Mechanical Design Handbook

In post [ Timing Diagram (Part 1 - No Overlap Movement) ], we saw the design requirement that we have to design the die to work together with the indexing mill with the construction as shown below. Without detailed calculation, we could end up with a very simple timing diagram as shown below. But it's not good enough. The die has to wait for the indexing to finish its movement before moving. This reduces the indexing time of the die, and get high acceleration on the die. In post [ Timing Diagram (Part 2 - Maximum acceleration calculation) ], we calculated the maximum acceleration of Cycloidal motion cam profile and saw the opportunity to reduce the acceleration by extending the indexing time. In post [ Timing Diagram (Part 3 - Cycloid Cam Profile Analysis) ], we analyzed the cycloid cam profile and see opportunity of overlap motion. Some calculations have been made and we end up with new timing diagram which is smarter than the original one as shown below. We calculat

In previous post [ Timing Diagram (Part 2 - Maximum acceleration calculation) ], we calculated the maximum acceleration of the die using cycloid cam profile. We found out that this maximum acceleration of the die can be reduced if we can extend the indexing angle (B m ) or indexing time (t m ) through overlap motion. Then, let's see how we can calculate for the suitable indexing angle to reduce the acceleration of the die. Cycloidal motion cam profile has movement equation as follows. h = h m x [t/t m - 1/(2 x pi) x sin(2 x pi x t/t m )] Rearrange the equation to get h/h m = t/t m - 1/(2 x pi) x sin(2 x pi x t/t m ) The displacement profile can be plotted as shown below (dimensionless). We can see that at the first 10% of indexing time, the movement is just only 0.65% of the total movement (stroke) and at 90% of time, the remaining movement for the die is only 0.65% of the total movement (stroke). Or we can say that, there is not much movement at the first and last 1

Let's calculate the acceleration of the die from previous post [ Timing Diagram (Part 1 - No Overlap Movement) ] The die moves using Cycloid cam profile. So first we have to get the formula to calculate the maximum acceleration of cycloid cam profile. If the machine speed is N (pcs/h) and the indexing angle (degree) is B m , the indexing time (second) t m can be calculated as follows. Cycle time (sec) = 3600/N Indexing time t m (sec) = (B m /360) x Cycle time = (B m /360) x (3600/N) Hence, Indexing time t m (sec) = 10B m /N Cycloid cam profile has the equation of displacement as follows. h = h m x [t/t m - 1/(2 x pi) x sin(2 x pi x t/t m )] where: h m : Maximum displacement (m) t m : Indexing time (s) pi: 3.141592654 We can get velocity equation by differentiation. v = dh/dt = h m x [1/t m - (2 x pi)/(2 x pi x t m ) x cos(2 x pi x t/t m )] v = h m /t m x [1 - cos(2 x pi x t/t m )] Then, the acceleration is as follows. a = d 2 h/dt 2 = dv/dt = h m /t

When I search in Google for " timing diagram ", I found a lot of results about electrical timing diagram software but they're not about what I'm going to tell. Timing Diagram in my meaning is a tool that represents the sequences of movement of mechanisms. It is a very useful diagram for mechanical design engineers to understand how each part of the machine works together. " By properly design the timing diagram, we can make machine moves smoother even at higher speed. " We often draw the timing diagram using cam angle (in degree) in horizontal axis and use the movement of mechanism (in mm) in vertical axis. From the timing diagram, we can find the opportunity to reduce the acceleration (force) of the moving parts so as to reduce the wear in machine. Experience shows that a lot of mechanisms have been designed without using "overlap" movement. This makes the machine parts move from one point to another point in short period. But if we provide

In the previous post ( Standards of limits and fits for mating parts ), we talked about the definitions of each term related to limits and fits as well as the formulas to determine the values of tolerances. In this post, we're going to convert those information into the real calculation using Microsoft Excel (as usual). As stated earlier, the calculation results may be different from the real values used in general mechanical design handbook. So please use this just for educational purpose only, but use the real table from general limits and fits table if you want to get higher accuracy values. This is the screen shot of excel file to calculate upper deviation and lower deviation according to the selected shaft diameter and tolerance grade. Let's see how to manually calculate the deviation values before using the program. Example: To calculate the upper deviation and lower deviation of a shaft with diameter of 40 mm and tolerance g6. Please refer to previous post (