Zhi-ming CHENG，Bo YAN，Xiao-fei ZHAO

(ShanxiⅠnstitute of Mechanical＆Electrical Engineering，Changzhi 046011，China)

1 Introduction

At present，the design of slider-crank mechanism in diaphragm pump power end mainly depends on designers’experience［1］．Therefore，due to the lack of experimental prototype，potential defects cannot be avoided in the early design stage［2］，or conservative design phenomena is preferred in order to meet the requirements．With the rapid development of computer technology，Virtual Prototype(VP)technology is gradually used in diaphragm pump mechanism design．Virtual prototype is based on the simulation model of the product or system on a computer，it is essentially consistent with the physical prototype both on the function and performance．Based on the physical，functional simulation，by the means of visualization，improving the ability of the user interaction with virtual reality，VP tries to show the performance of physical prototype in different environment，instead of real test［3-4］．Virtual prototype technology can greatly simplify the design and development process of mechanical products，shorten the product development cycle，reduces product development costs，improve the quality and the system-level performance of products，and make the optimized and innovative design products．

This article takes a certain triplex single-acting diaphragm pump as an example and centers on the key structure of the diaphragm pump power end—slidercrank mechanism．Virtual prototype technology is used here to realize dynamic analysis．The analytical kinematics data can tell the operation of the virtual prototype，and provide the connecting rod small-end speed for the speed check of its sliding bearing．The analytical dynamics data can provide load basis for finite element calculation．The main parameters are as follows:stroke length:s=510 mm，connecting rod length:L=1 700 mm;Speed:n=43 r/min;the crankshaft total quality:8400 kg;cross quality:1 294 kg;connecting rod quality:930 kg;rotational inertia of connecting rod:Ⅰc=1．585 227 319 4×102 kg·mm，F(xiàn)ull loading in the diaphragm pump stroke:1 176 kN．

2 3D model of diaphragm pump slidercrank mechanism

ADAMS software is specially used for kinematics，dynamics analysis and simulation of mechanical system．The ADAMS/View provides some basic modeling tool library［5］，but it is not suitable for more complex 3D model．So firstly，3D model is established in professional CAD software，and then it is entered into ADMAS in a certain format［6］．This article uses Pro/E software for the part modeling and the whole assembly of diaphragm pump slider-crank mechanism，the model is shown in Fig．1．

Fig．1 diaphragm pump

3 Virtual prototype of diaphragm pump slider-crank mechanism

3．1 The import of 3D model

ADAMS/Exchange can provide model data exchange interface in such formats as Parasolid，STEP，IDES，SAT，DXF，DWG．This article uses the Parasolid file standard，as shown in Fig．2．

3．2 Add physical properties to model in ADAMS

ADAMS/View has conventional material database．So after importing model artifacts，the user can edit the properties of the component and component elements，including color，location，name and material properties etc．If not given a certain material property to the imported component，error message will appear in the process of calculation．Here we respectively define the name and color of each component，and we define them as a rigid body at the same time．

Fig．2 model import window

3．3 The definition of model constraints and drive of diaphragm pump slider-crank mechanism

1)The definition of constraints

After adding the physical properties，we can restrict some relative motion between the components through constraints，which connect different components to form a mechanical system．This paper is considering the actual movement situation of the system when setting constraints．The specific objects of kinematical constraints and their corresponding relations are shown in Table 1．

Table 1 Relations between kinematic pair and components

After the definition，the diaphragm pump component details in ADAMSare shown in Fig．3．

By defining constraints in the virtual prototype of the diaphragm pump，kinematic relations between all components of the prototype model assembly relations．the virtual prototype model of diaphragm pump in this study contains 22 rigid bodies，10 revolute pairs，12 fixed pairs and 6 prismatic pairs．

2)External force and drive

The external force added on performing mechanism are medium pressure and the torque on the crankshaft forced by actuating mechanism．Load:the crosshead maximum load of 1 176 kN，crankshaft:uniform rotation-43 r/min，rotating drive:258 d*time，drive type:Displacement．

Pressures are different according to different positions，so we use the IF-function of ADAMSto simulate approximate loading，and replace the pressure with the concentrated force．The load function of crosshead is:

Shizitou1:if(time-0．330:-1176000，-1176000，if(time-1．020:0，0，if(time-1．5:-1176000，-1176000，0)));Shizitou2:if(time-0．635:0，0，if(time-1．299:-1176000，-1176000，if(time-1．5:0，0，-1176000)));

Fig．3 The definition of prototype constraints

3)Add friction coefficient among kinematic pairs

The kinematic component of performing mechanism only has the relative movement and relative rotation．Every kinematic pair is made of different types of alloy steel，and it needs lubricating in the actual working environment，so we use the kinetic friction coefficient 0．08 of steel and the static friction coefficient 0．12 under lubricating conditions［7］．The friction coefficient between sliding plate and guide plate is the one between aluminum bronze and nodular cast-iron，and 0．01 is used here．

Based on the above physical parameters，the virtual prototype simulated analysis model of the diaphragm pump driving system is shown in Fig．4．

Fig．4 Dynamic simulation of diaphragm pump virtual prototye

4 Simulation and analysis of kinematics and dynamics

Before the simulation analysis，we should use the self-check tool to check the diaphragm pump prototype model，in order to remove hidden error and ensure the accuracy．The self-inspect tool of ADAMSmodel is a powerful tool．We can start it by clicking the Tools menu and select the ModelVerify command．The selfcheck result of this model is shown in Fig．5．

Fig．5 Test results of the prototype

After the check，the model simulation can be carried out．1．5 s and 150 steps are adopted here，and the following simulation results can be got．

4．1 Analysis of kinematics simulation results

The displacement curve of the crosshead is shown in Fig．6，which shows that the crosshead stroke is 510 mm．The displacement curves of three crossheads are in the shape of trigonometric function and they have a differential of 1/3 cycle in time．Crank eccentricity is 255 mm，the crosshead displacement value in theory is 510 mm，they are the same as this simulation results．So it’s proved that the simulation precision is very high．it shows that this paper has certain validity on diaphragm pump modeling to some extent，and it also provide certain theoretical basis for the following simulation．

Crosshead speed curve and acceleration curve are shown in Fig．7 and Fig．8．

From the crosshead speed diagram and the acceleration diagram，we can see that diagrams are in the shape of trigonometric function curve，and they have a differential of 1/3 cycle in time，and the curve is smooth．All of these show that the prototype runs smoothly．The maximum speed of the crosshead is 1．20 m/s，it provides the basis for the axis pin bearing substitution speed of linkage small ends．

Fig．6 Crosshead displacement curve

Fig．7 Crosshead speed curve

Fig．8 Crosshead acceleration curve

Angular velocity curve and angular acceleration curve of the connecting rod around Y axis are shown in Fig．9 and 10．The figures illustrate the maximum acceleration of the connecting rod is 0．68 rad/s，the maximum angular acceleration is 3．14 rad/s2．These data provide basis for the static analysis of the connecting rod on inertial load．

4．2 Analysis of dynamics simulation results

The positive force curve of crankshaft and the rotation pair of connecting rod is shown in Fig．11．The maximum positive force of the connecting rod added to the crankshaft is 2．71 x 105 n．If the initial state is that crankshaft 1 is at 180°in the horizontal direction，and each of the crank angle relative to the axis of rotation is seen as its respective reference，then Table 2 can be got．Fig．12 shows the horizontal force of the crankshaft and the rotation pair of connecting rod．We can conclude from Fig．12，when the force on the crank throw is in the positive direction，the horizontal force is1．21 x 106 N，when the force is0 N，the horizontal force is 0 N too．

Fig．9 Angular velocity curve of connecting rod

Fig．10 Angular acceleration curve of connecting rod

Fig．11 Positive force curve of crankshaft

Fig．12 Horizontal force curve

From Table 2，we can get the following conclusions:

1)The force is the biggest when the crank throw is at 270°，and now only one crank throw gets the force;

2)In the position of 1，2，3，5，6，7，9，10，11，two crank throw get the force at the same time．

The force curves of the connecting rod and the crosshead pin are not listed in this paper，because these two forces are action and reaction，and they are equal in the opposite direction．The force of the connecting rod added on the crosshead pin and its force added on the crankshaft are equal in the opposite direction．As a result，these forces can be obtained directly by the crank force curve［8-9］．

Table 2 Force of crankshaft in the positive direction

5 Conclusions

ADAMS simulation software is used for setting up the virtual prototype of the slider-crank mechanism in diaphragm pump and the simulation analysis．From the simulation results，we can see that the crosshead displacement changes by the trigonometric function pattern，and the precision of displacement value is very high．The force curve of constraints pair shows that the crank horizontal force is equal to the applied loads．Forces on the crankshaft have a differential of 1/3 cycle at every turn，and it is consistent with the alternate angle of 120°of the three throws．In conclusion，high precision of the simulation results can provide the basis for the design of the slider-crank mechanism in diaphragm pump and can also provide reliable load data for the following finite element analysis［10-11］．

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