Optimizing Rotary Toolholder Performance: Navigating the Nuances of Balancing Quality and Tolerance

Article is based upon information provided by Haimer
​written and edited by Bernard Martin

With rotating bodies, imbalance is an omnipresent phenomenon. A typical example are rotating tools on machine tools.

Because unbalance creates a centrifugal force, it increases linearly with the unbalance and squares with the number of rounds. The faster the rotor rotates, the more noticeable the unbalance. But how does unbalance arise, how can it be measured and how can it be eliminated by balancing?
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On the following page we have put together the theoretical fundamentals of balancing, the basis for tool balancing.

As a side note to this discussion, there is sometimes confusion over use of the words "imbalance" and "unbalance". Imbalance is the noun meaning the state of being not balanced, while unbalance is the verb meaning to cause the loss of balance.

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Causes of Unbalance

In rotating toolholder, addressing imbalance is crucial for efficiency and longevity. Imbalances arise from uneven mass distribution, design asymmetry, or manufacturing inaccuracies, leading to detrimental centrifugal forces during operation.

Balancing, achievable through mass adjustment or component alignment, mitigates these forces. This process involves precise measurement and correction to adhere to industry quality standards, though achieving absolute balance is challenging due to inherent mechanical and environmental factors.

Here's a quick overview:

• Unsymmetrical design of the rotor (e.g. gripping groove on tool holders as specified in DIN 69871 or clamping screw on Weldon tool holders).
• Unsymmetrical distribution of mass due to concentricity errors caused by manufacturing tolerances, e.g. concentricity of the tool outer diameter with respect to the taper.
• Alignment errors during assembly of a rotor consisting of several components, e.g. milling spindle and tool holder, tool holder and tool.
• Concentricity errors in the bearings of a rotor, e.g. the spindle bearing.

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What is Unbalance?

Static balance in rotary toolholders refers to the condition where the center of gravity is aligned with the axis of rotation, ensuring no lateral movement when the toolholder is stationary or rotating.

Dynamic balance, on the other hand, addresses both the static imbalance and the couple imbalance, ensuring that the toolholder remains stable and does not wobble during high-speed rotation, which involves balancing across two planes. Achieving dynamic balance is crucial for toolholders in high-speed applications to minimize vibration and wear.

Let's dig into some details:

​​STAT­IC UN­BAL­ANCE

Static unbalance in rotary toolholders manifests when their center of gravity doesn't align with the axis of rotation, leading to centrifugal forces that can cause significant issues when the rotor spins. This kind of imbalance can be detected even in non-moving rotary toolholders and is correctable by adjusting the mass distribution within a single plane. However, correcting static unbalance (a.k.a. Single Plane Balancing) might not address other types of imbalance, like couple unbalance, that can still affect the rotor's operation.
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MU = unbalance mass (in g)
r = distance of the unbalance mass from the axis of rotation (in mm)
M = rotor mass (in kg)
e = distance of the centre of gravity from the axis of rotation (in μm)
S = center of gravity
FF = centrifugal force
Value of static unbalance: U = MU • r = M • e
Unit of unbalance: [U] = g • mm = kg • μm

Static Unbalance

COUPLE UNBALANCE
Couple imbalance occurs when a toolholder's center of gravity is aligned with its rotation axis but still experiences a tilting moment during operation due to the distribution of mass. This condition, detectable only when the toolholder is in motion, results from opposing centrifugal forces that create no lateral movement but cause a rotational tilt.
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Correcting this type of imbalance requires adjustments in two different planes (a.k.a. Dual Plane Balancing) to ensure smooth rotation without wobble
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​MU1, MU2 = unbalance masses (in g)
S = center of gravity
r = distance of the unbalance masses from the axis of rotation (in mm)
M = rotor mass (in kg)
FF1, FF2 = centrifugal forces
MU1 = MU2
FF1 = FF2

Couple Unbalance

DY­NAM­IC UN­BAL­ANCE
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Dynamic imbalance in a rotary toolholder refers to a scenario where both static imbalance and couple imbalance are present, causing the toolholder to experience tilting and wobbling during operation. This complex form of imbalance necessitates correction in two planes for the toolholder to rotate smoothly at varying speeds, thereby reducing vibration and wear on associated machinery.

In case you were wondering the ideas of dynamic balance was developed by R.S. Berkof, G.G. Lowen​ in the seminal work A New Method for Completely Force Balancing Simple Linkages. ​

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What is "Balancing"?

Balancing aims to rectify the unsymmetrical distribution of mass ensuring even distribution of the mass for optimal harmonic performance.

This is done by:

1. applying mass - a clamped weight to balance car tire
2. removing mass - by drilling a hole
3. adjusting mass - by adding balancing rings, screws
   

Three methods of correcting unbalance in a rotary toolholder

BAL­AN­CING IN A SINGLE PLANE (STAT­IC BALANCING)

​Balancing in a single plane corrects the static imbalance by adjusting the toolholder's center of gravity to align with its axis of rotation, minimizing eccentricity. However, this method doesn't correct the couple imbalance associated with dynamic unbalance, which remains unaffected.

BAL­AN­CING IN TWO PLANES (DY­NAM­IC or DUAL PLANCE BALANCING)​

​Dynamic or dual plane balancing involves correcting both static and couple imbalances in a toolholder, achieving thorough compensation. The process allows for the selection of any two balancing planes, ideally positioned as far apart as possible, to ensure comprehensive balance throughout the toolholder's operation.

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Measuring Unbalance

The first step in correcting imbalance is to determine where unbalanced mass is located in a single plan or 3 dimensional plane.  To do this, the tool holder is inserted into the balancing spindle and made to rotate.

This process begins by rotating the toolholder on a balancing spindle, where force sensors detect centrifugal forces.

Measurements are taken in two planes, generating a sinusoidal signal that changes with the spindle's rotation.

The magnitude and angle of this signal are analyzed to calculate the imbalance, which informs the necessary compensation adjustments.

​This method ensures precise balance correction by adapting to changes in the balancing plane positions.

Balancing Quality - G Values

The two primary factors to determine permissible unbalance, also called the balancing tolerance, are the mass of the rotating part (G) and the maximum operational speed (RPM). To put a more technically, the grade G values in toolholder balancing are determined based on the permissible residual unbalance for a given rotation speed and the weight of the rotary toolholder, as outlined in standards such as DIN ISO 1940-1 (previously VDI guideline 2060).

​These values guide the maximum allowable unbalance to ensure operational safety and efficiency, factoring in specific operational conditions.

Each grade G value (previously: Q) corresponds to a different level of balancing precision, tailored to the rotor's intended use and operating environment.

G Values are most commonly described as a the number of gram-millimeters of imbalance at a given rational speed.  In other words how much mass is out of balance at a given RPM.  

Typically grinding machines are measured at a G1.0 while CNC machine tool spindles are held to G2.5. G6.3 is also used for many common toolholders that are not considered "balanced". G11 is sometimes used as well.  

Drive shafts in cars are measured at a G16 value while car wheels and rims are typically measured at G40 values. Larger G numbers cause more structural stress.

Permissible residual unbalance. The x axis is the spindle rotation speed while the y axis represents the residual unbalance in relation to the rotor weight.

Achievable Accuracy

Keep in mind that the balancing quality grade is only valid for a specific rotation speed of the the toolholder. e.g. G2.5 at 25,000 RPM.  This permissible residual unbalance is calculated from the balancing quality grade, the rotation speed and the weight of the toolholder. Here's the actual formula: 

Uper = (G•M)/n • 9549

• Uper = Permissible residual unbalance of the rotor in gmm
• G = balancing quality grade
• M = weight of the rotor in kg
• n = rotation speed of the rotor in rpm
• 9549 = a constant that is produced

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HERE IS AN EX­AMPLE

• A milling cutter is clamped in a collet chuck.
  
• The total weight is 0.8 kg.
• The milling cutter is to be used at a service speed of n = 15,000 rpm.
• The spindle manufacturer requires a balancing quality grade of G = 2.5.
• Permissible residual unbalance Uper = 1.3 gmm.
  

In the above example there is a permissible residual unbalance of 1.3 gmm. To illustrate
this value it is useful to convert the unbalance to eccentricity.

Uper = M • eper
eper = Uper/M =1.3 gmm/800g = 0.0016 mm = 1.6 μm
Therefore the centre of gravity of the tool holder can be offset by max. 1.6 μm from the axis of
rotation. During balancing the axis of rotation is assumed to be the axis of the taper or HSK.
However, in the milling machine the tool rotates about the axis of the spindle.

Even new spindles TIR of up to 5 μm (equivalent to eccentricity of e = 2.5 μm).

ANOTHER EXAMPLE

Balancing quality G = 1
Rotation speed n = 40.000 rpm
Tool weight M = 0.8 kg
Uper = 0.2 gmm
eper = 0.3 μm

This permissible eccentricity cannot be achieved in practice. Even good spindles have a repeatability of 1-2 μm when the tool is changed. Even small amounts of dirt, grime or swarf can worsen the result significantly.

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Complexities of Achieving
Ideal Balance in Milling Spindles

The total unbalance in a milling spindle is influenced by a multitude of factors, including the inherent unbalance of the spindle, errors in concentricity within the spindle  (The symmetry axis is not the axis of rotation, openings for coolant, etc), and distortions in the spindle clamping system (Springs, drawbar, etc).

Additionally, the alignment and unbalance of the tool holder, along with errors in the pullstud installation torque, and event the tool itself, play significant roles. Consequently, achieving a residual unbalance of less than 1 gmm in practical settings is often considered unrealistic.
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