# Optimization of a New High Rotary Missile-Borne Stabilization Platform

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## Abstract

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## 1. Introduction

## 2. Working Principle of Passive Semi-Strapdown Roll Stabilized Platform

#### 2.1. Composition and Working Principle of the Platform

#### 2.2. The Dynamic Model of Passive Semi-Strapdown Roll Stabilized Platform

## 3. Improvement Principle of Bearing Device

## 4. Calculation Model of Friction Moment in Bearing

#### 4.1. Calculation of the Traditional Signal Bearing Friction Moment

#### 4.2. Establishment of a Calculation Model for the Friction Moment of a Bearing Nested Structure

#### 4.3. Bearing Type Selection and Relevant Parameters

## 5. Simulation Verification

#### 5.1. Axial Reliability Verification of the Bearing Nested Structure

^{−5}mm, and that of a bearing nested structure under a 10g axial load is 3.5803 × 10

^{−6}mm. Obviously, under the same axial load, the maximum deformation of the bearing nested structure is reduced by an order of magnitude compared with that of the single bearing structure.

#### 5.2. Calculation of the Theoretical Frictional Moment of a Bearing Nested Structure

## 6. Test Verification

#### 6.1. Impact Test

#### 6.2. Vehicle Test

## 7. Conclusions

- Compared with the method of using only a single bearing, the scheme proposed in this paper has complementary advantages and can be better applied to the actual application environment Combining the large axial bearing capacity of angular contact ball bearings with the characteristic of the low cost and low friction coefficient of deep groove ball bearings to achieve the complementary advantages of bearing nested structure.
- The friction moment of the passive semi-strapdown roll stabilized platform is reduced effectively. The bearing nested structure effectively solves the problem of large friction of a single bearing in high speed and high overload environments by adopting the way of “multi-stage isolation and indirect drive”, and significantly reduces the swing angular rate of the platform inner cylinder, which is beneficial to realize the high-precision navigation solution of the platform.
- Improves the anti-overload capability and environmental adaptability of the platform. The bearing nested structure improves the axial overload resistance of the whole platform by means of multiple bearings bearing together.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The structural composition diagram of the passive semi-strapdown roll stabilized platform.

**Figure 14.**Simulation of the platform inner cylinder swing angular rate based on the single bearing and two-stage bearing nested structure under 900 r/min.

**Figure 16.**(

**a**) The state of a single bearing after the impact test. (

**b**) The state of the bearing nested structure after the impact test.

**Figure 18.**Actual value of the platform inner cylinder swing angular rate based on the single bearing and two-stage bearing nested structure under 900 r/min.

**Figure 19.**(

**a**) The yaw angle error of the platform based on the single bearing and two-stage bearing nested structure. (

**b**) The pitch angle error of the platform based on the single bearing and two-stage bearing nested structure. (

**c**) The roll angle error of the platform based on the single bearing and two-stage bearing nested structure.

**Figure 20.**(

**a**) The eastern position error of the platform based on the single bearing and two-stage bearing nested structure. (

**b**) The northern position error of the platform based on the single bearing and two-stage bearing nested structure. (

**c**) The upper position error of the platform based on the single bearing and two-stage bearing nested structure.

Bearing Type | Rolling Friction Variable ${\mathit{G}}_{\mathbf{rr}}$ | Sliding Friction Variable ${\mathit{G}}_{\mathbf{sl}}$ |
---|---|---|

Deep groove ball bearing | ${G}_{\mathrm{rr}}={R}_{1}{d}_{\mathrm{m}}{({F}_{\mathrm{r}}+\frac{{R}_{2}}{\mathrm{sin}{\alpha}_{\mathrm{F}}})}^{0.54}$ ${\alpha}_{\mathrm{F}}=24.6\times {({F}_{\mathrm{a}}/{C}_{0})}^{0.24}$ | ${G}_{\mathrm{sl}}={R}_{1}{d}_{\mathrm{m}}^{-0.145}{({F}_{\mathrm{r}}^{5}+\frac{{S}_{2}{d}_{\mathrm{m}}^{1.5}}{\mathrm{sin}{\alpha}_{\mathrm{F}}}{F}_{\mathrm{a}}^{4})}^{1/3}$ |

Angular contact ball bearing | ${G}_{\mathrm{rr}}={R}_{1}{d}_{m}^{1.97}{\left[{F}_{r}+{F}_{g}+{R}_{2}{F}_{a}\right]}^{0.54}$ ${F}_{\mathrm{g}}={R}_{3}{d}_{\mathrm{m}}^{4}{n}^{2}$ | ${G}_{\mathrm{sl}}={S}_{1}{d}_{\mathrm{m}}^{0.26}\left[{({F}_{\mathrm{r}}+{F}_{\mathrm{g}})}^{4/3}+{S}_{2}{F}_{\mathrm{a}}^{4/3}\right]$ ${F}_{\mathrm{g}}={S}_{3}{d}_{\mathrm{m}}^{4}{n}^{2}$ |

Parameter | Deep Groove Ball Bearing SKF6200 | Angular Contact Ball Bearing SKF7008AC |
---|---|---|

Outer diameter D (mm) | 30 | 68 |

Inner diameter d (mm) | 10 | 40 |

Limit speed (r·min ^{−1}) | 34,000 | 26,000 |

Rated static load C_{0} (kN) | 2.36 | 5.3 |

Friction coefficient μ | 0.0015 | 0.0020 |

R_{1} | 3.9 × 10^{−7} | 5.03 × 10^{−7} |

R_{2} | 1.7 | 1.97 |

R_{3} | / | 1.90 × 10^{−12} |

S_{1} | 3.23 × 10^{−3} | 1.30 × 10^{−2} |

S_{2} | 36.5 | 0.68 |

S_{3} | / | 1.91 × 10^{−12} |

Material | Elastic Modulus/GPa | Density/(kg·m^{−3}) | Poisson’s Ratio | Yield Strength/MPa |
---|---|---|---|---|

GCr15 bearing steel | 210 | 7810 | 0.29 | 1458 |

Parameter | Numerical Value |
---|---|

m/kg | 1 |

${J}_{o}$/(kg·mm^{2}) | 5860 |

L/mm | 14 |

g/(m/s^{2}) | 9.8 |

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## Share and Cite

**MDPI and ACS Style**

Wei, X.; Li, J.; Zhang, D.; Feng, K.; Zhang, J.; Li, J.; Lu, Z.
Optimization of a New High Rotary Missile-Borne Stabilization Platform. *Sensors* **2019**, *19*, 4143.
https://doi.org/10.3390/s19194143

**AMA Style**

Wei X, Li J, Zhang D, Feng K, Zhang J, Li J, Lu Z.
Optimization of a New High Rotary Missile-Borne Stabilization Platform. *Sensors*. 2019; 19(19):4143.
https://doi.org/10.3390/s19194143

**Chicago/Turabian Style**

Wei, Xiaokai, Jie Li, Debiao Zhang, Kaiqiang Feng, Jiayu Zhang, Jinqiang Li, and Zhenglong Lu.
2019. "Optimization of a New High Rotary Missile-Borne Stabilization Platform" *Sensors* 19, no. 19: 4143.
https://doi.org/10.3390/s19194143