Guide Rails and Bearing Blocks: Selection & Modeling

1. Final Validation of the Ball Screw

Before we move on, let's complete a crucial validation step we previewed in the last lesson: the critical speed check.

Critical speed is the rotational speed at which a long, spinning shaft becomes dynamically unstable and starts to vibrate or "whip." Operating near this speed can lead to excessive vibration, noise, and even catastrophic failure.

The formula for critical speed (n) is:

Where:

• n is the critical speed in RPM.
• d_r is the root diameter of the screw shaft in mm. For our 15 mm nominal diameter screw, a typical d_r is about 12.5 mm.
• L is the unsupported length between the support bearings in mm. We'll use our stroke length of 600 mm.
• f is a coefficient for the bearing support method. A common and robust configuration is "Fixed-Supported," for which f = 1.5.

Let's calculate the critical speed for our screw:

Our required operating speed is 360 RPM. Since 360 RPM is well below the calculated critical speed of 520 RPM (we are operating at about 70% of critical speed), our 15 mm diameter selection is acceptable. For a greater margin of safety in a real-world design, we might consider a slightly larger diameter or a different support method if the operating speed were closer to the critical speed.

2. Selecting the Linear Guides

With the ball screw validated, we can now design the support system. We will use linear guide rails with recirculating ball bearing blocks.

The selection process involves analyzing the loads on the blocks and ensuring they have a sufficient static load capacity.

Understanding the Loads

For our vertical lift, the 15 kg toolbox will be mounted on a platform that sits on the bearing blocks. Let's assume the center of gravity of the toolbox is offset from the plane of the guides. This offset creates a moment load, which is often the most significant load on the guides.

To provide stability, we'll use a standard configuration: two parallel rails, with two bearing blocks on each rail (four blocks total).

Let's define our layout:

• Distance between rails (l_0): 250 mm
• Distance between blocks on a single rail (l_1): 150 mm
• Load: 15 kg (~147 N)
• Load offset (distance from platform face to CoG, l_x): 100 mm

This offset creates a pitching moment:
$M_p=\text{Force}\times \text{distance}=147\text{N}\times 0.1\text{m}=14.7\text{N⋅m}$
This moment is resisted by upward and downward forces on the front and back pairs of blocks. The force on each of the two blocks in the front (or back) pair due to the moment is:
$F_{\text{moment}}=\frac{M_p}{l_1}\times \frac{1}{2}=\frac{14.7\text{N⋅m}}{0.15\text{m}}\times \frac{1}{2}=49\text{N}$
The static weight is distributed among all four blocks:
$F_{\text{weight}}=\frac{147\text{N}}{4}=36.75\text{N}$
The highest load occurs on the blocks that are supporting both the weight and the moment reaction.
$P_{\text{max}}=F_{\text{moment}}+F_{\text{weight}}=49\text{N}+36.75\text{N}=85.75\text{N}$
This maximum calculated load on a single block is very small.

Applying a Static Safety Factor

Now we check this against a catalog. The most important initial check is the static load capacity, C_0. We must ensure we have an adequate static safety factor (f_s).

As the video explains, manufacturers recommend safety factors based on the application. For a general industrial application with potential for light vibration, a safety factor (f_s) of 3 to 5 is appropriate. This means our selected block's C_0 should be 3 to 5 times our calculated maximum load P_max.

Required C_0 = P_max × f_s = 85.75 N × 5 = 428.75 N

This required static capacity is extremely low. If we look at the datasheet for even the smallest standard size, like a 15 mm rail (e.g., HRC 15 in the image LINK), the static load capacity is typically in the thousands or tens of thousands of Newtons. For example, a standard size 20 block might have a C_0 of over 20,000 N.

This tells us that for this specific application, the load is not the driving factor. Instead, the choice of size will be driven by factors like general robustness, availability, and the size of fasteners needed for assembly. We will select a Size 20 linear guide (e.g., HRC 20, or a standard Hiwin HG/EG series). This is a very common size that provides good rigidity.

Our safety factor with a size 20 block would be enormous (f_s = 20000 / 85.75 > 200), so it is more than adequate.

For a deeper dive into the manual formulas, you can review this document from Rockford Ball Screw. It shows the full complexity of the calculations we approximated.

3. Modeling the Linear Guides in OnShape

Now that we've selected a Size 20 linear guide system, let's model it. As an engineer, you'll almost never model standard components like these from scratch. You'll download them from a supplier or a content library.

A great resource for this is McMaster-Carr. You can search for the component, configure it, and download a STEP file, which is a universal 3D CAD format.

Your Task:

1. Go to the McMaster-Carr website (www.mcmaster.com).
2. Search for "Linear Guide Rails and Carriages".
3. Find a standard (e.g., Hiwin compatible) system. Select a 20 mm Rail Size.
4. Download the STEP file for one rail (choose a length > 600 mm) and one carriage (block).
5. In your OnShape project document, use the + menu and select Import to bring these two STEP files in.

Once imported, create a new Assembly tab. Now, we'll mate them.

As you saw, the Slider Mate constrains 5 of the 6 degrees of freedom, leaving only translation along a single axis.

Let's assemble the first rail and block:

1. Insert the rail and block into your assembly.
2. Right-click the rail and select Fix. This locks your base component in space.
3. Select the Slider Mate tool from the toolbar.
4. Define the first mate connector: Move your cursor over the end face of the rail. OnShape will offer several potential points. Choose the point at the center of the rail's profile.
5. Define the second mate connector: Move your cursor over the block. Choose a corresponding point, for example, the center of the opening where the rail goes through.
6. Click the green checkmark to accept the mate.
7. Now, try dragging the block with your mouse. It should slide smoothly along the rail but be unable to move in any other direction.

Conclusion

Fantastic work today. You've successfully navigated a complete component selection and modeling workflow, moving from high-level requirements to a functional CAD assembly.

Key Takeaways:

• You validated our ball screw selection by performing a critical speed check.
• You learned that for linear guides, moment loads are often the critical design driver.
• You followed an engineering process to select a guide size: analyze loads, apply a static safety factor (f_s), and consult manufacturer ratings (C_0).
• You sourced a standard component CAD model and used the Slider Mate in OnShape to create a realistic linear motion assembly.

Preview of the Next Lesson:
We now have our two key motion components specified: the ball screw and the linear guides. The next step is to model the ball screw assembly itself in OnShape and prepare to integrate it into our larger system. We will explore how to represent the screw, nut, and bearing supports in our CAD model.