Foreword
The dynamic analysis of mechanical systems is a very old research topic, and there are many solutions. With the continuous development of larger computer software, a simple, practical, intuitive and accurate research method is needed. The author found that the three-dimensional design software SolidWorks modeling is relatively simple, beginners easy to use, plus later integrated seamlessly full-featured motion simulation software COSMOSMotion, can perform complex kinematics simulation and dynamic static analysis of complex mechanical systems. If a large number of mechanical system motions and dynamic parameters (such as the kinetic energy curve of each component, the system balance torque curve, etc.) obtained by the simulation are used, the dynamic model of the mechanical system can be established by processing with an Excel spreadsheet and then used. The numerical solution of differential equations - the difference method can easily solve the real motion law of the mechanical system in the stable operation phase.
Based on this idea, the author took the planer as an example, after repeated trial and error, a relatively simple mechanical system dynamics analysis method was finally obtained. That is, first use Solidworks software to build a three-dimensional model of the mechanical system, and then use COSMOSMotion software for motion simulation, and its simulation results are exported to an Excel spreadsheet. Then the data of these simulation results are analyzed and processed in an Excel spreadsheet to obtain the equivalent parameters of the mechanical system (such as the equivalent moment of inertia, equivalent torque, etc.), establish the dynamic equation of the mechanical system, and finally use the formula of Excel. Calculate the function and solve the numerical solution of the dynamic equation - the real motion law of the mechanical system.
The biggest advantages of this method of dynamic analysis of mechanical systems are: SolidWorks operation technology is easy to grasp; COSMOSMotion simulation function is powerful, and the definitions of constraints, forces, moments, motions, and other concepts are consistent with the definition in the mechanical principle; easy to understand; Excel Software is more commonly used; the entire solution process is not programmed.
The following describes the application of this method in the dynamics analysis of the mechanical planer.
1 Create a virtual prototype
B650 planer mainly consists of rams, rocker arms, large helical gears, gear shifting/deceleration devices, belt drives, motors, worktables, feed devices and airframes. According to the measured data, all parts are manufactured and assembled in SolidWorks. Finally, the virtual prototype shown in Figure 1 is obtained (the fuselage and other parts are hidden in the figure). From Figure 1 can reflect the main drive route: motor belt drive (small pulley large pulley) a spline shaft - slip gear set a gear shaft a large helical gear - slider 1 (not visible in the figure) - Rocker and slider 2 a connector, pin 1 and 2 a ram, cutter bar.
2 motion simulation
The COsM0sMotion software has strong simulation capabilities, supports multiple constraints and virtual constraints, and can define various motions according to displacement, velocity, or acceleration, including fixed-value, stepping, harmonics, spline curves, and functions. With COSMOsMotion it is possible to simulate the precise movement and dynamic static analysis of various complex mechanical systems.
The key to the success of simulation is the setting of simulation parameters. COSMOSMotion simulation settings include dividing motion and stationary components, adding motion constraints, defining motion of the original move, adding working resistance, and more.
2.1 Component Grouping
In COSMOSMotion, components need to be divided into two categories: moving parts and stationary parts. The author puts the components related to motion analysis on the moving parts group, and the parts that are not related to the motion analysis or the motion analysis are fixed parts (the V band can be set as the stationary part). In order to observe conveniently, the static parts that affect the observation are generally compressed or hidden.
2.2 Add Constraints
When entering the COSMOSMotion interface, the software automatically adds constraints to components based on the fit between the components in the assembly drawing. But in the simulation, according to the specific analysis objects and analysis content, some constraints must be added, deleted, and adjusted.
The "fixed pair" constraint in C0SMOSMotion is used to lock two rigid components so that they cannot do relative motion, which is equivalent to welding two components together in the real world. There is no relative movement between the arbor, the connecting piece and the ram in the shaper, the pin 1, the pin 2 and the connecting piece, the large pulley, the slipping gear set and the spline shaft, so they have The constraint is "fixed pair".
The "rotary pair" constraint allows only one degree of relative rotation between two rigid members. Between the motor and the small pulley (including the motor rotor), the spline shaft and the bearing (equivalent to the frame), between the gear shaft and the bearing (equivalent to the frame), the large helical gear (crank) and Between the frame (fuselage), between the large helical gear (corresponding to the crank) and the slider l, between the slider 2 and the frame (body), between the rocker arm and the connector (or pin 1) There is only one relative rotation, so the constraint between them uses "rotation pair".
The "moving pair" constraint allows only 1 degree of relative movement between 2 rigid members. Between the slider l, the slider 2 and the rocker in the shaper, there is only one relative movement between the ram and the frame (airframe), so the constraint between them is "moving pair". In the COSMOSMotion software, the motion simulation of the gear transmission and the belt drive is realized by "coupling". The belt between the small pulley and the large pulley in the shaper is the belt transmission. The gear between the slip gear set (or the spline shaft) and the gear shaft and between the gear shaft and the large helical gear are all geared, so the The "coupled" approach defines the motion relationship between them. The three "coupled" ratios are 355/75, 36/55 and 84/21.
2.3 Enter movement
For analysis convenience, the large helical gear (equivalent to the crank of the guide rod mechanism) is selected as the moving part during the system motion analysis, and the rotation speed can be set according to the rotation speed n4 in the real system.
The original moving speed can also be optional. Because when establishing the equivalent dynamic model, the ratio of the speed of each component to the original moving part is used in the calculation of the system equivalent moment of inertia and the equivalent torque, and has nothing to do with the actual speed.
2.4 Add working resistance
2.5 Simulation and Result Output
At this point, you can run the simulation and output the total kinetic energy curve (including moving kinetic energy and rotational kinetic energy) of each part of the shaper to Excel. In addition, it is also necessary to separately simulate the movement of the mechanical system under the action of "no working resistance and gravity" and "with working resistance and gravity", and output the balance between these two conditions acting on the large helical gear. The couple moment curve is shown in Figure 3.
Any mechanical system can be reduced to the following equivalent dynamic model:
In dynamic static analysis, if the system is not affected by working resistance and gravity, the system balance moment is caused by the inertia force and inertia moment of each component, and the system balance moment under the action of resistance and gravity. It also contains the effects of gravity and working resistance. Therefore, subtracting the moment of equilibrium under the former condition with the latter is the equivalent moment of working resistance and gravity (the author has verified the validity of this conclusion). According to this equal relationship, the equivalent moment (resistance moment) curve of working resistance and gravity in the planer shown in FIG. 3 can be obtained through Excel analysis and calculation.
Assuming that the equivalent driving torque is a constant torque, its value can be used as a formula
According to the principle of equivalent kinetic energy before and after the system, the equivalent moment of inertia of the system can be calculated.
3.3 Solve the true speed of the equivalent component
It can be seen from the above that the equivalent dynamic model of the planer is formula (3), in which the system equivalent moment and the equivalent moment of inertia have been obtained in the form of a curve (Figs. 3 and 4). The difference method can now be used to find the equivalent The angular velocity of the component, ω, is the actual speed of the large helical gear in a real system. The solution formula is as follows:
4 Conclusion
This article makes full use of the modeling function of SolidWorks and the motion simulation function of COSMOSM0tion, and combines Excel's analysis, calculation and graph display functions to realize the dynamic analysis of the planer system. The software used in this research method is easy to learn, the method used is practical and reliable, and the results obtained are accurate and true. It is applicable to the kinematics and dynamics of any mechanical system.
The dynamic analysis of mechanical systems is a very old research topic, and there are many solutions. With the continuous development of larger computer software, a simple, practical, intuitive and accurate research method is needed. The author found that the three-dimensional design software SolidWorks modeling is relatively simple, beginners easy to use, plus later integrated seamlessly full-featured motion simulation software COSMOSMotion, can perform complex kinematics simulation and dynamic static analysis of complex mechanical systems. If a large number of mechanical system motions and dynamic parameters (such as the kinetic energy curve of each component, the system balance torque curve, etc.) obtained by the simulation are used, the dynamic model of the mechanical system can be established by processing with an Excel spreadsheet and then used. The numerical solution of differential equations - the difference method can easily solve the real motion law of the mechanical system in the stable operation phase.
Based on this idea, the author took the planer as an example, after repeated trial and error, a relatively simple mechanical system dynamics analysis method was finally obtained. That is, first use Solidworks software to build a three-dimensional model of the mechanical system, and then use COSMOSMotion software for motion simulation, and its simulation results are exported to an Excel spreadsheet. Then the data of these simulation results are analyzed and processed in an Excel spreadsheet to obtain the equivalent parameters of the mechanical system (such as the equivalent moment of inertia, equivalent torque, etc.), establish the dynamic equation of the mechanical system, and finally use the formula of Excel. Calculate the function and solve the numerical solution of the dynamic equation - the real motion law of the mechanical system.
The biggest advantages of this method of dynamic analysis of mechanical systems are: SolidWorks operation technology is easy to grasp; COSMOSMotion simulation function is powerful, and the definitions of constraints, forces, moments, motions, and other concepts are consistent with the definition in the mechanical principle; easy to understand; Excel Software is more commonly used; the entire solution process is not programmed.
The following describes the application of this method in the dynamics analysis of the mechanical planer.
1 Create a virtual prototype
B650 planer mainly consists of rams, rocker arms, large helical gears, gear shifting/deceleration devices, belt drives, motors, worktables, feed devices and airframes. According to the measured data, all parts are manufactured and assembled in SolidWorks. Finally, the virtual prototype shown in Figure 1 is obtained (the fuselage and other parts are hidden in the figure). From Figure 1 can reflect the main drive route: motor belt drive (small pulley large pulley) a spline shaft - slip gear set a gear shaft a large helical gear - slider 1 (not visible in the figure) - Rocker and slider 2 a connector, pin 1 and 2 a ram, cutter bar.
Figure 1 Main Drive of B650 Planer
2 motion simulation
The COsM0sMotion software has strong simulation capabilities, supports multiple constraints and virtual constraints, and can define various motions according to displacement, velocity, or acceleration, including fixed-value, stepping, harmonics, spline curves, and functions. With COSMOsMotion it is possible to simulate the precise movement and dynamic static analysis of various complex mechanical systems.
The key to the success of simulation is the setting of simulation parameters. COSMOSMotion simulation settings include dividing motion and stationary components, adding motion constraints, defining motion of the original move, adding working resistance, and more.
2.1 Component Grouping
In COSMOSMotion, components need to be divided into two categories: moving parts and stationary parts. The author puts the components related to motion analysis on the moving parts group, and the parts that are not related to the motion analysis or the motion analysis are fixed parts (the V band can be set as the stationary part). In order to observe conveniently, the static parts that affect the observation are generally compressed or hidden.
2.2 Add Constraints
When entering the COSMOSMotion interface, the software automatically adds constraints to components based on the fit between the components in the assembly drawing. But in the simulation, according to the specific analysis objects and analysis content, some constraints must be added, deleted, and adjusted.
The "fixed pair" constraint in C0SMOSMotion is used to lock two rigid components so that they cannot do relative motion, which is equivalent to welding two components together in the real world. There is no relative movement between the arbor, the connecting piece and the ram in the shaper, the pin 1, the pin 2 and the connecting piece, the large pulley, the slipping gear set and the spline shaft, so they have The constraint is "fixed pair".
The "rotary pair" constraint allows only one degree of relative rotation between two rigid members. Between the motor and the small pulley (including the motor rotor), the spline shaft and the bearing (equivalent to the frame), between the gear shaft and the bearing (equivalent to the frame), the large helical gear (crank) and Between the frame (fuselage), between the large helical gear (corresponding to the crank) and the slider l, between the slider 2 and the frame (body), between the rocker arm and the connector (or pin 1) There is only one relative rotation, so the constraint between them uses "rotation pair".
The "moving pair" constraint allows only 1 degree of relative movement between 2 rigid members. Between the slider l, the slider 2 and the rocker in the shaper, there is only one relative movement between the ram and the frame (airframe), so the constraint between them is "moving pair". In the COSMOSMotion software, the motion simulation of the gear transmission and the belt drive is realized by "coupling". The belt between the small pulley and the large pulley in the shaper is the belt transmission. The gear between the slip gear set (or the spline shaft) and the gear shaft and between the gear shaft and the large helical gear are all geared, so the The "coupled" approach defines the motion relationship between them. The three "coupled" ratios are 355/75, 36/55 and 84/21.
2.3 Enter movement
For analysis convenience, the large helical gear (equivalent to the crank of the guide rod mechanism) is selected as the moving part during the system motion analysis, and the rotation speed can be set according to the rotation speed n4 in the real system.
The original moving speed can also be optional. Because when establishing the equivalent dynamic model, the ratio of the speed of each component to the original moving part is used in the calculation of the system equivalent moment of inertia and the equivalent torque, and has nothing to do with the actual speed.
2.4 Add working resistance
2.5 Simulation and Result Output
At this point, you can run the simulation and output the total kinetic energy curve (including moving kinetic energy and rotational kinetic energy) of each part of the shaper to Excel. In addition, it is also necessary to separately simulate the movement of the mechanical system under the action of "no working resistance and gravity" and "with working resistance and gravity", and output the balance between these two conditions acting on the large helical gear. The couple moment curve is shown in Figure 3.
Fig. 3 Balanced couple moment to equivalent moment
Any mechanical system can be reduced to the following equivalent dynamic model:
In dynamic static analysis, if the system is not affected by working resistance and gravity, the system balance moment is caused by the inertia force and inertia moment of each component, and the system balance moment under the action of resistance and gravity. It also contains the effects of gravity and working resistance. Therefore, subtracting the moment of equilibrium under the former condition with the latter is the equivalent moment of working resistance and gravity (the author has verified the validity of this conclusion). According to this equal relationship, the equivalent moment (resistance moment) curve of working resistance and gravity in the planer shown in FIG. 3 can be obtained through Excel analysis and calculation.
Assuming that the equivalent driving torque is a constant torque, its value can be used as a formula
According to the principle of equivalent kinetic energy before and after the system, the equivalent moment of inertia of the system can be calculated.
Figure 4 System equivalent moment of inertia
3.3 Solve the true speed of the equivalent component
It can be seen from the above that the equivalent dynamic model of the planer is formula (3), in which the system equivalent moment and the equivalent moment of inertia have been obtained in the form of a curve (Figs. 3 and 4). The difference method can now be used to find the equivalent The angular velocity of the component, ω, is the actual speed of the large helical gear in a real system. The solution formula is as follows:
4 Conclusion
This article makes full use of the modeling function of SolidWorks and the motion simulation function of COSMOSM0tion, and combines Excel's analysis, calculation and graph display functions to realize the dynamic analysis of the planer system. The software used in this research method is easy to learn, the method used is practical and reliable, and the results obtained are accurate and true. It is applicable to the kinematics and dynamics of any mechanical system.