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 北京化工大学学报(自然科学版)  2017, Vol. 44 Issue (6): 70-75  DOI: 10.13543/j.bhxbzr.2017.06.011 0

### 引用本文

FAN ZhengTian, SHANG YanLong, ZHANG YiDan, MAO ZhiWei, JIANG ZhiNong. An angle-domain conversion method based on the instantaneous rotational speed signal of a diesel engine[J]. Journal of Beijing University of Chemical Technology (Natural Science), 2017, 44(6): 70-75. DOI: 10.13543/j.bhxbzr.2017.06.011.

### 文章历史

1. 北京化工大学 机电工程学院 高端机械装备健康监控与自愈化北京市重点实验室, 北京 100029;
2. 海军装备技术研究所, 北京 102442

An angle-domain conversion method based on the instantaneous rotational speed signal of a diesel engine
FAN ZhengTian 1, SHANG YanLong 2, ZHANG YiDan 1, MAO ZhiWei 1, JIANG ZhiNong 1
1. Beijing Key Laboratory of Health Monitoring Control and Fault Self-Recovery for High-end Machinery, College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029;
2. Naval Institute of Technology and Equipment, Beijing 102442, China
Abstract: In the fault diagnosis of reciprocating machinery, the traditional fault diagnosis method involving dividing the angle into equal intervals using the average rotational speed is inaccurate. A method of using the instantaneous rotational speed to transform the time-domain signal of a diesel engine into the angle-domain has been developed in this work. The main factors influencing the phase deviation in the method of the angular division of the average rotational speed under the condition of large rotational speed fluctuation are discussed, and the threshold parameter set according to the magnitude of the speed fluctuation rate and the expected angle-domain accuracy range. It is possible to automatically determine which method should be selected to perform the angle-domain conversion based on the threshold parameter. The results showed that phase deviation can be avoided by using the instantaneous rotation speed to transform the time-domain signal into the angle-domain under the conditions of speed fluctuation, which provides a basis for the fault diagnosis of diesel engines based on the angle-domain.
Key words: diesel engine    instantaneous rotational speed    angle-domain signal

1 瞬时转速的测量

 图 1 瞬时转速测量原理图、示意图及装置实物图 Fig.1 Schematic diagram of the instantaneous speed measurement, schematic diagram of the device and photograph of the device object

 $T = N{t_0}$ (1)

 $\bar n = \frac{{60}}{{360}}\frac{\theta }{T} = \frac{\theta }{{6T}}$ (2)

 $n \approx \bar n = \frac{\theta }{{6T}}$ (3)
2 柴油机时域信号的角域转换 2.1 基于平均转速信号

 $t = N/\left( {60{f_{\rm{s}}}} \right)$ (4)

 ${n_{\rm{r}}} = 2/t$ (5)

 ${\theta _{\rm{r}}} = 2{\rm{ \mathsf{ π} }}{n_{\rm{r}}}/60t \times 180/{\rm{ \mathsf{ π} }} = 6{n_{\rm{r}}}t$ (6)
2.2 基于瞬时转速信号

 ${\theta _{\rm{i}}} = 2{\rm{ \mathsf{ π} }}\int_0^t {{n_{\rm{i}}}{\rm{d}}t/60} \times \left( {180/{\rm{ \mathsf{ π} }}} \right) = 6\int_0^t {{n_{\rm{i}}}{\rm{d}}t}$ (7)
2.3 角域转换方法判断

 $\omega = {\omega _{\rm{m}}} + A\sin \left( {Bt} \right)$ (8)

 ${\theta _{\rm{t}}} = 6\int_0^t {\omega {\rm{d}}t} = 6\int_0^t {\left[ {{\omega _{\rm{m}}} + A\sin \left( {Bt} \right)} \right]{\rm{d}}t} = {\theta _{\rm{m}}} + \Delta \theta$ (9)
 $\left| {\Delta \theta } \right| = \frac{A}{B}\left( {1 - \cos Bt} \right) \le 2\frac{A}{B}$ (10)

 $B = 2{\rm{ \mathsf{ π} }}f = 2{\rm{ \mathsf{ π} }}\frac{{x{f_{\rm{c}}}}}{2} = {\rm{ \mathsf{ π} }}x{f_{\rm{c}}}$ (11)

 $\Delta {\theta _{\max }} = 2\frac{A}{{{\rm{ \mathsf{ π} }}x{f_{\rm{c}}}}}$ (12)

 $A = \frac{{360\Delta n}}{{60}} = 6\Delta n,{f_{\rm{c}}} = \frac{{{n_{\rm{m}}}}}{{60}}$ (13)

 $\Delta {\theta _{\max }} = \frac{{2 \times 6\Delta n}}{{{\rm{ \mathsf{ π} }}x{f_{\rm{c}}}}} = \frac{{2 \times 6\Delta n}}{{{\rm{ \mathsf{ π} }}x\frac{{{n_{\rm{m}}}}}{{60}}}} = \frac{{720\Delta n}}{{{\rm{ \mathsf{ π} }}x{n_{\rm{m}}}}} \propto \frac{{\Delta n}}{{{n_{\rm{m}}}}}$ (14)

 图 2 角域转换方法的判断流程图 Fig.2 Flow chart for the angle domain conversion method
3 角域转换方法试验验证 3.1 基于瞬时转速信号的角域转换方法验证

 图 3 启机点火相位异常工况下曲轴转角与缸内压力关系 Fig.3 Relationship between crank angle and cylinder pressure during the abnormal ignition phase of enginestart-up

3.2 角域转换方法试验对比

 图 4 转速波动较大工况下时间与曲轴转角及时间与相位偏差关系 Fig.4 The relationships between time and crank angle, and time and phase deviation under high speed fluctuation

 图 5 转速波动较大工况下曲轴转角和缸盖振动值关系 Fig.5 Relationship between crankshaft angle and cylinder head vibration under high speed fluctuation

 图 6 转速波动平稳工况下时间与曲轴转角及时间与相位偏差关系 Fig.6 The relationships between time and crank angle, and time and phase deviation under steady speed fluctuation
 图 7 转速波动平稳工况下曲轴转角和缸盖振动值关系 Fig.7 Relationship between crankshaft angle and cylinder head vibration under steady speed fluctuation

 图 8 不同转速波动下Δn/nm与相位偏差的关系曲线 Fig.8 The relationship between Δn/nm and phase deviation under different speed fluctuations
4 结论

(1) 根据Δn/nm的大小可以判定柴油机组是否需要利用瞬时转速进行角域转换。针对不同机组转速波动量大小及预期角域精度范围，可设定与Δn/nm正相关的参数α，当Δn/nm大于α时，需利用瞬时转速进行角域转换。

(2) 对于试验柴油机组，在转速波动较为平稳的工况下，即Δn/nm < 0.1时，利用平均转速进行角域转换是可行的，此时引起的相位偏差较小可以忽略。

(3) 在转速波动较大的工况下，即Δn/nm>0.1时，利用平均转速进行角域转换存在4°的相位偏差，可能导致故障误判。此时利用瞬时转速进行角域转换较为精确，能够有效减小相位偏差。

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