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Dynamic analysis of shaper based on COSMOSMOTION and excel

preface

Dynamic Analysis of mechanical system is a very old research topic, and there are many solutions now. With the continuous development of larger computer software, such as tuna and pet food, a simple, practical, intuitive and accurate research method is needed. The author found that the modeling of the three-dimensional design software SolidWorks is relatively simple and easy for beginners. In addition, the full-function motion simulation software COSMOSMOTION is seamlessly integrated in the later version, which can carry out complete kinematic simulation and dynamic static analysis of complex mechanical systems. If a large number of mechanical system motion and dynamic parameters (such as kinetic energy curve of each component, system balance torque curve, etc.) obtained from the simulation are processed by Excel spreadsheet, the dynamic model of the mechanical system can be established, and then the real motion law of the mechanical system in the stable operation stage can be easily solved by using the numerical solution of differential equations -- difference method

based on this idea, the author took the shaper as an example, and finally obtained a relatively simple mechanical system power credit after repeated experiments. Plastic has become the core material composition analysis method of most electronic and electrical products. That is, first use SolidWorks software to establish the three-dimensional model of mechanical system, then use COSMOSMOTION software to carry out motion simulation, and output the simulation results to excel spreadsheet. Then, these simulation results are analyzed and processed in Excel spreadsheet, so as to obtain the equivalent parameters of the mechanical system (such as equivalent moment of inertia, equivalent torque, etc.), establish the dynamic equation of the mechanical system, and finally use the formula calculation function of Excel to solve the numerical solution of the dynamic equation - the real motion law of the mechanical system

the biggest advantage of this mechanical system dynamics analysis method is that SolidWorks operation technology is easy to master; COSMOSMOTION simulation has powerful functions, and the definitions of constraints, forces, moments, motions and other concepts are consistent with those in mechanical principles, which is easy to understand; Excel software is commonly used; The whole solution process does not need programming

the application of this method in dynamic analysis of mechanical system of shaper is introduced below

1 establish a virtual prototype

b650 shaper is mainly composed of ram, rocker arm, large helical gear, gear speed change/reduction device, belt drive, motor, workbench, feeding device and body. According to the measured data, all parts are manufactured and assembled in SolidWorks, and finally the virtual prototype shown in Figure 1 is obtained (the body and other parts in the figure have been hidden). The main transmission route can be reflected in Figure 1: motor belt transmission (small belt pulley and large belt pulley) - spline shaft - sliding gear set - gear shaft - large helical gear - slider 1 (not visible in the figure) - rocker arm and slider 2 - connector, pins 1 and 2 - ram and cutter bar

Figure 1 b650 shaper main drive

for the convenience of analysis, it is assumed that the gear speed change device of the shaper is in the meshing state shown in the figure. The transmission parameters are as follows: the reference diameter of the small pulley is 75mm, the reference diameter of the large pulley is 355mm, the number of gears engaged between the spline shaft and the gear shaft is 55 and 36 respectively, and the number of gears engaged between the gear shaft and the large helical gear is 21 and 84 respectively

2 motion simulation

cosm0smotion software has strong simulation function, supports a variety of constraints and virtual constraints, and can define various motions according to displacement, speed or acceleration, including fixed value, step, harmonic, spline curve and function. COSMOSMOTION can be used to simulate the precise motion of various complex mechanical systems and carry out dynamic static analysis

the key to the success of simulation lies in the setting of simulation parameters. COSMOSMOTION simulation settings include dividing moving and stationary components, adding kinematic pair constraints, defining prime mover motion, adding working resistance, and so on

2.1 parts grouping

in COSMOSMOTION, parts need to be divided into two categories: moving parts and static parts. The author puts the parts related to motion analysis into the moving parts group, and the parts irrelevant to motion analysis or fixed during motion analysis are set as static parts (the V-belt can be set as static parts). For convenience of observation, static parts that affect observation are usually compressed or hidden

2.2 add constraints

when entering the COSMOSMOTION interface, the software will automatically add constraints for components according to the matching relationship between components in the assembly drawing. However, some constraints should be added, deleted and adjusted according to the specific analysis object and content

c0smosmosmotion's "fixed pair" constraint is used to lock two rigid members so that they cannot make relative motion, which is equivalent to welding two members together in the real world. In the shaper studied by the author, there is no relative movement between the cutter bar, the connecting piece and the ram, between the pin 1, pin 2 and the connecting piece, and between the large pulley, the sliding gear set and the spline shaft, so the constraint between them adopts "fixed pair"

"rotating pair" constraint only allows the relative rotation of 1 degree of freedom between 2 rigid members. In the shaper, there is only one relative rotation between the motor and the small pulley (including the motor rotor), between the spline shaft and the bearing (equivalent to the frame), between the gear shaft and the bearing (equivalent to the frame), between the large helical gear (crank) and the frame (body), between the large helical gear (equivalent to the crank) and the slider L, between the slider 2 and the frame (body), and between the rocker arm and the connecting piece (or pin 1), so the constraint between them adopts "rotating pair"

"moving pair" constraint only allows the relative movement of 1 degree of freedom between 2 rigid members. In the shaper, there is only one relative movement between the slider L, slider 2 and the rocker arm, and between the ram and the frame (body), so the constraint between them adopts the "moving pair". In COSMOSMOTION software, the dynamic simulation of gear transmission and belt transmission depends on "coupling". The belt drive is used between the small belt pulley and the large belt pulley in the shaper, and the gear drive is used between the sliding gear set (or spline shaft) and the gear shaft, and between the gear shaft and the large helical gear. Therefore, the "coupling" method should be used to define the lifting angle between them α Sports relationship. The transmission ratios of the three "coupling" are 355/75, 36/55 and 84/21 respectively

2.3 input motion

for the convenience of analysis, the large helical gear (equivalent to the crank of the guide rod mechanism) is selected as the prime mover in the system motion analysis, and its speed can be set according to the speed N4 in the real system

therefore, in the COSMOSMOTION interface, set the speed of the large helical gear to "constant value" 720 (°)/s

the speed of the prime mover can also be selected. Because when establishing the equivalent dynamic model, the ratio of the speed of each component to the prime mover is used in the calculation of the equivalent moment of inertia and equivalent moment of the system, which is independent of the real speed

2.4 add working resistance

because the tool bar only has working resistance when cutting the workpiece, it is necessary to carry out motion simulation first to obtain the displacement curve of the tool bar (Fig. 2), so as to determine the functional relationship between the working resistance P and the simulation time t:

in this way, the working resistance can be added to the "tool bar" parts in the form of function in COSMOSMOTION, The expression is: if (time-0.0472:0, 7000, if (time-0.256 25:7000, 0, if (time-0.5:0, 0, 0)))

2.5 simulation and result output

at this point, the simulation can be run and the total kinetic energy curve (including moving kinetic energy and rotating kinetic energy) of each part of the shaper can be output to excel. In addition, it is also necessary to simulate the movement of the mechanical system under the action of "no working resistance and gravity" and "with working resistance and gravity" respectively, and output the balance couple moment curve acting on the large helical gear under these two conditions, as shown in Figure 3, so that the pressure film can be used to convert the oil pressure into the change of the resistance of the strain gauge

Figure 3 balance couple moment and equivalent moment

3 system dynamics analysis

any mechanical system can be simplified into the following equivalent dynamics model:

3.1 calculation of equivalent moment

in dynamic statics analysis, if the system is not affected by working resistance and gravity, the system balance moment is caused by the inertia force and inertia couple moment of each component; Besides, the balance moment of the system under the action of working resistance and gravity also includes the influence of gravity and working resistance. Therefore, the equivalent combined torque of working resistance and gravity is obtained by subtracting the balance torque under the former working condition from the balance torque under the latter working condition (the author has verified the correctness of this conclusion). According to this equivalent relationship, the equivalent torque (resistance torque) curve of working resistance and gravity in the shaper shown in Figure 3 can be obtained through Excel analysis and calculation

assuming that the equivalent driving torque is a constant torque, its value can be calculated by the formula

3.2 system equivalent moment of inertia

according to the principle that the kinetic energy of the system is equal before and after equivalence, the equivalent moment of inertia of the system can be calculated

according to formula (4), the system equivalent moment of inertia curve shown in figure 4:

system equivalent moment of inertia

can be obtained in Excel spreadsheet

3.3 solve the real speed of the equivalent member

from the above, the equivalent dynamic model of the shaper is formula (3), in which the system equivalent moment and equivalent moment of inertia have been calculated in the form of curves (Fig. 3 and Fig. 4). Now the angular velocity of the equivalent member can be calculated by the difference method ω， That is, the actual speed of the large helical gear in the real system. The solution formula is as follows:

(5) the actual speed curve on the large helical gear of the shaper system can be obtained in the Excel spreadsheet, as shown in Figure 5. It is worth noting that if ω If the initial value of is too small, negative rotation speed will appear in the solution process (unreasonable)

4 Conclusion

this paper makes full use of the modeling function of SolidWorks and the motion simulation function of cosmosm0tion, and combines the analysis and calculation and chart display functions of Excel to realize the dynamic analysis of the shaper system. The software used in this research method is simple and easy to learn. The method used is practical and reliable, and the results obtained are accurate and true. It is suitable for the kinematics and dynamics of any mechanical system. (end)

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