Application Note | Spring Rate Testing
Nano Mechanical Characterization of Spring Constants
Measuring the Spring Rate of Small Coil Springs from Load-Depth Curves with Sub-mN to 400 N Loads
Research & Experimental Testing
Xavier Herrera-Keehn & Jocelyn Esparza
Visual Design & Editorial
Andrew Shore
Introduction
A spring’s ability to store mechanical energy has a long history of use. From bows for hunting to locks for doors, spring technology has been around for many centuries. Nowadays we rely on springs, be it from mattresses, pens, or automotive suspension, as they play a vital role in our daily lives. With such a wide variety of use and designs, the ability to quantify their mechanical properties is necessary.
Determining Spring Constant with the NANOVEA Mechanical Tester
One important mechanical property of springs is their ability to compress or stretch when a load is applied, this is quantified by the spring constant. The spring constant can be found by looking at the slope of the load vs. depth curve; a linear spring will follow Hooke’s Law: F = −kx, where F is the force applied, x is the spring’s displacement, and k is the spring constant. With the variety of modules offered with the NANOVEA Mechanical Tester, loads ranging from sub mN to 400 N can be applied onto a spring. The NANOVEA Mechanical Tester can precisely record the changes in depth as it applies a load onto the spring, as well as recording a spring’s deflection up to 20 mm. Keep in mind as the spring constant increases, higher loads will be needed to accurately obtain the spring constant.
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Measurement Objectives
The objective of this application note is to demonstrate the versatility of the NANOVEA Mechanical Tester by measuring the spring rate of three distinct coil springs with the Nano Module.
NANOVEA PB1000 Large Platform
Mechanical Tester
Measurement Parameters
| Test parameter | All samples |
|---|---|
| Maximum force | 150 mN |
| Loading rate | 300 mN/min |
| Unloading rate | 300 mN/min |
| Indenter type | Flat |
Table 1: Test parameters used.
Results and Discussion
Shown below is the data for the three spring samples, three tests were performed on each spring and their respective spring constants were found. A linear trend was fitted onto the loading curve to obtain the slope, the slope being the spring constant. The R² value describes how well the linear trend was fitted to the dataset (1 being a perfect fit).
Spring 1
| Spring 1 | Spring constant k (mN/µm) |
|---|---|
| Test 1 | 0.9358 |
| Test 2 | 0.9319 |
| Test 3 | 0.9344 |
| Average | 0.9340 |
| Standard deviation | 0.001613 |
Table 2: Spring constants of Spring 1 from three tests.
Spring 2
| Spring 2 | Spring constant k (mN/µm) |
|---|---|
| Test 1 | 1.5057 |
| Test 2 | 1.5149 |
| Test 3 | 1.5224 |
| Average | 1.5143 |
| Standard deviation | 0.00683 |
Table 3: Spring constants of Spring 2 from three tests.
Spring 3
| Spring 3 | Spring constant k (mN/µm) |
|---|---|
| Test 1 | 2.2293 |
| Test 2 | 2.2518 |
| Test 3 | 2.2396 |
| Average | 2.2402 |
| Standard deviation | 0.009196 |
Table 4: Spring constants of Spring 3 from three tests.
As you can see, the data for each of the three coil springs is repeatable and consistent, with the highest standard deviation being 0.009196 mN/µm for the third spring, but this is to be expected as the spring constant becomes greater.
Conclusion
Since springs are used in many different industries, quantifying their mechanical energy is necessary. In this study we were able to accurately and precisely measure the spring constant for 3 different coil springs. With the large variety of modules offered with the NANOVEA PB1000 Mechanical Tester, spring deflection up to 20 mm can be recorded.
Frequently Asked Questions About Spring Constant Measurement
What is a spring constant?
The spring constant k quantifies a spring’s ability to compress or stretch under load. A linear spring follows Hooke’s law, F = −kx, where F is the applied force and x the displacement, so k is the slope of the load versus depth curve.
How is a spring constant measured on a mechanical tester?
The tester applies a controlled load to the spring with a flat indenter while precisely recording depth, and a linear trend fitted to the loading curve gives the slope, the spring constant. Here springs were loaded to 150 mN at 300 mN/min.
What spring constants were measured?
Three coil springs averaged 0.9340, 1.5143 and 2.2402 mN/µm over three tests each, with standard deviations of 0.001613, 0.00683 and 0.009196 mN/µm.
How repeatable are the measurements?
Very repeatable: the largest standard deviation was 0.009196 mN/µm, for the stiffest spring, which is expected as the spring constant increases. The linear fits had R² values from 0.9991 to 1.
What range of springs can be tested?
NANOVEA mechanical tester modules apply loads from sub-mN to 400 N and record spring deflection up to 20 mm. Stiffer springs need higher loads to obtain their constant accurately.
Which NANOVEA instrument was used?
The NANOVEA PB1000 Mechanical Tester with its nano module, a multi-module platform for scratch, indentation and wear testing.
