Detailed explanation of SolidWorks mass characteristics (inertia tensor, moment of inertia, inertia spindle)

SolidWorks Detailed explanation of quality characteristics （ Inertia tensor 、 Moment of inertia 、 Inertial spindle ）

Reprinted from ：SolidWorks Detailed explanation of quality characteristics （ Inertia tensor 、 Moment of inertia 、 Inertial spindle ） - CAD2D3D.com

Catalog ： Technical tutorials    author ：CAD2D3D.com   date ：2014/04/21

SolidWorks Quality characteristics include quality 、 Volume 、 Surface area 、 Focus 、 Inertial spindle 、 Main moment of inertia 、 Inertia tensor 、 Moment of inertia, etc , The above values are Mechanical design Commonly used values in calculation , Therefore, we must correctly understand SolidWorks The calculation principle and formula of these values in .

see SolidWorks Method of quality characteristics ：

stay menu bar   Tools   Drop down menu choice   Quality characteristics , The quality characteristic dialog box pops up , The specific cases are as follows ：

notes ： Before viewing the quality properties , The part must be assigned a material , In this way, we can get the correct result . The above case is for calculation purposes , Set the material to 1000Kg/m3 The quality above 、 Volume 、 Surface area 、 There is no need to say more about the center of gravity , To be specific   Inertial spindle 、 Main moment of inertia 、 Inertia tensor .

The meaning of moment of inertia ：

Moment of inertia is also called moment of inertia （Moment of inertia）, Usually, the I or J Express , The basic unit of the international system of units is kg·m2. Moment of inertia is used to describe the resistance of an object to changes in its rotational motion , Is the inertia of an object with respect to its rotational motion . The role of moment of inertia in rotational dynamics is equivalent to that of mass in linear dynamics , Describe angular momentum 、 angular velocity 、 The relationship between torque and angular acceleration . For a particle ,I=mr2, among m It's the quality ,r Is the vertical distance between the particle and the axis of rotation . For a system with multiple particles ：

. The moment of inertia of a regular rigid body , There are usually specific calculation formulas , For example, the calculation formula of a rectangular rigid body is as follows ：

Definition of inertia tensor

Definition of principal moment of inertia and principal axis of inertia

When the rigid body rotates around the inertia axis , The binding force of the bearing is 0. Knowing the above definition , Let's see how to use it 3D Software SolidWorks  Calculated inertia principal axis 、 Main moment of inertia 、 Inertia tensor, etc .

Above mentioned 1 Item description

The origin of the coordinate system is the position of the center of gravity ,Ix = (0.00, 1.00, 0.00),Iy = (-1.00, 0.00, 0.00), Iz = (0.00, 0.00, 1.00) yes 3 eigenvectors , The direction of the inertia principal axis is pointed out .Px,Py,Pz Around their respective axes   Main moment of inertia , Also known as the principal moment of inertia .

Above mentioned 2 Item description

The origin of the coordinate system and the 1 It's the same , It's just  xyz 3 The direction of the axis changes to   Align the output coordinate system .

Above mentioned 3 Item description

Calculate the origin and direction of inertia tensor coordinate system and   Output coordinate system equally . Using the moment of inertia   Parallel axis theorem , The first 3 Term Ixx、Iyy、Izz It can be determined by 2 Term  Lxx、Lyy、Lzz  calculated . Let's calculate Ixx Make an example ： Parallel axis theorem ：Ixx（ The first 3 term ）=Lxx（ The first 2 term ）+md2=544.00+0.48×(502+302)=2176.00

This case SolidWorks 3D File download address ： Micro disk   Extract password ：U77B