Mechanism Design and Optimization for a Trebuchet
Mechanism design and optimization for a trebuchet in this assignment, which namely focus on some key components, such as main arm, fulcrum bar, steel ropes and welds holding the main arm to the fulcrum. To work out this design assignment, the physical process analysis of the trebuchet is necessary make it clear that what is the worst-loading condition and how it impacts the key components’ mechanical property. Three key methods of material mechanics are used, and some kinetics and kinematics methods are used to reveal physics laws about the trebuchet. Calculation results shows that an optimal main arm should be 8m with size 30x30 to 65x65, and the axis length of the fulcrum should be 110mm, and the optimize radius should 73mm. the bearings’ size is deep groove ball bearing with its size 6208, and the length of steel rope KIL is 4.5m, the length of steel rope BFD is 23.074m. The cost, maintenance, machine life and assembly are also kept in mind.
In nowadays, trebuchet, the siege weapon used in the Dark Ages, is attractive for its delicate design and enjoyment.Mechanism design and optimization of the trebuchet is complex, because it includes bar, ropes, welds, bearings, hinge and so on. The design process of trebuchet’s key components should consider many factors, such as multi-parameter optimization, static analysis, dynamic analysis et, Computer simulation is necessary in optimization as well. According to the research in this field, Physical process Analysis is the first step of mechanism design, and several key parameters are proposed after this analysis[5,6]. Machine reliability analysis is very important and necessary as well, and the best way to prove it is to test in the extreme case, such as high or low temperature, heavy shock load or alternating force.What’s more, a conclusive product also need to take into account several factors, such as its cost, maintenance, machine life and assembly and so on. The cost and machine life can also be calculated by component’s size and the extreme case it comes across.
The above mentioned methods are used to design and optimize the key components of the trebuchet in this assignment, and the worst conditions of each key component are stated. Only a few assumptions are made to simplified calculation.
2 Main Body
2.1 Physical Process Analysis of the trebuchet
Some assumptions are made before analysis:
A. The radius of double-drum winch and the length of is ignored;
B. The weight of loading packet is ignored;
C. The windage during the trebuchet operates is ignored for its tiny effect;
Then the physical process of the trebuchet can be divided into 3 phases:
Stage 1: The phase from releasing main arm to the position that the main arm is vertical to the horizon. During this period, it is difficult to tell the worst condition trebuchet comes accross, because the dynamic factor the acceleration caused is much bigger than the static condition;
Stage 2: The phase that the main arm swings. When the axis of main arm raise is vertical to the horizon, it can not rotate any more because the ropes have reached thier biggest length, which is thought the best way for cost saving, and the main arm swings in the effect of impact. At this time,the first shock plays a key role to the strength of the ropes and main arm. The other shocks is weaken due to the damping and consumption, which have an influence on the ropes and main arm’s life. The worst condition is the first shock and an impulsive loading derivation is needed.
Stage 3: Reloading, which can be seen as a static-loading process. During this period, it is difficult to tell the worst-loading for the combination effort of axial force along the main arm and the moment of torque act on the main arm. A general condition function is need at this situation and the worst condition is based on the calculation result. The static-loading process is important because it is the basis of the other physical process.
Figure 1 Physical Process Analysis of the trebuchet. Figure 1.a shows the first stage,
Figure 1.b shows the second stage, and Figure 1.c shows the third stage.
2.2 Stress Analysis
Figure 2 and Figure 3 show the force and moment condition in Stage 3 and Stage 1, and the derivation is as the Appendix. The figures show that moment and force at point A is bigger than the other points, the ropes act in Stage 2 is more dangerous for the shock, and the load on the bearings and fulcrum is bigger than on other components and always change with time. The fact gives a tip that the coaxiality has a big influence on the fulcrum and bearings life.
Figure 2 force and moment analysis in static condition in Stage
Figure 3 force and moment analysis in dynamic condition in Stage 1
Key components dimensions can be derived according to the above figures.Take the above Stages calculation into consideration, expression of the key components stress is as followed:
The results are as followed:
2.2.1 The dimensions of the SHS steel bar
Because the SHS steel bar is the plastic material, the safe factor ranges from 1.2 to 2.5. consider that the operating condition of main arm is relatively poor, the safe factor should be a higher value, here and the yield stress and tensile strength of SHS steel bar is as appendix table
1. Calculation results shows that the expression of an optimal main arm should be at 8m length and its size is 30x30 to 65x65.
2.2.2 The dimensions of the fulcrum bar and
According to the calculation results, the axis length of the fulcrum should be 110mm, and the optimize shaft shoulder radius should be 73mm.
Compared to its mechanical property, the fulcrum’s geometric construction is more important, because it determine the bearings’s size and the life itself in a big degree. A shaft shoulder is necessary to assemble with the bearing and its the other part coordinates with the bearing’s inner hole.
2.2.3 The size of the bearings
In the trebuchet, the bearings need to bear a big radial force and smaller axial load cause by the poor air-opening condition with a relatively low rotate speed, and they are paired mounting. The deep groove ball bearing is chosen and its size is 6208.
2.2.4 The type and size of the ropes
According to the calculation, the length of steel rope KIL is 4.5m, the length of steel rope BFD is 23.074m.
2.2.5The size of the welds holding the SHS steel bar to the fulcrum
There are many types of welds with individual characteristic, the welds on the main arm should bear a large bending moment and a frequently altering force. The slit bonding is the best choice for this condition. The welding technology is as important as the weld size. The Standard AS 1554.1-2004 gives many details of welding, and the material of W40XYshould be chosen during the submerged-arc welding. Some optimal method is introduced in Section 4, where lists some other ways to connect the fulcrum to the main arm.
The trebuchet’s work condition is in the open air, necessary maintenance is important to improve its machine life. Compared to the rules for the client, an optimization for trebuchet shows more competitiveness in nowadays market. Figure 4 shows the assembly at the bearings.
Numbers’ meaning in Figure 4 is as followed:(1)left bearing;(2)left seal ring;(3)left bearing cover;(4)main arm(5)right bearing cover;(6)right seal ring;(7)right bearing.
What’s more, spray paint and quenching can improve machine life as well.