Measuring and managing drawbar forces

Figure 1: Measured FRFs for a CAT 50 holder in a spindle with 12kN drawbar force (left) and 32kN drawbar force (right).

The metal-removal rate that can be achieved while milling depends largely on the dynamic characteristics of the machining system—including toolholder and cutting tool—as seen at the tool tip.

In particular, the dynamic stiffness as characterized by the frequency response function (FRF) sets limits on machining performance. The dynamic characteristics as seen at the tool tip are often strongly affected by the characteristics of the connection between the toolholder and the spindle. 

Considerable effort has been devoted recently to the computation and measurement of the static stiffness, dynamic stiffness, accuracy, repeatability, torque capacity and maximum speeds of various toolholder/spindle interfaces.

Intuitively, it would seem the best connection would be the stiffest one. If that were the case, the surface finish should be as smooth as possible, meaning that a polished, shiny surface would be preferable. A close fit between the toolholder and the spindle would also be desirable, as would a high drawbar force. However, intuition is often wrong, and measurements clearly indicate that those interface conditions can be detrimental to cutting performance.

The reason that intuition can fail is we often think statically. Static stiffness is an easy-to-understand concept. The higher the static stiffness, the smaller the tool deflection in response to an applied static force.

However, when milling, the cutting force is not static. It is variable because the teeth enter and leave the cut as the tool rotates, and because as the tool vibrates it changes the thickness of the chip. Therefore, the cutting performance depends on the dynamic stiffness (a combination of static stiffness and damping), and the relationship is usually expressed in a FRF. 

Figure 2: The product of static stiffness and damping vs. drawbar force for four different spindle connections. Stiffness and damping play the same role in cutting performance. High drawbar forces increase the stiffness, but reduce the damping. In these ranges, they decrease the damping more than they increase the stiffness.

The spindle/toolholder interface provides stiffness and damping, and the conditions of the interface affect both parameters. Increasing the drawbar force, for example, increases the static stiffness, which is good, but it reduces the damping, which is bad. 

Figure 1 on page 19 shows two measured FRFs. In these FRFs, small peaks mean the dynamic stiffness is high, and large peaks mean the dynamic stiffness is low. Static stiffness and damping play the same role in the FRF. They appear side by side in the equation, and it is their product that controls the size of the peaks. The measured system in both cases is the same CAT 50 toolholder mounted in a spindle, but in the left figure the toolholder has a 12kN drawbar force, and in the right figure it has a 32kN drawbar force. 

The graphs show that the increased stiffness resulting from the increased drawbar force is overpowered by the loss of damping. Surprisingly, the mrr for the case with the higher drawbar force is about 20 percent lower than the case with the lower drawbar force. This trend is also seen for other connections (Figure 2). Here, the product of damping and static stiffness is shown vs. drawbar force for two CAT 40 and two CAT 50 connections. In each case, the higher mrr would have been achieved with the lower drawbar force for the range of drawbar forces tested.

Clearly, there is a limit to how low the drawbar force can be. If the drawbar force were too low, the toolholder could wallow in the spindle taper, and accuracy and fretting corrosion could become issues. Generally, the drawbar force is not easily changed intentionally by an end user. 

However, machine tool cutting performance is directly connected to the drawbar force. Ensuring repeatable cutting performance from the machine tool means ensuring repeatable drawbar force. As a result, drawbar force should be measured periodically to verify that it is within the manufacturer’s specifications. Several manufacturers offer drawbar dynamometers, the instrument used to measure drawbar force. This equipment is easy to use, inexpensive and should be a standard machine tool maintenance item in every shop. 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 kssmith@uncc.edu.