Cutting Tool Engineering
April 2010 / Volume 62 / Issue 4

Limit the bending moment

By Dr. Scott Smith, University of North Carolina at Charlotte

All images courtesy of S. Smith

Figure 1: Static load is applied through a hydraulic cylinder at the right side and the deflection is measured using capacitance gages during toolholder tests for stiffness, damping and capability to support bending moment loads.

Bending moment is an important consideration in machine tool spindles because it causes the tool to separate from the toolholder or the toolholder to separate from the spindle.

A moment is a force multiplied by the distance between that force and the point of interest measured in foot-pounds or newton-meters. A bending moment exists in a mechanical structure when an applied moment causes that structure to bend. All tool/spindle connections have bending moment limits, beyond which the connection may break or the toolholder pulls out of the spindle.

Let’s look, for example, at milling a slot in aluminum with a 2-flute tool at a chip load of 0.2mm per tooth and an axial DOC of 5mm. The maximum force seen by the tool is about 850 N. If the distance from the spindle face is 150mm, then the toolholder supports a bending moment of about 127 Nm. This number will increase if there are more teeth simultaneously cutting, the material has a higher specific power, the axial DOC is larger, the chip load is higher or the distance from the tool tip to the spindle face increases.

Figure 2: Bending moment vs. rotation and drawbar force.

Figure 3: Bending moment vs. rotation for a CAT and an HSK connection.

Different styles of toolholders exhibit different responses to applied bending moments. In a project at the University of North Carolina at Charlotte sponsored by the National Center for Manufacturing Science, a variety of toolholder styles, classes of fit and drawbar forces were tested for stiffness, damping and capability to support bending moment loads. In the evaluation of bending moment, a static load was applied to the end of the tool in a test stand and the resulting tool rotation was measured. Figure 1 shows the measurement setup, with the static load being applied through a hydraulic cylinder at the right side and the deflection being measured using capacitance gages.

Figure 2 shows the measured tool rotation for an HSK 63A connection, with drawbar forces from 25 to 55 kN. It can be seen that increasing the drawbar force makes the connection stiffer, that is, a lower slope means less rotation for the same force. That makes sense because a higher drawbar force does a better job of keeping the spindle face in contact with the toolholder.

The HSK connection derives much of its stiffness from the face contact. As the drawbar force increases, the improvement decreases (45 kN and 55 kN are almost the same). There is a significant change in slope for all of the lines toward the right side of the graph. That means as the bending moment increases, the rotation begins to increase at a faster rate. In other words, when the bending moment gets large enough to separate the toolholder from the spindle face, stiffness decreases.

In machining, this is a dangerous situation because the toolholder can pull out of the spindle with only a small change in load once separation starts. All HSK connections have a bending moment limitation that should not be exceeded during machining.

A CAT 40 connection does not exhibit a similar change in slope. The separation happens gradually along the tapered surface. While such connections are significantly less stiff than HSK connections, they do not exhibit sudden decreases in stiffness. Figure 3 shows the bending moment compared to the rotation for an HSK 63A connection with a 10-kN drawbar force and a CAT 40 connection with a 17-kN drawbar force. The curve for the CAT connection is almost a straight line, meaning that there is almost no stiffness change in the connection as the bending moment increases. When the face contact exists, the HSK connection is significantly stiffer than the similar-sized CAT connection. However, once the face separation starts, the HSK connection rapidly loses stiffness. For large bending moments, the CAT connection is stiffer than the HSK connection. CTE

About the Author: Dr. Scott Smith is a professor and chairman of the Department of Mechanical Engineering at the William States Lee College of Engineering, University of North Carolina at Charlotte. He specializes in machine tool structural dynamics. Contact him via e-mail at

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