Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.

Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

Keyless Bushings for power transmission

There are several methods to connect shaft and hub together for power transmission. Let's find the advantage of using keyless bushings from Fenner compared with other traditional connection methods.

Traditional Connection Methods

Interference Fits (Shrink and Press)
A shrink fit is a procedure whereby heat is used to facilitate a mechanical interference fit between two pieces of metal, such as a steel shaft and hub. Extreme heat is applied to the hub, causing it to expand and increasing the size of its machined bore. The expanded hub is removed from the heat source and quickly positioned onto the shaft. As the hub cools, its bore contracts back to its original machined dimension, effectively “shrinking” the hub onto the shaft.

A press fit achieves the same end as a shrink fit — a mechanical interference fit between a steel shaft and hub — but does so through different means. Press fits rely on the application of simple brute force to “press” the hub onto the shaft. Interference fits offer several advantages, such as zero backlash and uniform fit pressures, but these advantages come at a price. High capacity interference fits require long fit lengths, close tolerances, expensive and sometimes hazardous heat sources or hydraulic presses, and field maintenance is extremely difficult. Finally, separated components can rarely be re-used.

Keys, Keyways and Splines
The centuries-old industry standard shaft-to-hub mounting technique is the key and keyway. While ubiquitous and intuitively easy to understand, the key and keyway is a remarkably ineffective technology. Machining a keyway into a shaft is not inexpensive, nor is the equipment required to do so, though these costs are often unknown or overlooked. Keyways introduce notch factors, which account for the reduced effective cross section and abridged fatigue life that occurs when a shaft is keyed and lead, in turn, to systematic over-sizing of shaft diameters. This translates to more shaft material and weight, larger bearings and other drive components, and increased cost.
The combined effect of these clearances is backlash. In applications with frequent starts/stops, direction changes, and/or shock overloads, this backlash can lead to pounded out keyways, fatigue failures, fretting corrosion or some combination of these failure modes. Nor do keys and keyways lend themselves to motion control applications, since backlash erodes the accuracy of motion profiles over time.

A splined connection is simply a series of keys and keyways that suffers the same limitations and drawbacks associated with a single keyed connection. Manufacturing costs are high, especially on hollow shafts, and special surface treatment is often required to increase strength.

Why Go Keyless

Today’s global marketplace demands precise, efficient machines that optimize productivity while minimizing material and fabrication costs. When compared to traditional connection methods, Fenner Drives Keyless Bushings offer the following advantages:
  • A mechanical interference fit with a uniform pressure distribution similar to that achieved through a shrink or press fit.
  • A true zero backlash shaft-to-hub connection with none of the operational drawbacks of keyways or splines.
  • The ability to mount on plain shafting, which need not be
over-sized to compensate for notch factors. This allows the use
 of smaller shafts and bearings for more cost effective designs.
  • The flexibility to mount over existing keyways if desired.
  • Straight bore machining of the mounted component, generous machining tolerances and as-turned surface finishes.
  • Complete axial and radial adjustability.
  • Simple installation, adjustment and removal, even in the field.

Principles of Operation
Though offered in many shapes and sizes, Fenner Drives Keyless Bushings and Specialty Locking Devices all operate using the simple wedge principle. An axial force is applied — by either a hex nut or a series of annular screws — to engage circular steel rings with mating tapers. In the case of keyless bushings, the resulting wedge action creates a radial force on the tapered rings, one of which contracts to squeeze the shaft while the other expands and presses into the component bore.
In the case of specialty locking devices, similar tapered geometry generates a radial force that is concentrated (in the case of Shrink Discs) around a solid steel hub, squeezing so tightly that the hub “shrinks” onto the underlying shaft, or (in the case of WK Series Couplings) simultaneously onto two solid shaft ends to form a high- capacity rigid coupling.
In all cases, the product of the radial force applied to the shaft, the radius of that shaft and the coefficient of friction between the surfaces being joined equals the rated torque capacity of the connection.


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