What causes ball screw whip in mechanical systems. How does whip affect the critical speed of ball screws. Why is ball screw length inversely related to maximum operating speed. Can ball screw whip be mitigated or prevented in high-speed applications.
The Phenomenon of Ball Screw Whip: An In-Depth Analysis
Ball screws are crucial components in many precision mechanical systems, prized for their ability to deliver high thrust forces with exceptional positioning accuracy and repeatability. However, these systems face a significant challenge known as ball screw whip, which can severely limit their performance in certain applications.
Ball screw whip is a dynamic phenomenon that occurs when the screw shaft rotates at high speeds. As the rotation rate increases, the shaft begins to deflect laterally, much like a jump rope being swung. This deflection can lead to several issues, including reduced accuracy, increased wear, and potential system failure if not properly managed.
What Causes Ball Screw Whip?
The primary cause of ball screw whip is the centrifugal force acting on the rotating shaft. As the shaft spins, any slight imbalance or eccentricity can lead to a radial force that causes the shaft to bow outward. This effect becomes more pronounced as the rotation speed increases, eventually leading to a self-reinforcing whipping motion.
- Shaft length: Longer shafts are more susceptible to whip due to their increased flexibility.
- Rotation speed: Higher speeds amplify the centrifugal forces causing whip.
- Shaft diameter: Thinner shafts are more prone to deflection and whip.
- Material properties: The shaft’s stiffness and damping characteristics affect its resistance to whip.
Critical Speed: The Limiting Factor in Ball Screw Performance
The concept of critical speed is crucial in understanding the limitations of ball screw systems. Critical speed is defined as the rotational speed at which the shaft’s natural frequency matches its operating frequency, leading to resonance and potentially catastrophic failure.
How is Critical Speed Calculated?
Critical speed (Nc) for a ball screw can be calculated using the following formula:
Nc = (60 * π * dn * fn) / L2
Where:
- dn is the root diameter of the screw shaft
- fn is a factor based on the end fixity of the screw
- L is the unsupported length of the screw
This formula clearly illustrates the inverse relationship between screw length and critical speed. As the length increases, the critical speed decreases quadratically, severely limiting the maximum operational speed of longer ball screws.
The Inverse Relationship Between Ball Screw Length and Speed
One of the most significant limitations of ball screw technology is the inverse relationship between screw length and maximum operational speed. This relationship stems directly from the physics of ball screw whip and critical speed considerations.
Why Does This Relationship Exist?
The inverse relationship between ball screw length and speed exists due to several factors:
- Increased flexibility: Longer shafts are inherently more flexible, making them more susceptible to deflection and whip.
- Lower natural frequency: The natural frequency of a shaft decreases with increasing length, lowering the critical speed.
- Amplified centrifugal forces: Longer shafts experience greater centrifugal forces at their midpoint, exacerbating the whip effect.
This relationship poses a significant challenge for designers who require both long travel distances and high speeds in their applications.
Characteristic Speed: Another Limiting Factor in Ball Screw Design
While critical speed is primarily determined by the properties of the screw shaft, characteristic speed is another important parameter that can limit ball screw performance. Characteristic speed is influenced by factors related to the ball nut assembly.
What Determines Characteristic Speed?
Characteristic speed is influenced by several factors:
- Ball return system design
- Mass of the balls
- Ball size and number
- Lubrication system efficiency
- Manufacturing precision of the ball nut
Advances in manufacturing techniques and ball recirculation methods have significantly increased the characteristic speeds of modern ball screw assemblies. However, in many cases, critical speed remains the primary limiting factor for high-speed operation.
Mitigating Ball Screw Whip: Strategies and Solutions
While ball screw whip presents a significant challenge, various strategies can be employed to mitigate its effects and extend the operational range of ball screw systems.
How Can Ball Screw Whip Be Reduced?
Several approaches can be taken to reduce ball screw whip:
- Increased shaft diameter: A larger shaft diameter increases stiffness and raises the critical speed.
- Support bearings: Adding intermediate support bearings can effectively reduce the unsupported length of the screw.
- Material selection: Using materials with higher stiffness-to-weight ratios can improve whip resistance.
- Preloading: Proper preloading of the ball nut can increase system stiffness and damping.
- Balancing: Precision balancing of the screw shaft can reduce eccentricity and minimize whip.
Implementing these strategies can significantly extend the operational range of ball screw systems, allowing for longer travel distances at higher speeds.
Advanced Ball Screw Technologies: Overcoming Traditional Limitations
As the demand for high-speed, long-travel ball screw systems continues to grow, manufacturers are developing innovative solutions to overcome the traditional limitations imposed by ball screw whip.
What New Technologies Are Addressing Ball Screw Whip?
Several cutting-edge technologies are being developed to address ball screw whip:
- Composite materials: Carbon fiber reinforced polymers offer high stiffness and low weight, potentially increasing critical speeds.
- Active damping systems: Electromagnetic or piezoelectric actuators can actively counteract whip motion.
- Hollow ball screws: Reducing shaft mass while maintaining stiffness can improve whip resistance.
- Optimized ball return systems: Advanced designs minimize turbulence and allow for higher characteristic speeds.
- Hybrid systems: Combining ball screws with linear motors can allow for high speeds over long distances.
These technologies promise to extend the capabilities of ball screw systems, opening up new possibilities in fields such as machine tools, robotics, and aerospace applications.
Applications and Industries Affected by Ball Screw Whip
Ball screw whip is a critical consideration in many industries that rely on precise linear motion over long distances. Understanding the impact of this phenomenon is essential for engineers and designers working in these fields.
Which Industries Are Most Affected by Ball Screw Whip?
Ball screw whip significantly impacts several key industries:
- Machine tools: High-speed machining centers require long travel and rapid acceleration, making whip a critical concern.
- Semiconductor manufacturing: Wafer handling systems demand extreme precision over long distances.
- Aerospace: Flight control surfaces and landing gear actuators must operate reliably under varying conditions.
- Robotics: Industrial robots with long reach capabilities face challenges in maintaining accuracy at high speeds.
- Medical equipment: CT scanners and other imaging devices require precise, high-speed linear motion.
In these industries, engineers must carefully balance the need for speed, precision, and travel distance when designing ball screw systems.
Future Trends in Ball Screw Technology and Whip Mitigation
As technology continues to advance, the future of ball screw systems looks promising. Researchers and engineers are constantly developing new methods to mitigate whip and extend the operational limits of these crucial components.
What Advancements Can We Expect in Ball Screw Technology?
Several exciting trends are emerging in ball screw technology:
- Smart ball screws: Integrated sensors and control systems for real-time whip detection and correction.
- Nanomaterials: Advanced coatings and materials to reduce friction and improve performance.
- AI-driven design optimization: Machine learning algorithms to create ball screw designs tailored for specific applications.
- Additive manufacturing: 3D printing technologies allowing for complex, optimized ball screw geometries.
- Hybrid drive systems: Combining ball screws with other linear motion technologies for optimal performance.
These advancements promise to push the boundaries of what’s possible with ball screw technology, enabling new applications and improving performance in existing systems.
In conclusion, ball screw whip remains a significant challenge in the design and implementation of high-speed, long-travel linear motion systems. However, with ongoing research and technological advancements, engineers are finding innovative ways to mitigate its effects and extend the capabilities of ball screw systems. As industries continue to demand higher speeds and greater precision, understanding and addressing ball screw whip will remain crucial for pushing the boundaries of mechanical design and automation.
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What is ball screw whip and why does it happen?
Ball screws are often the drive mechanism of choice in applications that require high thrust forces with excellent positioning accuracy and repeatability.
But one of the drawbacks of ball screw technology is that speed is inversely related to length — the longer the ball screw shaft, the more likely it is to whip, like a jump rope, as it turns. This behavior limits the maximum travel distance that can be achieved when high speeds are necessary, and vice-versa.
As a ball screw shaft rotates, it begins to whip – much like a jump rope. This behavior limits the screw’s critical speed.
What is critical speed?
The permissible operating speed of a ball screw assembly depends on two parameters — critical speed and characteristic speed. Characteristic speed is determined by factors related to the ball nut, including the ball return system and the mass of the balls. However, improvements in ball nut manufacturing and ball recirculation methods have provided most ball screw assemblies with very high characteristic speeds, so the limiting factor is typically the critical speed.
For a rotating shaft, such as a ball screw assembly, critical speed is defined as the angular velocity that excites the natural frequency, or first resonant frequency, of the assembly.
If the shaft is operated at its natural frequency, it can begin to resonate, causing severe damage — or even destruction — to the assembly.
Why do ball screws experience resonance?
In theory, a shaft is perfectly balanced — that is, its mass is perfectly distributed about its volume — so that when it rotates, there is no bending of the shaft and the center of mass lies along the axis of rotation. But in the real world, even the most precisely manufactured and machined shafts are not perfectly balanced, so the center of mass is very slightly offset from the axis of rotation. In addition, because the screw shaft is supported only at its ends, it bends somewhat under its own weight, moving the center of mass even farther from the axis of rotation. As the ball screw shaft rotates, the discrepancy between the center of mass and the axis of rotation produces centrifugal forces, which cause the shaft to deflect, or whip, like a jump rope.
If this vibration — or ball screw whip — approaches or reaches the natural frequency of the screw shaft, resonance can ensue and lead to increased noise, damage, and, in extreme cases, yielding of the shaft.
How to calculate ball screw critical speed
The critical speed of a shaft depends on its mass, length and diameter, the amount of deflection it experiences, and the end support method (type of end bearings).
The equation for critical speed of a ball screw is:
nc = critical speed (rpm)
k1 = factor depending on end bearing arrangement
Lcr = unsupported length of screw shaft (mm)
E = modulus of elasticity of screw shaft (N/mm2)
I = planar moment of inertia (mm4)
g = acceleration due to gravity (mm/s2)
γ = specific weight of screw shaft (N/mm3)
A = cross-sectional area of screw shaft (mm2)
It’s important to remember that if the ball nut is preloaded, the unsupported length (Lcr) is based on the greatest distance between the ball nut and the end of the screw that will occur in operation. For non-preloaded ball nuts, the unsupported length is simply the length between bearings (l).
Image credit: Bosch Rexroth
This equation can be simplified by combining all the non-variable components (k1, π, E, I, g, γ, and A). First, we’ll simplify the I/A component of the equation….
The inertia of a shaft is given as:
dn = root (minor) diameter of screw shaft (mm)
And the area is given as:
Dividing inertia by area gives us:
Since diameter is a variable, we’ll pull it out for now, but we need take the square root of dn2, so the variable for diameter becomes simply dn, and the 1/16 part stays within the square root.
Now we’ll define the non-variable part of the equation as “k.”
We know the values for pi (π), for the modulus of elasticity (E) and specific weight (γ) of steel, and for acceleration due to gravity (g):
π = 3.1415
E = 2.06 x 105 N/mm2
γ = 7.85 x 10-5 N/mm3
g = 9.8 x 103 mm/s2
So we can determine the value of the combined variables:
Typical values of k1 for different end bearing arrangements are as follows:
Fixed-Free: k1 = 1.
875
Floating-Floating: k1 = 3.142
Fixed-Floating: k1 = 3.927
Fixed-Fixed: k1 = 4.730
Now we can construct the simplified equation for ball screw critical speed, using “k” to represent all the non-variable components.
Notice that because we’re working in millimeters, the factor k is a very large number (42,000,000 for example). For the critical speed equation, k is typically expressed in scientific notation (notice the “107” factor included at the end of the equation).
Also note that some manufacturers include a safety factor of 0.8 when determining the value of k, since it’s generally recommended that a ball screw not be operated at more than 80 percent of its critical speed. The equations above do not include this 0.8 safety factor, so be sure to check if the manufacturer has included it in their published “k” values, or if it needs to be included during calculation.
How to brew matcha tea?
Matcha tea appeared in Russia relatively recently and quickly gained immense popularity.
The name 抹茶 – “matcha” or “matcha”, is translated from Japanese as “pulverized tea”. Contrary to popular myth, this tea was invented in China, and not in Japan, as is commonly believed.
During the Chinese Tang Dynasty (618-907), tea leaves were roasted and ground into a powder, and then brewed with salt and mint. During the Song Dynasty (960-1279), powdered tea became more popular: it was brewed by pouring boiling water over the tea powder in a cup and whisking it until frothy. The preparation of powdered tea has become a ritual among Chan Buddhists. They also brought tea to Japan along with Buddhism, which turned out to be the name of the Zen school, and turned the tea drinking process into a complex ceremony with a lot of rules and conventions.
A person who has not drunk tea is at odds with the universe.
— Japanese proverb
In today’s world, powdered tea has gained popularity due to its tonic properties and high content of vitamins. Now this tea can be bought in many specialized stores and even in the mass market, because a simpler grade of powder is used in tea cocktails and cooking.
We have matcha tea grown and produced in China, in Zhejiang province, in a large certified facility. On the site you will find two options for powdered tea – a ceremonial matcha, and a simpler, everyday version.
For the manufacture of powder tea, a young leaf is used, at an early stage of vegetation, processing is minimal. As a result, we get a powder very rich in useful elements, which is easily absorbed by the body. With one bowl of matches you will get cheerfulness, a lot of vitamins and energy for the whole day!
Studies have shown that matcha’s antioxidant levels are up to 140 times higher than regular green teas. It also contains the amino acid L-theanine, which is an uplifting and mood-stabilizing ingredient without the side effects of caffeine. Matcha contains a lot of calcium, potassium and vitamins A, B, C, E and P. In addition, the powder fraction is very easily and quickly absorbed by the body.
Matcha is often counterfeited and anything is passed off as quality powdered tea.
Matcha from our range has the necessary organic certificates and is supplied to the markets of Europe and the USA. The powder is packaged directly at the factory in sealed metallized bags, which guarantees freshness and minimal contact with oxygen.
You will need powdered tea, a bamboo whisk, a chawan tea bowl, and a special bamboo spoon.
Prepare the dishes. The tyavan must be warmed up before use and wiped dry, the whisk should be moistened a little, the bamboo stick should be wiped dry and free of dust;
Prepare water (80-85⁰C) and pour one spoonful of powdered tea into the chawan. Stronger tea is brewed at the rate of 50 ml of water per 4 g of matcha, less strong – about 100 ml of water per 2 g.
Slowly pour hot water over the powder, immerse the whisk, mix the contents of the bowl and begin to slowly whisk the tea until frothy.
For more details on how it looks, see our video below.Drink the entire drink, without residue, along with crushed green tea leaves. Enjoy the vivacity and benefits!
For more details on how it looks, see our video below.More about matcha tea, its benefits and preparation features – in our video:
How to make ice cream in a ball – “Food”
How to make ice cream in a ball – “Food”
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Mikhail Fedorov
The relaxing effect of playing ball at lunchtime definitely affects the efficiency of work.
We decided that energy should not be wasted, but transformed into another, and the break should end with dessert.
And so they made ice cream in the ball.
Because all it takes to turn sweet cream into ice cream is cold and regular stirring.
A rubber ball TU 84–612.28–2008 was used as an ice cream maker.
1. For ice cream we needed heavy cream, vanilla, egg, powdered sugar, lots of ice, salt and a hollow rubber ball.
2. Use scissors to cut a round hole in the ball about two centimeters in diameter.
3. Whip cream with powdered sugar, egg yolk and vanilla sugar with a mixer.
4. Fill a ball halfway with crushed ice, add three tablespoons of salt and stir.
5. First, we put a bag inside the ball, then filled it with whipped cream and tied it tightly with a rope.
6. Having cut off the extra tails from the bag, they drowned it in the ball, covered it completely with ice and sealed the hole with a patch.
7.
