The Lead to Linear Speed

A Readers Faces Torsional Issues. Can They Overcome Them With Better Sensing or Control? Should They Look to an Electronic Answer?

By Control Design

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"We've used lead screws in our linear motion applications for years because they give us high stiffness, very acceptable backlash, and simplicity. As performance requirements increase, we're going to have problems with the lead screws not accelerating quickly enough to high speeds. It looks like we have some torsional issues as well. Can we overcome this with better sensing and control? Is it time to look to an electronic answer?"

—From July '12 Control Design


Performance Limitations
As the market for linear actuators grows, so too will the demand for faster and longer actuators. When it comes to electrical actuators, lead screws have been the main go-to solution because they provide a high mechanical advantage in a compact envelope. Their position, speed and force can also be easily monitored with the application of a feedback device such as an encoder or a load cell. However, there are limitations to increased performance at longer strokes and higher speeds.

One of the potential problems when seeking higher speeds is not being able to accelerate fast enough to achieve a given peak velocity. For example, if an application has an actuator with a really short stroke of 7 in. and it needs to accelerate to a peak velocity of 20 in./s, it will have only 3.5 in. of stroke in which to accelerate, given a typical motion profile. However, the actuator may only be capable of a maximum acceleration of 90 in./s². In actuality, for this actuator to reach the target speed, acceleration would need to be 114.3 in./s².

The limiting factor is mass, as in Newton's second law, where force is equal to mass times acceleration. For rotation applications, the required torque would be equal to the polar moment of inertia times the angular acceleration.

This means that, given the same torque, the more mass the lead screw or motor has, the slower the acceleration will be. The same applies to its inertia. One solution could be to install a larger motor with more torque, but it will have greater rotational inertia because its mass is farther from the axis of rotation. A better solution would be a coreless motor with high acceleration and low inertia.

Another option would be to eliminate the motor's inertia altogether by having it rotate in one direction, using a simple transmission to reverse its output. A screw with a higher lead could also be used.

A problem inherent to long lead screws is that the angle of twist makes it behave like a torsional spring, storing and releasing energy with changes in angular momentum. This could lead to small errors in position. A method to correct for this would be to drive a little past the desired position to compensate for the position error. Another method would be to change the lead screw's geometry by switching to a larger-diameter hollow screw or preloading it in tension.

The only electronic solution is to monitor what is happening and respond accordingly. Proper placement of these monitoring devices is critical, and the closer the monitoring is to the output, the better the response. Most linear actuators monitor the angular position of the lead screw, but this does not account for the error caused by lead screw twist, backlash and changes in length from compression or tension.

It would be better to monitor the position with a linear-style encoder such as an optical transmissive, optical reflective or absolute magnetic style. The magnetic style is unique in that it has tiny grooves etched in it that a read head can sense (Figure 1). Magnetic-style encoders are robust and do not require recalibration.

Andrew Oudhraj,
mechanical engineer,

The Cost of Speed
Screws are, by design, mechanical reduction devices. They increase the torque output of the motor while reducing top end speed and acceleration. Speed and acceleration can be increased by changing the pitch; however, this will typically result in increased backlash and reduced accuracy.

Travel length will also limit the top end speed because the resonant frequency of the screw decreases as the length increases. Going with direct-drive linear motor technology eliminates all these problems, and will result in improved accuracy and a longer operational lifetime.

The higher speed and acceleration come at a cost. Linear feedback devices and linear motors tend to be more expensive than a rotary motor with a lead screw, and the technology requires a counterbalance system when used in a non-horizontal orientation.

Ron Rekowski,
director of product management,

Consider the Lead
As with most technical questions, I typically like to ask about 10 more clarifying questions before I make a recommendation.

For starters, it would help to understand what acceleration you are trying to obtain. Under ideal conditions, a lead screw can accelerate at 20 m/s2. If you require accelerations that are significantly larger, you will likely need to look at alternate drive train technologies, such as a linear motor, which is capable of 50 m/s2 or greater. If an acceleration of 20 m/s2 would satisfy your application's requirements, please read on to see what might be limiting your current system's performance.

There are several factors that will limit the acceleration that any screw is capable of. The most common limitation is the critical speed of the screw, also known as "whip." Critical speed is defined as the eccentric motion of the drive screw that occurs when the rotational velocity (rps) of a screw is exceeded. If the screw's critical speed is too low, then the ability to accelerate will also be limited.

Fundamentally, a screw's critical speed is a function of two variables: the diameter and the length of the screw.

where N is the critical speed, d is the screw diameter, and L is the length between bearing supports. Note that the formula assumes both ends of the screw are rigidly fixed.

The critical speed and the screw diameter have a direct relationship, so an increase in diameter will increase the critical speed. However, the critical speed and the screw length have an inverse relationship, so the longer the screw is, the lower the critical speed will be (Figure 2). Knowing this, the acceleration capability can be improved by either increasing the screw diameter, shortening the screw length, or some combination of both.

Another way to avoid critical speed issues, while increasing acceleration capability, is to change the lead of the screw you are using. The screw lead is the axial advance that is realized from one complete turn (360°) of the screw. For example, a 5 mm lead screw will have a linear translation of 5 mm per screw rotation. Increasing the lead of the screw will increase the speed and acceleration attainable without increasing the critical speed. Please note that by increasing the lead of the screw, you will sacrifice some mechanical advantage, and the torque required from the motor will increase as well.

If critical speed is not the issue, then there could be an issue with the amount of torque available. If you consider the components that make up the total required thrust force (acceleration force, force of gravity, and force of friction), the force required to accelerate your load is the largest contributor. It is possible that the motor you are using does not have enough torque to reach the accelerations that you are trying to achieve. There are relatively simple calculations that can be done to see what your maximum required torque is. Once that is known, you can make sure that your motor is properly sized to reach your desired accelerations.

Your question also refers to a solution with "better sensing and control." You don't mention what your current setup is, but if you are using a stepper motor that is an open-loop system, switching to a closed-loop servo motor solution, which certainly could be considered to have better sensing and control capabilities, could help in a roundabout way. As I mentioned, acceleration is all about torque. When you look at the continuous torque of a similarly sized stepper motor and servo motor (NEMA 23, 3 stack, for example), you will find that their torque densities are relatively close. The servo motor, however, has a peak torque region that a typical stepper motor will not have. This peak torque region allows the motor to put out some multiple of the continuous torque (our motors are rated at 3x) for a specified amount of time (our motors are rated for roughly 10–30 s based on winding and frame size). The ability to increase the torque output for a short period of time allows a smaller servo motor to solve applications where the acceleration torque requirements exceed that of the continuous torque rating on the stepper. With all of that said, though, increasing the size of the stepper motor —  to, say, a NEMA 34 — could give you a continuous torque rating that is large enough to satisfy the application's acceleration torque requirements.

If none of the above suggestions yields the acceleration performance you require, I would recommend that you start looking at alternate drive trains to meet your acceleration requirement. If high stiffness, low backlash and high accelerations are the goal, then we will likely be looking at a linear motor to meet your application's requirements. The linear motor does not have the mechanical limitations that screw solutions do. Additionally, if the linear motor solution you go with is a servo, you will gain the sensing and control functionality associated with a closed-loop system. The downside of this path is that a servo-driven linear motor system is typically more expensive than a rotary motor screw-driven solution.

Mike Szesterniak,
marketing manager — life sciences,
Parker Hannifin,

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