Motion System Design
Settling the stage

Settling the stage

Many factors influence the positioning accuracy of a linear stage on a machine tool. The one most often overlooked, settling time, may be the most important.

The goal is to produce the perfect part. Machine tool designers are inching closer with new motion technology that squeezes almost every micron of imprecision out of cutting, positioning, shaping, and assembly functions. But even new technology has limits. To chip away at those last few microns, designers need to refocus on machine dynamics, particularly settling time.

Settling time is a measure of how long it takes a motion system to come within a set distance of a desired point after the initial positioning move. It can also be a measure of how long it takes to lock in on a desired velocity. For equipment that makes short, quick, repetitive moves, such as punch presses, pick-and-place machines, and laser cutters, settling time can mean everything in terms of performance, drive sizing, and stage design.

Linear motion stages can take 1.5 to 2 times longer than the programmed move time to settle within the positioning tolerance (static accuracy). For example, if a stage moves to a rough position, 2 to 5 times the tolerance, in 30 msec, it may take an additional 30 msec to pull within tolerance. Over a series of moves, settling times quickly accumulate, effecting the desired throughput.

Tolerances and resolutions

To shorten settling times, designers should look at the whole system. It may even be necessary to conduct an FEA analysis on the interactions between resolution and tolerance.

Digital motion controllers determine position by counting. The number of counts per unit distance determines system resolution. For example, a motion stage using a linear encoder with 25 lines/mm and a 4x multiplier in the controller has a resolution of 100 counts/mm, or 10 μm. For a 40-mm move, the controller sees 4,000 counts and sends the appropriate command to the motion programmer. The programmer sends instructions to the stage, which then moves the commanded distance to its programmed position tolerance. That tolerance depends on the mechanical capability of the stage.

Tolerances are set in controls as a number of counts. They affect the overall commanded static accuracy of the stage, measured at the stage feedback device. This accuracy is different from the total mechanical system accuracy at the part because of the design of the machine, stiction, traveling friction, temperature, encoder location, load location, and other factors. For a tolerance of ± 20 counts, a move of 4,000 counts could be considered complete when the stage reaches 3,980 to 4,020 counts. With a 10 μm resolution, this is a position accuracy of ± 200 μm, which may be insufficient for the application.

So it's important to specify the tolerance when defining position accuracy for one or more moves in a time frame. Customers will usually state this as: "The stage will move 1 mm and settle to within ± 3 μm in less than 40 msec." The machine tool builder then knows to control the motion and stage settling oscillations to within ± 3 μm. If this tolerance is large enough, the machine tool builder may not have to alter the design to gain the desired throughput.

Weighty matters

But many machining functions, such as those called for in contouring moves, require increasingly tighter tolerances. The settling time of a linear stage can have a dramatic affect here. The machine controller does not consider a move complete, and therefore will not execute the next command, until the stage is in position. If settling takes too long, it can ruin the part.

The material used in the stage can hinder or help settling times. While all materials respond to step and vibration inputs, steel and aluminum take longer to settle, making them unsuitable for motions with small tolerances. Cast iron meehanite, the mainstay of most machine tools, and polymer concrete quickly dampen vibrations induced by stage motion.

Designers must examine the individual components of each subsystem to develop a light, stiff system with good vibration dampening features.

Motion stages are made up of three main sections: a moving platform, a stationary base, and the drive system. The motion energy that drives the moving component transfers to the stage base by Newton's third law of motion (every motion has an equal and opposite reaction . . .). From here, the energy moves to the machine base. If the base is not sufficiently massive or securely anchored to the floor, the stage base may oscillate, increasing the settling time of the whole system.

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For example, consider a linear scale. The scale usually attaches to the machine base and the reader head to the moving element. When the stage slows to a stop, part of the braking energy transfers to the base, which may cause it to move. Whether the reader head or base scale moves, though, the controller sees signal counts indicating a change in position. If the new position is outside the tolerance window, the controller issues commands to move the stage to the new position. The same effect can occur from machine vibration or drive screw oscillation.

Controller drive algorithms can produce a similar effect. A step input will command a full digital ac output, causing the drive to start the motor full on for high acceleration. This results in a large energy transfer to the motion stage. Deceleration must remove this energy to limit residual vibration to the system.

Some controllers will gently accelerate and decelerate a stage, leaving less residual motion and speeding settling times. These controllers often use PID algorithms, velocity feedforward, look-ahead processing, or bell-shaped acceleration profiles to impart less jerk to the system.

Driving the motion

Most motion systems can be defined as spring-mass systems. Applying a step-function force to one usually results in an oscillation. This natural frequency can be found through:

k = spring constant
m = mass

Typical natural frequencies for positioning stages are 50 to 150 Hz.

This factor affects the amount of time available for a move and the subsequent settling. With friction, mass, and spring forces, however, the problem changes from a simple exponential equation to a second order differential equation.

The system's drive must move the stage to the desired position within the tolerance to allow time for any residual stage oscillations to subside. This may mean using an oversized motor and drive amplifier to decrease acceleration and deceleration time.

Friction in the stage ways can help dampen stage-motion oscillations. However, it should not be so large that the stage can't oscillate back to the intended position or that it increases the load on the motor during acceleration and linear motion. Changing the amount of friction may be as simple as changing the lubrication type or as complicated as determining new preloads on the ways.

The greatest contributor to stage oscillation is the drive screw itself. Anyone who has tapped a steel rod or hit a baseball with an aluminum bat can attest to its vibration capability.

To decrease the drive-screw oscillation time, engineers can:
• adjust the preload of the ballnut
• use a fully supported mounting
• select larger diameter drive screws
• choose drive screws made of other material
• install stiffer duplex drive bearings
• use special motor couplings

All of these methods, though, have drawbacks including increased cost, assembly, and test times.

Linear motor option

Another option is eliminating the mechanical drive system altogether. Many machine builders are doing this, replacing the mechanical system with a linear motor.

In its simplest form, this device is a directly coupled force producer. Accuracy and settling time, therefore, depend on the positioning controller, servo stiffness, and machine design.

In addition, a linear motor drive contains few parts. Its two pieces do not touch, so it operates well in high duty-cycle machines. Dynamic stiffness is on the order of 355 N/μm (2.5 μm deflection for a 889.6 N force). It eliminates drive screw ringing, windup, motor coupling windup, support bearing deflection, and mounting errors.

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Eliminating the mechanical portion of the drive train greatly eases the restrictions on the control. There is no gear slop or drive stiction and friction to overcome. Signals sent to the drive can be acted on almost instantaneously. As a result, amplifier gain can be increased over that of a mechanical drive system. Coupled with digital feedforward techniques, these effective gains can be more than double those of a mechanical system.

In addition, the higher the gain, the less the axis lags behind the commanded position. This reduces the dynamic error, and brings the machine one step closer to producing the perfect part.

Minimizing settling time

The factors that directly influence system behavior include:
• natural frequency of the motion stage
• natural frequency of the drive screw
• stiffness of the drive nut
• friction of the ways or linear bearings
• applied step input force
• move distance
• motor inertia
• system inertia
• lead screw compliance
• motor coupling compliance
• encoder placement and resolution
• load inertia

Indirect factors include:
• control system processing capability
• servo control (step function, PID, acceleration and deceleration type, and so on) and implementation
• torque feedback
• servo amplifier response and bandwidth

Finding the natural frequency of a stage

If the move time for a laser piercing operation calls for a process time of 10 msec per hole and the goal is to produce 1,000 holes per minute with each hole 1-mm apart, the calculations would be:

Without accounting for settling, multiply the process time (10 msec) by the number of holes (1,000) for a time of 10 sec. Subtracting this time from production time (60 sec - 10 sec) leaves 50 sec for moves between the holes. Dividing this result by the number of holes leaves the engineers with 50 msec of time available per move.

Assuming a triangular move profile this allows 25 msec each for acceleration and deceleration.

The designer needs a motor and drive that can provide an acceleration of 1,600 mm/sec2 or 0.16 g.

Accounting for a 30 msec settling time using the same information as above, subtract the settling time from the move time (50 msec - 30 msec) for a result of 20 msec per move. Using the same triangular profile, this allows 10 msec each for acceleration and deceleration. The selected motor would have to provide an acceleration of 10,000 mm/sec2 or 1 g.

Higher acceleration, however, does not always mean quicker settling. In some applications, it increases settling time to a point where performance degrades by the amount of energy the system must dissipate.

Preston Miller is CNC manager, drive products, at GE Fanuc Automation, Charlottesville, Va.

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