Belt, spindle, rack and pinion or linear motor?

Hi, Mechatronitians! Welcome to a new chapter of SINADRIVES’ blog.

Today we will be dealing with how to choose a transmission system.

November 2020

Belt, spindle, rack and pinion or linear motor? This is the million-dollar question every engineer faces when it comes to designing a linear motion system. Sometimes the answer might be an obvious one, other times it is a very complicated decision. Here we would like to share some tips with you. There is a wide range of transmission systems available today. For simplification, here we are going study the following systems: toothed belt, trapezoidal thread, ball screw, rack and pinion and linear motor. These are the most commonly used in speed-controlled applications, when it comes to speed and acceleration of positioning. In doing so, we leave aside other systems such as chains, cables, rollers or flat belts.

1. Duty cycle

The first thing to be taken into account is the duty cycle. This is defined as the ratio between working time and pause time. For example, if a machine works for 1 second and pauses for 1 second, the duty cycle is 50 %. If the machine works for 8 seconds and stops for another 2, then the duty cycle is 80 %.

Trapezoidal spindles are not recommended if the duty cycle is high (cycles over 30%), as their wearing off is too quick in such applications.

2. Stroke

The second factor to take into account is the stroke. Speed is limited by rotation speed if the stroke is over 2000 mm. In this case, the spindle’s rotation speed is highly limited and impedes dynamic movements or movements requiring very high precision. Furthermore, in addition to vibrations, the appearance of resonances makes position control very difficult.

3. Force

The third factor is the force required to move a given weight. The following formula can be used for a quick calculation:

F = Fvc + Fac

where Fvc is the force required for movement at constant speed, and Fac is the force required for the movement, with acceleration or deceleration.

For a load in horizontal movement at constant speed:

Fvc = m x g x µ

m, kg – load to move

g, m/s² – acceleration of gravity, g = 9.81 m/s²)

µ – friction, 0.05 for ball guide, 0.15 for rods and Vulkollan wheels, and 0.2-0.3 for friction guides.

For a load in horizontal movement with acceleration:

Fac = m x a

m, kg – load to move

a, m/s²– acceleration

For a load in vertical movement at constant speed:

Fvc = m x g x µ + m x g

For a load in vertical movement with acceleration:

Fac = m x a

Force indicates whether a rack and pinion transmission system will be good enough for the job, or if another type of transmission will be more efficient. It is mainly in vertical applications where this factor is decisive. Special attention is required in terms of the diameters of the belt or pinion, as the force the system may deliver depends on them. The higher the number of teeth at work, the more force they can deliver. The same goes for the toothed belt: the wider it is, the more force it can deliver.

4. Performance and efficiency

Below are the average performances of the systems described:

Type of machine	Trapezoidal screw	Ball screw	Toothed belt	Rack and pinion	Linear motor
Efficiency	0.2 – 0.3	0.9-0.95	0.9-0.95	0.9	0.97

5. Precision and repeatability

Out of the 5 systems mentioned, the linear motor, the ground ball screws, and the trapezoidal spindles (machined) offer the best precision. The rack offers somewhat lower precision, and finally the spindle offers the least precision of the five. Resonances and vibrations appear since the toothed belt is an elastic element, although repeatability may be below 0.1 mm.

6. Some general rules of thumb

• The spindle axis is still the best alternative for high force applications with a stroke up to 2000 mm.

• The trapezoidal spindle offers an economical solution for very low duty cycle applications.

• Linear motors and rack and belts are the best options for dynamic applications requiring low maintenance, as they do not need greasing.

• Linear motor or rack and belt are recommended in applications with a stroke over 2000 mm.

The table below sums up the main features of the transmission systems discussed in this post:

SYSTEM Type / Feature	Trapezoidal screw	Ball screw	Toothed belt	Rack and pinion	Linear motor
Velocity	–	0	+	+	+
Acceleration	–	0	+	+	+
Duty cycle	–	+	+	+	+
Precision	0	+	0	+	+
Repeatability	+	+	0	+	+
Long stroke	–	0	+	+	+
Maintenance	–	0	+	0	+
Price	+	–	+	0	+

NOTE: “-“negative or limiting feature; “0” neutral or average feature, “+” positive feature or strength.

Linear motor technology is an improvement on traditional transmission systems, although it has its limitations. This is true in the case of vertical axes and in tool machining applications, due to the heat such systems generate.

That is all for today. Use the blog’s menu to add any comments. Please let us know if there are any subjects you would like us to discuss.

We hope you find the information provided useful. Please subscribe to our blog to keep up to date with the latest news and technical features about Linear motor stages and Co. See you in the next chapter.

Best wishes,

The SINADRIVES Team