ISO 1940-1: Mechanical vibration – Balance quality requirements for rotors in a constant (rigid) state

Summary

ISO 1940-1 is one of the most important and frequently referenced standards in the field of rotor balancing. It provides a systematic method for classifying rotors by type, determining an appropriate balance quality level, and calculating a specific balancing tolerance. The core of the standard is the concept of Balance Quality Grades (G-Grades), which allows manufacturers and maintenance personnel to specify and verify the precision of a balance job in a standardized way. This standard applies specifically to rigid rotors—those that do not flex or bend at their service speed.

Note: This standard has been formally replaced by ISO 21940-11, but its principles and G-Grade system remain the fundamental basis for rigid rotor balancing worldwide.

Table of Contents (Conceptual Structure)

The standard is structured to guide the user through the process of determining a permissible residual unbalance:

1. 1. Scope and Field of Application:

   This initial section establishes the boundaries and purpose of the standard. It explicitly states that its rules and guidelines apply to rotors that behave rigidly throughout their operating speed range. This is the fundamental assumption of the entire standard; it means the rotor does not experience significant bending or deformation due to unbalance forces. The scope is broad, intended to cover a wide variety of rotating machinery across all industries. However, it also clarifies that this is a general-purpose standard, and for certain specific types of machinery (e.g., aerospace gas turbines), other, more stringent standards may take precedence. It sets the objective: to provide a systematic method for specifying balance tolerances, which are essential for quality control in manufacturing and repair.

2. 2. Balance Quality Grades (G-Grades):

   This section is the heart of the standard. It introduces the concept of Balance Quality Grades (G-Grades) as a way to classify the balance requirements for different types of machinery. The G-Grade is defined as the product of the specific unbalance (eccentricity, e) and the maximum service angular velocity (Ω), where G = e × Ω. This value represents a constant vibration velocity, providing a standardized measure of quality. The standard provides a comprehensive table that lists a wide variety of rotor types (e.g., electric motors, pump impellers, fans, gas turbines, crankshafts) and assigns a recommended G-Grade for each. These grades are based on decades of empirical data and practical experience. For example, a G6.3 might be recommended for a standard industrial motor, while a precision grinding spindle would require a much stricter G1.0 or G0.4. A lower G-number always signifies a tighter, more precise balance tolerance, meaning less permissible residual unbalance.

3. 3. Permissible Residual Unbalance Calculation:

   This section provides the essential mathematical bridge from the theoretical G-Grade to a practical, measurable tolerance. It details the formula to calculate the permissible specific unbalance (e_per), which is the allowable displacement of the center of gravity from the axis of rotation. The formula is derived directly from the definition of the G-Grade:

   e_per = G / Ω

   For practical use with common engineering units, the standard provides the formula:

   e_per [g·mm/kg] = (G [mm/s] × 9549) / n [RPM]

   Once the permissible specific unbalance (e_per) is calculated, it is multiplied by the rotor’s mass (M) to find the total permissible residual unbalance (U_per) for the entire rotor: U_per = e_per × M. This final value, expressed in units like gram-millimeters (g·mm), is the target that the balancing machine operator must achieve. The rotor is considered balanced once its measured residual unbalance is below this calculated value.

4. 4. Allocation of Residual Unbalance to Correction Planes:

   This section addresses the critical step of distributing the calculated total permissible unbalance (U_per) into specific tolerances for each of the two correction planes. A two-plane balance is required to correct for both static and couple unbalance. The standard provides formulas for this allocation, which depends on the rotor’s geometry. For a simple, symmetrical rotor, the total unbalance is often split equally between the two planes. However, for more complex geometries, such as overhung rotors or rotors with the center of gravity not centered between the bearings, the standard provides specific formulas. These formulas take into account the distances of the correction planes and the center of gravity from the bearings, ensuring that the tolerance for each plane is correctly apportioned. This step is vital because a balancing machine measures the unbalance in each plane independently; therefore, the operator needs a specific target value for each plane (e.g., “Permissible unbalance in Plane I is 15 g·mm and in Plane II is 20 g·mm”).

5. 5. Sources of Error in Balancing:

   This final section serves as a practical guide to the real-world factors that can compromise the accuracy of a balancing job, even when a precise tolerance has been calculated. It highlights that achieving a perfect balance is impossible and that the goal is to reduce the residual unbalance to a level below the calculated tolerance. The standard discusses several key sources of error that must be managed, including: errors in the calibration of the balancing machine itself; geometric imperfections of the rotor’s journals or mounting surfaces (runout); errors introduced by the tooling used to mount the rotor on the machine (e.g., an unbalanced arbor); and operational effects that are not present during low-speed balancing, such as thermal expansion or aerodynamic forces. This chapter serves as a crucial checklist for quality control, reminding the practitioner to consider the entire balancing process, not just the final number on the machine’s display.

Key Concepts

• Standardization: The G-Grade system provides a universal language for balance quality. A customer can specify “balance to G6.3” and any balancing shop in the world will know exactly what tolerance is required.
• Speed Dependence: The standard makes it clear that balance tolerance is critically dependent on the machine’s operating speed. A faster rotor requires a tighter balance (a smaller permissible residual unbalance) to produce the same level of vibration as a slower rotor.
• Practicality: The standard provides a proven, practical framework based on decades of empirical data, helping to avoid both under-balancing (which leads to high vibration) and over-balancing (which is unnecessarily expensive).

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