# Design and Development of a Tri-Axial Turning Dynamometer Utilizing Cross-Beam Type Force Transducer for Fine-Turning Cutting Force Measurement

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Concept Design of Turning Dynamometer

#### 2.1. Cutting Force Component in Turning Process

_{a}, is the result of the combination of the cutting force, F

_{c}, and the feed force, F

_{f}, in the direction of the cutting action. The passive or radial force, denoted by the symbol F

_{r}, does not contribute to the power conversion, since the tool and the workpiece do not move relative to one another in the direction of movement. The resultant force on the turning process can be expressed by the following equation:

#### 2.2. Design of Force Transducer and Dynamometer

_{c}in the vertical direction or the direction of the spindle rotation, the feed force F

_{f}in the feed direction, and the radial force F

_{r}perpendicular to the axis of the workpiece axis or in the direction of the tool holder.

_{c}, the feed force F

_{f}, and the radial force F

_{r}, they may correspond to forces in the co-ordinate system, namely the forces F

_{x}, F

_{y}, and F

_{z}. The three components of the cutting force will be focused on the central cross beam that is in a free condition, as shown in Figure 3a,b. Under ideal circumstances, when a force F

_{x}is applied to a force transducer, it only results in beams b

_{1x}and b

_{2x}, which generate deformation and strain. When only force F

_{y}is applied, beams b

_{1y}and b

_{2y}are deformed and strain is apparent on the surface. When the z-axis co-ordinates are subjected to a force F

_{z}, the beams b

_{1z}, b

_{2z}, b

_{3z}, and b

_{4z}will deform.

_{z}. The measurement points S-01 and S-03 are symmetrical about the neutral surfaces of the cantilever beams b

_{1y}and b

_{2y}, while the measurement points S-05 and S-07 are symmetrical about the neutral surfaces of the cantilever beams b

_{1x}and b

_{2x}. The locations of the measuring points for the forces F

_{x}and F

_{y}in cantilever beams are similar to one another, as are their geometric constructions. However, with regard to the measuring point of force F

_{z}, the geometry and dimensions are the same from points S-09 until S-24. So, the measurement concept of a force transducer can be shown by looking at how two types of cantilever beams are used to measure the force (Figure 4).

_{1x}and b

_{2x}components to detect F

_{x}. Cantilever beams b

_{1y}and b

_{2y}only need to detect F

_{y}, while cantilever beams b

_{1z}, b

_{2z}, b

_{3z}, and b

_{4z}only need to detect F

_{z}. The cantilever beam is composed of two symmetrical grooved holes that allow for the measurement of three-dimensional forces to be achieved. The strain value at measurement point S-01 is insensitive to the effects of forces F

_{y}and F

_{z}because the hole weakens the stiffness of the beam, and the strain value at measurement point S-05 is similarly unaffected by forces F

_{x}and F

_{z}.

_{xx}= 1/2 F

_{x}, F

_{yy}= 1/2 F

_{y}, and F

_{zz}= 1/8 F

_{z}. By using the mechanical theory of the bending stress of a cantilever beam, which can be written as follows:

_{xx}l, and I = wh

^{3}/12, the strain value at measurement point S-01 can be expressed as follows:

_{b}

_{1x}is the strain values of measurement in beam b

_{1}x at point s-01 under the action of F

_{x}and E is the modulus of elasticity of stainless steel 316.

_{z}is applied to the transducer, beam b

_{z}will detect stress, and the value of strain on beam b

_{4z}at point S-16 can be obtained using the following equation:

#### 2.3. Analysis by Finite Element Method (FEM)

^{3}, Young’s modulus of 193 GPa, a Poisson ratio of 0.27, and a yield strength of 520 MPa.

_{x}, εF

_{y}, and εF

_{z}are the total strains from the Wheatstone bridge for each direction of force and S

_{i}is the strain measured on the cross-beam surface in a certain position (i = 1 to 16).

_{x}operating on the force transducer, the maximum strain on the x-axis was 0.75 microstrain at locations 4 to 6 mm in Figure 6a. In comparison, the strains on the y and z axes were 0.005 and −0.2 microstrain at the same position. This suggests that the interference strain that was caused by a force F

_{x}on the y and z channels was relatively small or even nonexistent. The highest amount of strain that was measured as a result of a radial force, denoted by F

_{z}, was 0.13 microstrain, whereas the amount of strain that was measured in the x and y channels was around 0.004 and −0.0002 microstrain, respectively.

## 3. Fabrication of the Tri-Axial Turning Dynamometer

#### 3.1. Piezoresistive Strain Gauge Arrangement in Cross-Beam Force Transducer

_{f}, is detected by strain sensors S-06 and S-08, which are subjected to compressive stress, as indicated in Figure 7b, whereas strain sensors S-05 and S-07 are exposed to tensile stress. As seen in Figure 7c, the z-direction force or radial force, F

_{r}, is detected by strain sensors S-09, S-10, S-11, and S-12; and S-13, S-14, S-15, and S-16 are exposed to a tensile stress, whereas strain sensors S-17, S-18, S-19, and S-20 and S-21, S-22, S-23, and S-24 are subjected to compressive stress. All strain sensors used in this work were linear semiconductor or piezoresistive strain gauges SSC-350-B-F5 (UTOP) with the nominal resistance of 350 Ω. The gauge factor (GF) of this sensor was 150, the length of the gauge was 6 mm, and the width of the gauge was 3.5 mm. The actual strain could be obtained from the following equation [1]:

#### 3.2. Constraction of Dynamometer and Data Acqusition System

## 4. Testing of Tri-Axial Turning Dynamometer

#### 4.1. Static Calibration Test

_{x}), the y-direction (F

_{y}), and the z-direction (F

_{z}), as well as their interactions, have been displayed.

#### 4.2. Dynamic Test of Dynamometer

^{2}was mounted onto the dynamometer component. A sampling rate of 50 kHz was used in the LabVIEW program in order to acquire the signal, which was then collected by the data acquisition device (NI-9250). After that, a modal analysis was carried out in order to determine the frequency response function of the dynamometer in three co-ordinate directions in accordance with the three-axis force components. The graphs of the natural frequencies acquired by dynamic testing and modal analysis are shown in Figure 10. The turning dynamometer’s construction had natural frequencies of 2253 Hz, 2317 Hz, and 2957 Hz, respectively, when measured along the axes x, y, and z. These results revealed that the specified dynamometer construction was excellent for both conventional turning and high-speed turning.

#### 4.3. Performance Test of Dynamometer in Turning Operation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Structure of the cross-beam force transducer: (

**a**) isometric view; (

**b**) front view; (

**c**) left side view.

**Figure 4.**Cantilever beam model in cross-beam force transducer: (

**a**) force in x-direction; (

**b**) force in z-direction.

**Figure 5.**Strain distribution on cross-beam surfaces while under: (

**a**,

**b**) F

_{x}force; (

**c**,

**d**) F

_{z}force.

**Figure 6.**Normal strain along the midline of cross-beam surfaces: (

**a**) when F

_{x}force is applied; (

**b**) when F

_{z}force is applied.

**Figure 7.**Wheatstone bridge circuits for detection of forces in cross-beam force transducer: (

**a**) F

_{x}; (

**b**) F

_{y}; (

**c**) F

_{z}.

**Figure 9.**Dynamometer calibration curves: (

**a**) F

_{x}direction; (

**b**) F

_{y}direction; (

**c**) F

_{z}direction.

**Figure 10.**Frequency response of the dynamometer: (

**a**) x-direction; (

**b**) y-direction; (

**c**) z-direction.

**Figure 12.**Cutting forces in turning operation under three different depths of cut: (

**a**) time domain; (

**b**) frequency domain.

Force Direction | Cross-Talk Error (%) | ||
---|---|---|---|

F_{x} | F_{y} | F_{z} | |

F_{x} | - | 1.62 | 5.13 |

F_{y} | 0.79 | - | 4.66 |

F_{z} | 5.17 | 1.62 | - |

Force Direction | Avg. of Linearity Error (%) | Hysteresis Error (%) | Repeatability Error (%) | ||
---|---|---|---|---|---|

10 N | 50 N | 100 N | |||

F_{x} | 0.02 | 0.36 | 0.27 | 0.38 | 0.86 |

F_{y} | 0.06 | 0.62 | 0.77 | 1.63 | 1.94 |

F_{z} | 0.13 | 0.46 | 0.82 | 2.79 | 2.91 |

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**MDPI and ACS Style**

Rizal, M.; Ghani, J.A.; Mubarak, A.Z.
Design and Development of a Tri-Axial Turning Dynamometer Utilizing Cross-Beam Type Force Transducer for Fine-Turning Cutting Force Measurement. *Sensors* **2022**, *22*, 8751.
https://doi.org/10.3390/s22228751

**AMA Style**

Rizal M, Ghani JA, Mubarak AZ.
Design and Development of a Tri-Axial Turning Dynamometer Utilizing Cross-Beam Type Force Transducer for Fine-Turning Cutting Force Measurement. *Sensors*. 2022; 22(22):8751.
https://doi.org/10.3390/s22228751

**Chicago/Turabian Style**

Rizal, Muhammad, Jaharah A. Ghani, and Amir Zaki Mubarak.
2022. "Design and Development of a Tri-Axial Turning Dynamometer Utilizing Cross-Beam Type Force Transducer for Fine-Turning Cutting Force Measurement" *Sensors* 22, no. 22: 8751.
https://doi.org/10.3390/s22228751