Tiêu chuẩn iso 01940 1 2003

Microsoft Word C027092e doc Reference number ISO 1940 1 2003(E) © ISO 2003 INTERNATIONAL STANDARD ISO 1940 1 Second edition 2003 08 15 Mechanical vibration — Balance quality requirements for rotors in[.]

General

Balancing is a critical procedure that ensures the proper mass distribution of a rotor, preventing excessive vibrations It involves checking and adjusting the rotor's mass to keep residual unbalance within specified limits Proper balancing reduces vibrations at the journals and bearings, especially at the rotor's service speed, enhancing equipment reliability and lifespan This process is essential for maintaining optimal performance and minimizing mechanical stress on rotating components.

Rotor unbalance can be caused by design, material, manufacturing and assembly Every rotor has an individual unbalance distribution along its length, even in a series production.

Representation of the unbalance

One and the same unbalance of a rotor in a constant (rigid) state can be represented by vectorial quantities in various ways, as shown in Figures 1a) to 1f)

Figures 1a) to 1c) show different representations in terms of resultant unbalance and resultant couple unbalance, whereas Figures 1d) to 1f) are in terms of a dynamic unbalance in two planes

The resultant unbalance vector can be positioned in any radial plane without altering its magnitude or angle However, the associated resultant couple unbalance depends on the specific location of the unbalance vector This relationship highlights the importance of vector positioning in analyzing system unbalance and its effects on overall stability Understanding how the location influences the couple unbalance is essential for accurate imbalance correction and system optimization.

NOTE 2 The centre of unbalance is that location on the shaft axis for the resultant unbalance, where the resultant moment unbalance is a minimum

For single-plane balancing or when evaluating resultant and couple unbalance, the preferred representations are shown in Figures 1a) to 1c) Conversely, for typical two-plane balancing considerations, it's more advantageous to use the representations in Figures 1d) to 1f).

This article discusses various types of unbalance in rotating machinery, starting with the general case where a resultant unbalance vector is accompanied by an associated couple unbalance in the end planes It then covers the static unbalance scenario, where the unbalance vector is located at the center of mass (CM), resulting in a specific couple unbalance in the end planes The article further explores the case where the resultant unbalance vector is positioned at the center of unbalance (CU), leading to a minimal associated couple unbalance that lies in a plane orthogonal to the unbalance vector Finally, it addresses situations involving an unbalance vector in each of the end planes, highlighting the complexities of balancing in such configurations.

Copyright International Organization for Standardization

The unbalance analysis includes various components with different magnitudes There are two 90° unbalance components in each of the end planes, indicating a specific unbalance pattern Additionally, an unbalance vector is present in each of two other planes, contributing to the overall imbalance The unbalance values range from 1 g⋅mm to 5 g⋅mm, with measurements such as 1.12 g⋅mm, 1.41 g⋅mm, 2 g⋅mm, 2.24 g⋅mm, 2.69 g⋅mm, 3 g⋅mm, 3.16 g⋅mm, and 5 g⋅mm, highlighting the varying degrees of imbalance across different components.

CM is the centre of mass

CU is the centre of unbalance

Figure 1 — Different representations of the same unbalance of a rotor in a constant (rigid) state

Unbalance effects

Resultant unbalance and resultant moment unbalance (resultant couple unbalance) differently affect bearing forces and machine vibration, so they are often analyzed separately in practice Even when a dynamic unbalance is specified in two planes, the predominant effects depend on whether the unbalance mainly manifests as a resultant unbalance or a resultant couple unbalance Understanding these distinctions is crucial for accurate machine diagnostics and balance correction.

Correction planes

Rotors that exceed balance tolerance require correction to ensure optimal performance These unbalance corrections are often not feasible in the original balancing planes; instead, they must be performed in areas where material can be added, removed, or relocated to achieve proper balance Proper balancing of rotors is essential for preventing equipment failure and extending operational lifespan Conducting precise unbalance corrections in the appropriate planes helps maintain machinery efficiency and reduces vibration-related issues.

The required number of correction planes is determined by the extent and distribution of the initial unbalance and the rotor design, including the shape and placement of correction planes relative to the tolerance planes.

4.5.2 Rotors which need one correction plane only

For some rotors, only the resultant unbalance is out of tolerance, the resultant moment unbalance is in tolerance This typically happens with disc-shaped rotors, provided that

 the bearing distance is sufficiently large,

 the disc rotates with sufficiently small axial runout, and

 the correction plane for the resultant unbalance is properly chosen

The suitability of single-plane balancing can be assessed by analyzing each individual case to determine if the balancing criteria are met After balancing multiple rotors, the largest residual moment unbalance is identified and divided by the bearing distance to calculate the couple unbalance If these remaining unbalances are acceptable even in the worst-case scenario, it indicates that single-plane balancing is likely sufficient for the application.

For single-plane balancing, the rotor does not need to rotate; however, for enhanced sensitivity and accuracy, rotational balancing machines are typically used These machines accurately determine the resulting unbalance, allowing it to be corrected within specified limits, ensuring optimal rotor performance and stability.

4.5.3 Rotors which need two correction planes

If a rotor in a rigid, constant state does not meet the conditions outlined in section 4.5.2, it is essential to reduce the moment unbalance Typically, resultant unbalance and moment unbalance are combined into a dynamic unbalance, represented by two unbalance vectors in different planes—referred to as complementary unbalance vectors.

For two-plane balancing, it is necessary for the rotor to rotate, since otherwise the moment unbalance would remain undetected

4.5.4 Rotors with more than two correction planes

Although all rotors in their constant (rigid) state theoretically can be balanced in two planes, sometimes more than two correction planes are used, for instance

When correcting for unbalance, it is essential to address both the resultant unbalance and the couple unbalance; failing to correct the resultant unbalance in both or either of the couple planes can lead to persistent vibration issues, compromising equipment performance and longevity Proper correction ensures balanced operation and reduces mechanical stresses, highlighting the importance of comprehensive balancing procedures.

 if the correction is spread along the rotor

In certain situations, spreading the correction across the rotor may be essential due to limitations in the correction planes, such as when adjusting crankshafts by drilling into counterweights This approach can also be recommended to maintain the overall function and strength of the components, ensuring optimal engine performance and durability.

Permissible residual unbalance

In the case of an inboard rotor with a small axial length, the effect of couple unbalance can be neglected Under these conditions, the rotor's unbalance state is effectively represented by a single vector quantity called the unbalance UG This simplified approach allows for more straightforward analysis and diagnosis of rotor imbalance issues Understanding the unbalance UG is essential for optimizing rotor performance and ensuring system stability.

To obtain a satisfactory running of the rotor, the magnitude of this unbalance (the residual unbalance U res ) should not be higher than a permissible value U per , i.e

More generally, the same applies to any type of rotor

NOTE The SI unit for U per is kilogram metres (kg⋅m), but for balancing purposes a more practical unit is gram millimetres (g⋅mm)

U per is defined as the total tolerance in the mass centre plane For all two-plane tasks, this tolerance shall be allocated to the tolerance planes (see Clause 7)

General

Some considerations on similarity may help in the understanding and calculation of the influences of rotor mass and service speed on the permissible residual unbalance.

Permissible residual unbalance and rotor mass

In general, for rotors of the same type, the permissible residual unbalance U per is proportional to the rotor mass m:

The permissible residual specific unbalance, denoted as e per, is directly related to the rotor mass when the residual unbalance limit is considered It can be calculated using the equation e per = U per / m, where U per represents the allowable residual unbalance, and m is the rotor mass This relationship helps ensure balanced rotor operation by correlating unbalance limits with rotor weight, facilitating precise maintenance and design standards.

The SI unit for U per meter is kilogram meters per kilogram (kg·m/kg), though a more practical alternative is gram millimeters per kilogram (g·mm/kg) This latter unit corresponds to micrometres, as explained in Note 2, providing a more convenient measure for specific applications.

Note 2 explains that the SI unit for e per is either kilogram metres per kilogram (kg⋅m/kg) or metres (m), with micrometres (µm) being a more practical unit due to typical residual unbalances ranging from 0.1 µm to 10 µm The term e per is particularly useful for relating geometric tolerances such as runout and play to balance tolerances, facilitating precise measurements and assessments in mechanical balancing applications.

In rotor dynamics, if a rotor has only a resultant unbalance, such as a disc perpendicular to the shaft axis, e_per represents the distance from the mass center to the shaft axis For more complex rotors with multiple unbalance types, e_per becomes an artificial parameter that combines the effects of both the resulting unbalance and the moment unbalance Consequently, e_per cannot be directly observed or measured in a general rotor with complex unbalance conditions.

NOTE 4 There are limits for achievable residual specific unbalance e per depending on the set-up conditions in the balancing machine, for instance: centring, bearings and drive

Achieving small values of e per can requires precise accuracy of shaft journals, including roundness and straightness In certain situations, rotor balancing must be performed while the rotor is in its service bearings using methods such as belt, air, or self-drive systems Alternatively, balancing may need to be conducted with the rotor fully assembled within its housing, bearings, and self-drive, under actual service conditions and temperature to ensure optimal performance.

Permissible residual specific unbalance and service speed

For rotors of the same type, experience shows that, in general, the permissible residual specific unbalance value e per varies inversely with the service speed n of the rotor: e per ∼ 1/n (4)

Differently expressed, this relationship is given by the following equation, where Ω is the angular velocity of the rotor at maximum service speed: e per ⋅Ω = constant (5)

Geometrically similar rotors operating at equal peripheral velocities experience identical stresses and bearing specific loads caused by centrifugal forces This fundamental relationship underpins the balance quality grades, as detailed in Table 1 and Figure 2 of section 6.2, ensuring consistent balancing standards across similar rotor designs.

For rotors operating at a significantly lower service speed than their maximum designed speed—such as certain AC motors rated for 3,000 RPM but used at 1,000 RPM—the standard similarity rule may be overly restrictive In these situations, a higher permissible value of e per can be considered, scaled proportionally to the ratio of the maximum to operating speed (e.g., 3,000/1,000).

General

The balance tolerances may be determined by five different methods as described in 6.2 to 6.5 The methods are based on

 balance quality grades, derived from long-term practical experience with a large number of different rotors (see 6.2),

 experimental evaluation of permissible unbalance limits (see 6.3),

 limited bearing forces due to unbalance (see 6.4.1),

 limited vibrations due to unbalance (see 6.4.2), and

 established experience with balance tolerances (see 6.5)

The choice of method should be agreed between the manufacturer and user of the rotor.

Balance quality grades G

Based on global experience and similarity considerations (see Clause 5), balance quality grades G have been established to classify the balance quality requirements for various typical machinery types (see Table 1), ensuring optimal performance and adherence to industry standards.

Balance quality grades G are determined based on the magnitude of the product e per Ω, expressed in millimeters per second (mm/s) When the magnitude reaches 6.3 mm/s, the balance quality grade is classified accordingly, ensuring precise assessment of balance performance This standard helps in maintaining accurate and reliable balancing processes across various applications.

Balance quality grades are distinguished by a factor of 2.5, with finer grading potentially needed for high-precision balancing, but not less than a factor of 1.6 The values of e per (equivalent to U per /m) are plotted against maximum service speed in Figure 2, providing important data for assessing balancing requirements at different operational velocities.

NOTE Figure 2 contains some additional information on generally used areas (speed and quality grade G), based on common experience

The balance quality grades are based on typical machine design, where the rotor mass is a certain fraction of the complete machine In special cases modifications are needed

Electric motors with shaft heights less than 80 mm are classified under G 6,3, which determines their permissible unbalance (see 6.2.3) This unbalance limit applies when the rotor mass is approximately 30% of the total machine mass, but for lightweight rotors like iron-less armatures, where rotor mass may be only 10%, the permissible unbalance can be increased up to three times the standard value.

In external-rotor motors, a high rotor mass can reach up to 90%, necessitating stricter balance standards To ensure optimal performance and safety, the permissible unbalance may need to be reduced by a factor of three Proper unbalance control is crucial in high-mass rotors to prevent vibrations and mechanical issues, highlighting the importance of precise manufacturing and maintenance practices.

The permissible residual unbalance U per can be derived on the basis of a selected balance quality grade G by the following equation:

U per is the numerical value of the permissible residual unbalance, expressed in gram millimetres

(e per ⋅Ω) is the numerical value of the selected balance quality grade, expressed in millimetres per second

(mm/s); m is the numerical value of the rotor mass, expressed in kilograms (kg);

Ω is the numerical value of the angular velocity of the service speed, expressed in radians per second (rad/s), with Ω ≈ n/10 and the service speed n in revolutions per minute (r/min)

As an alternative, Figure 2 may be used to derive e per , then: per = e per m

When considering permissible residual unbalance (U) and the balance quality grade (e), it's essential to account for their specific SI units with appropriate prefixes Proper application of the balancing equation requires careful attention to these units An illustrative example is provided in Annex A to ensure clarity and accurate understanding of the balancing process.

U per is defined as the total tolerance in the mass centre plane For all two-plane tasks, this tolerance shall be allocated to the tolerance planes (see Clause 7).

Experimental evaluation

Experimental evaluation of balance quality is essential for mass production applications and is typically conducted through in-situ testing During these tests, permissible residual unbalance is determined by successively introducing various test unbalances in each correction plane The evaluation relies on the most representative criteria, such as vibration, force, or noise caused by unbalance, to ensure optimal performance and quality control.

In two-plane balancing, it is important to account for the effects of unbalances with the same phase angle and those 180° apart when no tolerance planes are used, as outlined in section 4.4.

Table 1 — Guidance for balance quality grades for rotors in a constant (rigid) state

Crankshaft drives for large slow marine diesel engines (piston speed below

Crankshaft drives, inherently unbalanced, elastically mounted G 630 630

Crankshaft drives, inherently unbalanced, rigidly mounted G 250 250

Complete reciprocating engines for cars, trucks and locomotives G 100 100

Cars: wheels, wheel rims, wheel sets, drive shafts

Crankshaft drives, inherently balanced, elastically mounted

Crankshaft drives, inherently balanced, rigidly mounted

Drive shafts (cardan shafts, propeller shafts)

Electric motors and generators (of at least 80 mm shaft height), of maximum rated speeds up to 950 r/min Electric motors of shaft heights smaller than 80 mm

Electric motors and generators (of at least 80 mm shaft height), of maximum rated speeds above 950 r/min Gas turbines and steam turbines

Spindles and drives of high-precision systems

NOTE 1 Typically completely assembled rotors are classified here Depending on the particular application, the next higher or lower grade may be used instead For components, see Clause 9

NOTE 2 All items are rotating if not otherwise mentioned (reciprocating) or self-evident (e.g crankshaft drives)

NOTE 3 For limitations due to set-up conditions (balancing machine, tooling), see Notes 4 and 5 in 5.2

NOTE 4 For some additional information on the chosen balance quality grade, see Figure 2 It contains generally used areas (service speed and balance quality grade G), based on common experience

Crankshaft drives in Note 5 may include components such as the crankshaft, flywheel, clutch, vibration damper, and the rotating portion of the connecting rod Inherently unbalanced crankshaft drives are theoretically impossible to balance, while inherently balanced crankshaft drives can be balanced according to design specifications Additionally, some machinery may require adherence to specific International Standards for balance tolerances, which are outlined in relevant standards and bibliographies.

NOTE The white area is the generally used area, based on common experience

Figure 2 — Permissible residual specific unbalance based on balance quality grade G and service speed n (see 6.2)

Methods based on special aims

The primary goal is to restrict bearing forces resulting from unbalances Initially, these limits are expressed in terms of bearing forces, which must then be converted into unbalance quantities When dealing with a stationary bearing housing, this conversion is straightforward and utilizes the centrifugal force equation outlined in Annex B.

In all other cases, the dynamic behaviour of the structure under service condition shall be considered There are no simple rules available for these cases

The primary goal is to limit vibrations in specific planes, which is especially important for hand-held machines Ensuring optimal balance quality is essential and can be determined based on these vibration limits For detailed guidelines, refer to Annex C.

Methods based on established experience

If a company has gained sufficient established experience to assess the balance quality of its products, it may make full use of this Annex D gives some guidance

7 Allocation of permissible residual unbalance to tolerance planes

Single plane

In the case of single-plane correction, U per is used entirely for this plane (see 4.5.2) In all other cases, U per shall be allocated to the two tolerance planes.

Two planes

The permissible residual unbalance, U per, is allocated proportionally based on the distances from the mass center to the opposite tolerance planes, such as bearing planes A and B This allocation ensures compliance with precision standards, as demonstrated in Figures 3 and 4 The specific calculations follow established equations that relate the unbalance to the distances from the mass center to the respective tolerance planes, facilitating accurate balancing and minimizing operational vibrations.

U per A is the permissible residual unbalance in bearing plane A;

U per B is the permissible residual unbalance in bearing plane B;

U per is the (total) permissible residual unbalance (in the mass centre plane);

L A is the distance from mass centre plane to bearing plane A;

L B is the distance from mass centre plane to bearing plane B;

For a comprehensive overview, refer to Figure 3 When the mass center is located close to one bearing, the calculated tolerance for that bearing increases significantly, approaching the value of U per, while the tolerance for the distant bearing decreases towards zero To prevent such extreme tolerance variations, it is recommended to implement specific design measures ensuring balanced load distribution and maintaining acceptable tolerance levels across all bearings.

 the larger value should not be larger than 0,7 U per , and

 the smaller value should not be smaller than 0,3 U per

Figure 3 — Inboard rotor with mass centre in an asymmetric position

For general outlines, see Figure 4 The values are calculated according to Equations (8) and (9) However, to avoid extreme tolerance conditions, it is stipulated that

 the larger value should not be larger than 1,3 U per , and

 the smaller value should not be smaller than 0,3 U per

The upper unbalance limit is different from that of the inboard rotor This assumes that bearing B and the supporting structure are designed to take the static load exerted by the overhung mass Thus it will also support a proportionately higher load caused by unbalances If this is not the case, the limitations for inboard rotors should be applied

Figure 4 — Outboard rotor with mass centre in an overhung position

8 Allocation of balance tolerances to correction planes

General

It is strongly recommended to use special reference planes to state balance tolerances, but many of today's balancing processes still apply balance tolerances at the correction planes

Correction planes are selected based on the correction process, which may not be ideal for balance tolerances When allocating tolerances to correction planes, it is essential to consider both the magnitude of residual unbalances and their relative angular position, although tolerances are typically defined solely by amount Any allocation rule must balance these factors and account for the worst-case angular relationship between residual unbalances in both correction planes, as other conditions usually result in lower effects on the rotor.

Thus, using balance tolerances in correction planes, many rotors are balanced to smaller unbalance values than necessary

The balance tolerances may be determined by the methods described in Clause 6

 In the case of experimental determination (see 6.3), the permissible residual unbalance is generally gained for each correction plane: no further allocation is required

When using tolerance planes based on balance quality grades (see 6.2), specific aims (see 6.4), or established experience (see 6.5), it may be necessary to subsequently allocate corrections to the correction planes to ensure precise alignment and quality control.

Single plane

For rotors which need one correction plane only, the permissible residual unbalance U per in this plane is equal to the sum of the tolerance amounts in the tolerance planes

NOTE When applying balance quality grades (see 6.2) to determine U per , allocating to two tolerance planes (see Clause 7) is omitted

Two planes

When correction planes I and II are close to the tolerance planes A and B, tolerances can be transferred directly using a factor of 1, meaning the original tolerance value of the adjacent plane is maintained For additional details and specific conditions related to tolerance transfer, refer to Annex E.

General

Assembled rotors can be balanced either as complete units or at the component level Unbalances from individual components combine, and assembly errors such as runout and play introduce additional unbalances, affecting overall rotor stability For optimal performance, it is essential to consider these factors during balancing procedures, following standards like ISO 1940-2.

NOTE If assembly errors are not decisive, the choice of balancing process may be governed by the availability of balancing machines.

Balanced as a unit

The best way to take care of all unbalances in the rotor and all related assembly errors in one step is to balance the rotor as a fully assembled unit

When disassembling a balanced rotor assembly for mounting into the housing, it is essential to mark each component angularly This practice ensures that during reassembly, all parts are positioned exactly as they were, maintaining the rotor's balance and optimal performance Proper marking helps preserve the integrity of the initial balancing process, preventing imbalances caused by incorrect reassembly Following these steps is crucial for maintaining rotor reliability and extending equipment life.

NOTE The above-mentioned problems with runout and play can still exist.

Balanced on component level

When balancing individual components, it is important to ensure that each part maintains a specific residual unbalance, typically aligned with the assembly's overall residual unbalance (see Clause 5) To accommodate assembly errors described in ISO 1940-2, each component's residual unbalance should be less than that of the final assembly If balancing specific components results in issues—such as a lightweight fan mounted on a heavy armature—any distribution method can be employed, provided the total unbalance of the assembled system remains within specified tolerances Additionally, prior agreement between the manufacturer and user regarding the attachment of connecting elements, like keys (see ISO 8821), is essential to ensure proper balancing and functionality.

When it is not possible to achieve the desired balance tolerance by balancing individual components, the entire assembly should be balanced as a single unit In these situations, it is advisable to reevaluate whether component-level balancing is truly necessary or if it can be skipped to streamline the process.

General

It is advisable to verify the residual unbalance in the tolerance planes (see 4.4) and not in the correction planes

Any measurement contains errors In order to verify the residual unbalance of a rotor, the balancing errors cannot be neglected (see ISO 1940-2 for assessment and consideration)

Acceptance criteria

Systematic errors in the readings have been corrected, and ∆U is the remaining combined error (see ISO 1940-2) For bearing planes A and B, let

U per A be the magnitude of the permissible residual unbalance in plane A;

U per B be the magnitude of the permissible residual unbalance in plane B;

U r m A be the magnitude of the measured residual unbalance in plane A of a single reading;

U r m B be the magnitude of the measured residual unbalance in plane B of a single reading;

∆U A be the magnitude of the combined error in plane A;

∆U B be the magnitude of the combined error in plane B

During the balancing process, the rotor balance should be considered acceptable if the following conditions are both satisfied:

If a separate balance check is performed, the rotor balance should be considered acceptable if the following conditions are both satisfied:

If ∆U A or ∆U B is found to be less than 5 % of U per A or U per B , respectively, it may be disregarded

The magnitude of the combined error ∆U A or ∆U B will usually be different on different balancing machines Therefore different values for the manufacturer and the user may apply

Repeating measurements more often, using more than one piece of equipment, and having more than one person performing the measurements may statistically reduce the errors.

Verification on a balancing machine

Systematic errors shall be checked/treated first in accordance with ISO 1940-2

During balancing machine verification, residual unbalance can be measured directly to ensure accurate results It is essential that the machine's characteristics, along with the unbalance reduction ratio (URR) and the minimum achievable residual unbalance (U_mar), meet the requirements outlined in ISO 2953 Proper verification guarantees precise unbalance assessment and optimal balancing performance.

The procedure described in section 10.4 can be applied using a balancing machine; however, its effectiveness may be limited to the rotor’s service speeds At lower speeds, the vibration signals may be too faint to provide accurate measurements, which could affect the balancing process.

Verification outside a balancing machine

The residual unbalance may be determined outside a balancing machine, for example in situ by means of a device capable of measuring amplitude and phase of the once-per-revolution vibration

Check the vibrational behaviour and scale it by the following measuring sequence without and with test unbalances:

 measure the rotor “as it is”;

 apply a test unbalance in one plane, then measure again;

 remove the test unbalance in the previous plane, apply a test unbalance in the other plane, then measure again;

 evaluate the readings using the influence coefficient method or equivalent

The in-situ balancing process involves measuring vibrations without performing final unbalance corrections It is crucial that all measurement changes are solely due to test unbalances, ensuring accurate results To achieve this, measurements must be taken under consistent conditions, such as maintaining the same speed and stationary vibrations throughout testing.

If the measuring accuracy, especially the linearity, is in doubt, it is recommended to repeat the procedure with different test unbalances, in angle and/or amount

Example of the specification of permissible residual unbalance based on balance quality grade G and allocation to the tolerance planes

Consider a turbine rotor with the following data (see Figure A.1): rotor mass: m = 3 600 kg service speed: n = 3 000 r/min distances: L A = 1 500 mm

Selected: Balance quality grade was selected according to Table 1, for machinery type “gas turbines and steam turbines”: G 2,5

Calculated: Angular velocity of service speed, from

A.2 Specification of U per based on Equation (6)

U per is the numerical value of the permissible residual unbalance, expressed in gram millimetres

(e per ⋅Ω) is the numerical value of the selected balance quality grade, expressed in millimetres per second

(mm/s); m is the numerical value of the rotor mass, expressed in kilograms (kg);

Ω is the numerical value of the angular velocity of the maximum service speed, expressed in radians per second (rad/s)

NOTE For the permissible unbalance U per , and the balance quality grade (e per ⋅Ω), the SI units are used here with prefixes, so special care is needed to apply this equation.

A.3 Specification of U per based on Figure 2

For the given service speed and balance quality grade (see Figure A.2): e per ≈ 8 g mm/kg

Multiplied by the rotor mass, the permissible residual unbalance is U per ≈ 8 × 3 600 = 28,8 × 10 3 g⋅mm

A.4 Allocation to tolerance planes (bearing planes)

According to 7.2, the permissible residual unbalance (as calculated in A.2) can be allocated to the bearing planes as follows:

A.5 Check on limitations (see 7.2.2 for inboard rotor)

The larger value should not be larger than 0,7 U per , i.e U per max u 20,0 × 10 3 g⋅mm

The smaller value should not be smaller than 0,3 U per , i.e U per min W 8,6 × 10 3 g⋅mm

U per A is larger than U per min

U per B is smaller than U per max

Both limits are kept, U per A and U per B as calculated apply

NOTE White area is the generally used area, based on common experience

Figure A.2 — Example of specification of e per using Figure 2

Specification of balance tolerances based on bearing force limits

One of the primary objectives of balancing is to limit bearing forces, as outlined in section 6.4.1 When these bearing forces are specified, they must be converted into unbalances for effective analysis This transformation is straightforward only if the bearing housing remains stationary; in such cases, the calculation can be simplified using the centrifugal force equation Proper balancing ensures the reduction of undue bearing forces, thereby extending the lifespan of machinery and improving operational stability.

U per A is the permissible residual unbalance in bearing A;

U per B is the permissible residual unbalance in bearing B;

F A is the permissible bearing force caused by unbalances in bearing A;

F B is the permissible bearing force caused by unbalances in bearing B;

Ω is the angular velocity of the maximum service speed

This equation is based on SI units, as outlined in ISO 1000, ensuring standardized measurements Permissible residual unbalances are typically expressed with dimensional prefixes (see 4.6), requiring careful application of the formula Special attention is needed when applying this equation to ensure accurate and reliable results in engineering practices.

For the rotor described in Annex A, the maximum permissible bearing forces caused by unbalances are stated with

The permissible residual unbalances in bearing planes are

Specification of balance tolerances based on vibration limits

Elaborated models and detailed calculations are essential for analyzing the dynamic behavior of rotors and complete machines, as well as assessing their vibrational response to unbalances However, this comprehensive approach is too extensive and beyond the scope of this section of ISO 1940.

A simplified method seems to be applicable in easy cases, but a proven basis is not yet available

Specification of balance tolerances based on established experience

A company with substantial documented experience in assessing product balance quality can effectively utilize this knowledge to set new balance tolerances By leveraging insights gained from previous rotor evaluations, the company can establish more accurate and reliable balance standards This approach ensures continuous improvement in product quality while maintaining alignment with overall operational goals.

For a new rotor size, almost identical to others that have been successfully balanced, identical balance tolerances apply.

Use the same limits in similarly located tolerance planes

For a new rotor size, similar to others that have been successfully balanced, balance tolerances may be derived in different ways, as given in D.3.2 and D.3.3

A graph illustrates the relationship between balance tolerance and rotor size, including diameter, mass, and power, for known rotors This visual data enables the determination of the required balance tolerance for new rotor dimensions Refer to Figure D.1 to accurately derive the necessary balance specifications for different rotor sizes, ensuring optimal performance and stability.

NOTE For different types of rotors, different graphs may be needed

Use adjusted limits in similarly located tolerance planes

For rotors of the same type, similarity rules dictate that the permissible residual unbalance (U) depends on the rotor’s mass (m) and operating speed (n) Specifically, the residual unbalance U is proportional to the rotor mass, meaning heavier rotors can tolerate greater imbalance Conversely, U is inversely proportional to the service speed, indicating that higher operating speeds require more precise balancing These principles, outlined in Clause 5, ensure proper rotor performance and safety during operation.

To determine the permissible residual unbalance for a new rotor size based on a known one, use the formula: permissible residual unbalance for the new rotor equals the known residual unbalance multiplied by the ratio of the new rotor mass to the known rotor mass This calculation ensures accurate balancing when upgrading or modifying rotor components, maintaining optimal machine performance Understanding how to adjust residual unbalance according to rotor size is essential for minimizing vibrations and avoiding mechanical issues Proper application of this equation allows engineers to precisely evaluate and control rotor balancing requirements during design and maintenance processes.

If permissible residual unbalances for the tolerance planes are known, similar equations may be used to calculate the values for a new rotor size

Use recalculated limits in similarly located tolerance planes

Figure D.1 — Interpolation of balance tolerance for a new rotor size

Evaluating differences in function, design, and arrangement can help determine balance tolerance requirements; however, this process is complex and requires extensive background knowledge Unlike simple examples, no universal rule exists for establishing these tolerances, making careful analysis essential for accurate assessment.

Rules for allocating balance tolerances from tolerance planes to correction planes

It is recommended to use the tolerance planes, often identical to the bearing planes, rather than the correction planes for specifying balance tolerances, as outlined in sections 4.4 and 8.1 However, in cases where balance tolerances must be applied to correction planes, Clauses E.2 to E.4 provide essential guidelines to ensure proper balancing procedures.

E.2 Correction planes in-between tolerance planes

For a situation as given in Figure E.1, the solution according to 8.3 is as follows Use the balance tolerance value of the adjacent tolerance plane:

U per I is the permissible residual unbalance in correction plane I;

U per II is the permissible residual unbalance in correction plane II;

U per A is the permissible residual unbalance in tolerance (bearing) plane A;

U per B is the permissible residual unbalance in tolerance (bearing) plane B

NOTE Tolerance (bearing) planes are A and B; correction planes are I and II

Figure E.1 — Allocation to inboard correction planes

E.3 Correction planes outside tolerance planes

In the scenario depicted in Figure E.2, it is recommended to reduce the balance tolerance value proportionally to the ratio of the bearing span to the correction plane distance Adjusting these tolerances ensures improved accuracy and stability in the correction process, aligning with best engineering practices This method optimizes structural performance by maintaining precise tolerances based on the specific geometric ratios involved.

U per I is the permissible residual unbalance in correction plane I;

U per II is the permissible residual unbalance in correction plane II;

U per A is the permissible residual unbalance in tolerance (bearing) plane A;

U per B is the permissible residual unbalance in tolerance (bearing) plane B;

L is the bearing span; b is the distance between correction planes I and II

For rotors with complex geometries, simple balancing guidelines are not applicable It is essential to specify permissible residual unbalances at the bearing planes to ensure proper rotor performance, as detailed in section 4.4.

NOTE Tolerance (bearing) planes are A and B; correction planes are I and II

Figure E.2 — Allocation to outside correction planes

[1] ISO 1000, SI units and recommendations for the use of their multiples and of certain other units

[2] ISO 2041, Vibration and shock — Vocabulary

[3] ISO 2953, Mechanical vibration — Balancing machines — Description and evaluation

[4] ISO 8821, Mechanical vibration — Balancing — Shaft and fitment key convention

[5] ISO 11342, Mechanical vibration — Methods and criteria for the mechanical balancing of flexible rotors

[6] ISO 14694, Industrial fans — Specifications for balance quality and vibration levels

Tiêu đề	Mechanical Vibration — Balance Quality Requirements For Rotors In A Constant (Rigid) State — Part 1: Specification And Verification Of Balance Tolerances
Trường học	International Organization for Standardization
Chuyên ngành	Mechanical Vibration
Thể loại	standard
Năm xuất bản	2003
Thành phố	Geneva

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