# An Empirical Study on the Friction of Reciprocating Rod Seals at Predefined Lubrication Conditions and Shear Rates

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Components of the Analyzed Sealing Systems

#### 2.1.1. Seal Rings

#### 2.1.2. Hydraulic Oil

#### 2.1.3. Hydraulic Rod

#### 2.2. Ellipsometer Used for Film Thickness Meausrements

#### 2.3. Test Rigs for Hydraulic Rod Seals

#### 2.3.1. Common Test Rig for Friction Measurement on Two Seals

#### 2.3.2. New Test Rig

^{−1}are possible. An outstroke or instroke can only be performed at ambient pressure ${p}_{0}$. A force transducer is used to measure the resulting friction between the rod and the seal ring. Due to the radial load of the seal a concentric alignment between the rod and the seal is ensured.

#### 2.4. Novel Measurement Procedure

## 3. Results

#### 3.1. Common Test Method

^{−1}. All measurements were carried out at an operating pressure $p=5\mathrm{bar}$. The surface temperature of the rod $\vartheta \approx 25\xb0\mathrm{C}$ was checked during the tests with a contact thermometer.

#### 3.1.1. Measured Friction

#### 3.1.2. Measured Friction vs. Hydrodynamic Parameter

#### 3.2. New Procedure

#### 3.2.1. Measured Friction and Film Thickness

#### 3.2.2. Measured Friction vs. Calculated Fluid Friction

## 4. Discussion

#### 4.1. New Measurement Procedure

^{5}to 10

^{7}s

^{−1}and the gap height in a range of approximately 5 to 100 nm. In such narrow gaps and at such high shear rates, tribological phenomena such as wall slip, shear thinning, or an increase in the lubricant’s viscosity were observed by other authors; see Section 1. Those phenomena depend on the film thickness, shear rate, and intermolecular forces between the lubricant and the surfaces. Besides the film thickness and the shear rate, the new measurement procedure can be used to analyze the influence of intermolecular forces and interfacial phenomena in the sealing gap on the resulting friction. In a next step, lubricants with different additives and made from different base oils can be compared at various shear rates and gap heights. Furthermore, the materials of the rod and the sealing ring can be varied. Using the new procedure, it is now possible to analyze whether and to what extend certain tribological phenomena influence the friction of rod seals. It can be clarified as to which phenomena should be considered when modelling linear reciprocating contacts.

#### 4.2. On the Analyis of Friction of Rod Seals

## 5. Conclusions

^{5}to 10

^{7}s

^{−1}can be controlled. In other words, rod seals can be utilized as an oil film generator and as part of a thin film tribometer for linear contacts.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$A$ | Contact area between a seal ring and a rod |

$d$ | Nominal diameter of a rod |

${F}_{\mathrm{fluid}}$ | Newtonian fluid friction |

${F}_{\mathrm{R}}$ | Measured friction at the test rig for two seals |

${F}_{\mathrm{R},\mathrm{i}}$ | Friction of one rod seal at instroke |

${F}_{\mathrm{R},\mathrm{o}}$ | Friction of one rod seal at outstroke |

${G}_{\mathrm{hyd}}$ | Hydrodynamic parameter |

${h}_{\mathrm{o},1}$ | Film thickness on the rod after the 1st outstroke when using the new procedure |

${h}_{\mathrm{o},2}$ | Film thickness on the rod after the 2nd outstroke when using the new procedure |

${l}_{\mathrm{b}}$ | Contact width between the seal ring and the rod, measured in axial direction |

${p}_{0}$ | Ambient pressure |

$p$ | Operating pressure |

${u}_{\mathrm{o}}$ | Rod speed at outstroke |

${u}_{\mathrm{o},1}$ | Rod speed at 1st outstroke when using the new procedure |

${u}_{\mathrm{o},2}$ | Rod speed at 2nd outstroke when using the new procedure |

$\dot{\gamma}$ | Shear rate |

$\eta $ | Dynamic viscosity |

$\vartheta $ | Temperature |

## Appendix A

U-Cup | Oil | $\frac{\mathit{\eta}\left(25\xb0\mathbf{C}\right)}{\mathbf{mPas}}$ | Rod Speed $\mathit{u}$ in mms^{−1} | |||||||
---|---|---|---|---|---|---|---|---|---|---|

10 | 20 | 30 | 50 | 100 | 200 | 350 | 500 | |||

Friction Force ${\mathit{F}}_{\mathit{R}}\left(\mathit{u}\right)$ in N | ||||||||||

T20 | FVA1 | 22 | 294 | 215 | 170 | 127 | 100 | 95 | 100 | 105 |

T20 | FVA2 | 54 | 228 | 185 | 155 | 128 | 113 | 113 | 122 | 133 |

T20 | FVA2 | 54 | 202 | 159 | 126 | 104 | 101 | 109 | 121 | 134 |

T20 | FVA3 | 205 | 100 | 96 | 98 | 105 | 119 | 139 | 157 | 169 |

T20 | FVA4 | 1040 | 99 | 107 | 114 | 125 | 143 | 167 | 190 | 205 |

T20 | ISO VG 68 | 119 | 120 | 95 | 92 | 96 | 107 | 121 | 133 | 141 |

EW-rough | FVA2 | 54 | 87 | 71 | 65 | 61 | 64 | 72 | 79 | 84 |

EW-rough | FVA4 | 1040 | 68 | 78 | 86 | 97 | 113 | 131 | 146 | 154 |

EW-smooth | FVA2 | 54 | 75 | 59 | 54 | 52 | 54 | 60 | 67 | 72 |

EW-smooth | FVA4 | 1040 | 51 | 61 | 68 | 79 | 98 | 121 | 143 | 156 |

**Table A2.**Measured friction and film thickness of rod seals at outstroke using the new measurement procedure and T20 U-cups at room temperature.

U-Cup | Oil | $\frac{\mathit{\eta}\left(23\xb0\mathbf{C}\right)}{\mathbf{m}\mathbf{P}\mathbf{a}\mathbf{s}}$ | $\frac{{\mathit{u}}_{\mathbf{o},2}}{\mathbf{m}\mathbf{m}{\mathbf{s}}^{-1}}$ | $\frac{{\mathit{h}}_{\mathbf{o},2}}{\mathbf{n}\mathbf{m}}$ | $\frac{{\mathit{F}}_{\mathbf{R},\mathbf{o},2}}{\mathbf{N}}$ | U-Cup | Oil | $\frac{\mathit{\eta}\left(23\xb0\mathbf{C}\right)}{\mathbf{m}\mathbf{P}\mathbf{a}\mathbf{s}}$ | $\frac{{\mathit{u}}_{\mathbf{o},2}}{\mathbf{m}\mathbf{m}{\mathbf{s}}^{-1}}$ | $\frac{{\mathit{h}}_{\mathbf{o},2}}{\mathbf{n}\mathbf{m}}$ | $\frac{{\mathit{F}}_{\mathbf{R},\mathbf{o},2}}{\mathbf{N}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

T20 | FVA1 | 24 | 10 | 0.4 | 70.7 | T20 | FVA3 | 234 | 40 | 14.8 | 71.1 |

T20 | FVA1 | 24 | 10 | 0.8 | 61.8 | T20 | FVA3 | 234 | 100 | 7.8 | 222.5 |

T20 | FVA1 | 24 | 10 | 0.9 | 57.3 | T20 | FVA3 | 234 | 100 | 8.0 | 210 |

T20 | FVA1 | 24 | 20 | 1.1 | 49.4 | T20 | FVA3 | 234 | 100 | 9.2 | 189.4 |

T20 | FVA1 | 24 | 20 | 2.5 | 41.5 | T20 | FVA3 | 234 | 100 | 29.3 | 74.8 |

T20 | FVA1 | 24 | 20 | 3.6 | 41.4 | T20 | FVA3 | 234 | 100 | 33.8 | 61.6 |

T20 | FVA1 | 24 | 40 | 4.3 | 53.5 | T20 | FVA3 | 234 | 100 | 35.2 | 63.4 |

T20 | FVA1 | 24 | 40 | 4.6 | 51.1 | T20 | FVA3 | 234 | 200 | 28.2 | 122.3 |

T20 | FVA1 | 24 | 40 | 5.1 | 48.8 | T20 | FVA3 | 234 | 200 | 30.1 | 123.6 |

T20 | FVA2 | 60 | 20 | 4.1 | 41.2 | T20 | FVA3 | 234 | 200 | 34.7 | 100.3 |

T20 | FVA2 | 60 | 20 | 5.1 | 37.3 | T20 | FVA3 | 234 | 200 | 34.7 | 100.0 |

T20 | FVA2 | 60 | 20 | 5.3 | 38.8 | T20 | FVA3 | 234 | 200 | 35.7 | 112.7 |

T20 | FVA2 | 60 | 40 | 7.0 | 45.4 | T20 | FVA3 | 234 | 200 | 36.0 | 104.3 |

T20 | FVA2 | 60 | 40 | 7.1 | 48.8 | T20 | FVA3 | 234 | 200 | 55.0 | 65.0 |

T20 | FVA2 | 60 | 40 | 7.5 | 48.7 | T20 | FVA3 | 234 | 200 | 60.3 | 66.6 |

T20 | FVA2 | 60 | 100 | 11.7 | 50.0 | T20 | FVA3 | 234 | 200 | 70.9 | 63.0 |

T20 | FVA2 | 60 | 100 | 11.7 | 54.6 | T20 | FVA4 | 1214 | 20 | 32.4 | 88.3 |

T20 | FVA2 | 60 | 100 | 12.7 | 48.3 | T20 | FVA4 | 1214 | 20 | 36.1 | 81.2 |

T20 | FVA2 | 60 | 200 | 10.2 | 100.8 | T20 | FVA4 | 1214 | 20 | 47.5 | 59.1 |

T20 | FVA2 | 60 | 200 | 10.7 | 95.1 | T20 | FVA4 | 1214 | 50 | 35.3 | 153.8 |

T20 | FVA2 | 60 | 200 | 11.5 | 90.4 | T20 | FVA4 | 1214 | 50 | 38.5 | 155.8 |

T20 | FVA2 | 60 | 200 | 20.1 | 53.4 | T20 | FVA4 | 1214 | 50 | 40.3 | 159.5 |

T20 | FVA2 | 60 | 200 | 21.0 | 56.7 | T20 | FVA4 | 1214 | 75 | 34.1 | 249.2 |

T20 | FVA2 | 60 | 200 | 21.5 | 47.4 | T20 | FVA4 | 1214 | 75 | 34.3 | 238.7 |

T20 | FVA3 | 234 | 10 | 2.7 | 63.5 | T20 | FVA4 | 1214 | 75 | 34.3 | 250.6 |

T20 | FVA3 | 234 | 10 | 2.8 | 56.2 | T20 | FVA4 | 1214 | 100 | 33.1 | 273.4 |

T20 | FVA3 | 234 | 10 | 3.5 | 74.6 | T20 | FVA4 | 1214 | 100 | 36.3 | 264.2 |

T20 | FVA3 | 234 | 20 | 7.0 | 65.5 | T20 | FVA4 | 1214 | 100 | 36.4 | 271.9 |

T20 | FVA3 | 234 | 20 | 8.0 | 65.2 | T20 | FVA4 | 1214 | 100 | 218.4 | 46.7 |

T20 | FVA3 | 234 | 20 | 8.4 | 57.1 | T20 | FVA4 | 1214 | 100 | 232.6 | 47.7 |

T20 | FVA3 | 234 | 40 | 10.5 | 76.6 | T20 | FVA4 | 1214 | 100 | 232.6 | 46.2 |

T20 | FVA3 | 234 | 40 | 11.6 | 81.9 |

**Table A3.**Measured friction and film thickness of rod seals at outstroke using the new measurement procedure and EW U-cups.

U-Cup | Oil | $\frac{\mathit{\eta}\left(23\xb0\mathbf{C}\right)}{\mathbf{m}\mathbf{P}\mathbf{a}\mathbf{s}}$ | $\frac{{\mathit{u}}_{\mathbf{o},2}}{\mathbf{m}\mathbf{m}{\mathbf{s}}^{-1}}$ | $\frac{{\mathit{h}}_{\mathbf{o},2}}{\mathbf{n}\mathbf{m}}$ | $\frac{{\mathit{F}}_{\mathbf{R},\mathbf{o},2}}{\mathbf{N}}$ | U-Cup | Oil | $\frac{\mathit{\eta}\left(23\xb0\mathbf{C}\right)}{\mathbf{m}\mathbf{P}\mathbf{a}\mathbf{s}}$ | $\frac{{\mathit{u}}_{\mathbf{o},2}}{\mathbf{m}\mathbf{m}{\mathbf{s}}^{-1}}$ | $\frac{{\mathit{h}}_{\mathbf{o},2}}{\mathbf{n}\mathbf{m}}$ | $\frac{{\mathit{F}}_{\mathbf{R},\mathbf{o},2}}{\mathbf{N}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

EW-smooth | FVA2 | 60 | 80 | 12.0 | 46.7 | EW-rough | FVA2 | 60 | 80 | 13.3 | 38.4 |

FVA2 | 60 | 80 | 13.0 | 44.0 | FVA2 | 60 | 80 | 15.6 | 36.6 | ||

FVA3 | 234 | 75 | 9.7 | 102.8 | FVA3 | 234 | 75 | 7.8 | 118.4 | ||

FVA3 | 234 | 75 | 13.4 | 84.0 | FVA3 | 234 | 75 | 11.2 | 84.8 |

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**Figure 1.**Schematic of a hydraulic cylinder (

**left**) and the sealing gap of the rod seal at outstroke (

**right**).

**Figure 6.**Measured friction of two seals as a function of rod speed; the results were obtained using the common method ($u=10\dots 500{\mathrm{mms}}^{-1}$, $\vartheta =25\xb0\mathrm{C}$, $p=5\mathrm{bar}$, various mineral oils, T20 U-cups).

**Figure 7.**Measured friction of two seals as a function of the hydrodynamic parameter ${G}_{\mathrm{hyd}}$; the results were obtained using the common method ($u=10\dots 500{\mathrm{mms}}^{-1}$, $\vartheta =25\xb0\mathrm{C}$, $p=5\mathrm{bar}$, various mineral oils, T20 and EW U-cups).

**Figure 8.**Measured friction (

**a**) and film thickness (

**b**) at first and second outstroke using the new method with constant speed at first outstroke ${u}_{\mathrm{o},1}=10{\mathrm{mms}}^{-1}$ (room temperature, ambient pressure, ISO VG 460 mineral oil with $\eta \left(23\xb0\mathrm{C}\right)=1214\mathrm{mPas}$, T20 U-cups).

**Figure 9.**Measured friction (

**a**) and film thickness (

**b**) at first and second outstroke using the new method with constant speed ratios ${u}_{\mathrm{o},1}/{u}_{\mathrm{o},2}=0,5$ (room temperature, ambient pressure, ISO VG 32 mineral oil with $\eta \left(23\xb0\mathrm{C}\right)=60\mathrm{mPas}$, T20 U-cups).

**Figure 10.**The measured friction at the second outstroke with predefined lubrication conditions is plotted against the calculated fluid friction based on the measurement results obtained with the new procedure (room temperature, ambient pressure, mineral oils, T20 and EW U-cups).

**Table 1.**Viscosity classes (ISO VG) and dynamic viscosities $\eta \left(\vartheta \right)$ at different temperatures $\vartheta $ for the mineral oils used in this study.

Oil | Viscosity Class | Dynamic Viscosity $\mathit{\eta}\left(\mathit{\vartheta}\right)/$mPas | ||
---|---|---|---|---|

$\mathit{\eta}\left(20\xb0\mathbf{C}\right)$ | $\mathit{\eta}\left(25\xb0\mathbf{C}\right)$ | $\mathit{\eta}\left(30\xb0\mathbf{C}\right)$ | ||

FVA1 | ISO VG 15 | 28 | 22 | 18 |

FVA2 | ISO VG 32 | 72 | 54 | 42 |

FVA2 + FVA3 | ISO VG 68 | 161 | 119 | 90 |

FVA3 | ISO VG 100 | 288 | 205 | 150 |

FVA4 | ISO VG 460 | 1543 | 1040 | 720 |

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## Share and Cite

**MDPI and ACS Style**

Feuchtmüller, O.; Hörl, L.; Bauer, F.
An Empirical Study on the Friction of Reciprocating Rod Seals at Predefined Lubrication Conditions and Shear Rates. *Lubricants* **2022**, *10*, 56.
https://doi.org/10.3390/lubricants10040056

**AMA Style**

Feuchtmüller O, Hörl L, Bauer F.
An Empirical Study on the Friction of Reciprocating Rod Seals at Predefined Lubrication Conditions and Shear Rates. *Lubricants*. 2022; 10(4):56.
https://doi.org/10.3390/lubricants10040056

**Chicago/Turabian Style**

Feuchtmüller, Oliver, Lothar Hörl, and Frank Bauer.
2022. "An Empirical Study on the Friction of Reciprocating Rod Seals at Predefined Lubrication Conditions and Shear Rates" *Lubricants* 10, no. 4: 56.
https://doi.org/10.3390/lubricants10040056