Name: application of design aspects in uniaxial loading machine development
Uploaded: 2018-09-19T14:00:00.000+00:00
Duration: 5 min 23 s
Description: Watch this Scientific Journal Video about Application of Design Aspects in Uniaxial Loading Machine Development at JoVE.com

This work was supported by the National Institutes Health NIDCR [DE022664].

NOTE: The finished device is shown in Figure 2. The device enables pure uniaxial testing of specimens in a horizontal position.
1. Component Parts
<ol>
	<li>Prepare two programmable actuators with a 30 mm (1.2 in) travel per actuator capable of spanning 60 mm (2.3 in) when programmed to pull/push together. To accommodate a variety of potential uses, select actuators having a reasonable force capacity [67 N (15 lb)], peak thrust [58 N (13 lb)], speed resolution [0.9302 &#181;m/s (0.00004 in/s)], and a unidirectional accuracy [25 &#181;m (0.001 in)].</li>
	<li>Daisy-chain the actuators to sync them for an equal application of extension/retraction.</li>
	<li>Prepare a 24 V controller to provide the driving motion to the actuator; these systems enable a precise linear motion by the rotation of a screw, the leadscrew.</li>
	<li>Prepare two load cells with a maximum force capacity of 44.5 N (10 lb). Select a low profile or canister-style load which is ideal for confined spaces.</li>
	<li>Prepare the rail/carriage block system. Prepare one rail and two carriages; one to hold each actuator. Because steel will rust, select stainless-steel material if the device will be utilized for materials that require hydration; for all other purposes, steel is acceptable. 
	NOTE: An exploded view of the loading platform with the rail/carriage block shown in purple is provided in Figure 3.</li>
</ol>
2. Frame Construction
NOTE: For explanatory purposes, the platform is color-coded in the graphics.
<ol>
	<li>Prepare aluminum stock material. Select aluminum for its cost-effectiveness and ease of machining. Prepare both plate and &#39;L&#39;-shaped angle stock.</li>
	<li>Prepare stock material to machine fixtures. Select plexiglass; it is strong while lightweight.</li>
</ol>
3. Metal Base and Side Plate (Frame) Assembly
<ol>
	<li>Cut the base plate from the aluminum stock, making sure it is approximately 64 x 15 x 1.3 cm (25 x 6 x 0.5 in). Clean up the edges in the mill and cut the base plate to its final dimensions.</li>
	<li>Machine the plate flat in the mill, according to the specifications provided in the supplemental files.</li>
	<li>Face it, ensuring the plane is level.</li>
	<li>Machine a track into the base plate to align the side plates with a tolerance of 0.0126 mm (0.0005 in).</li>
	<li>Machine the side plates according to specifications provided in the supplemental files.</li>
	<li>Drill and tap the side plates on their bottom face.</li>
	<li>Mount the side plates upright in the track.</li>
	<li>Fasten the side plates to the base plate from underneath (Figure 4).</li>
</ol>
4. Attaching the Rail/Carriage Assembly to the Frame
<ol>
	<li>Machine tracks into the front face of each side plate to enable the mounting of the rail/carriage assembly according to the specifications provided in the drawing links (Figure 5).</li>
	<li>Fasten the rail to the track through the clearance holes in the rail via drilled and tapped holes (to accommodate #10-32 screws) in each side plate.</li>
</ol>
5. Rear Mount Attachment of the Actuators
<ol>
	<li>Machine rear mount attachments from the &#39;L&#39;-shaped angle stock according to the specifications provided in the supplemental files.</li>
	<li>Machine a bar to attach to the bottom of the mount to serve as a keyway and ride it in the machined track on the face of the side plate according to the specifications provided in the supplemental files. Screw the bar into the bottom of the mount.</li>
	<li>Drill a through hole in the base of the rear mount for the actuator clearance.</li>
	<li>Attach the rear mount to the body of the actuator via the hole pattern in the commercial actuator. 
	NOTE: One reason for making a rear mount is to eliminate the need to repeatedly attach the actuator directly to the frame using the small #2 metric screws that come stock on the actuators. The mount eliminates the concern of stripping the internal threads of the actuator with repeated use.</li>
	<li>Slot the base of the mount to attach the rear actuator mount to the frame via two screws.</li>
	<li>Drill and tap a series of holes (to accommodate #10-32 screws) flanking the track on the front face of the side plates to allow for an adjustable mount attachment if it is desirable to accommodate specimens of varying sizes.</li>
</ol>
6. Front Mount Attachment of the Actuators via Connectors
NOTE: The front mount is an &#39;L&#39;-shaped piece that attaches the front of the actuator to the carriage. The actuator does not physically contact the mount; it attaches via a series of connectors that extend from the actuator tip.
<ol>
	<li>Machine front mount attachments from the &#39;L&#39;-shaped angle stock according to the specifications provided in the supplemental files.</li>
	<li>Drill a hole in the base of the front mount to accommodate the tapered connector.</li>
	<li>Machine a track in the side of the front mount to accommodate a plate.</li>
	<li>Machine the plate with a track to accommodate the fixtures.</li>
	<li>Machine an aluminum, cylindrical connector according to the specifications provided in the drawing links. This adaptor connects the load cell to the actuator.</li>
	<li>Drill and tap the connector for a #2 metric screw on the actuator end and a #6 metric screw on the load cell end to support the axial mounting and alignment of the load cell and actuator.</li>
	<li>Repeat this process to machine two identical connectors, one for each load cell.</li>
	<li>Machine an aluminum, tapered, cylindrical connector according to specifications provided in the drawing links. This adaptor connects the load cell to the fixture and the carriage.</li>
	<li>Drill and tap the connector to the threaded load cell connection on one end.</li>
	<li>Pass the cylinder into the hole of the front actuator mount and use a set screw to anchor the cylinder end.</li>
	<li>Duplicate the system for the right and left actuators. 
	NOTE: As shown in Figure 6, once assembled, the base of the actuator is rigidly attached to the side plate. The front of the actuator is attached to the carriage and, as the actuator is extended and retracted, the carriage is pushed and pulled. This provides the framework for the fixture attachment and specimen loading.</li>
</ol>
7. Fixtures
<ol>
	<li>Machine the fixtures according to the specifications provided in the supplemental files (Figure 7).</li>
	<li>Machine a central, vertical slot in the fixture holder to accommodate the height.</li>
	<li>Attach the actuator front mounts to the rectangular plate with three drilled and tapped holes (to accommodate #10-32 screws) vertically aligned in the center of the plate.</li>
	<li>Raise or lower the holder as necessary, for example, if a saline bath for hydrated testing is being used, and secure it with screws.</li>
</ol>
8. Operating Procedure:
<ol>
	<li>Download the actuator software to remotely control the device16.</li>
	<li>Create a link between the computer and the 24 V controller with a 6-pin mini-din male-to-female PS/2 extension cable; each actuator controller has two 6-pin mini-din connector cable links.</li>
	<li>Use a USB-to-6-pin mini-din converter to connect the actuators to a standard computer; the converter contains one female 6-pin mini-din connector end and a USB connection port.</li>
	<li>Daisy-chain the actuators so that a single computer cable is sufficient for the operation, or alternatively, use an HDMI adapter in place of the USB adapter.</li>
	<li>Connect the actuators to the 24 V power supply.</li>
	<li>Once connected and powered, select the devices and customize the actuator performance.</li>
	<li>Alternatively, control the actuators manually by the dial on each actuator, which is useful for the set-up. 
	NOTE: This software is applicable to any standard operating system. With this software, the actuators can be moved at varying speeds to any set distance, synced at a set distance or synced to each other to move in unison.</li>
</ol>

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Standard practice for torque calibration of testing machines Available from: <a target="_blank" href="https://www.astm.org/Standard/standards-and-publications.html">https://www.astm.org/Standard/standards-and-publications.html</a> (2017)</li><li>. ASTM C39 &#8211; Standard test method for compressive strength of cylindrical concrete specimens Available from: <a target="_blank" href="https://www.astm.org/Standard/standards-and-publications.html">https://www.astm.org/Standard/standards-and-publications.html</a> (2018)</li><li>. ASTM A370-17a. Standard test methods and definitions for mechanical testing of steel products Available from: <a target="_blank" href="https://www.astm.org/Standard/standards-and-publications.html">https://www.astm.org/Standard/standards-and-publications.html</a> (2017)</li><li>. ASTM D4761-13. Standard test methods for mechanical properties of lumber and wood-base structural material Available from: <a target="_blank" href="https://www.astm.org/Standard/standards-and-publications.html">https://www.astm.org/Standard/standards-and-publications.html</a> (2013)</li><li>Green, M. L., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mechanical+properties+of+cheese,+cheese+analogues+and+protein+gels+in+relation+to+composition+and+microstructure.">Mechanical properties of cheese, cheese analogues and protein gels in relation to composition and microstructure.</a> Food Structure. 5 (1), 169-192 (1986).</li><li>. ASTM D76/D76M-11. Standard specification for tensile testing machines for textiles Available from: <a target="_blank" href="https://www.astm.org/Standard/standards-and-publications.html">https://www.astm.org/Standard/standards-and-publications.html</a> (2011)</li><li>Papini, M., Zdero, R., Schemitsch, E. 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The authors have nothing to disclose.

The goal of this work was to design and fabricate a cost-effective and reliable uniaxial loader for its use with small-scale specimens such as tissue and fibers. A device was constructed that met the requirements set forth while also being flexible enough in design to allow for new attachments to be fabricated as the user needs grow. For example, the device will allow for the testing of dry and wet specimens in a uniaxial or fixed-end configuration.
Critical steps in the design and fabrication...

Mechanical testing has an interesting history that can be traced back to hardness testing equipment developed by Stanley Rockwell in the early in the twentieth century. While technology has grown to the extent that standard, documented practices guide everything from the verification of machine performance to the guidelines for carrying out specific tests1,2,3,4. Today, mechanical tests are conducted on everything from building materials such as concrete, steel, and wood to food and textile products5,6,7,8,9. Given that the fields of biomedical engineering and, more specifically, biomechanics utilize mechanical testing, loading machines are commonplace in biomechanics labs.
Loading machines run the range of scale in biomechanics. As an example, larger loading machines can be used to conduct full-body impact studies or determine human femoral mechanical properties, while smaller loading machines can be used to test murine bones or stimulate cells10,11,12,13,14. Two types of loading machines are found in the testing laboratory; those that are purchased commercially and those that are built by the user. Loading machines developed in-house are often favored for their personalization and customization options15.
In testing, a specimen is secured in the machine so that a displacement can be applied, generating a measurable force. If the load is used as the driving feedback, the test is load-controlled; if the displacement is used as the driving feedback, the test is displacement-controlled. Loading machines, in general, are built upon a frame that connects a mover to a fixed support. As such, testing generally involves one end of the specimen being moved while the other end remains fixed.
Shown in Figure 1 is a sketch of a simple loading machine demonstrating its basic components. Fundamental to all loading machines is a base or frame. Whereas the vast majority of commercial brands utilize a fixed base, the drawing depicts a platform that allows planar (XY) movement. The mover, in this case, is the upper arm that holds a load cell and is driven by a stepper motor. Attached to the frame are the fixtures which hold the specimen and dictate the type of test that is run. Shown in the drawing are three-point bend fixtures. The top fixture (the single contact) is mounted to the moving arm; the bottom fixture (the double contact) is mounted to the stationary base. During testing, the motor drives the upper fixture downward to where the center contact engages the specimen. As the contact engages the specimen, the load cell records the increase in resistance or the force placed upon the specimen.
There are occasions where machines are designed and built in-house to accomplish a motion not attainable with the existing machines in the laboratory. Here we describe in detail one such device. It is a loading platform that enables pure uniaxial specimen loading or equal and opposite motion at both ends. The device incorporates commercial load cells and actuators (movers); a frame is machined to hold the commercial parts and loading fixtures for specimen testing. Understanding the basic principles of testing machine construction can aid in the design of one&#39;s own machine. We have provided the drawing files we created as a starting point to assist researchers with their own machine development. The video will focus on the assembly of the device and the application of mechanical design principles to ensure alignment and reliable testing.

<table><tbody><tr><td>Power supply, 24 V DC 2.5 A out, 100-240 V AC in, plug for North America&amp;nbsp;</td><td>Zaber Technologies inc</td><td>PS05-24V25</td><td></td></tr><tr><td>6 pin mini din-male to female PS/2 extension cable</td><td>Zaber Technologies inc</td><td>T-DC06</td><td></td></tr><tr><td>Stepper motor controller, 2 phase</td><td>Zaber Technologies inc</td><td>A-MCA</td><td></td></tr><tr><td>Linear actuator, NEMA size 11, 30 mm travel, 58 N maximum continuous thrust</td><td>Zaber Technologies inc</td><td>NA11B30</td><td></td></tr><tr><td>Corrosion resistant maintenance-Free Ball Bearing Carriages and Guide Rails</td><td>McMaster-Carr</td><td>9184T31</td><td></td></tr><tr><td>6061-t6 Aluminum Stock</td><td>McMaster-Carr</td><td>NA</td><td></td></tr><tr><td>Plexiglas Stock</td><td>McMaster-Carr</td><td>NA</td><td></td></tr><tr><td>Canister load cell, 4.5N</td><td>Honeywell Sensotec</td><td>NA</td><td></td></tr><tr><td>USB to 6 pin mini-din</td><td>Universal&amp;nbsp;</td><td>NA</td><td></td></tr></tbody></table>

application of design aspects in uniaxial loading machine development

In terms of accurate and precise mechanical testing, machines run the continuum. Whereas commercial platforms offer excellent accuracy, they can be cost-prohibitive, often priced in the $100,000 - $200,000 price range. At the other extreme are stand-alone manual devices that often lack repeatability and accuracy (e.g., a manual crank device). However, if a single use is indicated, it is over-engineering to design and machine something overly elaborate. Nonetheless, there are occasions where machines are designed and built in-house to accomplish a motion not attainable with the existing machines in the laboratory. Described in detail here is one such device. It is a loading platform that enables pure uniaxial loading. Standard loading machines typically are biaxial in that linear loading occurs along the axis and rotary loading occurs about the axis. During testing with these machines, a load is applied to one end of the specimen while the other end remains fixed. These systems are not capable of conducting pure axial testing in which tension/compression is applied equally to the specimen ends. The platform developed in this paper enables the equal and opposite loading of specimens. While it can be used for compression, here the focus is on its use in pure tensile loading. The device incorporates commercial load cells and actuators (movers) and, as is the case with machines built in-house, a frame is machined to hold the commercial parts and fixtures for testing.

In order to verify the use of the system, actuator speed and performance tests were conducted17. These tests consisted of measuring the actuator speed and distance in comparison to the input values. To verify the sample travel distance accuracy, arbitrary travel distances along the shaft between 254 - 2540 &#181;m (0.01 - 0.10 in) were selected. The device was run to these distances and compared to the actual distance measured using combinations of gauge blocks and...

Watch this Scientific Journal Video about Application of Design Aspects in Uniaxial Loading Machine Development at JoVE.com

Application of Design Aspects in Uniaxial Loading Machine Development

Here we present a protocol to develop a pure uniaxial loading machine. Critical design aspects are employed to ensure accurate and reproducible testing results.

In terms of accurate and precise mechanical testing, machines run the continuum. Whereas commercial platforms offer excellent accuracy, they can be ...

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5.8K Views.  University of Akron. Here we present a protocol to develop a pure uniaxial loading machine. Critical design aspects are employed to ensure accurate and reproducible testing results.

Video: Application of Design Aspects in Uniaxial Loading Machine Development

Design of a Biaxial Mechanical Loading Bioreactor for Tissue Engineering

We designed a loading device that is capable of applying uniaxial or biaxial mechanical strain to a tissue engineered biocomposites fabricated for transplantation. While the device primarily functions as a bioreactor that mimics the native mechanical strains, it is also outfitted with a load cell for providing force feedback or mechanical testing of the constructs. The device subjects engineered cartilage constructs to biaxial mechanical loading with great precision of loading dose (amplitude and frequency) and is compact enough to fit inside a standard tissue culture incubator. It loads samples directly in a tissue culture plate, and multiple plate sizes are compatible with the system. The device has been designed using components manufactured for precision-guided laser applications. Bi-axial loading is accomplished by two orthogonal stages. The stages have a 50 mm travel range and are driven independently by stepper motor actuators, controlled by a closed-loop stepper motor driver that features micro-stepping capabilities, enabling step sizes of less than 50 nm. A polysulfone loading platen is coupled to the bi-axial moving platform. Movements of the stages are controlled by Thor-labs Advanced Positioning Technology (APT) software. The stepper motor driver is used with the software to adjust load parameters of frequency and amplitude of both shear and compression independently and simultaneously. Positional feedback is provided by linear optical encoders that have a bidirectional repeatability of 0.1 &mu;m and a resolution of 20 nm, translating to a positional accuracy of less than 3 &mu;m over the full 50 mm of travel. These encoders provide the necessary position feedback to the drive electronics to ensure true nanopositioning capabilities. In order to provide the force feedback to detect contact and evaluate loading responses, a precision miniature load cell is positioned between the loading platen and the moving platform. The load cell has high accuracies of 0.15% to 0.25% full scale.

We designed a novel mechanical loading bioreactor that can apply uniaxial or biaxial mechanical strain to a cartilage biocomposite prior to transplantation into an articular cartilage defect.

We  designed a loading device that is capable of applying uniaxial or biaxial  mechanical strain to a tissue engineered biocomposites fabricated for  ...

Bioengineering

A Novel Biaxial Testing Apparatus for the Determination of Forming Limit under Hot Stamping Conditions

The hot stamping and cold die quenching process is increasingly used to form complex shaped structural components of sheet metals. Conventional experimental approaches, such as out-of-plane and in-plane tests, are not applicable to the determination of forming limits when heating and rapid cooling processes are introduced prior to forming for tests conducted under hot stamping conditions. A novel in-plane biaxial testing system was designed and used for the determination of forming limits of sheet metals at various strain paths, temperatures, and strain rates after heating and cooling processes in a resistance heating uniaxial testing machine. The core part of the biaxial testing system is a biaxial apparatus, which transfers a uniaxial force provided by the uniaxial testing machine to a biaxial force. One type of cruciform specimen was designed and verified for the formability test of aluminum alloy 6082 using the proposed biaxial testing system. The digital image correlation (DIC) system with a high-speed camera was used for taking strain measurements of a specimen during a deformation. The aim of proposing this biaxial testing system is to enable the forming limits of an alloy to be determined at various temperatures and strain rates under hot stamping conditions.

This protocol proposes a novel biaxial testing system used on a resistance heating uniaxial tensile test machine in order to determine the forming limit diagram (FLD) of sheet metals under hot stamping conditions.

The hot stamping and cold die quenching process is increasingly used to form complex shaped structural components of sheet metals. Conventional ...

Biaxial Mechanical Characterizations of Atrioventricular Heart Valves

Extensive biaxial mechanical testing of the atrioventricular heart valve leaflets can be utilized to derive&#160;optimal parameters used in constitutive models, which provide a mathematical representation of the mechanical function of those structures. This presented biaxial mechanical testing protocol involves (i) tissue acquisition, (ii) the preparation of tissue specimens, (iii) biaxial mechanical testing, and (iv) postprocessing of the acquired data. First, tissue acquisition requires obtaining porcine or ovine hearts from a local Food and Drug Administration-approved abattoir for later dissection to retrieve the valve leaflets. Second, tissue preparation requires using tissue specimen cutters on the leaflet tissue to extract a clear zone for testing. Third, biaxial mechanical testing of the leaflet specimen requires the use of a commercial biaxial mechanical tester, which consists of force-controlled, displacement-controlled, and stress-relaxation testing protocols to characterize the leaflet tissue&#39;s mechanical properties. Finally, post-processing requires the use of data image correlation techniques and force and displacement readings to summarize the tissue&#39;s mechanical behaviors in response to external loading. In general, results from biaxial testing demonstrate that the leaflet tissues yield a nonlinear, anisotropic mechanical response. The presented biaxial testing procedure is advantageous to other methods since the method presented here allows for a more comprehensive characterization of the valve leaflet tissue under one unified testing scheme, as opposed to separate testing protocols on different tissue specimens. The proposed testing method has its limitations in that shear stress is potentially present in the tissue sample. However, any potential shear is presumed negligible.

This protocol involves characterizations of atrioventricular valve leaflets with force-controlled, displacement-controlled, and stress-relaxation biaxial mechanical testing procedures. Results acquired with this protocol can be used for constitutive model development to simulate the mechanical behavior of functioning valves under a finite element simulation framework.

Extensive biaxial mechanical testing of the atrioventricular heart valve leaflets can be utilized to derive&#160;optimal parameters used in constitutive ...

Layer Microdissection of Tricuspid Valve Leaflets for Biaxial Mechanical Characterization and Microstructural Quantification

The tricuspid valve (TV) regulates the unidirectional flow of unoxygenated blood from the right atrium to the right ventricle. The TV consists of three leaflets, each with unique mechanical behaviors. These variations among the three TV leaflets can be further understood by examining their four anatomical layers, which are the atrialis (A), spongiosa (S), fibrosa (F), and ventricularis (V). While these layers are present in all three TV leaflets, there are differences in their thicknesses and microstructural constituents that further influence their respective mechanical behaviors. 
This protocol includes four steps to elucidate the layer-specific differences: (i) characterize the mechanical and collagen fiber architectural behaviors of the intact TV leaflet, (ii) separate the composite layers (A/S and F/V) of the TV leaflet, (iii) carry out the same characterizations for the composite layers, and (iv) perform post-hoc histology assessment. This experimental framework uniquely allows the direct comparison of the intact TV tissue to each of its composite layers. As a result, detailed information regarding the microstructure and biomechanical function of the TV leaflets can be collected with this protocol. Such information can potentially be used to develop TV computational models that seek to provide guidance for the clinical treatment of TV disease.

This protocol describes the biaxial mechanical characterization, polarized spatial frequency domain imaging-based collagen quantification, and microdissection of tricuspid valve leaflets. The provided method elucidates how the leaflet layers contribute to the holistic leaflet behaviors.

The tricuspid valve (TV) regulates the unidirectional flow of unoxygenated blood from the right atrium to the right ventricle. The TV consists of three ...

Compression Testing of Mouse Vertebra for Determination of Mechanical Strength

Mouse Lumbar Vertebra Uniaxial Compression Testing with Embedding of the Loading Surface

There is increasing awareness that cortical and cancellous bone differ in regulating and responding to pharmaceutical therapies, hormone therapies, and other treatments for age-related bone loss. Three-point bending is a common method used to assess the influence of a treatment on the mid-diaphysis region of long bones, which is rich in cortical bone. Uniaxial compression testing of mouse vertebrae, though capable of assessing bones rich in cancellous bone, is less commonly performed due to technical challenges. Even less commonly performed is the pairing of three-point bending and compression testing to determine how a treatment may influence a long bone's mid-diaphysis region and a vertebral centrum similarly or differently. Here, we describe two procedures to make compression testing of mouse lumbar vertebrae a less challenging method to perform in parallel with three-point bending: first, a procedure to convert a three-point bending machine into a compression testing machine, and second, an embedding method for preparing a mouse lumbar vertebra loading surface.

Author Spotlight: Enhancing Small Animal Bone Compression Testing for Research

In this protocol, two approaches are described to make uniaxial compression testing of mouse lumbar vertebrae more attainable. First, the conversion of a three-point bending machine to a compression testing machine is described. Second, an embedding method for preparing the loading surface that uses bone cement is adapted for mouse lumbar vertebrae.

There is increasing awareness that cortical and cancellous bone differ in regulating and responding to pharmaceutical therapies, hormone therapies, and ...

Biology

Design of Transmission Shafts - Stress Analysis

Designing a transmission shaft requires a thorough understanding of the stresses induced by bending moments and torques, especially in systems where power is transferred through gears. These forces create force-couple systems at the centers of the shaft&#39;s cross-sections, leading to both transverse and torsional loading. Although shearing stresses from transverse loads are typically smaller than those from torques and are often overlooked, the significant normal stresses from these loads contribute to the maximum shearing stress.
<img alt="Equation 1" src="/files/ftp_upload/15663/15663_Equation_1.svg" style="text-align: center; height: 48px;" />
Calculating the normal stress exerted on a shaft section involves examining the shaft&#39;s cross-section at a specific point, considering both the torque and bending couples. The maximum normal stress typically occurs at the ends of the diameter perpendicular to the resultant of the bending moment couple. Determining the cross-section&#39;s minimum allowable polar moment ratio J/c is essential to ensure the shaft&#39;s integrity and functionality.
<img alt="Equation 2" src="/files/ftp_upload/15663/15663_Equation_2.svg" style="text-align: center; height: 38px;" />
This ratio is vital as it accounts for both the maximum resultant bending moment and torque on the shaft, in addition to the allowable shearing stress. This analytical approach is fundamental in designing both solid and hollow circular shafts, enabling the creation of optimized shaft configurations that can reliably withstand operational stresses. Such methodology ensures that the designed shafts are robust, efficient, and tailored to their specific applications, guaranteeing mechanical systems&#39; safety and functionality.

Projektowanie wałów napędowych - analiza naprężeń

The design of a transmission shaft involves understanding the stresses due to bending moments and torques.
When power is transferred through gears, the ...

Principal Stresses under a Given Loading

KEY TERMS AND CONCEPTS

Projektowanie wałów napędowych

Transmission Shafts: Problem Solving

Designing a solid shaft that transmits power from a motor to a machine tool involves a series of calculations to ensure the shaft can withstand the stresses applied by bending moments and torques. First, calculate the torque exerted on the gear, considering the power transmitted by the shaft and its rotational speed. Following this, compute the tangential forces acting on the gears, which directly relate to the torque and the gear radius.
Next, use bending moment diagrams for the shaft to identify the bending moment values due to forces acting in horizontal and vertical planes. At potentially critical transverse sections of the shaft, determine the combined stresses from these bending moments and torsion by calculating the square root of the sum of the squares of these values. This analysis helps assess whether the shaft can handle the stress without failing. Then, calculate the polar moment of inertia, which is crucial for linking shearing stress with torsion and bending moments.
<img alt="Equation 1" src="/files/ftp_upload/15664/15664_Equation_1.svg" style="text-align: center; height: 58px;" />
This calculation verifies the shaft&#39;s capacity to endure the applied forces. Finally,&#160; calculate the shaft&#39;s minimum required diameter based on the polar moment of inertia, ensuring it can withstand the calculated stresses with minimal material use while meeting safety and performance standards.

Wały transmisyjne: rozwiązywanie problemów

A solid shaft rotates, transmitting power from the motor to a machine tool connected to the gear. Given the allowable shearing stress, calculate the ...

Wały napędowe: rozwiązywanie problemów

Unsymmetric Loading of Thin-Walled Members

Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
The concept of the shear center is crucial in countering the effects of unsymmetrical loading. The shear center is the point in the cross-section where a load causes pure bending without twisting. The shear center&#39;s location, which depends on the cross-section&#39;s geometry, is vital for optimal load application. By applying loads at the shear center, engineers can significantly reduce twisting, enhancing structural integrity.
Identifying the precise location of the shear center enables engineers to strategically apply loads, breaking them down into components that avoid causing twisting. This method preserves structural stability and performance under unsymmetrical loads. Understanding the shear center&#39;s role in load distribution is essential for designing and analyzing thin-walled members, preventing failures, and promoting material efficiency. Grasping these principles is critical for creating innovative and resilient structural designs.

Niesymetryczne obciążenie prętów cienkościennych

When thin-walled members with non-symmetrical cross-sections are subjected to unsymmetric loading, they experience bending and twisting.
This dual effect ...

Application of Design Aspects in Uniaxial Loading Machine Development

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Mouse Lumbar Vertebra Uniaxial Compression Testing with Embedding of the Loading Surface

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Wały transmisyjne: rozwiązywanie problemów

Wały transmisyjne: rozwiązywanie problemów

Niesymetryczne obciążenie prętów cienkościennych