Mechanical Design Handbook

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Showing posts from November, 2009

Timing Diagrams Part 4: Motion Simulation & Verification in Excel

In post [ Part 1 - No Overlap Movement ] , we established the core design requirement: The die must work synchronously with the indexing mill. Advertisement Figure 1: The physical system requires precise synchronization. The Problem: Rigid Sequencing Without detailed calculation, inexperienced designers often end up with a rigid timing diagram. The die waits for the indexing to completely finish before moving. The Consequence: This compressed movement window results in extremely high acceleration ( 4.15 m/s² ). This leads to massive inertial forces, vibration, and premature equipment failure . The Solution: Optimized Overlap In post [ Part 3 - Cycloid Cam Profile Analysis ] , we utilized the "Soft Start" properties of the Cycloid profile. By allowing the motions to overlap safely, we extended the indexing angle significantly without causing collisions. The Engineering Impact: ...

Timing Diagram (Part 3 - Cycloid Cam Profile Analysis)

In the previous post [ Timing Diagram Part 2: Max Acceleration ] , we calculated the maximum forces acting on a die driven by a cycloid cam profile. We discovered a critical rule of physics: inertial forces are inversely proportional to the square of the time allowed for movement. The Engineering Strategy: If we can extend the indexing angle (time) by allowing Overlap Motion , we can drastically reduce wear. This is the heart of Predictive Maintenance —designing machines that inherently last longer. Advertisement 1. The Cycloid Cam Profile The Cycloidal motion curve is the industry standard for high-speed automation because it has zero acceleration at the start and end of the move. The displacement equation is: h = h m × [ (t / t m ) - 1/(2π) × sin(2π × t / t m ) ] To solve for the Displacement Ratio (percentage of travel), we rearrange it: h / h m = (t / t m ) - 0.159 × sin(6.28 × t / t m ) Figure 1: The ...

Timing Diagram (Part 2 - Maximum acceleration calculation)

In the previous post [ Timing Diagram (Part 1 - No Overlap Movement) ], we determined that without overlap, our die must travel 50mm within a tight cam angle of just 55 degrees. Advertisement Now, we must ask: What is the physical cost of this rapid movement? To answer this, we calculate the Maximum Acceleration . In Machine Dynamics , acceleration is directly proportional to Force (F = m × a). High acceleration means high inertial forces, which lead to severe wear, vibration, and the need for expensive oversized servo motors . Step 1: The Time Calculation First, we need to convert our "Cam Angle" into actual "Time" in seconds. Let: N = Machine Speed (pieces per hour) B m = Indexing Angle (degrees) Cycle time (sec) = 3600 / N Indexing time t m = (B m / 360) × Cycle time Indexing time t m = (B m / 360) × (3600 / N) t m (sec) = (10 × B m ) / N Step 2: Cycloid Cam Profile Equations The...

Timing Diagram (Part 1 - No Overlap Movement)

When you search Google for " timing diagram ", you typically find results about electrical timing diagram software for digital logic or PLC programming. However, in the context of Mechanical Machine Design , a Timing Diagram is a critical engineering tool that represents the sequential kinematics of mechanism movement. Advertisement It is the standard visualization for engineers to ensure synchronization between cam drives , servo motors , and pneumatic actuators in complex automation cells. The Cost of Poor Timing: By properly designing the timing diagram, we can optimize motion profiles to be smoother even at higher speeds. This directly improves OEE (Overall Equipment Effectiveness) and significantly reduces operational costs. We typically draw the timing diagram using the Master Cam Angle (degrees) on the horizontal axis and the Mechanism Displacement (mm) on the vertical axis. The Goal: Reducing Inertial Forces & M...

Standards of limits and fits for mating parts (Part 2)

In the previous post ( Standards of limits and fits for mating parts ), we defined the core terms of the ISO 286 standard . Now, we translate that theory into real-world Precision Metrology calculations. While manual math is good for understanding the "why," modern manufacturing relies on Tolerance Analysis Software to prevent costly scrap in CNC Machining . Advertisement Automated Calculation Logic Below is an example of how logic is structured in engineering spreadsheets or professional Quality Control (QC) software to determine upper and lower deviations. Step-by-Step Manual Calculation Let's verify the software's logic by calculating the deviations manually. Example: Calculate the deviations for a shaft with a diameter of 40 mm and a tolerance class of g6 (40g6). Step 1: Determine the Geometric Mean (D) First, we find the basic size range. For a 40 mm shaft, the range is "Over 30 up ...