Rigid Body Dynamics Analysis of Pirate Ship Based on ADAMS

Wang wei,Tang Dewen

（School of Mechanical Engineering,University of South China,Hengyang 421001）

Abstract:Pirate ship is a common amusement machine,because of the high-speed swings of the pirate ship outdoors,and due to the complicated external environment and high working load,the safety of the pirate ship has been greatly weakened,in order to ensure the movement stability and security of pirate ships,this paper,by using the dynamics analytical software ADAMS of mechanical simulation analysis to the pirate ship.Through analyzing the structure of the pirate ship,the components with less influence on the results are simplified,the 3d model is drawn in the solid works,then imported into the ADAMS,the load and constraints are added to the model,and the rigid body dynamics of the pirate ship is analyzed.the velocity,angular velocity and angular acceleration values of the hull vary with time.Through the calculation of theoretical formula,the corresponding calculation results are compared with the simulation values.The results show that the theoretical calculation values are consistent with the simulation results within a certain error range,which provides theoretical guidance for the design of pirate ships.

Key words:ADAMS;The pirate ship;Rigid body dynamics analysis;Safety

1 Introduction

In recent years,entertainment facilities have been constructed on a large scale.As one of the most commonly used entertainment facilities[1],amusement machines have been gaining more and more popularity.However,while enjoying the excitement and stimulation[2],the safety of amusement machines has also attracted wide attention,and the consequences caused by design defects,structural fatigue and so on are very severe.

In 2017,a major safety accident happened in an amusement park in Ohio,the United States.When the meteor hammer in the amusement park was running at a high speed,one of the pendulums suddenly broke,causing one of the supports to fall off.Under the great impact force,passengers were thrown out instantly,resulting in one death and seven injuries[3].

On July 14,2019,the main shaft pipe of the Pendulum at Ganglia Adventure Park in Ahmedabad,India,was broken in the air during operation due to design flaws,resulting the main shaft to crash directly into the ground,causing at least two deaths and more than a dozen injuries.

2 Basic Structural Parameters

Corsair ship is mainly composed of support structure,hull,suspension arm,driving parts,spindle platform,etc.,as shown in Fig.1.The support structure is made up of two symmetrical cylindrical steel tubes,the bottom of which is fixedly connected with the ground,and the top is connected with the main shaft,the upper end is connected with the main shaft through a rotating pair,while the lower end is connected with the hull.The hull of a pirate ship adopts box girder structure and forms a V shape,and under the action of driving force,the left and right reciprocating swing can be realized[4].Table 1 shows the mass of various parts of the Corsair ship and the connection between them.

Fig.1 Schematic diagram of the structure of a pirate ship

Table 1 the mass of each part of a pirate ship and the connection between them(unit:kg)

In reality,the structures of pirate ships are more complex,this paper uses the SolidWorks and the rigid body dynamics simulation of ADAMS software,the pirate ship is made up of many small artifacts,the more you add constraint in the simulation analysis,the longer the simulation time is,so the solid model works,the need to structure analysis was carried out on the pirate ship,impact on the results of simulation is to simplify the small parts,as shown in table 2 the parameters of the pirate ship.A 3D model is built in SolidWorks and saved as X_T type,then,it was imported into ADAMS through SolidWorks and ADAMS intermediate common format,the material of each part was set as low carbon steel,and the technical parameters of the material are shown in Table 3.

Table 2 Basic parameters of a pirate ship

Table 3 Technical parameters of materials

3 Theoretical Calculation of Parameters

Pirate ship is a kind of horizontal axis reciprocating swing,equipped with driving mechanism on the bottom of the hull,driving around the hull and suspension arm perpendicular to the direction of the axis of the main shaft do reciprocating swing,every once in a while,a driving force in the direction of the transformation,under the action of periodic driving force,the pirate ship swing Angle increases gradually,until the swing to the preset level,stop driving moment,pirate ships landed on driving force,under the action of each branch office under periodic changes of load[5-6].Take the pirate ship,passengers and seats as mass points,and the cantilever as a cycloid,then the whole hull moves in a single pendulum,and the load it receives in the swinging process is shown in Fig.2.

Figure 2: Schematic diagram of operating load of Corsair ship

The height of the pirate ship from the highest swing point in the process of movement is:

Where:θ—the included Angle between the cycloid and the vertical direction,namely the pendulum Angle;

R—the distance from the Corsair ship to the center of rotation,namely the radius of rotation;

In the process of swinging,the pirate ship is always affected by the gravity of the earth,which can be obtained by the conservation of mechanical energy:

Where:M—the total mass of the hull,seats and passengers;g—standard gravity acceleration,9.8m/s^2;

V 1—the instantaneous velocity of the ship's motion

When the pirate ship is swinging back and forth around its main shaft,it is affected by the centripetal force,which can be derived from the centripetal force of circular motion:

When the pirate ship moves to the position shown in Figure 2,the force analysis on the pirate ship can be obtained as follows:

Wherein:F 1—the tension of the cycloid;

Formulas (2-1),(2-2),(2-3) and (2-4) can be obtained:

When the Corsair ship is working,it moves in a single direction,with the maximum swing Angle of 45 ° for 15s under the action of three driving forces.At this time,the gravitational potential energy reaches the maximum.When the motion reaches the lowest point,all the potential energy is converted into kinetic energy,and the Corsair ship reaches the maximum speed at the lowest point.To analyze of the forced state of a figure 2 pirate ship,the pirate ship only in the process of movement by the pull of gravity and cantilever rack,the formula (2-5) shows that when the pendulum Angle q=0 °,the pirate ship's motion is at the lowest point,will be affected by 1.59 g acceleration,overweight,at this time all the gravitational potential energy is converted into kinetic energy,tension of the cantilever rack is the biggest=1.59 mg,until the bottom of pirate ship motion analysis,by the table a pirate ship quality known hull total quality of the parts:

Where:—the total mass of the hull;

m5—Average quality of passengers;

Substituting the above equation into Formula (2-5),we can get:

According to the law of conservation of energy,the Corsair ship reaches the maximum rotational speed at the lowest point,and its instantaneous velocity is:

The maximum acceleration of passengers in a Corsair ship along the direction of the center of rotation is:

When the Corsair is fully loaded,the total weight of the swinging parts is:

M=m+m6=16996 kg

Where m 6—the total mass of the suspension arm

When the hull swings at the maximum speed,the corresponding rotational speed is:

The moment of inertia of a pirate ship when fully loaded:

The driving torque exerted by the Corsair in the process of motion is:

T—Total drive time

4 Rigid Body Dynamics Analysis of Pirate Ship

Pirate ship is a kind of round spindle reciprocating swinging amusement machine,rides in connected with the cantilever rack on the hull of the ship at the bottom of the driving force to achieve the reciprocating swing of the hull under the action of various forces[7],because in this paper,the height of the pirate ship design is higher,swinging is bigger,therefore potential security problems may exist in the working process,so rigid body dynamics analysis is needed.Structural dynamic analysis using the method of virtual experiment,to accurately predict the performance of the product,by using the virtual experiment to the product under various conditions,we can know the possible problems which may arise in working conditionso,and then figure out ways to improve,and solve product in dynamics,life,strength,and deformation problems.

4.1 Defining Materials

Simplified model will be imported into the ADAMS,the simplified model is shown in figure 3,the material properties are defined,parts of material properties affect the ADAMS of rigid body dynamics simulation analysis result,in the need analysis of the dynamic simulation of parts material type,density,young's modulus and poisson's ratio are defined,in this paper,all the parts using low carbon steel,meets the design requirements,also save the simulation time.

Figure 3.A simplified model of a pirate ship

4.2 Add Constraints and Loads

Before defining the constraints between the parts,it was necessary to understand the connection between the parts of the Corsair.Adams provides a variety of constraints:fixed pairs,rotating pairs,moving pairs,spherical pairs,etc.The fixed pair is used to restrict the movement and rotation of the parts in three directions without relative motion between the two parts.The rotating pair is used for the rotation of only one direction between two parts,which restricts the movement of three directions and rotation of two directions.The moving pair is used to constrain the rotation of a part in two directions and three directions by moving a part in one direction relative to another.Spherical pair is used for one part to rotate arbitrarily along another part to constrain its movement in three directions.The support structure of the pirate ship is fixed with the ground and belongs to the fixed pair.It imposes fixed constraints on the base of the four columns,and the top of the bracket is fixed together with the spindle platform through welding.The cantilever frame and the hull swing reciprocately around the main shaft under the action of the bottom driving force,which belongs to the rotating pair and restricts the rotation of the cantilever frame[8].Corsair ship will be subjected to a variety of conditions in the process of swinging,such as zero load,partial load,full load,wind load,seismic load,etc.This paper mainly aimed at full load condition of the Corsair ship movement simulation analysis.In the process of reciprocating swing,the Corsair ship is always affected by the gravity of the earth,and a gravitational acceleration is applied in the direction of vertical downward.Under the action of the driving force at the bottom,the hull and the suspension arm swing back and forth in the plane perpendicular to the main shaft,and finally reach the maximum speed,and a rotating torque is added to the suspension arm.The constraints and loads added throughout the Corsair ship are shown in Figure 4.

Figure 4.Corsair ship added loads and constraints

4.3 Extraction and Analysis of Simulation Results

The motion diagram of the ship's velocity and swing Angle changing with time is extracted from ADAMS.Fig.5 shows the curve of the ship's swing Angle changes with time.It can be seen from the figure that the ship's swing Angle gradually increases within 0～15s and finally reaches the preset value of 45°,and the direction changes once every certain period.During 0～6s,the Corsair ship is in the initial stage of motion,and the swing Angle changes little.During 6～15s,the Angle increases gradually under the action of driving force,and finally reaches the highest point after three driving times.

Fig.5 Curve of swing Angle over time

Fig.6 Curve of velocity over time

As shown in figure 6 for hull speed changing with time curve,in each cycle speed curve of the wave of successive increases over time,the peak velocity increases gradually,which can be seen from the diagram of hull within 0～ 15s speed rising wave gradually,when t=13.8 s,hull ranges from high to low,at this time all the gravitational potential energy.is converted into kinetic energy,maximum speed,maximum speed is:9.5 m/s,and the theoretical calculation of the maximum speed js 9.49 m/s,compared to both within a certain range of error,show that the correctness of the pirate ship rigid body dynamics simulation.Under the action of periodic driving force,the velocity of the hull increases first and then decreases in each cycle.When the hull swings to the highest position,the velocity is 0m/s,and when the hull swings to the lowest position,the velocity reaches the maximum.Fig.7 shows the angular acceleration curve of the lowest point of the hull.It can be seen from the figure that the internal angular acceleration from 0 to 15s gradually increases from 0m/s to the maximum,and the peak value of the wave gradually increases in each cycle.By the figure 8 figure 9 available velocity and angular velocity curve of change over time,the figure 8 can get velocity and angular acceleration value,on the contrary,when the hull moves to the lowest point,maximum speed,angular acceleration is zero at this time the rad/s2,when the pirate ship moves to the highest point,the speed of 0 m/s,reached the maximum angular acceleration 47 rad/s2.

Fig.7 Curve of angular acceleration over time

Fig.8 Curve of angular acceleration and velocity over time

Fig.9 Curve of velocity,angular velocity and angular acceleration over time

5 Conclusion

In this paper,the pirate ship under load conditions are analyzed in rigid body dynamics,the pirate ship hull under working state of the speed,acceleration and driving forces has carried on the theoretical calculation,in order to simulate the operation condition of the hull in the real environment,rigid body dynamics analysis was carried out on the pirate ship in Adams,the results showed that within the scope of permissible error pirate ship speed of the simulation values are in accordance with the basic theoretical calculation value,within 0～15s velocity,angular velocity and angular acceleration and angular change over time curve complys with the design requirements.The rigid body dynamics analysis of Corsair ship provides data support for the subsequent design and verification of Corsair ship,and also provides reference for the design and verification of large-scale entertainment machines,which can greatly shorten the equipment research and development cycle,reduce the cost,and improve the safety performance of the equipment.However,this method also has some shortcomings.It neglects the influence of external environment on the working state of the equipment,so this method still has some room for improvement.