Publish Time: 2026-05-08 Origin: Site
The Three Brothers of Vibration: Differences and Conversion of Displacement, Velocity, and Acceleration Units
In the field of vibration measurement, mm, mm/s, and mm/s ⊃2; represent three different physical quantities of vibration, which describe the characteristics of vibration from different dimensions.
The core answer can be summarized in one sentence:
mm: represents vibration displacement, and is concerned with the amplitude of vibration.
mm/s: represents the vibration velocity, and is concerned with the intensity of the vibration.
mm/s ⊃2;: represents vibration acceleration, and is concerned with the "impact force generated by vibration".
Below we will provide a detailed explanation.
1.Displacement - Unit: Millimeters (mm)
What is it?
Vibration displacement refers to the maximum distance that an object deviates from its equilibrium position during the vibration process. Usually measured is the peak to peak value, which is the total distance between the highest and lowest points on the vibration trajectory.
What does it reflect?
It directly reflects the magnitude of the vibration. It can be intuitively understood as' how far the object has shaken '.
Main application scenarios:
Assessment of Gap and Safety: For rotating machinery such as turbines and large generators, vibration displacement is directly related to the gap between rotating and stationary components. Excessive displacement may lead to collisions and serious damage.
Low frequency vibration evaluation: In the low-frequency field (such as the vibration of buildings, bridges, and large structures), displacement is a commonly used evaluation index because low-frequency vibration may produce large amplitudes even if the speed is not fast.
Measuring deformation: applications that focus on the dynamic deformation of the structure itself.
2.Velocity - Unit: millimeters per second (mm/s)
What is it?
Vibration velocity is the rate of change of displacement over time, that is, the velocity of vibration. In engineering, its effective value (RMS) is commonly used, and velocity RMS is strongly correlated with vibration energy. Therefore, velocity RMS is commonly used as a health evaluation indicator in standards.
What does it reflect?
It directly reflects the energy and intensity of vibration. The speed value is the best indicator to determine the overall vibration state of the equipment.
Main application scenarios:
Equipment status monitoring and evaluation standards: This is the most commonly used and universal vibration evaluation parameter. International standards and most industry standards use the effective value of vibration velocity to define the health status of equipment (good, qualified, unqualified, dangerous).
Fault diagnosis: Many common faults, such as imbalance, misalignment, looseness, etc., will produce significant responses in vibration speed.
Predictive maintenance: By monitoring the trend of vibration speed changes over the long term, equipment failures and maintenance cycles can be effectively predicted.
3.Acceleration - Unit: millimeters per second ⊃2; (mm/s ⊃2;) or gravitational acceleration g (1 g ≈ 9.8 m/s ⊃2;)
What is it?
Vibration acceleration is the rate of change of velocity over time, that is, the speed at which the vibration velocity changes. It is directly related to the force generated by vibration (Newton's second law: F=m × a).
What does it reflect?
It reflects the impact force and high-frequency components of vibration.
Main application scenarios:
High frequency fault diagnosis: It is very sensitive to early high-frequency impact faults such as bearing damage, gear meshing problems, and cavitation phenomena. These faults may not cause significant speed or displacement changes in the initial stage, but they will generate high acceleration.
Impact and force analysis: used to analyze transient events such as collisions and impact tests.
Structural dynamics: used for modal analysis to study the natural frequencies and modes of vibration of the structure itself.
The impact of actual conversion and frequency
In practical vibration analysis, the most crucial concept is that for the same vibration, the magnitude relationship between displacement, velocity, and acceleration strongly depends on the frequency of the vibration.
Why?
Because velocity is the derivative of displacement with respect to time, and the higher the frequency of a sinusoidal vibration, the faster its displacement changes, the velocity value will increase linearly with increasing frequency. Similarly, the acceleration value will increase with the square of the frequency.
Conversion formula (for peak harmonic vibration):
Assuming a vibration frequency of f (Hz), a single amplitude of D (mm), a velocity amplitude of V (mm/s), and an acceleration amplitude of A (mm/s ⊃2;), the following approximate relationship exists:
1)Velocity (V) ≈ 2 π f × displacement (D)
V (mm/s) ≈ 6.28 × f (Hz) × D (mm)
2)Acceleration (A) ≈ (2 π f) ⊃2; × Displacement (D) ≈ 2 π f × Velocity (V)
A (mm/s⊃2;) ≈ 39.5 × [f (Hz)]⊃2; × D (mm)
A (mm/s⊃2;) ≈ 6.28 × f (Hz) × V (mm/s)
Intuitive example: Comparison at different frequencies
This example best illustrates the problem. Assuming two vibrations with the same velocity value (both 10 mm/s) but different frequencies:
Parameter | Low frequency vibration (10 Hz) | High frequency vibration (1000 Hz) | Explanation |
Velocity V | 10 mm/s | 10 mm/s | Same vibration intensity |
Displacement D | ≈ 0.16 mm | ≈ 0.0016 mm | Low frequency vibration amplitude is large, with visible oscillation to the naked eye; The amplitude of high-frequency vibration is extremely small. |
Acceleration A | ≈ 628 mm/s⊃2; | ≈ 62,800 mm/s⊃2; | High frequency vibration has a huge impact force (about 6.4 g), which is 100 times that of low frequency! |
Summary and Analogy
To help you better understand the relationship between these three, let's make a vivid metaphor:
Imagine a child sitting on a swing.
Displacement (mm): The vertical height of the swing from the lowest point to the highest point. It tells you how much swing the swing has.
Speed (mm/s): The instantaneous speed at which the swing passes through the lowest point. It best represents the "momentum" and energy of swinging on a swing.
Acceleration (mm/s ⊃2;): At the moment when the swing is ready to swing back at its highest point, the speed changes from zero, and the acceleration is at its maximum. It reflects how strong the force is to make the child "cling" tightly to the swing seat.
Mutual Relationship and Selection Guide
These three physical quantities can be converted into each other through differentiation (differentiation) or integration (summation):
Velocity ≈ Differential of displacement ≈ Integral of acceleration
Acceleration ≈ differential of velocity ≈ second-order differential of displacement
In practical measurement, piezoelectric acceleration sensors are most commonly used because of their small size and wide frequency range. Through the built-in integration circuit, the measured acceleration signal can be integrated once into a velocity signal and twice into a displacement signal.
Application focus in engineering analysis and fault diagnosis
Parameter | Advantages and application scenarios | Corresponding to typical faults |
Acceleration | Extremely sensitive to high-frequency vibrations Suitable for high-frequency impact faults. Gear meshing, bearing defects (early stage), cavitation, impact friction. Commonly used for equipment status monitoring and early warning. | Bearing peeling, gear tooth breakage, blade impact. |
Velocity | The best correlation with vibration energy and destructive force International universal standards (such as ISO 10816) are parameters used to evaluate the overall vibration intensity (health status) of equipment. Good response to mid low frequency faults and stable spectrum morphology. The preferred choice for daily inspections and status assessments. | Imbalance, misalignment, looseness, resonance. |
displacement | Sensitive to low-frequency vibrations and static position changes. Pay attention to the absolute swing amplitude. Suitable for low-speed equipment (as displacement amplitude may be large) and situations where gap changes need to be monitored. The core parameters of rotor dynamics analysis. | Shaft bending, oil film vortex, surge, and excessive clearance between sliding bearings. |
Conclusion: Understanding the differences between these three units is the cornerstone of effective vibration analysis and equipment diagnosis.
Simple memory: mm tells you "how far to swing", mm/s tells you "how intense", mm/s ⊃2; tells you "how strong the impact is". They are linked together through a key bridge - vibration frequency.
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