What is ball screw whip. How does it affect the performance of linear motion systems. Why does ball screw whip occur in longer shafts. How can critical speed be calculated for ball screws. What methods can be used to mitigate ball screw whip.
The Phenomenon of Ball Screw Whip: An In-Depth Analysis
Ball screws are crucial components in many linear motion systems, prized for their ability to deliver high thrust forces with exceptional positioning accuracy and repeatability. However, these mechanical marvels are not without their limitations. One significant challenge that engineers and designers must contend with is the phenomenon known as ball screw whip.
Ball screw whip occurs when the rotating shaft of a ball screw begins to oscillate laterally, much like a jump rope being swung. This behavior becomes more pronounced as the length of the shaft increases and as rotational speeds rise. The occurrence of whip can severely impact the performance and longevity of a ball screw assembly, making it a critical factor to consider in system design.
The Mechanics of Ball Screw Whip
To understand ball screw whip, we must first examine the forces at play during operation. As the screw shaft rotates, it experiences centrifugal forces that cause it to deflect slightly. In shorter shafts, this deflection is negligible. However, in longer shafts, the deflection can become significant, leading to a whipping motion that amplifies as speed increases.
Critical Speed: The Limiting Factor in Ball Screw Performance
The concept of critical speed is fundamental to understanding the limitations imposed by ball screw whip. Critical speed refers to the rotational velocity at which the natural frequency of the shaft coincides with the frequency of rotation, leading to resonance and potentially catastrophic failure.
Critical speed is inversely proportional to the square of the shaft length. This relationship explains why longer ball screws are more susceptible to whip at lower speeds compared to shorter ones. Engineers must carefully consider this factor when designing systems that require both high speed and long travel distances.
Calculating Critical Speed
The formula for calculating the critical speed of a ball screw is:
Nc = (60 * 4.76 * 106 * dr) / L2
Where:
- Nc is the critical speed in rpm
- dr is the root diameter of the screw in mm
- L is the unsupported length of the screw in mm
This calculation provides a theoretical maximum speed, but in practice, it’s recommended to operate at no more than 80% of the calculated critical speed to ensure safe and reliable operation.
Factors Influencing Ball Screw Whip
Several factors contribute to the occurrence and severity of ball screw whip:
- Shaft length: Longer shafts are more prone to whip at lower speeds.
- Rotational speed: Higher speeds increase the likelihood and magnitude of whip.
- Shaft diameter: Thicker shafts are more resistant to whip but may increase inertia.
- Material properties: The stiffness and damping characteristics of the shaft material affect whip behavior.
- Support configuration: The type and placement of bearings can significantly influence whip.
Mitigating Ball Screw Whip: Strategies for Improved Performance
While ball screw whip poses a significant challenge, various strategies can be employed to mitigate its effects and extend the operational range of ball screw assemblies:
1. Optimizing Shaft Design
One effective approach is to optimize the shaft design. This can involve:
- Increasing the shaft diameter to improve stiffness
- Using materials with higher stiffness-to-weight ratios
- Implementing hollow shaft designs to reduce mass while maintaining stiffness
2. Enhanced Support Systems
Improving the support system can significantly reduce whip:
- Utilizing fixed-fixed end supports instead of fixed-free configurations
- Implementing intermediate support bearings for longer shafts
- Using preloaded bearings to increase overall system rigidity
3. Speed Reduction Techniques
When high linear speeds are required, alternative approaches can be considered:
- Employing multiple shorter ball screws in series
- Using a ball screw with a larger lead to achieve higher linear speeds at lower rotational speeds
- Implementing a hybrid system combining ball screws with belt drives or linear motors
Advanced Technologies for Combating Ball Screw Whip
As engineering continues to evolve, new technologies are emerging to address the challenge of ball screw whip:
Active Damping Systems
Active damping systems use sensors and actuators to detect and counteract whip in real-time. These systems can significantly extend the operational range of ball screws, particularly in high-precision applications.
Composite Materials
Advanced composite materials offer the potential for creating ball screw shafts with superior stiffness-to-weight ratios, potentially allowing for longer shafts that resist whip at higher speeds.
Optimized Ball Circulation Systems
Innovations in ball circulation systems can reduce internal vibrations and improve overall stability, indirectly contributing to whip resistance.
The Impact of Ball Screw Whip on System Performance
Understanding the consequences of ball screw whip is crucial for system designers and engineers. The effects of whip can manifest in various ways:
Reduced Accuracy and Repeatability
As whip increases, the positional accuracy of the ball screw system deteriorates. This can lead to inconsistent results in precision applications such as machining or metrology.
Increased Wear and Reduced Lifespan
The lateral forces introduced by whip can accelerate wear on ball bearings, raceways, and support structures. This increased wear can significantly reduce the operational life of the ball screw assembly.
Noise and Vibration Issues
Ball screw whip often manifests as increased noise and vibration in the system. This can be problematic in applications where quiet operation is essential or where vibration can interfere with sensitive processes or measurements.
Energy Efficiency Concerns
The energy required to overcome the effects of whip represents a loss in system efficiency. In high-duty cycle applications, this can translate to increased power consumption and operating costs.
Balancing Performance and Limitations in Ball Screw Design
Designing an optimal ball screw system often involves a delicate balance between performance requirements and the limitations imposed by ball screw whip. Engineers must carefully consider factors such as:
- Required travel distance
- Desired speed and acceleration profiles
- Positioning accuracy and repeatability requirements
- Load capacities (both static and dynamic)
- Environmental factors (temperature, contamination, etc.)
- Cost constraints
By thoroughly analyzing these factors in the context of ball screw whip limitations, designers can create systems that maximize performance while ensuring reliability and longevity.
Case Study: High-Speed, Long-Travel Application
Consider a scenario where a system requires both high speed and long travel distance—two requirements that are typically at odds due to ball screw whip. One innovative solution might involve:
- Dividing the travel distance into segments, each served by a separate ball screw
- Implementing a transfer mechanism between segments
- Using high-lead ball screws to achieve high linear speeds at lower rotational speeds
- Incorporating active damping systems on each ball screw to further mitigate whip
This approach allows for high-speed operation over a long total distance while keeping individual ball screws within their critical speed limits.
Future Trends in Ball Screw Technology and Whip Mitigation
As technology continues to advance, we can anticipate new developments that will further address the challenge of ball screw whip:
AI-Driven Design Optimization
Artificial intelligence and machine learning algorithms may soon play a significant role in optimizing ball screw designs. These tools could analyze vast amounts of performance data to create designs that inherently resist whip while meeting specific application requirements.
Novel Materials and Manufacturing Techniques
Advancements in materials science and manufacturing processes may lead to ball screws with unprecedented stiffness-to-weight ratios. Techniques such as 3D printing of metal components could allow for complex internal structures that provide superior whip resistance.
Integrated Sensing and Control Systems
Future ball screw assemblies may incorporate built-in sensors and microcontrollers, allowing for real-time monitoring and adjustment of operating parameters to prevent whip. This could enable adaptive systems that push the boundaries of performance while maintaining reliability.
Hybrid Drive Systems
Innovative combinations of ball screws with other drive technologies, such as linear motors or piezoelectric actuators, may provide solutions that leverage the strengths of each technology while mitigating their individual limitations.
As we continue to push the boundaries of linear motion systems, understanding and addressing ball screw whip remains a critical area of focus. By combining innovative design approaches, advanced materials, and cutting-edge control strategies, engineers are continually expanding the capabilities of ball screw technology, enabling new applications and improving performance across a wide range of industries.
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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.
