2011 International Conference on Mechatronic Science, Electric Engineering and Computer August 19-22, 2011, Jilin, China
Design and kinematic simulation of ratchet mechanism based
Kunming university of science and technology Kunming, China firstname.lastname@example.org
Abstract—This paper designed a ratchet mechanism of a pastry slicer. In the first place, this discourse used SolidWorks software to model the ratchet mechanism, then imported the three-dimensional model into ADAMS by the nicer interface between SolidWorks and ADAMS to build a virtual machine and simulated it. The kinematic simulation result of ADAMS not only showed that the ratchet mechanism could fulfill the anticipative design requirements, but also offered the references to design and produce physical prototype of ratchet mechanism. The virtual prototype could be used to do a deeper analysis according to different requirements. Keywords-ratchet mechanism; kinematic simulation; slicer ADAMS; SolidWorks;
Haitao Wua and Hongbin Liub
Kunming university of science and technology Kunming, China a email@example.com, firstname.lastname@example.org radius(R) is equal to 180o / π (mm) . According to Eq.(1), if R=180o / π (mm) and ? = 5o , obviously, L is equal to 5(mm), therefore, the arc length that each turn of a ratchet tooth corresponding to is 5(mm), as a result, if pastry thickness is 10(mm), ratchet will turn 2 teeth, if pastry thickness is 15(mm), ratchet will turn 3 teeth, and if pastry thickness is 20(mm), ratchet will turn 4 teeth. The ratchet contour which is shown in Fig. 1 is obtained according to the above calculated data.
In some developed countries such as United States , Germany and Japanese, the virtual prototyping technology has already made an extensive application in the car manufacturing industry, engineering machine, aerospace industry, shipbuilding industry, machine electronics industry, defence industry, living physics, medical science and so on. II. ESTABLISHMENT OF RATCHET MECHANISM 3D MODEL
Figure 1. Ratchet contour sketches
A. Mathematical Model of The Ratchet The design requirements of a pastry slicer are as follows. First, the pastry thickness scope is 10~20 (mm). Second, the pastry high scope is 5~80(mm).Third, The pastry width is 300(mm).The pastry width is 300(mm). The feeding mechanism was designed by using SolidWorks according to these requests. Ratchet mechanism[2-3] and belt drive mechanism were used as the machine feeding mechanism of pastry slicer in order to alter the pastry thickness. According to the design requirements, the pastry thickness is 10~20(mm), according to (1):
B. Mathematical Model of The Crank-rocker Crank-rocker mechanism is an important part of the ratchet mechanism, the ratchet needs to turn four teeth when the pastry thickness is 20(mm), as a result, the maximum swing angle( ACB) of rocker is equal to 10o . As shown in Fig. 2, the relationships between the crank length and the distance that between the crank rotation center and the rocker rotation center are as follows: e=
l1 /sin( ACB)=50/sin(10 ) 288mm
L = R × ? × π /180o
where L is the arc length, in m; R is the ratchet radius, in m; ? is the circumferential angle, in degree. According to the design requirements, the maximum pastry thickness is 20mm, let L = 20(mm) , ? = 20o in Eq.(1), the ratchet
Figure 2. Kinematic diagram of crank-rocker
978-1-61284-722-1/11/$26.00 ?2011 IEEE
Establish the Crank angular displacement equation according to Fig. 2.
(12) is the angular velocity expression of rocker. If = 44 ? / s, III.
?1 = ω1t
Coordinates of points B are as follows.
?1 = 90 °, l1 = 50mm, ω2 is equal to 6.5 ? / s.
DYNAMIC SIMULATION AND ANALYSIS OF
? xB = l1 cos ?1 ? ? yB = l1 sin ?1
Establish the closed vector equation of the crank-rocker mechanism.
A. Put Three-dimensional Solid into ADAMS Both ADAMS and SolidWorks use ‘Parasolid’ as their modeling kernel[4-6], therefore, the pastry slicer 3D model was transmited into ADAMS by using ‘Parasolid’ format. The dynamic simulation can begin after constraints and external forces have been set up in ADAMS. The general assembly drawings of ratchet mechanism is shown in Fig.3.
uuu r uuu r uuu r CA + AB = CB
Projected the vector equation onto the x and y axis.
l1 cos ?1 = S cos ? 2 e + l1 sin ?1 = S sin ? 2
(7) divided by (6) are
Figure 3. Ratchet mechanism assembly drawing
e + l1 sin?1 (?1 ≠ 90o ,270o ) l1 cos?1
B. Dynamic Simulation and Analysis of Crank-Rocker Mechanism As shown in Fig. 4, the angular displacement of rocker satisfies a cyclical fluctuations, the amplitude ( ? ) of it is
e+l1 sin?1 ? (0o ≤?1 < 90o,270o <?1 < 360o ) ?arctan( l cos? ) 1 1 ? ? (?1 = 90o,270o ) ?2 = ?90o ? e +l sin? ?180o +arctan( 1 1 ) (90o <?1 < 270o ) l cos ? ? 1 1 ?
(9) is the angle function expression of rocker(BC).
9.9371o , the theoretical amplitude of it should be 10o , the simulation results are approximately equal to theoretical design requirements.
ω2 = ( tan ?2 ) ' =
ω1l1 + eω1 sin ?1 cos 2 ? 2 2 2 l1 cos ?1
Figure 4. Rocker angular displacement curve
where ω2 is the angular velocity of rocker(BC).(11) is obtained by (9).
cos2 ?2 =
l12 cos2 ?1 (0o ≤ ?1 < 360o ) e2 + l12 + 2el1 sin?1
As shown in Fig. 5, cyclical fluctuation in angular velocity, the maximum of the angular velocity is equal to 6.5066(°/s), the simulation results consistent with the mathematical model calculations results, therefore, the simulation results are accurate and reliable.
(12) is obtained by (10) and (11).
ω1l12 + el1ω1 sin ?1 o (0 ≤ ?1 < 360o ) e 2 + l12 + 2el1 sin ?1
Figure 5. Rocker angular velocity curve
C. Dynamic Simulation and Analysis of Ratchet Mechanism Ratchet mechanism is important to control the thickness of pastry. The simulation results are shown in Fig. 6, Fig. 7 and Fig. 8.
19.5o , therefore, the practical pastry thickness will be
about 14.6(mm) and 19.5(mm). Because of the theoretical pastry thickness is 15(mm) and 20(mm), the average error of the pastry thickness is 2.6% which is less than 5%, as a result, the simulation results are more in line with the design requirements. IV. CONCLUSIONS A ratchet mechanism of a pastry slicer was designed by using SolidWorks and ADAMS. It can be proved that the simulation results are accurate and reliable. On the one hand, the simulation model and it’s motion parameters could offer the theoretical basis to optimize the entire organization, on the other hand, the virtual prototype could be used to do a deeper analysis according to different requirements, what’s more, the application of virtual prototyping technology enables not only to shorten the pastry slicer design cycle, but also to reduce the design costs, what more important is that it can improve the quality of products. ACKNOWLEDGMENT This study was supported by The Third Installment of Specialty Professional Construction Projects of Chinese Ministry of Finance and Education(TS11137). REFERENCES
  Z.H. Ge, ADAMS2007 Virtual Prototyping Technology. China: Chemical Industry Press, 2010. D.Chen, Mechanical Design Manual. China: Chemical Industry Press, 2008. H.Sun,Z.M.Chen,W.J.Ge, Mechanical Principle. China: Higher Education Press, 2007. Y.X.Li, H.H.Hao, X.T.Liu. “Influences of rigidity and damping of conveyer belt on the dynamic characteristics of belt typed conveyor”. Journal of Machine Design. China: vol.27, 2010, No.2, pp.13-16. X.F.Ma, Y.B.Chen. “High-speed elevator system dynamic simulation research cased on virtual prototype technology”. Research and Design. China: vol.21, 2010, No.5, pp.48-51.
Figure 6. Ratchet angular displacement curve (Pastry thickness is 10 mm )
Figure 7. Ratchet angular displacement curve (Pastry thickness is 15 mm )
Figure 8. Ratchet angular displacement curve (Pastry thickness is 20 mm )
As shown in Fig.10, the ratchet angular displacement curve has two distinct fluctuations, because ratchet needs to turn two teeth when the pastry thickness is 10(mm), therefore, the theoretical angular displacement of the o o ratchet is 10 , but the actual angular displacement is 9.6 . Let ? = 9.6 and R = 180 / π ( mm) in (1), we can find that the practical pastry thickness is about 9.6(mm) which is approximately equal to the theoretical pastry thickness which is 10(mm). Similarly, as shown in Fig.11 o and Fig. 12, the actual angular displacement is 14.6 and