the rotor. Various alternates are available, such as twin rollers, plain bearings, rolling element hearings (including slave bearings), V roller bearings, nylon V-blocks, etc. (see also SECTION 6B, "Balancing Machine Nomenclature," and SECTION 6C.) The most frequently used and easiest to adapt are twin rollers. A rotor should generally be supported at its journals to assure that balancing is carried out around the same axis on which it rotates in service. Rotors with More than Two Journals Rotors which are normally supported at more than two journals may be balanced satisfactorily on only two journals provided that: 1. All journal surfaces are concentric with respect to the axis deter mined by the two journals used for support in the balancing machine. 2. The rotor is rigid at the balancing speed when supported on only two bearings. 3. The rotor has equal stiffness in all radial planes when supported on only two journals. If the other journal surfaces are not concentric with respect to the axis determined by the two supporting journals, the shaft should be straightened. If the rotor is not a rigid body, or if it has unequal stiffness in different radial planes (e.g., crankshafts), the rotor should be supported in a (non-rotating) cradle at all journals during the balancing operation. This cradle should supply the stiffness usually supplied to the rotor by the rotor housing in which it’s finally installed. The cradle should have minimum mass when used with a soft-bearing machine to permit maximum balancing sensitivity. Rotors with Rolling Element Bearings Rotors with stringent requirements for minimum residual unbalance and which run in rolling element bearings, should be balanced in their bearings, either in: 1. Special machines where the bearings are aligned and the outer races held in saddle bearing supports, rigidly connected by tie bars; or 2. In standard machines having supports equipped with V-roller carriages. Frequently, practical considerations make it necessary to remove the bearings after balancing, to permit final assembly. If this cannot be avoided, the bearings should be match-marked to the rotor shaft and returned to the location used during balancing. Rolling element bearings with considerable radial play or bearings with a quality less than ABEC (Annular Bearing Engineers Committee) Standard grade 3 tend to cause erratic indications in the balancing machine. In some cases the outer race can be clamped tightly enough to remove excessive radial play. Only "fair" or lesser balance quality can be reached when rotors are supported on bearings of a grade lower than ABEC 3. When maintenance requires antifriction bearings to be changed occasionally on a rotor, it’s best to balance the rotor on the journals on which the inner races of the antifriction bearings fit. The unbalance introduced by displacement of the shaft axis due to eccentricity of the inner races can be minimized by use of high-quality bearings. Driving the Rotor If the rotor has its own journals, it may be driven in a horizontal balancing machine through: 1. A universal-joint or flexible-coupling drive from one end of the rotor. 2. A belt over the periphery of the rotor, or over a pulley attached to the rotor. 3. Air jets. 4. Other power means by which the rotor is normally driven in the final machine assembly. The choice of end-drive can affect the residual unbalance substantially, even if the design considerations listed later in this text are carefully observed (see also "Balance Errors Due to Drive Elements"). Belt-drive has the advantage here, but it’s somewhat limited in the amount of torque it can transmit to the rotor. Driving belts must be extremely flexible and of uniform thickness. Driving pulleys attached to the rotor should be used only when it’s impossible to transmit sufficient driving torque by running the belt over the rotor. Pulleys must be as light as possible, must be dynamically balanced, and should be mounted on surfaces of the rotor which are square and concentric with the journal axis. The belt drive should not cause disturbances in the unbalance indication exceeding one quarter of the permissible residual unbalance. Rotors driven by belt should not drive components of the balancing machine by means of any mechanical connection. The use of electrical means or air for driving rotors may influence the unbalance readout. To avoid or minimize such influence, great care should be taken to bring in the power supply through very flexible leads, or have the airstream strike the rotor at right angles to the direction in which the balancing machine takes its readings. If the electronic measuring system incorporates filters tuned to a specific frequency only, it’s essential that means be available to control precisely the rotor speed to suit the filter setting. Drive System Limitation A given drive system has a certain rotor acceleration capability expressed in terms of the Wk2 n2 value. This limiting value is generally part of the machine specification describing the drive, since it depends primarily on motor horsepower, motor type (squirrel-cage induction, wound-rotor, DC), and drive line strength. The specified Wk2 n2 value may be used to determine the maximum balancing speed (n) to which a rotor with a specific polar moment of inertia (Wk2 ) can be accelerated; or conversely, to determine what maximum Wk2 can be accelerated to a specified speed (n). (In each case the number of runs per hour must stay within the maximum number of cycles allowed.) If a rotor is to be balanced which has a Wk2 n2 value smaller than the maximum specified for a given drive, the stated cycles per hour may generally be exceeded in an inverse ratio. On occasion it may happen that a large diameter rotor, although still within the weight capacity of the machine, cannot be accelerated to a given balancing speed. This may be due to the fact that the rotor's mass is located at a large radius, thus creating a large polar moment of inertia. As a result, a lower balancing speed may have to be selected. TBL. 2 Factor C for Approximating Radius of Gyration k for Typical Rotors Typical Rotor C-Factor Tube or Pipe 1 Solid Mass 0.7 Bladed Rotor 0.5-0.6 Propeller 0.4 A rotor's polar moment of inertia (Wk2 ) is found by multiplying the rotor weight (W) in pounds by the square of the radius-of-gyration (k) in feet. The radius-of-gyration is the average of the radii from the shaft axis of each infinitesimal part of the rotor. It may be approximated by multiplying the outside radius of the rotor by a factor (C), shown in TBL. 2. Example: With the polar moment of inertia known, the maximum speed n (in rpm) to which the machine can accelerate this rotor may now be computed. Example: To determine the maximum moment of inertia the machine can accelerate to a specific balancing speed, divide the limiting Wk2 n2). Weight-Speed Limitation (Wn2) The weight-speed limitation stated by a balancing machine supplier for a given size machine serves (a) to prevent damage to the supports of soft bearing machines, and (b) to prevent the hard-bearing machine support system from operating too closely to its natural frequency and giving false indications. The stated value of Wn2 is based on the assumption that the rotors are approximately symmetrical in shape, rigid, and mounted between the supports. Example: Machine specification limits Wn2 to 2,400 · 10^6 lb n2. A given symmetric rotor weighs 1,200 lb, and is to be balanced at 800 rpm. Its Wn2 value is: Wn2 = 1 200 800 768 10 =?=? , Therefore, the balancing speed of 800 rpm falls well within the capabilities of the machine. For nonsymmetrical load distribution between the supports, and for out board rotors, the following formula provides a fast approximation of (a) the maximum permissible balancing speed in a soft-bearing machine, and (b) the maximum balancing speed in a hard-bearing machine at which permanent calibration in the A-B-C mode is maintained. Where: We = Weight equivalent to be used in Wn2 formula, (lb). W = Weight of rotor, (lb). s = Distance from the rotor CG to the nearest support. (If the CG is outboard of the supports, s is positive; if the CG is inboard, s is negative.) D = Distance between the supports. Determining the Right Balancing Speed The question is often asked whether a given rotor such as a crankshaft, fan, roll or other rotating component should be balanced at its respective service speed. The answer, in most cases, is no. The next question, usually, is why not? Doesn't unbalance increase with the square of the rotational speed? The answer, again, is no. Only the centrifugal force that a given unbalance creates increases proportionately to the square of the speed, but the actual unbalance remains the same. In other words, an ounce-inch of unbalance represents a one ounce unbalance mass with its center-of gravity located at a one inch radius from the shaft axis, no matter whether the part is at rest or rotating (see also earlier in this SECTION on "Units of Unbalance"). What balancing speed should be used then? To answer that question, consider the following requirements: 1. The balancing speed should be as low as possible to decrease cycle time, horsepower requirement, wind, noise, and danger to the operator. 2. It should be high enough so that the balancing machine has sufficient sensitivity to achieve the required balance tolerance with ease. However, there is one other important consideration to be made before deciding upon a balancing speed substantially lower than the rotor's service speed; namely, is the part (or assembly) rigid? Is the Rotor "Rigid"? Theoretically it’s not, since no workpiece is infinitely rigid. However, for balancing purposes there is another way of looking at it (see definition of "Rigid Rotor" in SECTION 6A). Any rotor satisfying this definition can be balanced on standard balancing machines at a speed which is normally well below the service speed. When selecting the balancing speed, consider the following guidelines: 1. Determine the proper balance tolerance by consulting TBL. 5 and subsequent nomograms. 2. Select the lowest available speed at which the balancing machine provides at least 1/4 in. amount-of-unbalance indicator deflection or 5 digital units of indication for the required balance tolerance. It’s usually of no advantage to select a higher speed for achieving greater sensitivity, since the repeatability of a good quality balancing machine is well in line with today's exacting balance tolerances. Whether a given rotor can be termed "rigid" as defined in SECTION 6A depends on numerous factors that should be carefully evaluated. For instance: 1. Rotor configuration and service speed. Technical literature provides reference tables which permit approximating the critical speed of the first flexural mode from the significant geometric rotor parameters (see SECTION 6D). In most cases it can be assumed that a rotor can be balanced successfully at low speed if its service speed is less than 50 percent of the computed first flexural critical speed. 2. Rotor design and manufacturing procedures. Rotors which are known to be flexible or unstable may, nevertheless be balanced satisfactorily at low speed if certain precautions are taken. Rotors of this type are classified as "quasi-rigid rotors." Examples: • A gas turbine compressor assembly, consisting of a series of bladed disks which can all be balanced individually prior to rotor assembly. Considerable effort has been made by the turbine designers to provide for accurate component balancing so that standard (low speed) balancing machines can be employed in production and overhaul of these sophisticated rotor assemblies. • A turbine rotor with flexible or unstable mass components, such as governors or loose blades. To obtain, at low balancing speed, a position of governor or blades which most nearly approximates their position at the much higher service speed, it may be necessary to block the governor or "stake" the blades. • A large diesel crankshaft normally rotating in five or even seven journals. When running such a shaft on only two journals in a balancing machine, the shaft may bend from centrifugal forces caused by large counterweights and thus register a large (erroneous) unbalance. To avoid these difficulties, the balancing speed must be extremely low and/or the shaft must be supported in the balancing machine on a rigid cradle with three, five, or even seven precisely aligned bearings. • Rotors which can not be satisfactorily balanced at low speed, require special high-speed or "modal" balancing techniques, since they must be corrected in several planes at or near their critical speed(s)^2. Flexibility Test This test serves to determine if a rotor may be considered rigid for balancing purposes, or if it must be treated as a flexible rotor. The test is carried out at service speed either in the rotor service bearings or in a high-speed, hard-bearing balancing machine. The rotor should first be balanced fairly well at low speed. Then one test mass is added at the same angular position in each end plane of the rotor near its journals. During a subsequent test run, vibration is measured on both bearings. Next, the rotor is stopped and the test masses are moved to the center of the rotor, or where they are expected to cause the largest rotor distortion. In a second run the vibration is again measured at the bearings. If the total of the first readings is designated A, and the total of the second readings B, then the ratio of (B-A)/A should not exceed 0.2. Experience has shown that, if the ratio stays below 0.2, the rotor can be satisfactorily corrected at low speed by applying correction masses in two or three planes. Should the ratio exceed 0.2, the rotor will generally have to be balanced at or near its service speed. Direction of Rotation The direction of rotation in which the rotor runs while being balanced is usually unimportant with the exception of bladed rotors. On these (or others that create windage) it’s recommended to run in the direction that creates the least turbulence and thus, uses the least drive power. Certain fans need close shrouding to reduce drive power requirements to an acceptable level. Turbine rotors with loose blades should be run backward (opposite to operational direction) to approximate the blade position in service, while compressor rotors should run forward (the same as under service conditions). End-Drive Adapters Design Considerations End-drive adapters used on horizontal balancing machines to drive workpieces need to be carefully balanced so as not to introduce a balance error into the workpiece. Considerations should be given to the following details when designing an end-drive adapter: 1. Make the adapters as light in weight as possible, consistent with capability to transmit the required driving torque. This will reduce balance errors due to fit tolerances which allow the adapter to locate eccentrically, i.e., offset from the shaft axis of the workpiece. 2. Maintain close tolerances on fit dimensions between end-drive adapter and workpiece, and between adapter and balancing machine drive. Loose fits cause shifting of the adapter and consequent changes in adapter balance. Multiply the weight of the adapter in grams by one half of the maximum radial runout possible due to a loose fit to obtain the maximum balance error in gram-inches that may result. 3. Design adapters so that they may be indexed 180° relative to the workpiece. This will allow checking and correcting the end-drive adapter balance on the balancing machine. 4. Harden and grind adapters to be used in production runs to reduce wear and consequent increase in fit clearances. Balancing Keyed End-Drive Adapters An adapter for a keyed rotor shaft should be provided with two 180° opposed keyways. The correct procedure for balancing the adapter depends entirely on which of the two methods was used to take care of the mating keyway when balancing the component which, on final assembly, mounts to the keyed shaft end of the workpiece being balanced. Half-Key Method This is the method most commonly used in North American industry. Shafts with keyways, as well as the mating components are individually balanced with half-keys fitted to fill the void the keys will occupy upon final assembly of the unit (see FIG. 22A). To balance the end-drive adapter using this method, proceed as follows: 1. Mount the adapter to the workpiece shaft using a full key in the shaft keyway and fill the half-key void in the opposite side of the adapter with a half-key (see FIG. 22B). Balance the assembly by adding balancing clay to the workpiece. 2. Index the adapter 180° on rotor shaft (see FIG. 22C). If the adapter is out of balance, it will register on the balancing machine instrumentation. Note the gram-inch unbalance value in the plane closest to the adapter. Eliminate half of the indicated unbalance by adding clay to the adapter, the other half by adding clay to the workpiece. 3. Index the adapter 180° once again, back to the position shown in FIG. 22, and check unbalance indication. Repeat correction method outlined above. Then replace clay on adapter with permanent unbalance correction, such as drilling, grinding, etc., on opposite side. If it’s not possible to reduce the unbalance in the adapter to a satisfactory level by this method, it’s an indication that the tolerances on fit dimensions are not adequate. FIG. 22. Half-key method. FIG. 23. Full-key method. This is the method most commonly used in European industry. Shafts are balanced with full keys and mating components without a key. To balance the end-drive adapter using this method, proceed as follows: 1. Place a full key into the keyway of the workpiece shaft (see FIG. 23 A). Mount adapter to the workpiece shaft, leaving the opposite half-key void in the adapter empty (see FIG. 23B). Balance the assembly using balancing clay. 2. Follow the index balancing procedure outlined in paragraphs 2 and 3 of the half-key method. Balancing Arbors Definition A balancing arbor (or mandrel) generally is an accurately machined piece of shafting on which rotors that don’t have journals are mounted prior to balancing. Flywheels, clutches, pulleys and other disc-shaped parts fall into this category. Arbors are employed on horizontal as well as vertical balancing machines. Particularly when used on the latter, they are also referred to as "adapters," "fixtures," or "tooling." Since an arbor becomes part of the rotating mass being balanced, several criteria must be carefully observed during its design, manufacture, and use. Basic Design Criteria As is the case with most balancing machine tooling, an arbor should be as light as possible to have minimum effect on machine sensitivity. This is particularly important when using a soft-bearing machine. At the same time, the arbor must be rigid enough not to flex or bend at balancing speed. For ease of set-up in a horizontal machine, the arbor should be designed so that the rotor can be mounted near the center ( FIG. 24). Where this is not possible, perhaps because the rotor has a blind or very small bore, the rotor may be mounted in an outboard position ( FIG. 25). If the center-of-gravity of the combined rotor and arbor falls outboard of the machine supports, a negative load bearing is required on the opposite support to absorb the uplift. FIG. 24. Rotor in center of arbor. FIG. 25. Rotor mounted outboard. FIG. 26. Rotor held on arbor with clamping nut. A light push fit between arbor and rotor will facilitate assembly and disassembly, but may allow the rotor to slip during acceleration or deceleration. To prevent this, a hydraulically or mechanically expanding arbor is ideal. If none is available, a set screw may do. A small, flat area should be provided on the shaft for set screw seating. If the rotor has a keyway, the arbor should be provided with a mating key of the same length as the final assembly key. If the arbor has no keyway, the void of the rotor keyway should be filled with a half-key having the same length as the final assembly key, even if it differs from the length of the keyway. Threads are not a good locating or piloting surface. Sometimes a nut is used to hold the rotor on the arbor (see FIG. 26). The nut should be balanced in itself and have a piloting surface to keep it concentric with the arbor axis. Error Analysis The tighter the balance tolerance, the more important it’s to keep all working surfaces of the arbor as square and concentric as possible. Any eccentricity of the rotor mounting surface to the arbor axis and/or looseness in the fit of the rotor on the arbor causes balance errors. To determine the balance error U (i.e., unbalance) caused by eccentricity e of the rotor mounting surface (and by rotor clearance), use the following formula: U g in W g e inches ? () = () ? () Where: W = Weight of rotor (grams) e = eccentricity (inches) (= 1/2 Total indicator runout [TIR] of rotor mounting surface relative to arbor axis, plus 1/2 clearance between rotor and arbor) U(1-4) = Unbalance (gram· inches) caused by eccentric rotor mounting surface and/or rotor/arbor fit clearance. Example: W = 1,000 grams e = 1/2 TIR (mounting surface to shaft axis), say 1/2 of 0.004 in.= 0.002 in. + 1/2 the total clearance between in. rotor and arbor, say 1/2 of 0.002 = 0.001 in. = 0.003 in. 1. U1 = 1,000 g · 0.003 in. = 3 gram· inches. To this may have to be added: 2. Unbalance caused by eccentricity and thread clearance of the clamping nut, assume: W = 100 grams e = 0.001 in. U2 = 100 g · 0.001 in. = 0.1 g · in. (For simplification, the residual unbalance of the nut is ignored) 3. Residual unbalance U3 of the arbor, assume 0.1g·in. 4. Eccentricity plus 1/2 fit clearance in mounting surfaces of the final rotor installation. Assuming that similar tolerances prevail as were used in making the arbor, the same unbalance will result, or: UU gin 41 3 ==? . Total unbalance caused by arbor eccentricity and fit clearance U1, nut eccentricity U2, arbor residual unbalance, and installation error therefore may add up to a maximum of: Statistical Evaluation of Errors One can readily see that if the rotor balance tolerance is, say, 10g·in., 62 percent of it (6.2 g· in.) is already used up by tooling and mounting errors. Thus, the balancing machine operator is forced to balance each part to 10 - 6.2 = 3.8 (g · in.) or better, to be sure that the maximum permissible residual unbalance of 10 g· in. will be attained in the final assembly. This may be rather time consuming and, therefore, costly. To allow a larger working tolerance, the various tooling errors could be reduced by a more precisely machined arbor and final shaft. However, this too may be costly or impractical. A solution may be found in a statistical approach. Since the various unbalance errors are vectors and may have different angular directions, they add to each other vectorially, not arithmetically. If certain errors have opposite angular directions, they actually subtract, thus resulting in a smaller total error than assumed above. To determine the probable maximum error, the root of the sum of the squares (RSS) method should be used. This statistical method requires that the individual errors (U1 to U4) each be squared, then added and the square root drawn of the total. In the aforementioned example, the computation would look as follows: Now the operator is allowed a working tolerance of 10 - 4.25 = 5.75 g · in., or 50 percent more than when the unbalance errors were added arithmetically. If this still presents a problem, a more sensitive machine may be needed, or the rotor may have to be trim- or field-balanced after assembly. Under certain conditions "biasing" of the arbor may help. This method is described in the third subheading down. Balancing the Arbor Since residual unbalance in the arbor itself is one of the factors in the error analysis, every arbor should be carefully balanced and periodically checked. If the arbor has a keyway, it should be of the same length as the final assembly key and be filled completely during balancing with a half key (split lengthwise) for rotors of North American origin, with a full key for rotors of European origin (see FIGS. 22 and 23). If the arbor has a nut, the arbor should be balanced first without it. Then the nut should be added and any residual unbalance corrected in the nut. The nut should be checked in several angular positions to make sure it stays in balance. If it does not, its locating surface must be corrected. Special Design Features If the arbor is to be used on a horizontal balancing machine with end drive, one arbor face must be provided with a pilot and bolt hole circle to interface with the drive flange of the universal-joint shaft that transmits the driving torque from the balancing machine headstock. If a horizontal machine with belt-drive is to be used, and if the rotor has no surface over which the drive belt may be placed, the arbor must be provided with a belt pulley, unless the belt can run over the arbor itself. In either case, balancing speed and drive power requirements must be taken into consideration. On machines with fixed drive motor speeds, the ratio between drive pulley diameter and driven rotor (or arbor pulley) diameter determines the desired balancing speed. If arbors are to be used often, for instance for production balancing, they should be hardened and ground. Special care must be taken during storage to prevent corrosion and damage to locating and running surfaces. Biasing an Arbor This method is helpful whenever the runout (primarily radial runout) of the arbor surface which locates the rotor represents a significant factor in the error analysis. Biasing means the addition of artificial unbalance(s) to the (otherwise balanced) arbor. The bias masses are intended to compensate for the unbalance error caused by rotor displacement from the arbor's axis of rotation; rotor displacement being caused, for instance, by radial runout of the arbor surface which locates the rotor and/or, on vertical machines, runout of the machine spindle pilot. Since the attachment of masses to a (horizontal machine) arbor may prevent it from being inserted in the rotor bore, biasing is often accomplished by grinding or drilling two light spots into the arbor, equidistant to the left and right of the rotor. The light spots must have the same angular location as the high spot of the arbor surface which locates the rotor radially. The combined approximate unbalance value (g · in.) of the two high spots may be calculated by multiplying the rotor weight (g) by 1 /2 of the TJR (in.). On vertical machines the addition of bias masses to the arbor is often the simpler method. Whether the proper bias has been reached can be tested by balancing a rotor to the machine's minimum achievable residual unbalance, and then indexing it 180° on the arbor. One half of the unbalance which shows up after indexing is corrected in the rotor, the other half in the arbor. This indexing procedure is repeated until no further residual unbalance is detectable. The total correction made in the arbor is now considered its bias correction compensating for its runout, but only for the particular type of rotor used. If the rotor weight changes, the bias will have to be corrected again. Bias correction requires a good rotor fit. It won’t overcome locating errors caused by loose fits. To eliminate the need for physically biasing an arbor, balancing machine instrumentation can be furnished with a "double compensator." This feature permits biasing of the machine indication by means of suit able electrical circuits. FIG. 27. Schematic representation of double compensator. The Double Compensator As its name indicates, the double compensator has a two-fold purpose: to eliminate errors in unbalance caused by tooling (thereby biasing the tooling or arbor), and to compensate for initial workpiece unbalance during machine setup. Used in conjunction with 180° indexing, the compensator allows the machine to indicate only the rotor's true unbalance. Typically, this works as follows (see FIG. 27). 1. Mount first workpiece on adapter. Start machine, on Schenck Trebel equipment depress compensator switch "U + K1," and observe initial indication, I1. This represents the combination (vectorial addition) of workpiece unbalance, U1, and tooling error E (adapter eccentricity e and/or adapter-spindle unbalance), both of which are of unknown amount and angle. 2. Adjust compensator until indicator I1 becomes zero. Compensator voltage, K1, has now compensated for U1 and E. 3. Index workpiece 180° in reference to the adapter. This does not change the magnitude nor the angle of the tooling error E. The initial workpiece unbalance, however, moves 180° with the workpiece. Since the U1 component of K1 now adds to the reversed work piece unbalance U2, indication I2 will be opposite U1 and twice its magnitude. 4. Depress switch "U + K2" and adjust compensation voltage K2 until I2 is zero. 5. Depress switch "U + 1/2K2." This divides compensation voltage K2 in half. The remaining indication is U1, or the true initial unbalance in the workpiece. The tooling error E remains compensated by K1 and thus has no more influence on this reading or on readings taken on subsequent workpieces of the same type. If the workpiece type changes, the double compensator procedure described above must be repeated for a new setup. Just as the compensator is used to correct for unwanted errors, it can also be used to bias tooling, thereby producing a specified unbalance in a part. A typical example would be a crankshaft for a single or dual piston pump which might call for a given amount of compensating unbalance in the counterweights. Before using a compensator for this purpose, the required accuracy for the bias must be evaluated. For large biases with tight tolerances, it may be necessary to add precisely made (and located) bias masses to the tooling. An error analysis and statistical evaluation (see earlier SECTIONS) may then be required to take into account all error sources such as weight of bias mass, its CG uncertainty due to unbalance and mounting fit tolerance, distance of bias mass to the shaft axis of the arbor, angular location, etc. Unbalance Correction Methods Corrections for rotor unbalance are made either by the addition of mass to the rotor, by the removal of material, or in some cases, by relocating the shaft axis ("mass centering"). The selected correction method should ensure that there is sufficient capacity to allow correction of the maximum unbalance which may occur. The ideal correction method permits reduction of the maximum initial unbalance to less than balance tolerance in a single correction step. However, this is often difficult to achieve. The more common methods described below, e.g., drilling, usually permit a reduction of 10:1 in unbalance if carried out carefully. The addition of mass may achieve a reduction ratio as large as 20:1 or higher, provided the mass and its position are closely controlled. If the method selected for reduction of maximum initial unbalance cannot be expected to bring the rotor within the permissible residual unbalance in a single correction step, a preliminary correction is made. Then a second correction method is selected to reduce the remaining unbalance to its permissible value. Addition of Mass 1. Addition of solder or two-component epoxy. It’s difficult to apply the material so that its center-of-gravity is precisely at the desired correction location. Variations in location introduce errors in correction. Also, this method requires a fair amount of time. 2. Addition of bolted or riveted washers. This method is used only where moderate balance quality is required. 3. Addition of cast iron, lead, or lead masses. Such masses, in incremental sizes, are used for unbalance correction. 4. Addition of masses by resistance-welding them to a suitable rotor surface. This method provides a means of attaching a wide variety of correction masses at any desired angular locations. Care must be taken that welding heat does not distort the rotor. Removal of Mass 1. Drilling. Material is removed from the rotor by a drill which penetrates the rotor to a measured depth, thereby removing the intended mass of material with a high degree of accuracy. A depth gage or limit switch can be provided on the drill spindle to ensure that the hole is drilled to the desired depth. This is probably the most effective method of unbalance correction. 2. Milling, shaping, or fly cutting. This method permits accurate removal of mass when the rotor surfaces, from which the depth of cut is measured, are machined surfaces, and when means are pro vided for accurate measurement of cut with respect to those surfaces; used where relatively large corrections are required. 3. Grinding. In general, grinding is used as a trial-and-error method of correction. It’s difficult to evaluate the actual mass of the material which is removed. This method is usually used only where the rotor design does not permit a more economical type of correction. Mass Centering For the definition of mass centering see SECTION 6A. Such a procedure is used, for instance, to reduce initial unbalance in crankshaft forgings. The shaft is mounted in a balanced cage or cradle which, in turn, is rotated in a balancing machine. The shaft is adjusted radially with respect to the cage, until the unbalance indication for the combined shaft and cradle assembly is within a given tolerance. At this point the principal inertia axis of the shaft essentially coincides with the shaft axis of the balanced cage. Center-drills, guided along the axis of the cage, drill the shaft centers and thereby provide an axis in the crankshaft about which it’s in balance. The subsequent machining of the crankshaft is carried out between these centers. Because material removal is uneven at different parts of the shaft, the machining operation will introduce some new unbalance. A final balancing operation is therefore still required. It’s generally accomplished by drilling into the crankshaft counterweights. However, final unbalance corrections are small and balancing time is significantly shortened. Further more, final correction by drilling does not exceed the material available for it, nor does it reduce the mass of the counterweights to a level where they no longer perform their proper function, namely to compensate for the opposed masses of the crankshaft. Testing Balancing Machines Total verification of all purchase specification requirements may be possible for a production machine, but usually not for a general purpose machine, such as a machine in a motor repair shop, because a rotor of the maximum specified weight or polar moment of inertia may not be avail able at the time of acceptance tests. Nevertheless, essential conformance with the specification may be ascertained by a complete physical inspection and performance tests with typical workpieces and/or a "proving rotor." Physical inspection needs to take into account all specified dimensions, features, instrumentation, tooling, and accessories that are listed in the purchase specification and/or the seller's proposal. Performance tests are somewhat more involved and should be witnessed by a representative of the buyer who is well acquainted with balancing machines and the particular specification applying to the machine to be tested. Tests for Production Machines A production machine is usually purchased for balancing a given part or parts in large quantities. Acceptance tests, therefore, are generally performed by running samples of such parts, so that total compliance with specified indicating accuracy and cycle time can be ascertained under simulated production conditions. At the same time, tooling is checked for locating accuracy and balance. Additional tests, as described in the following paragraphs, may then be confined to just the first part (Umar Test), since compliance with the specified cycle time may already be considered sufficient proof that the machine achieves a satisfactory "Unbalance Reduction Ratio." This, however, is only the case if the initial unbalance of the sample rotors is representative of the whole range of initial unbalances that will be encountered in actual production parts. |