介绍
Vis_cal用于计算润滑油的粘度系数和温度，参考于ISO 6336-22$^{[1]}$
原理
运动粘度
The kinematic viscosity at bulk temperature, $\nu_{\theta M}$, can be calculated from the kinematic viscosity at 40 $^\circ C$, $\nu_{40}$, and the kinematic viscosity at 100 $^\circ C$, $\nu_{100}$. Extrapolation for temperature higher than 140$^\circ C$ should be confirmed by measurement.
$$
log[log(\nu_{\theta M}+0.7)]=A·log(\theta_{M}+273)+B
$$
where
$$
A=\frac{log[log(\nu_{40}+0.7)/log(\nu_{100}+0.7)]}{log(313/373)}
$$
$$
B=log[log(\nu_{40}+0.7)]-A·log(313)
$$
where
$\theta_M$ is the bulk temperature.
$\nu_{40}$ is the kinematic viscosity of the lubricant at 40$^\circ C$
密度
If the density of the lubricant at bulk temperature, $\rho_{\theta M}$, is not available, it can be approximated based on the density of the lubricant at 15 $^\circ C$ according to
$$
\rho_{\theta M}=\rho_{15}·[1-\frac{(\theta_M+273)-288}{15\rho_{15}}]
$$
where
$\rho_{15}$ is the density of the lubricant at 15 $^\circ C$ according to the lubricant data sheet
$\theta_M$ is the bulk temperature
If no data for $\rho_{15}$ is available, then below formula can be used for approximation of mineral oils
$$
\rho_{15}=43.37log\nu_{40}+805.5
$$
类结构
输入 input：
- T : 温度
参数 params:
- Material ：润滑油的材料属性
输出 output :
- Rou : 润滑油在该温度下的密度
- Vis1 : 该温度下运动粘度系数
- Vis2 : 该温度下动力粘度系数
- B : 参数B
- A : 参数A
案例
以ISO-VG 100为例，计算70℃时的运动粘度系数。
%% Caculate the vis
S=RMaterial('Lubricant');
Mat=GetMat(S,3);
inputStruct1.T=70;
paramsStruct1.Material=Mat{1,1};
Vis=method.Vis_cal(paramsStruct1, inputStruct1);
Vis=Vis.solve();
%% Plot vis, rou&Tempearture curve
x=(30:10:150)';
y1=NaN(numel(x),1);
y2=NaN(numel(x),1);
for i=1:numel(x)
Vis.input.T=x(i);
Vis=Vis.solve();
y1(i)=Vis.output.Vis1;
y2(i)=Vis.output.Rou;
end
figure
plot(x,y1)
title('Kinematic Viscosity & Temperature Curve')
xlabel('Temperature (℃)')
ylabel('Kinematic Viscosity (mm2/s)')
figure
plot(x,y2)
title('Density & Temperature Curve')
xlabel('Temperature (℃)')
ylabel('Density (g/cm3)')
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参考文献
[1] ISO\TR 6336-22
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