Friday, September 30, 2022

A Tutorial on stepper motor torque calculations

 A Tutorial on stepper motor torque calculations

A question oft asked on MYCNCUK is "how big a motor do I need?". There is no simple answer to this, and the options are usually:
a) follow someone elses build and copy theirs;
b) take a guess and try again if you are wrong; or
c) work it out, which is the subject of this tutorial.

When choosing a stepper motor you need to know:
a) what power and torque output is required at a given speed
b) what electrical characteristics are appropriate to acheive that

What I have tried to do here is the engineering approach, by showing the calculations needed to get some idea of power, which then dictates motor size. I am concerning myself with a stepper motor directly driving a leadscrew to move the gantry, table, etc. Similar calculations can, however, be done for belt drive or geared up/down with timing pulleys.

DISCLAIMER: This tutorial is to give you an insight into how to approach the selection of a motor. I take no responsibility for any consequences of following this tutorial and you alone are responsible for your choice and purchase of motors etc.

So lets start with assessing what torque might be needed. The basic properties we need to be concerned with start with the moving element, be it table, gantry, milling head or whatever, and that is its mass. We need to know this, either by actually weighing it, or by estimation based on the volume of material and the density of the material or by adding up the weights of the component parts.

A gantry for a router would be the weight of the slides (from manufacturer data) plus the weight of the aluminium parts (calculated using 2750 as the density) and the weight of the steppers, router, etc. Typically on a small router this would be in the order of 20kg, which we will use as our worked example - yours will be different. If you work out the motor needed for the heaviest element, then this is the worst case and the same motor will work for everything else (although you may chose to do the calculations for each axis in turn to see if there are saving to be made).

So, we know what our moving part's mass is. The motor has to make this component move, first by accelerating it and then maintaining that velocity. To do so it must first overcome the initial friction (stiction) and then maintain the drive against the friction of the moving parts and against any cutting forces. Minimising that friction is therefore crucial. For linear or rolling bearings the friction can be calculated and the stiction is generally very small. For dovetails (as on a mill) it is not easy to calculate and is best measured with a spring balance, firstly to determine what pull is required to get the table moving and then to maintain that movement. This might be as much as 15kgf initially, dropping to 5kgf.

The second aspect to accelerating the moving item is to overcome its inertia (the tendency of something to remain at rest) - this is true even if friction were zero.

The motor turns the leadscrew to convert rotational motion into linear motion. There is friction here too, expressed as the efficiency of the leadscrew. This is typically 80% for ballscrews and as low as 30% for trapezoidal screws (bronze or delrin nuts on steel) and inertia, as the screw itself has inertia which is dependent on its mass and its length.

Now we have all the elements we need.

So, considering the frictional component of the torque, this is given by:

Torque = F * p/(2pi * e)

where F is the force to be overcome in Newtons, p is the screw pitch in metres and e is efficiency.

For this example I shall assume a TR12x3 trapzoidal screw 12mm dia, 3mm pitch.

The force to be overcome is, as said above, either the stiction or the kinetic friction plus the cutting forces. For the purposes of simplicity
assume the cutting forces range from 5N for wood to 20N for alloy using the sort of spindles/cutters found in hobby sized machines up to 75N for steel on a mill.

The frictional forces are calculated from the mass of the load and the friction coefficient:

F = M * g * Fc

where g is gravity, which can be taken as 10

Typical static friction coefficients for common sliding mechanisms are:
0.003 for a ball slide,
0.01 for low-end ball races on aluminum channel,
0.05 for teflon on steel,
0.16 for bronze on steel
1.10 for cast iron on cast iron.

For most of these the kinetic frictional coefficient can be taken as the
same, although it is around 0.2 for greased cast iron to cast iron.

Assuming a low cost router using ball races and our 20kg load the frictional force (from equation 2) is 20 * 10 * .01 = 2N. Add to this the cutting force for wood at 5N and the force to be overcome is 7N, therefore the torque (from equation 1) is:

T = 7 * .003/(2pi * .3) = 0.01Nm

This doesn't sound a lot when motors are rated at 1 - 3Nm, but we haven't finished yet.

The second calculation is the inertia of the moving item, expressed in terms of the inertia seen by the motor. The symbol we use for this is J(load) and it is calculated thus:

J(load) = mass(load) * pitch^2/(2 * pi)^2
where mass in Kg, pitch in metres gives inertia in kg m^2
[note: ^2 means raise to the 2nd power, e.g. square it]

In our example we will use a trapezoidal TR12x3 single start screw to move this 20Kg gantry, so from equation 3, J(load) = 20 * 0.003^2/40 = 4.5 x 10E-06 kgm^2 (the 40 is a good approximation to 2pi squared). To this we add the inertia of the screw, which is given by:

J(screw) = 1/2 Mass * radius^2

where the mass is given by:

mass(screw) = pi * radius^2* length * density

In our worked example a 12mm screw 800mm long has a mass of 3.1416 * .006^2 * .8 * 7800 = 0.71kg and therefore an inertia of J(screw) = 1/2 * 0.71 * .006^2 = 1.28 x 10E-05, so the screw has a higher inertia than the load!

The total inertia to be overcome is the sum of J(load) and J(screw) = 1.72x10E-05 kgm^2. (Note the spreadsheet also adds in the rotor inertia of the motor)

Next we have to decide how fast we want the gantry to move under load. Typically for a wood router anything from 500 to 1000mm/min would be suitable, for cutting aluminium you might want to look at 1800mm/min or better when using small cutting tools. The maximum traverse speed is given by:

Smax = max motor rpm * screw pitch.

In many cases the speed will be determined by the available drivers and the motor. Few motors will give much torque above about 1000steps/sec on low voltages (24v being the typical supply used), so the maxium speed we could reasonably expect under load for a 200step motor is going to be 1000/200 * 60 * .003 = 0.9m/min or 900mm/min. At this speed the angular velocity of the screw will be:

w = 2 * pi * screw revs/sec
In our example this becomes 6.28 * 1000/200 = 31.4 rads/sec.

Note that the spreadsheet also shows whether the screw is likely to whip at the chosen speed depending on the type of fixing. For most basic systems fixed/free or supported/supported would be a typical configration, but this may need to be adjusted (or a bigger diameter screw chosen) for larger/faster designs.

Now we need to decide what acceleration we want. There is a correllation between the speed of movement and the ideal acceleration to avoid loosing steps but allow rapid direction changes for accuracy of cut. Obviously as the speed increases the acceleration needed to maintain cut accuracy is higher, however for rapids a lower acceleration can be tolerated. A typical router at around a 1000mm/min would need an acceleration on the order of 2300rads/sec^2. The torque required to achieve this acceleration against the inertial loads is

T = J * A
Which gives 1.72x10E-05 * 2300 = 0.04Nm. (the spreadsheet assumes rapids need ~1/3 the acceleration of that used for cutting).

Adding the two components of torque together we have a total torque requirement of 0.052Nm at the motor speed of 1000steps/sec (i.e. 5rps, 300rpm). The spreadsheet also adds in the detent torque (the torque needed to overcome the magnetic attraction between stator and rotor - this is what gives rise to the 'cogging' feel of a stepper motor when turned by hand.)

You can see that the torque required is very different to the 'torque rating' of the motor. It is important to note that the holding torque of a stepper motor is to some extent of little relevance. This is the physical torque required to overcome the electromagnetic forces holding the rotor stationary and is the torque the motor tends towards as speed drops to zero. In practice this torque is rarely available or used. While the size of a stepper motor generally dictates the low speed torque, the ability of the drive electronics to force current through the windings of the motor dictates the high speed torque. Remembering that a stepper motors torque ratings are based on sinusoidal drive current; running it on a square wave signal of a switched driver is at best an approximation at low revs and is progressively worse at higher revs unless there is sufficient voltage to force the current through the winding. A good rule of thumb, for best performance, is:

Vd = 32 * sqrt(L)
where Vd is operating voltage, and L is the motor inductance in mH. If your drivers are limited in voltage a low inductance motor is essential if you want any reasonable speeds.

The inductance of the windings and the drive voltage used dictates the corner speed of the motor. The calculations are too complex to describe here but the spreadsheet allows you to put in the motor parameters to get a go/no go view. In an ideal world you would want to run the motor just below its corner speed to get maximum power output and a torque that is essentially constant across a range of revs. Once you get past the corner speed the torque falls off rapidly. This is a consequence if you design for high power at cutting speeds (to minimise the likelhood of loosing steps) but then want fast rapids which take you over the corner speed - if the torque drops too low you will either lose steps or worse the motor will stall.

So, lets look at the motors available. Pick any website, such as Zapp Automation's, and look at the list of NEMA17 and NEMA23 motors. Here are the options:

Motor V A mH Nm Inertia
SY42STH47-1684B 2.80 1.6 2.8 0.44 68
SY57STH51-1008B 9.24 0.7 32.8 1.00 275
SY57STH51-3008B 3.10 2.1 3.6 1.00 275
SY57STH56-2008B 5.04 1.4 10.0 1.24 300
SY57STH56-3008B 3.15 2.1 4.4 1.24 300
SY57STH76-3008B 4.00 2.1 6.4 1.85 480

Plugging any of these into the spreadsheet gives similar results, so which to choose? Next calculate the ideal voltage for each (the spreadsheet shows this as the 'ideal voltage')

Motor V A mH Vd
SY42STH47-1684B 2.80 1.6 2.8 54
SY57STH51-1008B 9.24 0.7 32.8 183
SY57STH51-3008B 3.10 2.1 3.6 60
SY57STH56-2008B 5.04 1.4 10.0 101
SY57STH56-3008B 3.15 2.1 4.4 67
SY57STH76-3008B 4.00 2.1 6.4 81

Lets assume we want to use a low cost driver board, such as the System3 from DIYCNC which is OK to 2.5A but limited to 30v max, or the TBA6560 boards available on eBay. None of those are going to manage 60v, indeed 24v is the likely voltage, but the motors that are the lower ideal voltage will perform better with those drivers. So on this basis the SY42STH47-1684B or the SY57STH51-3008B would be contenders. I'd probably opt for the 1Nm NEMA23 motor over the 0.44Nm NEMA17 motor to give a bit more leeway and scope for upgrades. Anything bigger would be a waste of money and would perform no better (and usually worse - there is such a thing as too big a motor).

Below shows similar calculations repeated for a number of examples

25kg gantry 4' Rockcliffe oilite bronze on steel, TR12x3 1.2m long. 1000mm/min. Torque = 0.1Nm, power = 3W so a 1Nm - 1.5Nm motor.

35kg gantry 2m ballrace on channel, 16mm ballscrew 5mm pitch, 1.8m long, 2000mm/min. dense hardwood capable. Torque = 0.4Nm, power = 12W (typical 2Nm NEMA23 motor)

50kg dovetail table + 5kg workpiece + 5kg vice, 20mm ballscrew 5mm pitch, 900mm long, 1200mm/min, light alloy/steel cutting. Torque = 0.9Nm , power = 32W (8Nm NEMA34 motor)

50kg dovetail table + 10kg workpiece + 5kg vice, 25mm ballscrew 5mm pitch, 900mm long, 1800mm/min (with slightly reduced acceleration), heavy alloy/steel cutting. Torque = 1.1Nm , power = 64W (possible with 12Nm NEMA34 motor, but this is starting to get into servo motor territory to meet that speed/accel requirement)

Friday, August 19, 2022

What are advantages and disadvantages of integrated stepper motor-drive combination?

Stepper motors and drives can be combined into one unit. Manufacturers offer a variety of combinations of integrated stepper motors and drive combinations. There are advantages and disadvantages to these integrated stepper motor-drive units. The advantages of integrated motor and driver units include ease-of-implementation, lower wiring complexity, quicker setup and construction of systems, and motor-drive compatibility. Also, there are integrated units that integrate systems on a chips (SoC). 


There are disadvantages, such as fewer configuration options, a lack of customization and vendor lock-in. These issues can also be troubleshooting and modifications to maintenance procedures.

The best thing about integrated drive-motor units is their ease of implementation. These units do not require wiring between the motor and drive. They can be simply "dropped" in place and connected to a control unit. This allows for faster setup, allowing a system go from blueprints into production in a shorter time.

Engineers don't have to worry about wiring inputs and outputs correctly connecting drive and motor.

There are no concerns about bipolar or unipolar wiring. Long wiring runs don't cause signal degradation.

Integrated drives are also guaranteed to work together with the motor and drive. They are guaranteed to work together because they are provided by the manufacturer. Because the curves already take into account the drive's torque-speed curves, this means less work. This means that you don't have to worry about whether or not the drive uses the correct voltages. An integrated unit with an SoC can be even simpler. The SoC can handle most control operations. The combined unit can also connect to other units, which is particularly useful for the Internet of Things.

This setup has one major drawback: it is not flexible enough to be customized and implemented in a way that suits your needs. The drive-motor combination is one unit so it works only for certain applications. If the driver needs to be changed, but the motor works fine or vice versa, it is impossible to replace the entire unit.

Because manufacturers don't have the same level of optimization or specialization for individual components that are available in integrated units, customization is limited. Any unique or unusual requirements cannot be met by a system.

Additionally, if more than one drive is required, but not all motors, integrated drives add unnecessary redundancy to the system. Other drawbacks include vendor lock in and changes to maintenance procedures. It may be difficult to determine if a fault is caused by the motor or drive.

Wednesday, January 22, 2020

Motion Controller and Driver Selection Tips You Should Know

Motion Controller
The first thing that should be checked when selecting a motion controller is compatibility with other system components such as the PLC/PC, stepper driver and voltage sources.Motor speed is controlled by the pulse rate (pulses per second) supplied by the driver via the controller.Depending on the speed required, one must ensure that the motion controller can output the corresponding pulse rate to reach that speed. The motion controller must be able to output this pulse rate, and the stepper drive must be able to receive this pulse rate and send over to the SMLA. The equation for determining required pulse rate is shown in the following page.

Motion Controller and Driver Selection Tips You Should Know

• Linear speed: desired linear travel speed (in/s)
• Lead: lead screw for stepper motor travel per one full revolution of the screw (in/rev)
• Motor steps per rev: how many steps per one full revolution of the motor (steps/rev). All SMLAs are 200 steps per revolution.
• Pulses per step: pulses per step (pulse/step). SMLAs are 1 pulse per 1 step.
• Microstep: Micro-stepping resolution (micro-step/step)
After calculating the required pulse rate, it may come to light that your PLC, PC or microcontroller is capable of sending out this frequency to the stepper drive without the need of a separate motion controller.

Stepper Drive
Like a controller, the user should select a drive based on its ability to interface with all other components in the system – specifically the stepper motor and controller. For Thomson standard SMLA stepper motors, a drive must be able to allow the connection of a four-wire, bipolar motor. Electrical properties of the system must also be taken into consideration. Items such as desired output current to the motor, max input voltage from the power supply, and motor inductance will need to be reviewed.Just like a controller, required pulse rate will also need to be considered to ensure the driver is capable of driving the motor to the required speed.

There are many unique stepper motor drives out there that offer various micro-stepping resolutions. Depending on your requirement, micro-stepping may be worth considering, specifically if a smoothmotion is required. Micro-stepping essentially takes the standard 200 steps per revolution of the SMLA motor and breaks down each step to smaller increments such as from ½ step, ¼ step and even all the way to 1/256 step. Figure 7 illustrates the difference between full-stepping and micro-stepping.

Figure 7: Simple illustration comparing the motion between full stepping and micro-stepping.An important thing to note about micro-stepping is that it does not improve positional accuracy by goingto finer resolutions. A typical rotational accuracy for a stepper motor is approximately +/- 0.09 degreesregardless of micro-stepping resolution.

Final Considerations
Ultimately, experience is the best tool at one’s disposal for building a stepper motor-based system.The guidance mentioned above should only be utilized as a way of getting in the ballpark for a system build.Some experimentation with trial and error may need to be conducted to get a completely functional system. Always utilize the help of an experienced system designer and add a decent margin to system calculations when possible. When it comes to SMLA selection, Thomson can help recommend a product to get the performance you need. PLC, motion controller and drive manufacturers will also have dedicated engineers to help assist you in selecting one of their products.

Additional benefits of linear stepping motors

Additional benefits of linear stepping motors

Linear stepping motors are an excellent solution for positioning applications that require rapid acceleration and high-speed moves with low mass payloads. Mechanical simplicity and precise open-loop operation are additional features of the Compumotor microstepping linear motor systems.

Additional benefits of linear stepping motors

High Throughput – The motors are capable of speeds to 100 ips and the low mass forcer allows high acceleration.
• Mechanical Simplicity – The need for leadscrews or belts and pulleys is eliminated. The mechanical design is preengineered.
• High Reliability – Fewer moving parts and a friction-less airbearing design results in a longer, maintenance-free life.
• Long Travel – Length of travel is limited only by the length of the platen; increasing length causes no degradation in performance.
• Precise Open-Loop Operation – Unidirectional repeatability to 2.5 microns without the added expense of feedback devices.
• Small Work Envelope – A linear motor is usually smaller in all three dimensions than comparable systems where rotary motion is converted to linear.
• Easily-Achieved X-Y Motion – The assembly of X-Y gantry systems is readily accomplished.
• Multiple Motion – More than one forcer can operate on the same platen with overlapping trajectories.

Construction of a Linear Step Motor
A linear hybrid stepping motor operates on the same electromagnetic principles as a rotary hybrid stepping motor.The moving element is called a forcer. The stationary part is called the platen. The stator or platen is a passive toothed steel bar extending over the desired length of travel. All permanent magnets, electromagnets and bearings are incorporated into the armature or forcer. The forcer moves bidirectional along the platen, assuring discrete locations in response to the state of the currents in the field windings

Monday, January 20, 2020

What is the maximum speed of a stepper motor?

What is the maximum speed of a stepper motor?
Modern stepper motors can reach rotation speeds of up to 1500 RPM, taking into consideration that the motor torque curve decreases considerably with the increasing of the step frequency. If a screw of 4 mm is run at 1500 RPM, we obtain a displacement speed of 1500*4mm=6000mm/min or 6 m/min. Therefore, in practice, the stepper motors runs at max 600 RPM because the torque decrease above that values.

What is the maximum speed of a stepper motor?

14hs13-0804s or 17hm08-1204s

Related Questions:
What temperatures are stepper motors able to run at?
Most stepper motors are made with Class B insulation. This allows the stepper motor internal wiring to sustain temperatures of up to 130 degrees Celsius. With an ambient temperature of 40 Celsius, the stepper motor has a temperature rise allowance of 90 Celsius. Stepper motors can run continuously at these temperatures.
What applications would a bipolar stepper motor be used for?
A bipolar stepper motor is best used in a situation that would require high torque at low speeds.

What is the difference between a Unipolar and a Bipolar stepper motor?
The main difference between unipolar and bipolar hybrid stepper motor is the center tap connections. A unipolar motor is wound with six lead wires, each of these having a center tap. These would be used in applications needing high torque with high speed. Whereas a bipolar stepper motor has four lead wires but has no center tap connections. Bipolar stepper motors are used when you require high torque at low speeds.

What applications would a unipolar stepper motor be used for?
A unipolar stepper motor would be best used in an instance where you would require a motor with high speed and high torque.

Tuesday, December 31, 2019

When to apply external Non-Captive and Captive Step Motor Actuators

When to apply external Non-Captive and Captive Step Motor Actuators

A common way to generate precise linear motion is to use an electric motor (rotary motion) and pair it with a lead screw to generate a linear actuation system. Depending upon what this linear actuator interfaces with it can be constructed in a number of different ways.

Here we will discuss several different ways to combine a lead screw and nut with a stepper motor to create a linear actuator system. The stepper motor is frequently used in motion control as it is a cost effective technology that does not require position feedback to operate correctly.

When to apply external Non-Captive and Captive Step Motor Actuators

3 Different Styles
There are three different styles of linear actuators that are commonly used they are the external nut linear actuator style, non-captive style and captive style. There are many reasons to use a certain style of linear actuator, the three main reasons for selecting one style over another are:

Size 23 stepper motor.
Stroke What is the amount of linear travel required?

Interface Point:
How will the actuator be mounted and how will the load be attached?
Options: What other options might be required from the linear actuator?

External Linear Actuator
The simplest way to envision this combination of parts is to simply affix the lead screw onto the shaft of the motor. The nut that rides on the lead screw must be restrained from rotating so that linear motion will be generated. This type of actuator  is commonly referred to as an external linear style actuator.

Non-Captive (through screw) Linear Actuator
Another option is to locate the nut inside the motor and allow the screw to move linearly through the actuator. In this case the screw must be prevented from rotating to generate the linear motion.This style of actuator is commonly referred to as a through screw or non-captive linear actuator.

Captive Linear Actuator
In instances where the application does not have a mechanism to prevent the rotation of either the nut or the screw a third style exists. This style locates the nut inside the actuator body just like the non-captive actuator above but on the front side a linear spline is attached to the screw, this linear spline engages a front sleeve that is rigidly fixed to the actuator this prevents the rotation of the screw and provides linear output. This style of actuator is referred to as a captive style actuator.

Friday, December 27, 2019

Block Diagram of a Stepper Motor System

A stepper motor actuator is a mechanical device which produces force, as well as motion along a straight path. A stepper actuator uses the core principles of a stepper motor, with some slight modifications. With the stepper actuator, the shaft of a normal stepper motor is replaced with a precision lead screw, and the rotor is tapped to convert it to a precision nut that is adjusted to the lead screw. As the rotor rotates, the lead screw rotates up and down the precision nut, allowing for linear motion. Minimizing outside mechanical systems to convert rotary into linear motion, greatly simplifies rotary to linear applications. The stepper actuator design allows for high resolution and accuracy, while minimizing extra mechanical components.

Block Diagram of a Stepper Motor System
Block Diagram for Stepper Motor System
Figure 1: Stepper Actuator System
Physical Properties of a Stepper Actuator
The physical properties of stepper actuators are made up of the same core properties of a stepper motor, with some modifications. The shaft of a normal stepper motor is replaced with a precision lead screw and the rotor is tapped precision nut that interacts with the lead screw to allow for linear motion. The stator and rotor laminations are comprised of silicon steel which allows for a higher electrical resistivity and lower core loss. There are a variety of magnets used: ferrite plastic, ferrite sintered and Nd-Fe-B (neodymium magnet).
Figure 2: Physical components of a PM stepper actuator with a threaded shaft and a mounting plate.
Figure 2: Physical components of a PM stepper actuator with a threaded shaft and a mounting plate.
Figure 3: Illustration of the threaded shaft with the pitch and lead.

Figure 3: Illustration of the threaded shaft with the pitch and lead.

How do Stepper Actuators Work?
A stepper actuator is driven by a stepper motor driver and/or controller, which provides the instructions to manipulate the stepper actuator to start or stop. The driver and/or controller sends the proper signal pulses to the windings of the stepper actuator, causing the rotor (Economy Linear Stepper or Precision Linear Actuator) to rotate and the lead screw to extend or retract. By the use of instructions, a stepper motor controller designates how far and how fast the stepper actuator should extend or retract. A controller can be pre-programmed or controlled in real time by inputs predefined on the stepper drive or controller.

A Tutorial on stepper motor torque calculations

  A Tutorial on stepper motor torque calculations A question oft asked on MYCNCUK is "how big a motor do I need?". There is no sim...