# 螺旋槽机械密封瞬态启动过程润滑特性

1.西安交通大学现代设计及转子轴承系统教育部重点实验室，西安，7100492.中国石油大学(华东)密封技术研究所，青岛，266580

## 1 物理模型

Fig.1 Schematic diagram of sealing structure

Fig.2 Schematic diagram of spiral groove seal
ring structure

## 2 研究方法

### 2.1 密封动力学模型

(1)

Fig.3 Dynamic model of mechanical seal

FclsFflFas三者计算公式如下：

(2)

(3)

(4)

(5)

(6)

v(k+1)=v(k)+aΔt

(7)

h(k+1)=h(k)+vΔt+aΔt2

(8)

### 2.2 接触模型

Fas=Fe+Fp

(9)

Fig.4 Model of the contact between a rough and an
ideally smooth flat surface

### 2.3 流体润滑模型

(10)

Φ=ρ/ρc

(11)

(12)

Fig.5 Diagram of unit grid for finite difference method

(1)强制性边界条件：

p=pi Φ(r=ri,θ)=1

p=po Φ(r=ro,θ)=1

(2)周期性边界条件：

(3)JFO(Jokobsson-Floberg-Olsson)空化边

A(i,j)p(i+1,j)+B(i,j)p(i-1,j)+
C(i,j)p(i,j+1)+D(i,j)p(i,j-1)-
E(i,j)p(i,j)-F(i,j)Φ(i,j)+
G(i,j)Φ(i-1,j)-K(i,j)-L(i,j)=0

(13)

E(i,j)=A(i,j)+B(i,j)+C(i,j)+D(i,j)

p(i,j)=(A(i,j)p(i+1,j)+B(i,j)p(i-1,j)+
C(i,j)p(i,j+1)+D(i,j)p(i,j-1)-
F(i,j)Φ(i,j)+G(i,j)Φ(i-1,j)-
K(i,j)-L(i,j))/E(i,j)

(14)

Φ(i,j)=(A(i,j)p(i+1,j)+B(i,j)p(i-1,j)+
C(i,j)p(i,j+1)+D(i,j)p(i,j-1)-
E(i,j)p(i,j)+G(i,j)Φ(i-1,j)-
K(i,j)-L(i,j))/F(i,j)

(15)

(16)

(17)

(18)

### 2.4 特性参数

(1)泄漏量

(2)液膜刚度

(3)摩擦扭矩[12]

(4)摩擦力为液膜与粗糙峰摩擦力之和,即

### 2.5 计算流程

Fig.6 Calculation flow chart

## 3 结果分析

Tab.1 Geometrical and operation parameters ofmechanical seals

### 3.1 润滑状态转变分析

Fig.7 Single period pressure distribution of liquid film

(a)液膜厚度

(b)轴向速度

Fig.8 Variation of film thickness and velocity
with speed

Fig.9 Variation of bearing force with speed

(a)泄漏量随转速变化曲线

(b)液膜刚度随转速变化曲线

Fig.10 Leakage and stiffness with speed variation

Fig.11 Variation of frictional torque with
speed variation

### 3.2 操作参数影响

3.2.1 启动加速度影响

Fig.12 Variation of film thickness under different
start-up accelerations

Fig.13 Variation of friction coefficient under
different start-up accelerations

3.2.2 介质压力影响

(a)内径压力

(b)外径压力

Fig.14 Effect of medium pressure

Fig.15 Effect of spiral angle

### 3.3 结构参数影响

3.3.1 螺旋角影响

3.3.2 槽数影响

Fig.16 Effect of groove number

3.3.3 槽坝比影响

Fig.17 Effect of groove width ratio

3.3.4 槽深影响

Fig.18 Effect of groove depth

## 4 结论

(1)混合摩擦状态下液膜刚度较大且振荡幅值明显，液膜厚度在该状态下增大缓慢，在由混合润滑向流体动压润滑状态转变临界时刻，动环轴向速度有显著的增大，之后液膜厚度与泵送量显著增大。

(2)受液膜扩张与端面分离速度对动压承载能力的影响，较小的启动加速度可以在更低的转速下实现端面脱开。密封环内外径压力对系统闭合力有不同程度影响，较高的外压或较低的内压均有利于润滑状态的转变。

(3)为提高启动过程螺旋槽机械密封的端面脱开能力，建议取螺旋角为16°～24°，槽深为5～7 μm，槽数为20～24，槽坝比为2/3～5/6。

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# LubricationCharacteristicsofSpiralGrooveMechanicalSealsduringTransientStart-up

XU Lushuai1 WANG Yunlei1 ZHANG Fan1 HAO Muming2 YUAN Xiaoyang1

1.Key Laboratory of Education Ministry for Modern Design and Rotor-bearing System,Xi’an Jiaotong University,Xi’an,710049 2.Institute of Sealing Technology,China University of Petroleum(East China),Qingdao,Shandong,266580

Abstract: A mathematical model of lubrication characteristics and sealing performance in spiral groove mechanical seals during transient start-up was established，which included the average Reynolds equation with flow factors, contact factor and JFO(Jakobsson-Floberg-Olsson) (mass conserving) cavitation boundary, elastic-plastic asperity peak contact equation as well as the equations of axial dynamics model. Furthermore, the influences of different working conditions and structural parameters on lubricate regime transformation were compared. Results show that fluid bearing capacity and film thickness increase while the asperity peak contact force gradually decreases to zero during acceleration periods. Mixed lubrication regimes have larger film stiffness and more obvious oscillation amplitude compared with hydrodynamic lubrication regimes. A distinct mutation of axial speed appears when reaching separation speed. The smaller accelerated speed may achieve hydrodynamic lubrication regime at low speed affected by squeezing effect. Both higher outer pressure and lower inner pressure are beneficial to the transformation of lubrication regimes. The separation speed ascends at first and then descends with the increment of groove number. The decrease of spiral angle, groove depth and the increase of groove width ratio play an effective role in the ability of lubrication regime transformation.

Key words: mechanical seal; transient start-up; lubrication regime； squeeze effect

DOI：10.3969/j.issn.1004-132X.2020.16.001

(编辑 王艳丽)