Factors Shaping Extension Precision in Servo-Based CRE Machines

Constant Rate of Extension (CRE) machines are central to materials testing, research and development. They apply a controlled, steady extension rate to a specimen so that its properties can be measured precisely.

At the heart of a CRE machine is the servo motor. It turns electrical signals into precise mechanical movement, driving the controlled extension and retraction that accurate, repeatable testing depends on. Getting the best extension precision out of a servo-driven machine is not a luxury; it is a requirement.

It is also a balancing act. Precision, resolution and displacement range pull against each other, and the settings that improve one can limit another. In this article we look at the factors that influence extension precision in servo-driven CRE machines and how to balance them.

The properties we want to control

A CRE machine stretches or compresses a material at a steady speed and records the force at each displacement point. These are the characteristics that define how well it does that:

• Displacement accuracy: how closely the actual position of the crosshead matches the intended extension.
• Displacement resolution: the smallest movement the system can detect and act on.
• Displacement range: the maximum distance the machine can extend the specimen.
• Speed precision: how consistently the machine holds a constant extension rate.
• Speed range: the range of extension rates the machine can achieve.
• Speed accuracy: how closely the achieved extension rate matches the set rate.

The factors that influence them

Some of these factors are within our control; others are fixed by the hardware.

• Gear ratio: most servo drives provide an electronic gear ratio. In principle it is equivalent to a mechanical gear ratio, but it can be changed in software.
• PPR (pulses per revolution): the number of external pulses needed to turn the servo motor through one full revolution.
• Lead of the ball screw: the distance the nut travels for one revolution of the screw. For a single-start screw this equals the pitch, the distance between adjacent threads.
• Word size: the number of bits the controller (for example a PLC) uses to hold a value.

Connecting the dots

In pulse-mode control, a controller such as a PLC sends pulses to the servo drive, which turns the motor. The motor turns the ball screw, and the ball-screw nut moves in a straight line. The task is to know exactly how far the nut moves for a given number of pulses.

In simple terms:

Current displacement = Np × Lead / PPR

Np   = number of external pulses sent for the current displacement
Lead = travel of the ball-screw nut per revolution
PPR  = number of external pulses for one revolution of the motor

That looks simple, but it isn’t. PPR depends on the electronic gear ratio of the drive, any mechanical gearing between motor and screw, and so on. The screw lead also carries some manufacturing error. So we can’t rely on nominal PPR and lead values to calculate displacement. Instead we use an indirect method, displacement calibration: we move the crosshead a known distance, count the pulses sent, and use that ratio from then on.

Current displacement = Np × Dc / Npc

Dc  = displacement used during calibration
Npc = number of external pulses sent during calibration

Does that make displacement independent of gear ratio and lead? Not quite. The details matter.

Where overflow comes in

Suppose the PLC holds Np, Dc and Npc in 32-bit signed registers (two 16-bit words). The largest value such a register can hold is 2³¹ − 1 = 2,147,483,647. If the product Np × Dc exceeds that, the calculation overflows.

Take an example, assuming no gearing and perfectly accurate components:

• PPR = 10,000 and lead = 5 mm, so one motor revolution moves the nut 5 mm.
• Calibration is done over 500 mm, stored with one decimal place, so Dc = 5,000.
• At a current displacement of 800 mm: Np × Dc = (800 / 5) × 10,000 × 5,000 = 8,000,000,000.

That is larger than 2,147,483,647, so the result overflows. With this configuration the maximum displacement we can calculate is:

2,147,483,647 × 5 / (5,000 × 10,000) = 214.7 mm

That’s too low. There are two ways to raise it:

1. Reduce the displacement used during calibration.
2. Reduce the PPR.

Option 1: calibrate over a shorter distance

Calibrate over 50 mm instead (Dc = 500). At 800 mm:

Np × Dc = (800 / 5) × 10,000 × 500 = 800,000,000   → no overflow
Maximum displacement = 2,147,483,647 × 5 / (500 × 10,000) = 2,147.4 mm

The catch is observational error. Manual calibration against a physical scale always carries some. Say the reading was out by 0.25 mm, so the crosshead really moved 50.25 mm while we entered 50 mm:

Npc = (10,000 / 5) × 50.25 = 100,500 pulses (instead of 100,000)
Error at 800 mm ≈ 3.98 mm

The shorter the calibration distance, the larger the displacement error. So we want to calibrate over a long distance, but a long calibration distance risks overflow.

Option 2: reduce the PPR

Instead of shortening the calibration, raise the electronic gear ratio by a factor of ten so that PPR drops to 1,000. Calibrate over 500 mm again (Dc = 5,000). At 800 mm:

Np × Dc = (800 / 5) × 1,000 × 5,000 = 800,000,000   → no overflow
Maximum displacement = 2,147,483,647 × 5 / (5,000 × 1,000) = 2,147.4 mm
Error at 800 mm (same 0.25 mm reading error) ≈ 0.40 mm

That’s a large improvement. But how far can PPR be reduced? Not indefinitely. Below a certain value it limits the precision and range of the speed, because each pulse now represents a larger movement. We’ll cover that in a future article.