By Dr. Scott Smith

The motion of a machine tool’s axes is often characterized by the range of motion and maximum feed. That’s because that information tells the user the part size the machine can accommodate and how long it will take to make the required axis motions.

However, as spindle speeds and feed rates have increased, axis acceleration is becoming a limiting factor, and axis acceleration largely determines machining time. If the acceleration is not high enough, then the machine does not reach the maximum feed during some—or most—machining operations.

To see how this works, let’s consider a permanent-magnet DC servomotor, a common type of machine tool axis drive. For DC servomotors, the achievable acceleration is generally limited by the maximum current the motor can support, and the motor controller prevents the current from exceeding that limit. The current produces torque, and torque produces acceleration.

There are two algebraic equations that relate the acceleration, the velocity and the position of an axis:

where a is axis acceleration, t is time, v is axis velocity (feed), and x is axis position. The subscript “0” refers to the starting velocity or position.

Let’s assume the machine tool in question will be used for high-speed machining of aluminum. As a general principle, we desire the highest spindle speed possible, but the spindle speed is limited by the bearings, and commercially available spindles with CAT 40 or HSK 63 tapers are typically available on machines in the 20,000- to 25,000-rpm range.

The milling feed for such a machine is calculated by the feed per tooth (chip load) times the number of teeth per revolution times the spindle speed. Using a tool with four teeth and a chip load per tooth of 0.2mm, the required feed is:

Only 20 m/min. is required for the working feed, yet many high-speed machines advertise substantially higher maximum feeds. Why? One reason is to speed up noncutting motions, such as rapid traverse and tool changes. Another reason is to account for chip thinning in small radial immersion cuts with ballnose tools.

Let’s say the machine in question has 0.5g acceleration, which is typical. The “g” refers to gravitational acceleration, which is about 9.8 m/sec.

^{2}. Starting from rest (v

_{0}= 0 and x

_{0}= 0) and using the maximum, current-limited acceleration, the time required to reach the full useful feed of 20m/min. is:

About 68 milliseconds isn’t much time, but, in that time, the machine travels:

Let’s take a typical move on one side of a rectangular pocket as starting from rest, moving 50mm and then stopping. For that move, acceleration and deceleration together would take 0.136 seconds and consume 22.68mm (nearly half of the total distance to be moved). Moving the remaining 27.32mm would take:

What’s the bottom line? The total time required for the 50mm move would be 0.218 seconds. Because acceleration is limited and the move is short, the axis would spend more than 45 percent of the distance (22.68mm out of 50mm) and more than 62 percent of the time (0.136 seconds out of 0.218 seconds) below the maximum feed.

One of the reasons NC verification software often miscalculates machining time, especially in HSM, is because it fails to account for acceleration and deceleration. Neglecting acceleration and deceleration would produce a machining time estimate of 0.150 seconds (distance/feed) for this 50mm move, while the real time would be 0.218 seconds—nearly 50 percent longer. That is a real danger when basing a cost estimate using machining time estimated in verification software. As long as acceleration is limited, the time estimation problem becomes worse as the average moves become shorter and as the programmed feed becomes higher.

Increasing the commanded feed of the machine doesn’t help, even if the tool could take the increased chip load. If the maximum commanded feed in this example were more than about 29.7 m/min., then the axis would not reach full feed before deceleration started, even at maximum acceleration.

Increasing acceleration is the only way to ensure the machine operates at full feed most of the time. There are essentially two options to increase acceleration: increase the power of the drive or decrease the mass that has to be accelerated. These parallel objectives have become the driving forces behind the design of new machine tools for HSM.